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This report is submitted in partial fulfilment of the requirements for the Masters Degree in Mechanical Engineering program, Faculty of Engineering and the Environment, University of Southampton

Mechanical Motion Rectifier

Supervisor: Dr. Mohamed Moshrefi- Torbati Individual Project Work Undertaken By Geoffrey Moore Academic Year 2015/2016 Word Count: 9919

Investigating the potential of a mechanical device for transforming bi-directional rotational motion into uni-directional rotational motion.

This report is submitted in partial fulfilment of the requirements for the Masters Degree in Mechanical Engineering program, Faculty of Engineering and the Environment, University of Southampton

Abstract A Mechanical Motion Rectifier is a device that translates bi-directional rotational motion into uni-directional rotational motion. If implemented within a regenerative damper, or energy harvesting device it allows for the performance of the generator to be optimised, and significantly reduces system wear. This report details the development of a new type of motion rectifier, based on a planetary type gear arrangement, from a design concept stage to the manufacturing of a full prototype device for suitable for future research purposes. Meanwhile a theoretical analysis of the device, including computational modelling, revealed its behaviour including response to input motion, and the effects of frequency, inertia and backlash. The effect of a flywheel was discussed, and found to improve the energy generation potential, at the cost of control over the oscillating system. Finally, a test rig concept was developed for the prototype MMR, and potential applications for the device were discussed. Contents Academic Integrity Statement ..........................................................................................................4 Acknowledgements ...........................................................................................................................4 Abbreviations & Nomenclature ........................................................................................................5 Word Count .......................................................................................................................................5 1. Introduction ..................................................................................................................................6

1.1 Project Aim ..............................................................................................................................7 1.2 Project Objectives ...................................................................................................................7

2. Literature Review ..........................................................................................................................7 3. Methodology .................................................................................................................................8

3.1 Design Concepts ......................................................................................................................8 3.1.1 Design Concept 1 - Bevel Gears .......................................................................................8 3.1.2 Design Concept 2 - Worm Gears ......................................................................................9 3.1.3 Design Concept 3 - Planetary Gears .................................................................................9 3.1.4 Concept Selection ......................................................................................................... 10

3.2 Basic System Design and Proof of Concept .......................................................................... 10 3.2.1 The Equal Ratio Rule ..................................................................................................... 10 3.2.2 The Concentricity Rule .................................................................................................. 11 3.2.3 Gear Geometry .............................................................................................................. 11 3.2.4 System Design Equations & System Variables .............................................................. 12 3.2.5 Proof of Concept - 3D Model ........................................................................................ 12 3.2.6 Proof of Concept - OpenModelica Model ..................................................................... 13

IP Report - Mechanical Motion Rectifier Geoffrey Moore - 25309218 3

3.3 Prototype Design .................................................................................................................. 14 3.3.1 Prototype Gear Selection .............................................................................................. 14 3.3.2 MMR Version 2 Design .................................................................................................. 17 3.3.3 Final MMR Design .......................................................................................................... 18 3.3.4 Manufacturing and Assembling the MMR .................................................................... 18

3.4 OpenModelica Modelling ..................................................................................................... 20 3.4.1 Developing a Full MMR Model ...................................................................................... 20

4. Results ........................................................................................................................................ 22 4.1 - The Completed MMR Prototype ........................................................................................ 22 4.2 - OpenModelica Modelling Results ...................................................................................... 24

4.2.1 Input Output Relationship ............................................................................................. 24 4.2.2 - The Effects of Backlash ................................................................................................ 26 4.2.2.1 - Introduction to Backlash .......................................................................................... 26 4.2.2.2 - Backlash Frequency Independency .......................................................................... 27 4.2.2.3 - Backlash 'Filter' Effect ............................................................................................... 27 4.2.3 - The Effect of Frequency ............................................................................................... 28 4.2.4 - Response to a Random Input ...................................................................................... 30

5. Discussion ................................................................................................................................... 30 5.1 - Theoretical Planetary-MMR Inertia .................................................................................... 30

5.1.1 - Prototype Planetary-MMR Inertia ............................................................................... 31 5.1.2 - Prototype Planetary-MMR Inertia Reductions ............................................................ 32

5.2 - Gear Meshing Force Analysis ............................................................................................. 33 5.3 - Flywheel Analysis ................................................................................................................ 35

5.3.1 Modelling the Flywheel ................................................................................................. 35 5.3.2 Flywheel Advantages ..................................................................................................... 37 5.3.3 - Disadvantages of a Flywheel ....................................................................................... 37

5.4 - MMR Rig Concept ............................................................................................................... 38 5.5 - Gear Ratio Inversion ........................................................................................................... 39 5.6 - Prototype Revisions ............................................................................................................ 40

5.6.1 - Revised Sprag Clutch Assembly ................................................................................... 40 5.6.2 - Reduced Length ........................................................................................................... 40 5.6.3 - Reduced Inertia ........................................................................................................... 41

5.7 - Potential Applications of the Planetary-MMR ................................................................... 41 5.7.1 - Automotive / Motorcycle Suspension Regenerative Damper ..................................... 41 5.7.2 - Wave Energy ................................................................................................................ 41


5.7.3 - Motion of Trees .......................................................................................................... 42 6. Conclusion .................................................................................................................................. 42 Appendix ........................................................................................................................................ 44

Appendix 1 - Gear Geometry Derivation ................................................................................... 44 Appendix 2 - Supplier Provided Component Geometry ............................................................ 45 Appendix 3 - Inertia Values for OpenModelica and Approximations ........................................ 45 Appendix 4 - Gear Meshing Force Analysis Matlab Script ......................................................... 46 Appendix A5 - Prototype Self-Manufacture and Assembly Photographs .................................. 48 Appendix A6 - Initial MMR Design Drawings ............................................................................. 49 Appendix A7 - Prototype MMR Design Drawings ...................................................................... 68 Appendix A8 - Getting Started with OpenModelica .................................................................. 83 Appendix A9 - Risk Assessment for Prototype Manufacturing .................................................. 89

References ..................................................................................................................................... 95 Image References ........................................................................................................................... 95

Academic Integrity Statement I, Geoffrey Moore declare that this thesis and the work presented in it are my own and has been generated by me as the result of my own original research. I confirm that: 1. This work was done wholly or mainly while in candidature for a degree at this University; 2. Where any part of this thesis has previously been submitted for any other qualification at this University or any other institution, this has been clearly stated; 3. Where I have consulted the published work of others, this is always clearly attributed; 4. Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work; 5. I have acknowledged all main sources of help; 6. Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself; 7. None of this work has been published before submission. Acknowledgements I would like to acknowledge the valued contributions to this project of a number of individuals not referenced in the main text. Firstly, I would like to thank project supervisor Dr. Mohamed Moshrefi- Torbati for all his time, assistance and advice throughout the duration of this project. The contributions and advice towards completion of the prototype design of Dr. Tim Woolman, John Young and Kevin Smith were greatly appreciated, along with the EDMC's technical staff for their contribution in building the prototype design. The assistance of Terry Webster and Dave


Williams for their assistance during the time spent in the Student Workshop on the self-manufactured elements of the prototype MMR, was also greatly appreciated. Finally, Dr. Neil Ferguson for his advice on the available rig testing laboratories, and the available electrodynamic shakers. Abbreviations & Nomenclature MMR Mechanical Motion Rectifier P1 Planetary Input Shaft Gear that Meshes with the Sun Gear P2 Planetary Input Shaft Gear that Meshes with the Ring Gear EDMC Engineering Design and Manufacturing Centre "Inertia" or "Rotational Inertia" Wherever these terms are used, they are in reference to the axis of rotation of a shaft or gear about which the component is designed to rotate. I.e. Inertia about the centreline of the length of a shaft. D Pitch Diameter of a Gear R Overall Gear Ratio of Mechanical Motion Rectifier N Number of teeth on a gear mod Gear teeth module t Time in seconds θ Angular Displacement in Radians η Efficiency A Amplitude of Vibration in m F Frequency of Vibration in Hz τ Torque in Nm J Rotational Inertia about the intended axis of rotation of a gear or shaft. Word Count 9919 words of main body text, including Titles and Figures.

IP Report - Mechanical Motion RGeoffrey Moore - 25309218

1. Introduction Conventional dampers have systems, by dissipating kinetic energy as heat. However in a worlsubjects including fuel efficiency andhave been designed to utilise oscillatory motion, and turn them into useful energy, most commonly electricity. Many regenerative damper designs move a magnet linearly though a coil, as illustrated in Figure 1, achieving damping by using the induced current to draw energy out of the system. However, more recent designs mechanically transform linear motion into rotato turn a conventional generator.

Figure 2 illustrates an existing design that utilises a rack and pinion arrangement to transform linear motion into rotational motionin particular, a mechanism known as a

Transform bi-directional input motion into u Removes The inertia of the motor is not being reversed, reducing system wear. Allows the use of a flywheel

Provide a gear ratio The gene harmonic Provide an efficient system of rectification.

Minimising losses in the mechanism potential. The focus of this Individual Project will be on designing and developing a new concept for an MMR mechanism, which generates an output motion with the desirable propertiesabove. It is also possible to use a lead screw to convert linear motion into rotational motprevious Southampton Group Design Projects have investigated this concept. It would be useful for a new MMR concept actuation.

Figure 1 - Magnet & Coil Type Regenerative Damper


Conventional dampers have long been utilised to reduce undesirable vibrations in mechanical

kinetic energy as heat. However in a world that is increasingly focussed including fuel efficiency and renewable energies, 'Regenerative Dampers' are devices that

have been designed to utilise oscillatory motion, and turn them into useful energy, most

Many regenerative damper designs move a magnet linearly though a coil, as illustrated in Figure 1, achieving damping by using the induced current to draw energy out of the system. However,

recent designs mechanically transform linear motion into rotational motion within damper, turn a conventional generator. [1]

Figure 2 illustrates an existing design that utilises a rack and pinion arrangement to transform linear motion into rotational motion. However, in order to optimise the system, and the generator

mechanism known as a Mechanical Motion Rectifier could directional input motion into unidirectional input motion into the generator

Removes the requirement for electrical voltage rectification.The inertia of the motor is not being reversed, reducing system wear.Allows the use of a flywheel

gear ratio on the input of the generator generator's optimum operating speed could be tuned to

harmonic frequencies. n efficient system of rectification.

Minimising losses in the mechanism allows greatest energy harvesting potential. Individual Project will be on designing and developing a new concept for an

MMR mechanism, which generates an output motion with the desirable properties

It is also possible to use a lead screw to convert linear motion into rotational motprevious Southampton Group Design Projects have investigated this concept. It would be useful

to be 'compatible' with either rack and pinion or lead screw type

Magnet & Coil Type Regenerative Damper Figure 2 - Rack and Pinion Type Regenerative Dampe

6

long been utilised to reduce undesirable vibrations in mechanical d that is increasingly focussed on

renewable energies, 'Regenerative Dampers' are devices that have been designed to utilise oscillatory motion, and turn them into useful energy, most

Many regenerative damper designs move a magnet linearly though a coil, as illustrated in Figure 1, achieving damping by using the induced current to draw energy out of the system. However,

tional motion within damper,

Figure 2 illustrates an existing design that utilises a rack and pinion arrangement to transform . However, in order to optimise the system, and the generator

be used to: motion into the generator.

the requirement for electrical voltage rectification. The inertia of the motor is not being reversed, reducing system wear.

be tuned to match the system's

greatest energy harvesting

Individual Project will be on designing and developing a new concept for an MMR mechanism, which generates an output motion with the desirable properties detailed

It is also possible to use a lead screw to convert linear motion into rotational motion, and a few previous Southampton Group Design Projects have investigated this concept. It would be useful

to be 'compatible' with either rack and pinion or lead screw type

Rack and Pinion Type Regenerative Damper


1.1 Project Aim To design, develop and evaluate a mechanism that facilitates mechanical motion rectification with a unidirectional, ratioed output velocity and a lead screw-type input. 1.2 Project Objectives

1. Generate mechanism design concepts that exhibit mechanical motion rectification, (with a unidirectional, variable-ratio output velocity and a lead screw-type input). 2. Build a Prototype Mechanical Motion Rectifier based on an original design concept, demonstrating its principle of operation, and is suitable for use in future research into the design.

3. Conduct a theoretical analysis into the MMR design. Investigate the physical and operational characteristics of the design and suggesting suitable applications.

4. Develop a design concept for a suitable Test Rig that would facilitate the physical testing of this MMR.

2. Literature Review A good place to start in the field of Regenerative Dampers is with Jin-qui et. al.'s 'Review on Energy-Regenerative Suspension Systems for Vehicles' [2]. Focusing on road vehicles, this paper summarises various designs of regenerative dampers and suspensions currently under investigation by academics globally. 'Direct drive electromagnetic' dampers are discussed, as well as ball screw type designs and the rack and pinion damper, which is praised for potential integration with active suspension controls to improve the vehicle road handling. Jin-qui et. al. also interestingly discusses another device that utilises a planetary gear actuated by a ball screw, improving the regenerative efficiency. Meanwhile, Li et al.'s 'Energy-Harvesting Shock Absorber with a Mechanical Motion Rectifier' [3] claims to have introduced the concept of rectifying bidirectional motion into unidirectional motion. The concept is developed with an 'electrical equivalent' theoretical model, and physical testing. The design of Li et al.'s MMR, Figure 3, utilises two contra-rotating bevel gears to turn an

output gear, driving the generator. Sprag clutches are used to disconnect the drive of one of the bevel gears depending on the direction of input motion, thus ensuring uni-directional output motion. This design could be adapted to work with a lead screw input, as explored by a University of Southampton Group Design Project [4]. The group design project also introduced an element of direct drive between the lead screw and 'output bevel' to improve efficiency. This restricted the MMR to a 1:1 gear ratio.

Figure 3 - Li et. al's MMR Design


The Southampton Group Design Project also discusses assembly to achieve motion rectification. It is cited that this design gear ratios in opposing directions, and it has high rotational inertia. However, I beliedifficulties might be overcome Another MMR concept, produced by Lin et al, integrated a rackMMR, and was used to generate power from rail tracks. On the subject of gear design, Dudley's Gear Handbook providing the theory relating to gear and gearparticularly useful given the number of terms used in gear design that can easily be confused, (for example Pitch, Pitch Diameter and Diametral Pitch are all different variablesexhaustive source of information on this subjec 3. Methodology3.1 Design ConceptsA mechanical motion rectifier functions by using rotationalcomponents (normally gears) in opposing directions, and then fixing these output shaft using contrarotation in one directionused as the basis of am MMR, so a few desigone for further analysis. 3.1.1 Design Concept 1

This first concept is very similar to that proposed by Li design is used as the output of the device produced by bevel gear aligns axes of the input and output shafts perpendicular in Li et al).

Figure 4 - Bevel GearSprag Clutches shown in yellow


The Southampton Group Design Project also discusses the prospect of utilising a planetary gear assembly to achieve motion rectification. It is cited that this design is poor because of differing gear ratios in opposing directions, and it has high rotational inertia. However, I belie

be overcome. Another MMR concept, produced by Lin et al, integrated a rack-and pinion mechanism into theMMR, and was used to generate power from rail tracks. On the subject of gear design, Dudley's Gear Handbook [5] is an extensive reference book

relating to gear and gear-train design required during thisparticularly useful given the number of terms used in gear design that can easily be confused, (for example Pitch, Pitch Diameter and Diametral Pitch are all different variables

source of information on this subject will provide consistent and correct nomenclature

3. Methodology Design Concepts

rectifier functions by using rotational input motion to turn two separate components (normally gears) in opposing directions, and then fixing these output shaft using contra-rotating sprag clutches. (A sprag clutch, or onerotation in one direction, but locks solid when turned the other way). Many mechanisms could be used as the basis of am MMR, so a few design concepts ought to be explored before selecting

Design Concept 1 - Bevel Gears

This concepttop bevel, turningbevels in opposing directions (one clockwise, one counterclockwise). These gears are not directly mounted to the central shaft, but onsprag clutchesthat they transmit drive to the central shaft when the side bevel turns in a givendrives the smaller internal bevel gear and output shaft.

This first concept is very similar to that proposed by Li et al, excepting that the input shaft of this design is used as the output of the device produced by Li et al. Furthermore, the small internal

axes of the input and output shafts such that they are co.

Bevel Gear MMR Design Concept Sprag Clutches shown in yellow

8

the prospect of utilising a planetary gear is poor because of differing

gear ratios in opposing directions, and it has high rotational inertia. However, I believe that these

and pinion mechanism into the

is an extensive reference book, n required during this project. This is

particularly useful given the number of terms used in gear design that can easily be confused, (for example Pitch, Pitch Diameter and Diametral Pitch are all different variables). Having one

t will provide consistent and correct nomenclature.

input motion to turn two separate components (normally gears) in opposing directions, and then fixing these components to an

rotating sprag clutches. (A sprag clutch, or one-way bearing, allows free any mechanisms could be

n concepts ought to be explored before selecting

This concept functions by driving the , turning the large side

bevels in opposing directions (one clockwise, one counterclockwise). These gears are not directly

to the central shaft, but on sprag clutches that are fitted such that they transmit drive to the central shaft when the side bevel

given direction. This shaft drives the smaller internal bevel gear and output shaft.

excepting that the input shaft of this Furthermore, the small internal

are co-linear, (as opposed to

IP Report - Mechanical Motion Rectifier Geoffrey Moore - 25309218

Figure 6 - Planetary Gear MMR Design

3.1.2 Design Concept 2 - Worm Gears

3.1.3 Design Concept 3 - Planetary Gears

opposite direction, motion rectification couldsprag clutches fitted to both the sun and ring gear to drivemotion, as shown in Figure 6. The gear ratios in either directiongears on the planetary (input) shaft, and meshing one witring gear (P2).

Figure 5 - Worm Gear MMR Design

MMR Design Concept

Gears This design concept uses worm gears to achieve opposing motion for rectification. Figure 5shows that a clockwise threaded worm gear turns in the opposing direction to an anticlockwise threaded worm gear. By mating these gears to sprag clutches, which drive a secondary set of gears as shown, a single shaft may be turned in unidirectional motion. Note that shafts A and B would be parallel in a real design.

Planetary Gears A planetary gear MMR was investigated during the Southampton GDP [4], however theconcept was cited as having differing gear ratios in opposing directions, and having a high rotational inertia. The design utilised the conventional wisdom that the sun and ring gears must be the input and output shaftsrespectively. The design shown in Figure 6 differs significantly from their proposal Because the ring gear rotates in the same direction as the planetgear, and the sun gear ro

ection, motion rectification could be achieved by driving the planetary gear and both the sun and ring gear to drive an output shaft in unidirectional

, as shown in Figure 6. The gear ratios in either direction are equilibrated by placing two gears on the planetary (input) shaft, and meshing one with the sun (P1), and the other with the

MMR Design Concept

9

design concept uses worm opposing

rectification. Figure 5 a clockwise threaded

in the opposing nticlockwise

. By mating to sprag clutches,

which drive a secondary set of gears as shown, a single output shaft may be turned in uni-Note that shafts A and B would be parallel in a real design.

was during the previous

, however the concept was cited as having differing gear ratios in opposing directions, and having a high

e design conventional wisdom

that the sun and ring gears must be the input and output shafts

igure 6 differs proposal .

e ring gear rotates in the tion as the planetary

sun gear rotates in the driving the planetary gear and using

in unidirectional by placing two

, and the other with the


3.1.4 Concept Selection Design Concept Discussion Bevel Gear MMR + Co-linear input and output shafts, make the design versatile and suitable for

many applications, including lead screw driven designs. + Fairly compact overall shape makes the design easy to package and reduces its total inertia. - Bevel gears generate axial loading, which represents reduced efficiency. Thrust bearings must be also used, as simple roller bearing will fail. - The concept is similar to that explored by Li et. al. and the Southampton GDP. Concept Not Selected for further investigation, primarily due to similarity to existing designs.

Worm Gear MMR + Design could be quite slim in the direction perpendicular to the input shaft. - Output shaft perpendicular to the input shaft would potentially result in compromised regenerative damper geometry with the generator axis perpendicular to axis of vibration. - Worm gears are typically inefficient due to high frictional losses. Concept Not Selected for further investigation, primarily due to propensity for mechanical inefficiencies.

Planetary Gear MMR + Low number of gear pairs improves efficiency. + Spur gears are highly efficient and produce negligible axial loading. + Potential for very compact design in the axial direction of the input and output shafts. - Potentially large size in the plane perpendicular to the input and output shafts, increasing inertia. Concept Selected for further investigation

Table 1 - Design Concept Discussion 3.2 Basic System Design and Proof of Concept By examining the Planetary-MMR design concept, two 'design rules' become evident, which must be satisfied for the system to work. That of equal ratio, and concentricity. 3.2.1 The Equal Ratio Rule To optimise the use of a generator, and potentially a flywheel, the magnitude of the gear ratio between the input and output shafts must be constant, regardless of the direction of input shaft motion. A gear ratio can be expressed as the pitch diameter (the effective diameter of the gear) of the driving gear divided by that of the driven gear. Therefore, to equilibrate the gear ratios in the planetary type MMR, the following equation must be satisfied:

= = Equation 1

Where: Ds = Pitch Diameter of the Sun Gear Dp1 = Pitch Diameter of the Planetary Gear that meshes with the Sun (P1) Dp2 = Pitch Diameter of the Planetary Gear that meshes with the Ring (P2) Dr = Pitch Diameter of the Ring Gear R = System Gear Ratio


Figure 7 - Spur Gear Nomenclature

The equal ratio rule also has particular significance on the rotational inertia of the MMR, a topic discussed in section 5.1.1. 3.2.2 The Concentricity Rule The equal ratio rule governs system dynamics, but a second rule is required to ensure that the MMR will actually fit together. The ring and sun gears must be concentric about a single output shaft, and the two planetary gears concentric about the input shaft. Satisfying the following equation ensures that concentricity is maintained:

2 + 2 + 2 = 2 Equation 2

3.2.3 Gear Geometry

Since the pitch diameter does not describe tooth geometry, gears tend to be specified according to theier number of teeth (N) and the module (mod) of the gear, which is the number of teeth per mm of pitch diameter.

= = ℎ For two gears to mesh, the must have an equal module, therefore:

= = Equations 3 & 4

Any meaningful system design equations should be in terms of the module and number of teeth present on each gear in the MMR, not the pitch diameters.


Figure 8 - 'Proof of Concept' Solidworks Model

3.2.4 System Design Equations & System Variables Equations 1, 2, 3, & 4 are used to derive Equations 5, 6 and 7, which give the number of teeth on each gear in the MMR, and govern the system design. For derivations see Appendix-A1.

= = − (1 + 1)(1 − 1) = (1 + 1 − 1 + 1

1 − 1 ) Equations 5, 6, & 7

Equations 3 -7 define the gearing of the MMR using four 'system variables': The number of teeth on P1 (The planetary gear that meshes with the sun gear. See Fig.6) The module of P1 The module of P2 (The planetary gear that meshes with the ring gear. See Fig.6) The overall gear ratio of the system.

These equations may generate non-integer values for the number of gear teeth given certain combinations of system variables. Clearly, this is not possible, restricting the combinations of system variables available for use. 3.2.5 Proof of Concept - 3D Model A proof of concept exercise is necessary to validate these design formulas.

Equations 3-7 were used to find a set of gears with appropriate geometries and ratio (R=1/3). These were developed into a Solidworks model featuring the involute spline geometry, as necessary to demonstrate the mechanism.

Modelling involute gear spline geometry is time consuming, so an involute spline gear generator produced by 'thingiverse.com' user 'Matt Ruggles' proved a useful starting point for the model. Having checked the spline generator for errors, the model shown in Figure 8 was constructed. Particular effort was made transforming the external spline geometry into the internal spline geometry required for the ring gear.

Motion analysis demonstrated that the magnitude of the ring gear velocity was equal to that of the sun gear, they rotated in opposing directions and that the intended gear ratio was achieved, validating the gear design formulas established in section 4.4.

This exercise also highlighted the difficulties of properly defining involute spline geometry. The ring gear didn't mesh perfectly with

the corresponding planetary gear (P2), although the geometry was sufficient for this proof of

Gear No. Teeth Module P1 20 1 P2 40 1 Sun 60 1 Ring 120 1

Table 2 - Prototype Gear Geometry


Figure 9 - 'Proof of Concept' Model - Shown in OMEdit graphical editing tool

concept exercise. It was decided to purchase gears from a supplier to produce the prototype MMR, rather than have them manufactured in house, making absolutely certain that the gears would run together properly. 3.2.6 Proof of Concept - OpenModelica Model Replicating sprag clutch frictional behaviour is very difficult in 3D-modelling programs like Solidworks. Several papers have modelled MMRs as an 'analogous electronic system' instead of generating a 3D model [3] [6]. Modelica is "an equation based [coding] language to conveniently model complex systems" [7]. It is freely available, and with the 'OpenModelica' simulation environment, is capable of modelling sprag clutch behaviour. It is a very powerful tool for simulating the behaviour of an MMR. The 'Modelica Standard Library' already contains a sprag clutch model, 'OneWayClutch.mo'. This model transmits drive when the input turns clockwise with respect to the output. A second model featuring reversed behaviour was required, i.e. locking when the input is turned anticlockwise with respect to the output. This was created by duplicating the original model, then understanding and reformatting the equations within to reverse its behaviour. This model is combined with others from the 'Modelica Standard Library' to form a rudimentary MMR model.

A test rig model was created to simulate the MMR model within. The 'rig' uses positional control to turn the input shaft through a sine curve. Running this simulation, and plotting the positions of the input and output shafts produces Figure 10, which demonstrates the MMR functioning as expected. It is believed to be the first instance of an MMR modelled using mechanical behaviour.


This model does not feature developing an accurate MMR model in Modelicato be conducted. 3.3 Prototype DesignIdeally, proving the functionality of characterisation of the system before designing a prototype. However, due to normal Engineering Design and Manufacture Centrestudy, then build a prototype within the project The prototype design wassystem carried out later. 3.3.1 Prototype Gear SelectionThe gear ratio is very influential onof the device, and the total size of the deviceEquation 7). As no specific application was ratios could be consideredselection process. For an RMS suspension velocity of 0.24:1, depending on the lead screw utilised, (friction). A 3:1 ratio (input : output) was selected for the prototype, as it represented between the velocities thatuseful prototype for further research.sprag clutch assembly. See Section 5.5


Figure 10 - 'Proof of Concept' OpenModelica Model Angle of Rotation (y) vs. Time (x)

Blue = Input Shaft, Red = Output Shaft model does not feature representative inertias or geartrain characteristics. Therefore

MMR model in Modelica will allow a great deal of system characterisation

Prototype Design functionality of the MMR concept would directly precede a theoretical

system before designing a prototype. However, due to normal Engineering e Centre (EDMC) lead times, it was unfeasible to co

a prototype within the project timeframe. was completed with the information available, and a detailed analysis

Selection

very influential on MMR design; it determines the basic input/outputof the device, and the total size of the device through the size of the required ring gear (see Equation 7). As no specific application was intended for the prototype MMR, a broad range of

could be considered. A brief analysis of a motorcycle damper was conducted to focus the

or an RMS suspension velocity of 0.2-0.6 m/s [8], a suitable gear ratio woulding on the lead screw utilised, (which, in this instance, was low pitch and

3:1 ratio (input : output) was selected for the prototype, as it represented that might be expected within a regenerative damper, and

further research. It is possible invert this gear ratio by reconfiguring the See Section 5.5 for further detail.

14

inertias or geartrain characteristics. Therefore will allow a great deal of system characterisation

the MMR concept would directly precede a theoretical system before designing a prototype. However, due to normal Engineering

conduct a theoretical

completed with the information available, and a detailed analysis of the

determines the basic input/output relationship required ring gear (see

prototype MMR, a broad range of . A brief analysis of a motorcycle damper was conducted to focus the

, a suitable gear ratio would be between 3:1 and low pitch and causing high

3:1 ratio (input : output) was selected for the prototype, as it represented a good compromise regenerative damper, and for developing a

gear ratio by reconfiguring the


Figure 11 - A Basic Spreasheet facilitates Parametric Design Understanding the system design equations (section 4.4) highlights that the system overall dimensions are very sensitive to small changes of the P1 gear. By manipulating the modules of P1 and P2, it is possible to reduce P1 down to a small diameter, 16 tooth gear. This reduced the pitch diameter of the ring gear to 57.6mm, making the MMR more compact, and lower inertia. However, 16 teeth is below the ANSI recommended minimum tooth number [5], and without tooth profile and centre distance correction, the gear may mesh incorrectly. The teeth on this gear arrangement are also very small, and concerns existed that they may fail during testing. The decision was made to produce a larger MMR, and the gear geometry used during the proof of concept exercise, as listed in table 2, was actually most suitable. These sizes are commonly available, and more affordable. 3.3.2 Full System Design Gears were sourced from HPCgears.com, while sprag clutches and bearings were sourced from simplybearings.co.uk. With these component dimensions fixed (listed in Appendix 2), full design of the MMR could begin. A few features were selected for inclusion within an ideal design:

A single layshaft positioned opposite the input shaft would counter balance the radial forces generated by gear meshing exerted on the bearings and frame.

A modular flywheel assembly, removable from the output of the MMR, for rig testing. The device should be easily modifiable to be contained within a fully sealed casing to

experiment with system lubrication in future projects. A keyway joint in the sun gear shaft to aid assembly/disassembly.

The MMR design was then completed in Solidworks. A full description of the design process is too lengthy for this report, however, a great deal of time and attention was paid to the design process.

A complete set of engineering drawings for the initial MMR design and flywheel assembly may be found in Appendix A6.


Figure 14 - Initial MMR Section View Bearings in Blue, Sprag cluches in yellow

Figure 13 - Modular Flywheel Design Sprag Clutch in yellow

Figure 12 - Initial MMR Design - Gear Teeth not shown Bearings in Blue, Outer Sprag Clutch in Red


Figure 15 - Initial MMR Lower Case Design

Frame

Sheet Metal Figure 16 - Final MMR Frame Design

Figure 17 - Section Through P2 Gear, Illustrating Grub Screw Fitment and Location Figure 18 - Modified Ring Carrier Design featuring

Plate Section Welded to Cylindrical Tube Section.

3.3.2 MMR Version 2 Design The EDMC estimated that producing the full complexity MMR design required 70 hours of technician time, where the project is allocated just 24. Achieving a 65% reduction in production time was a significant challenge, the majority of which was met through the following design changes: 1. Discarding the flywheel assembly; saving 15 hours of technician time. As a set of components not integral to the MMR itself, relinquishing the modular flywheel was an obvious means to substantially reduce production time. 2. Redesigning the MMR case.

It was originally intended that the lower MMR case would be fabricated from a sheet metal case fixed to a machined frame, as shown in Figure 15. However, the EDMC's capacity to produce the sheet metal components was limited, and the component would require machining from a solid billet. This was both time consuming and prohibitively expensive. The complexity of the case had


Figure 19 - Final MMR Design (Ring Gear Teeth Not Shown)

to be drastically reduced in order to meet the required production time. Figure 16 shows the final design frame design. 3. Grub Screw Gear Fitment. Gears P1 and P2 had been specified as an interference fit over the

8mm (+tolerance) shafts. This meant that 10mm shaft would require careful machining down to a precise tolerance. It was advised that utilising a stock 8mm shaft and attaching the gears using a grub screw threaded through the gears as shown in Figure 17 might be more appropriate. 'Loctite' adhesive could also be utilised to ensure a sufficiently strong connection between the gear and shaft is made.

4. Ring Carrier Modification. The ring carrier was subjected to amendments to ensuring it wouldn't require machining from a solid metal billet. Rather, joining a section of tube to a plate section, as illustrated in figure 18, saved both machining time and significant cost.

3.3.3 Final MMR Design These changes significantly simplified the design of the MMR. The final assembly is shown in the figure below, and full engineering drawings of each component may be found in Appendix A7.

3.3.4 Manufacturing and Assembling the MMR The above changes and numerous other smaller amendments brought the estimated technician time to approximately 30 hours. In order to meet the allocated 24 hours, it was agreed that certain components and final assembly stages would be completed by myself. These were:

Frame Tie Bar (x2) Frame Joint Input Shaft Drilling and Threading P1 and P2 for

Grub Screw Assemble Input Shaft and Fitment into Front Housing Output Shaft Assembly Fitment into Rear Housing Sun Gear Shaft Fitment into Front Housing Final Assembly


Figure 20 - Proper Operation of a Sprag Clutch Note how the surfaces of the sprag are in contact with the inner and outer race when the sprag clutch is

engaged, but are free (or sliding) when the sprag clutch is disengaged.

Figures 21 & 22 - Disassembly of the Outer Sprag Clutch Assembly

Producing these components required an understanding of milling, drilling, thread tapping and pressing operations. A few photographs taken during the self-manufacturing process are in Appendix 5. In addition to this work, inspection of the parts completed by the EDMC revealed that the outer sprag clutch was not operating as intended. It required a significant force to rotate the sprag clutch in the direction where it should have been rotating freely.

If the outer race of the sprag clutch is under compression, or the inner race being expanded, the disengaged condition may not occur, since the inner and outer races would remain tight against the sprag. It was therefore concluded that the outer sprag clutch assembly (Figure 21) must be disassembled, in order to re-machine whichever component was interfering with the sprag clutch.

The sprag operated normally with the ring carrier removed, since the inner bore of the ring carrier was found to be 0.17mm larger than the ideal tolerance for a bearing press fit. To maintain concentricity, the bore was very carefully re-machined, turning out 0.17mm. When pressed back over the outer sprag, the mechanism worked as intended. No similar problems were experienced with the smaller, inner sprag clutch. All components could then be assembled into the completed MMR prototype.

Bore to be re-machined


Figure 23 - Above: Full MMR Model produced in OpenModelica Connection Editor Left: Model Annotated to Illustrate Grouping of Components

3.4 OpenModelica Modelling Following the OpenModelica proof of concept exercise, it was felt that there was significant scope within the software to develop a fully parametric model of the MMR design as a mechanical system, and run a series of virtual rig tests. Appendix A8 contains an introduction into using OpenModelica. 3.4.1 Developing a Full MMR Model The model used in the proof of concept exercise was very simplistic, and bore little resemblance to a real MMR design. Developing a parametric model of the full complexity MMR design (see section 3.3.2 and Appendix A6) would be more representative of a real system. Rotational inertias for each component were calculated (see Appendix A3), which facilitated the initial construction of the MMR and Rig models in OpenModelica.


Figure 24 - MMR Rig Model - With Sinusoidal Input Signal

Figure 25 - Kinematic Loop Shown in Red

However, some debugging was required to ensure these models run and produce meaningful results. Particularly significant stages in the development of the model were:

The 'reverse sprag clutch' model, initially developed for the proof of concept exercise, was found to contain small errors which caused simulation failures in a more complex model. In particular, it must be modified to lock when the rotational velocity across the sprag is less than zero, as opposed to less than or equal to zero (the 'standard' configuration). This prevents an error occurring where both sprag clutches are instantaneously locked, causing the simulation to fail.

Resolving a closed kinematic loop within the system. A closed kinematic loop essentially means that the start and end conditions of a mechanism are equal. Figure 25 highlights where the inclusion of the layshaft in the MMR design introduces a kinematic loop. Modelica needs to be instructed how to resolve the loop. Following much research, Otter, Elmqvist and Mattsson's 'The New Modelica Multibody Library' [9] was useful in suggesting that setting the selectState parameter within an inertia component as 'always' forces Modelica to use rotational displacement and velocity as 'states' for the component, thus allowing the kinematic loop to be resolved. The 'P2_IS_Inertia' component with 'selectState = always', removed the error.

Introducing Backlash into the Gear model. Michael Tiller's 'Modelica by Example' [10] contains both excellent instructions for constructing a gear pair with lash model, and an example code for connecting the subsystem models required for a gear pair with lash. This code was later re-parameterised for use in the MMR model, after efforts to produce a bespoke gear lash model turned out further errors while compiling.

It was then possible to start running simulations, and gaining an understanding of the MMR's behaviour.


Figures 26 (Left) and 27 (Right) - Completed MMR Prototype. Input shaft shown in Figure 26, Output Shaft shown in Figure 27

Figures 28 (Left) and 29 (Right) - Completed MMR Prototype Detail. Figure 28 - Correctly toleranced centre distances ensures that the gears mesh correctly and run together well.

Figure 29 - The Sprag Clutch Assembly in detail.

4. Results 4.1 - The Completed MMR Prototype The design and manufacturing process produced a completed MMR prototype.

Small Inner Sprag

Large Outer Sprag


Figure 30 - Prototype MMR - Sun Shaft Keyway feature allows simple assembly and disassembly The finished MMR Prototype behaves as expected and the gears run together well demonstrating

that the engineering principles maintained throughout design and manufacturing were correct and appropriate. Several observations of the prototype design can be made: 4.1.1 Sprag Clutch Friction. When turning the input shaft by hand, it is obvious that it requires less torque to turn clockwise than to turn anticlockwise. This is because the large sprag clutch exerts a larger drag force when turning freely than the smaller inner sprag clutch does. Thus, the MMR frictional losses will have distinctly different behaviour dependent on input shaft direction. Section 5.6 discusses a potential design change that utilises two identical sprag clutches in the MMR. 4.1.2 Overall Size. The MMR is large in the radial direction (Height = 170mm approx.), but quite compact in the axial dimension (56mm, including frame). This type of geometry is an inherent trait of the Planetary-MMR, and affects the type of system the device might be used in. 4.1.3 Mass and Inertia. Due to manufacturing time and budgetary constraints throughout the project, opportunities to reduce the mass and inertia of the MMR were constrained, and the final prototype is relatively heavy, weighing 1.86kg. If the mass and inertia of the MMR is significantly large with respect to the system it is installed in, then the MMR will account for a measureable change in the dynamics of the system, particularly its resonant frequencies. Section 5.1 discusses inertia further. 4.1.4 Minimal Backlash. The appropriate tolerances used throughout the prototype's design mean the gear backlash is very small. This is beneficial, since energy is lost each time the direction of input motion is reversed, and the gear teeth must move through the lash before motion is transmitted. A hypothesis that, "the effect of lash within the prototype MMR is negligible when


Figure 31 - MMR Response to input function sin(2πt) - Angle of Rotation vs. Time θin = Red, θout = Blue

the angle of input shaft rotation is large," can be tested using the OpenModelica Model. (See Section 4.2.2)

4.2 - OpenModelica Modelling Results 4.2.1 Input Output Relationship It is relatively simple to verbally describe the function of the MMR as to translate bi-directional rotational motion into uni-directional rotational motion. However, it should be possible to mathematically describe the action of the MMR as transfer function. It could be initially hypothesized that:

= | | Equation 8

θout = Displacement of the Output Shaft in Radians θin = Displacement of the Input Shaft in Radians R = Gear Ratio

When the input = sin(2 ) is passed into the modelica model, the plot shown in Figure 31 is produced. (Where R=1/3, t = time in seconds). This plot demonstrates that equation 8 is valid where t<0.25s, the initial period of motion, before the direction of input shaft rotation changes, but does not hold true beyond t=0.25. For example, at t=0.5, θin = 0, and θout =0.66, where equation 8 suggests that θout should also be zero. A new hypothesis is therefore required. Figure 31 demonstrates that at t=0.5 the input shaft has rotated one radian clockwise, and one radian anticlockwise, two radians in total. The output shaft has rotated 0.66 radians clockwise. This indicates that the displacement of the output shaft corresponds the distance travelled by the input shaft rather than its displacement, given by the formula:


Figure 32 - MMR Response to input function 2sin(2πt) + 0.1sin(50πt) - Angle of Rotation vs. Time θin = Red, θout = Blue

= |∆ | + |∆ | + |∆ | Equation 9

ℎ ℎ ℎ = 0, = 0 = To solve Equation 9 for = sin(2 ) , the Z values (times where = 0) are found by:

= 2 cos(2 ) = 0, = 0.25, = 0.75, … These Z values are then used in equation to find at any given time, for example tmax = 0.5.

, . = 13 (|sin(2πZ )| + |sin(2πt ) − sin(2πZ )|)

, . = 1

3 (|sin(2π ∗ 0.25)| + |sin(2π ∗ 0.5) − sin(2π ∗ 0.25)|) = 13 (1 + |0 − 1|) = 0.666

Equation 10 The correlation between Equation 10 and Figure 31 suggests that an appropriate transfer function has been found. To test whether Equation 9 is true for all functions of input displacement, a more complex θin function may be compared with the output of the Modelica model. The Input formula = 2sin(2 ) + 0.1 sin(50 ) is designed specifically to undergo a significant number of motion reversals to test equation 9. A Matlab script calculated an array of Z values (times at which = 0, between t=0 and tmax), and implemented these in equation 9. When tmax =1 and R=(1/3), the script yielded , =3.887 . Implementing = 2sin(2 ) + 0.1 sin(50 ) in the modelica model produces the following plot:

The modelica software finds that , = 3.888 .


The correlation between the modelica model and theory function of the MMR is:

=

ℎ 4.2.2 - The Effects of BacklashIn section 4.1.4, it was hypothesised that when the angle of rotation of the input shaft is large, the effect of backlash would be negligibleaccount for backlash, and negligible lash for large amplitude vibration 4.2.2.1 - Introduction to Backlash

However, gear lash shouldn'tthe MMR, it is useful to understaclearance between mated teeth equal to the tooth spacing minus the tooth thi This clearance is required to stop the gears making contact on both sides of a single tooth, causing the mechanism to jam. When the direction of rotation of the driven gear is through this clearance, during which time, no drive is transmittedcritical angular displacementdisplacement depends on the toocorrection, but for the prototype MMR discussed in this report,is 0.0225 radians [11]. (Calculated Therefore:


Figure 33 - Gear Backlash

The correlation between the modelica model and theory is 99.97%, serving to validate the transfer

= |∆ | + |∆ | + |∆ |

ℎ ℎ = 0,

The Effects of Backlash In section 4.1.4, it was hypothesised that when the angle of rotation of the input shaft is large, the effect of backlash would be negligible. The 99.97% correlation between a

and a Modelica model that includes it, suggests that the hypothesis of for large amplitude vibration is valid.

Introduction to Backlash

lash shouldn't be disregarded entirely. To understand the impact lash will hasuseful to understand exactly what it is. Figure 33 illustrates that

mated teeth equal to the tooth spacing minus the tooth thiThis clearance is required to stop the gears making contact on both sides of a single tooth,

the mechanism to jam. However, too higher value of backlash causes excessive wear.When the direction of rotation of the driven gear is reversed, the mating teeth must move through this clearance, during which time, no drive is transmitted and energy is lost

displacement must be exceeded to transmit drive between the gearson the tooth size, manufacturing tolerances and gear centre distance

correction, but for the prototype MMR discussed in this report, the worst case value for (Calculated with PCD of P1 and P2).

, = 0.0225

26

is 99.97%, serving to validate the transfer

Equation 9

= 0 =

In section 4.1.4, it was hypothesised that when the angle of rotation of the input shaft is large, the theory that does not

model that includes it, suggests that the hypothesis of

impact lash will has on illustrates that there exists a

mated teeth equal to the tooth spacing minus the tooth thickness. This clearance is required to stop the gears making contact on both sides of a single tooth,

However, too higher value of backlash causes excessive wear. reversed, the mating teeth must move

and energy is lost. Therefore a between the gears. This

gear centre distance worst case value for total lash


Figure 34 - Effect of Gear Backlash at Low Amplitude - Angle of Rotation vs. Time θin = Red, θout = Blue

Figure 35 - Effect of Gear Backlash at 100Hz, Low Amplitude - Angle of Rotation vs. Time θin = Red, θout = Blue

i.e. any input rotation smaller than , will not be transmitted into the output shaft.

Note that the maximum displacement is equal to twice the amplitude of the sine wave. 4.2.2.2 - Backlash Frequency Independency It is worth emphasising that backlash is completely independent of frequency. It does not matter how many times per second the MMR rotates through the lash, no drive will be transmitted during this motion, as is illustrated by comparing Figures 34 and 35.

Many systems have some form of relationship between frequency and amplitude. In the most general of terms, vibration frequency tends to increase as amplitude decreases. However, unless a specific application of the MMR is defined, one cannot define a 'critical frequency for backlash'. 4.2.2.3 - Backlash 'Filter' Effect


Figure 36 - MMR response to 50Hz, 0.04 Radian Amplitude Sinusoid - Angle of Rotation vs. Time θin = Red, θout = Blue

When an nominal input is passed to the Modelica model which consists of one large amplitude vibration ( . . 10sin(2 )), and a second vibration with amplitude less than θcrit,,lash ( . . 0.01 sin(100 )), for example;

= 10sin(2 ) + 0.01 sin(100 ) the response of the system (θout) is identical to the response to:

= 10sin(2 ) The backlash is effectively 'filtering out' very low amplitude vibrations. This represents an inefficiency within the MMR, which might be calculated as:

= , , ℎ = 0.0110.01 = 0.1%

This demonstrates that the inefficiency caused by backlash becomes appreciable as ⟶

, , i.e. the maximum amplitude of rotation of the input shaft is small, within a factor of 100 (or so) of the critical amplitude for lash. It is unlikely that a gear based MMR design would be utilised in a system with very low amplitudes of vibration because of this loss of energy. It is also entirely possible that the 'backlash filter effect' may increase the service life of a motor generator in an energy harvester by removing potentially damaging high frequency vibration. 4.2.3 - The Effect of Frequency

Figure 31 (See Section 4.2.1) shows the output displacement profile is very non-linear given a low frequency, 1Hz input. If the frequency of the input is then increased to 50Hz, and the amplitude reduced to 0.04 radians, Equation 9 indicates that the output of the MMR will be displaced an equal amount when simulated over a one second period.


Plotting this higher frequency signal yields Figure 36. It is interesting to observe that as the frequency increases, the output shaft displacement has become quasi-linear, despite the total displacement being identical to that of Figure 31. This quasi-linearity occurs because a higher frequency may cover the same distance as a low frequency input, but in multiple smaller 'steps', making the motion appear more consistent. It is perhaps analogous to think of this like the frame rate of a video camera, if a man is filmed for one second walking from A to B at a frequency of 3 frames per second, he will appear to 'jump' along his path in discrete steps. If the frame rate is 100 frames per second, the man appears to be walking smoothly. This may be useful for basic calculations for the output of the MMR, by using the approximation that the output velocity is constant. However, a constant velocity implies zero acceleration of the MMR output shaft. This is far from the case:

= ℎ ℎ 1 =

= sin(2 ) , ⇒ = 2 (2 ) , ⇒ = −4 (2 ) Note that:

, is independent of frequency, but , ∝ . The maximum acceleration of the output shaft actually increases as a factor of frequency, rather than approaching zero as the 'quasi-linear' behaviour might suggest. This has a profound effect on the torque exerted upon the motor generator:

= ∗ ⇒ ∝

= ℎ ℎ ℎ ℎ ℎ Therefore, systems with higher operating frequencies need motor generators with higher torque capabilities. Equally, as the frequency increases, the effect of increased MMR inertia on the torques in the system will be more pronounced.


Figure 37 - MMR Response to Random Input - Angle of Rotation vs. Time θin = Red, θout = Blue

4.2.4 - Response to a Random Input It is now possible to examine the response of the MMR to a random input signal, and understand its behaviour.

Throughout the motion of the MMR Output, the established rules of MMR operation are maintained in Figure 37.

The displacement of the output shaft is always equal to the distance travelled by the input shaft multiplied by the gear ratio of the MMR, according to Equation 9.

The high frequencies have produced the appearance of a smooth output displacement. Although not visible in Figure 34, the vibrations with amplitude less than θcrit,,lash were

'filtered' out of the result. 5. Discussion 5.1 - Theoretical Planetary-MMR Inertia A basic principle of Planetary-MMR operation is that when the sun gear drives the output shaft, the ring gear and layshafts are also being driven by the input shaft, similarly, the sun gear is still driven by the input when the output is driven by the ring gear. This means that the rotational inertia of the MMR, (observed at the output shaft) must take into account both the rotational inertias of the components that are directly transmitting drive, and those that are not. When the ring gear is driving the output, Equation 11 gives the total system rotational inertia realised at the output shaft of the MMR:


= + + + + + 1

+

⇒ = + + + + + +

Equation 11 Where:

= ℎ ℎ ℎ ℎ ℎ = ℎ

= ℎ ℎ = = ℎ , 1 2

= ℎ ℎ ℎ ℎ ℎ ℎ ℎ .

= ℎ = ℎ , 1 2 = = = ℎ

( ℎ ) If drive is considered to be transmitted through the sun gear (opposed to through the ring gear), equation 11 is still derived. The total inertia of the MMR is therefore constant regardless of the direction of input motion. This occurs because when the ring gear is driving the output, the inertia of the sun gear and shaft realised at the output shaft is reflected through two gear ratios. Since = is stipulated by the 'Equal Ratio' design rule, (see section 3.2.1), the ratios must cancel while deriving equation 11, therefore the contribution of the sun gear and shaft does not carry a multiplication factor. The same cancelling of ratios occurs when the sun gear drives the output shaft. Therefore the inertia formula does not change depending on input shaft direction, and the total rotational inertia (Jt) is constant. Having non-constant values for rotational inertia could create an energy harvester with differing responses depending upon the direction it is actuated in, given that = . Indeed, the planetary gear MMR design discussed by the Southampton Group Project [4] cited that their concept's imbalanced gear ratios were a significant disadvantage. This highlights the crucial importance of the 'Equal Ratio' Design Rule, however simple it appears. 5.1.1 - Prototype Planetary-MMR Inertia Using Equation 11 and the inertia values from Appendix 3, the rotational inertia of the prototype MMR may be calculated (by neglecting the motor and actuation mechanism terms in Eq.11):

= 0.000007767


Figures 38 (Left) and 39 (Right) - Prototype Ring Gear vs. Revised Ring Gear Design

= 0.002533808 + 0.000293427 = 0.000000189 + 0.000000961 + 0.000015758 = 0.000079842 + 0.000000101 + 0.000000453 = 1/3

= + + + + + + ⇒ = 0.000007767 + 0.002533808 + 0.000293427

+ 0.000000189 + 0.000000961 + 0.000015758(1 3) + 0.000079842 + 0.000000101

+ 0.000000453 ⇒ = 0.002835002 + 0.000152172 + 0.000080396 ⇒ = 0.00306757 . For reference, the MMR has an approximately equivalent rotational inertia to a cylinder, length 100mm and radius 40mm, formed in mild steel (7850 kg/m3 approx.). Whether or not this inertia is significantly large depends on the inertia of the energy harvester the MMR is deployed in, however, it would be worthwhile to look into how inertia can be reduced. 5.1.2 - Prototype Planetary-MMR Inertia Reductions The component inertias, found in Appendix 3, make clear that the Ring Gear is the largest contributor to the inertia of the MMR, accounting for a massive 83% of JMMR out. Assuming the ring gear can be modelled as a hollow cylinder, its inertia is given by = ( − ). Inertia can therefore be reduced by:

Removing material from its outer radius. Reducing its width. Noting that the P2 gear must not contact the ring carrier.

IP Report - Mechanical Motion Rectifier Geoffrey Moore - 25309218 Figure 41

0 5 10 15-6000

-5000

-4000

-3000

-2000

-1000

0

1000

2000

3000

Force

[N]

Normal Force on P1Radial Force on P1Tangential Force on P1Normal Force on P2Radial Force on P2Tangential Force on P2

Figure 38 illustrates how the existing prototype riradius of 150mm to 130mm, leaving justreducing its thickness to 9mm. These simple measures reduce the rotational inertia of the original value, and the total rotational inertia of the MMR to original value. Other measures can reduce inertia further, such as machining out unnecessary material from the P2 and Sun gears, which can be seen in figure As the inertia of the MMR is reduced, so is the effect system's response to vibration. Equally, minimising the mass of the system widens the number of energy harvesting applications the MMR can be utilised in. This is e 5.2 - Gear Meshing Force AnalysisWhen gears mesh, the force generated between the teethalong the line of action of the gear, as is illustrated in Figure 40 The line of action is the line traced by the point of contact of the two gear teeth. The force acting on the gears, Fn is oftentangential and radial force (Ft and Fr). Tis the 'pressure angle' of the gear. Unlike Helidon't generate an axial force. These forces generate loads on the shaftteeth and bearings are typically the failure prone SESM3002 lecture, "Gear Trains & Automotive Gearboxescalculating the forces exerted upon these components

Figure 40 - Spur Gear Meshing Forces

Figure 41 - Forces on Gears P1 and P2

15 20 25 30 35 40 45Input Shaft Torque [Nm]

illustrates how the existing prototype ring gear can be machined back from an outer of 150mm to 130mm, leaving just four 3mm thick flanges to mount the ring carrier to

These simple measures reduce the rotational inertia of the ring gear to 0.000569 kg.m, and the total rotational inertia of the MMR to 0.001095275 kg.m3, 36%

reduce inertia further, such as machining out unnecessary material from the P2 and Sun gears, which can be seen in figures 51 and 52, section 5.6. As the inertia of the MMR is reduced, so is the effect the MMR has on the energy harvesting system's response to vibration. Equally, minimising the mass of the system widens the number of energy harvesting applications the MMR can be utilised in. This is explored further in Section

Gear Meshing Force Analysis , the force generated between the teeth (Fn) lies

, as is illustrated in Figure 40. of action is the line traced by the point of contact of the

is often broken down into a ). The angle between Fn and Ft

r. Unlike Helical gears, Spur gears

shafts and bearings within the MMR. In gear mechanisms,are typically the failure prone components. Using the principles outlined by

Automotive Gearboxes" [12], a Matlab script can be produced, exerted upon these components. This script may be found in appendix 4

33

Spur Gear Meshing Forces

50

ng gear can be machined back from an outer four 3mm thick flanges to mount the ring carrier to, and

kg.m3, 22% of its % of its

reduce inertia further, such as machining out unnecessary material from the

has on the energy harvesting system's response to vibration. Equally, minimising the mass of the system widens the number of

xplored further in Section 5.7.

In gear mechanisms, gear sing the principles outlined by

n be produced, appendix 4.


Figure 43 - Bearing Loads 0 5 10 15 20 25 30 35 40 45 50-5000

-4000

-3000

-2000

-1000

0

1000

2000

3000

Input Shaft Torque [Nm]

Force

[N]

Vertical Force on Input Shaft BearingHorizontal Force on Input Shaft BearingVertical Force on Sun Shaft BearingHorizontal Force on Sun Shaft BearingVertical Force on Output Shaft BearingHorizontal Force on Output Shaft Bearing

Figure 42 - Prototype MMR Construction Bearings Shown in Blue

Figure 41 shows the meshing forces varying linearly with torque, and that tangential forces are far higher than normal forces, which is to be expected. The forces on P1 are higher, since = ( = gear radius), and P1 has a smaller radius. Therefore the teeth on gear P1 may exhibit worse wear and be more failure prone than their counterparts on P2. Future MMR lubrication strategies should therefore prioritise effective lubrication of the P1-Sun gear mesh. The forces exerted upon the ring and sun gears will be of equal magnitude (but opposite sign) to that of the P2 and P1 gears respectively. These forces, and the positions of the gears on their shafts are used to calculate the bearing loads.

The horizontal forces on the bearings are typically larger than the vertical loadings, corresponding to the larger tangential meshing forces which are being transmitted into the bearings. It is interesting that despite the input shaft being supported by a single bearing, it does not experience as higher loads as the output shaft assembly bearings. This appears to be because the large force exerted by the Sun Gear is not sufficiently balanced by the Ring Gear, and is creating a moment in the shaft. Consequently, the entire assembly shown between the upper two bearings in Figure 42 is trying to rotate. This rotation is resisted by frame via the bearings. The output shaft bearing has largest loading for any given torque, making it the most likely bearing to fail.


Figure 44 - OpenModelica Flywheel Model

No moment is generated on the input shaft, despite the input shaft effectively being a cantilever beam, since the forces on it have been specifically designed to cancel one-another out:

= ( ∗ − ∗ ) Where:

= , ⇒ = 0.04 , = 0.02 = ℎ ℎ ℎ ℎ ℎ

By tuning the locations of the P1 and P2 gears, the moment on the input shaft is always zero.

= 0.01 , = 0.02 ⇒ = (0.04 ∗ 0.01) − (0.02 ∗ 0.02) = 0 5.3 - Flywheel Analysis 5.3.1 Modelling the Flywheel One of the benefits of utilising an MMR within an energy harvester was the possibility of it driving a flywheel, from which a motor generator can draw energy.

The flywheel assembly comprises of two main components, a sprag clutch and a mass. The sprag clutch will only engage and drive the flywheel while the rotational velocity of the MMR output is equal to that of the flywheel. When the MMR decelerates, the flywheel should continue spinning at the maximum velocity reached by the MMR output. When the flywheel output is attached to a generator, it is always being decelerated toward the MMR output velocity. When this velocity is reached, the sprag re-engages, and accelerates the flywheel. The motor generator may be modelled as a simple brake in OpenModelica. The heat dissipated by the brake is equivalent to the power that generated with a motor. This can be found in OpenModelica by enabling the 'heat port' option within the Brake, and by observing the heat flow into a lumped mass.


Figure 45 - Test Rig with Flywheel

Figure 46 - MMR Output and Flywheel Velocity - Radians/sec vs. time θMMR,-Output = Red, θFlywheel = Blue, Sprag Engaged (Boolean) = Green

Simulating the MMR rig model shown in Figures 45 generates Figures 46 and 47.

Figure 46 shows the flywheel maintaining a higher average velocity than the MMR Output. The green line is a Boolean reading 1 when the sprag is engaged, and 0 when disengaged. Where a solid green area exists, the deceleration of the MMR output is approximately equal to the deceleration of the flywheel, causing the sprag to engage and disengage very quickly.


Figure 47 - Power Output (W) with Flywheel vs. time Motor Generator modelled with 3N braking force

5.3.2 Flywheel Advantages The power dissipated by the brake is shown in Figure 43, and is direct proportionality to the flywheel velocity, with a peak power output of around 75 watts. Notice that during decelerations in the energy harvester's actuation system energy is being dissipated within it. However, during this period the flywheel is disconnected from the rest of the energy harvester, and the energy stored in the flywheel is used by the motor to generate energy. This is why utilising a flywheel has the potential to increase the energy generated by an energy harvester. A reasonable hypothesis is that the peak amount of energy extracted from an energy harvester with a flywheel is obtained by implementing motor control such that the flywheel velocity is maintained marginally higher than output speed of the MMR whenever the actuation system is decelerating. This ensures the sprag clutch is open while the system is decelerating, meaning that flywheel energy is harnessed by the motor, rather than dissipated by the actuation system. 5.3.3 - Disadvantages of a Flywheel Using a flywheel does bring significant compromise. 5.3.3.1 - Inertia Variation Because the sprag clutch disconnects the flywheel from the rest of the system while the energy harvester is decelerating means that the inertia that is directly attached to the vibrating mass varies during system acceleration and deceleration. This means that the energy harvester has a totally different response and harmonic frequencies depending on whether it is experiencing positive or negative acceleration. 5.3.3.2 - Loss of Control The motor generator is the only component that provides active control over the energy harvester. When the sprag clutch is open, the motor is no longer connected to the vibrating mass.


Figure 48 - MMR Test Rig Concept, Actuation System

This is extremely problematic in regenerative dampers as the system becomes intermittently undamped, as the motor generates most of the damping. Implementing a flywheel within a system where control over the vibrating mass is required, for example an automotive damper, would be very difficult to achieve. 5.4 - MMR Rig Concept No existing rig at the university is appropriate for physical testing of the Prototype MMR, and a new test rig would have had to been designed and built to test the device. Unfortunately, this would not be possible during this project. During time spent investigating the possibility of developing an MMR test rig, a concept rig was established that could generate the type of input motion required to test the MMR. No single device at the University is capable of controlling oscillating rotational motion across a reasonable range of frequencies. However, an electrodynamic shaker can produce linear vibrations, based upon a controllable input signal. If the shaker were used to drive a nut along a lead screw, the resulting rotation could drive the MMR. However, a problem arises if the shaker is directly driving the nut. The maximum amplitude of the shaker is around 10mm, and the pitch of the lead screw available is 50mm. Therefore, with the shaker directly actuating the nut, the lead screw would turn just 0.2 rotations, since = ℎ ∗

∗ . Figures 44 and 45 shows how a lever arm is used to amplify the motion of the shaker. The amplification factor is given by , where a and b are the distances between the fulcrum and the point where force is applied on the lever. In Figures 48 and 49, = 10.


Figure 49 - Test Rig Lever Arm

Figure 50 - Planetary-MMR Ratio Inversion

The input motion generated by the rig is given by:

= ℎ ∗ ∗ 602

Where:

= ℎ [ ] ℎ = ℎ ℎ[ ]

= [ ] Axial loading on the lead screw is generated by this rig. To avoid possible damage to the MMR input shaft bearing, mount the lead screw between thrust bearings, which can deal with these loadings. The output of the MMR may be attached to devices including:

Motor Generator Flywheel Hall Effect velocity sensors (input and

output shafts) to effectively characterise the behaviour of the system and complete the rig assembly. 5.5 - Gear Ratio Inversion The current configuration of the prototype MMR gears the input : output velocities at 3:1. However, it would be very simple to reconfigure the MMR to a 1:3 ratio. Figure 50 shows that by removing just one sprag clutch, turning it around, and then treating the existing output shaft as an input shaft (and vice versa), the ratio will be inverted. It is advisable to remove and re-fit the outer sprag clutch, which can be pressed from the output shaft, whereas the inner sprag must be pulled from inside it.


Figure 51 (Left) - Revised Prototype MMR Figure 52 (Right) - Revised Prototype Section View, Front Housing and Bearings not shown.

5.6 - Prototype Revisions Following completion of the Prototype MMR and the theoretical analysis of its behaviour, a few design revisions might be suggested to further enhance the prototype's performance.

5.6.1 - Revised Sprag Clutch Assembly In Section 4.1.1, it was noted that the two sprag clutches had different drag forces, meaning the MMR required more torque to turn in one direction than the other. To address this, the sun gear is modified to have a sprag clutch pressed into it, and a second identical sprag clutch is used to mount the ring gear. The sprags can be fitted to set the gear ratio as desired (See Section 5.5). 5.6.2 - Reduced Length Using a smaller sprag clutch to mount the ring gear to the output shaft provides sufficient clearance between the re-designed ring carrier and the P2 gear to flip the ring carrier around, and house the sprag within the ring gear, reducing the axial length of the MMR mechanism by 13mm (35%). The inclusion of an output shaft joint is now more difficult, and the MMR could not be assembled/disassembled so easily.


Figure 53 - PowerBuoy

5.6.3 - Reduced Inertia The reduced inertia ring gear suggested in 5.1.3 is integrated into the design. The Sun and P2 gears have been machined out, further reducing the rotational inertia of the design. 5.7 - Potential Applications of the Planetary-MMR 5.7.1 - Automotive / Motorcycle Suspension Regenerative Damper Automotive regenerative dampers are a relatively established technology, and many design variants exist. Li et al. produced a damper that features a bevel gear based MMR [3]. If the Planetary-MMR is to warrant further investigation in an automotive damper, it must compare favourably against the bevel-MMR for this application.

Size - Automotive dampers are typically tightly packaged components. The Planetary-MMR's large ring gear makes fitting it within a damper fairly challenging, restricting maximum gear ratio. This restriction is less significant for the radially compact bevel-MMR.

Lead Screw Input - The Planetary-MMR may utilise a lead screw input, although the frictional losses within a lead screw become increasingly significant its velocity increases. It is unlikely that a lead screw would be utilised in an automotive damper, versus Li's rack-and-pinion mechanism, for example.

Frequency - The vibration frequencies of a road input can be as high as 800Hz, [13] making the larger inertia of the Planetary-MMR a significant disadvantage versus the bevel concept.

It seems unlikely that an automotive regenerative damper is a well suited application for Planetary-MMR. 5.7.2 - Wave Energy Wave Energy Generators, such as PowerBuoy from Ocean Power Technologies, transfer relative linear motion between a float and heave plate into rotational motion, driving a generator [14]. Several characteristics of these devices seem to compliment the Planetary-MMR.

Size and Mass - The PowerBuoy is a vast device, the total mass of the PB10 model is 33,000kg. The generator is located within the spar, mounted to the heave plate, so mass added by the Planetary-MMR could be subtracted from the heave plate. In theory, the Planetary-MMR would fit well within the large cylindrical body.


Wave Motion - The higher amplitude and lower frequency of wave motion versus other sources (such as an automotive damper) reduces the impact of the Planetary-MMR's higher rotational inertia.

Flywheel Potential - A flywheel could be implemented on the output of the MMR to

increase energy generation potential. The mass of the flywheel could also be subtracted from the mass of the heave plate, maintaining the buoyancy of the device.

5.7.3 - Motion of Trees In recent years, novel concepts have emerged, generating energy from the motion of trees. McGarry and Knight [15] developed a system whereby a long cord is tethered to a tree at one end, and the other wrapped around a hub, which is actuated as the tree moves in the wind. The hub's rotation drives a generator which is affixed to the ground. In principle, there is scope to utilise an MMR and flywheel assembly between the output of the hub and the generator in order to rectify the motion of the hub, increasing the power output of the generator. However this technology still in its infancy, and far from optimised in its current state, so it is difficult to conclude whether a Planetary-MMR presents the best solution for rectifying the motion of this device. 6. Conclusion The aim of this project was, "To design, develop and evaluate a mechanism that facilitates mechanical motion rectification with a unidirectional, ratioed output velocity and a lead screw-type input." A series of MMR design concepts were established, and an idea based on a planetary geartrain was investigated throughout this report. Basic design parameters for the system were established, (Equations 5, 6 & 7), and a proof of concept exercise validated these principles of MMR design. An initial prototype design demonstrated how an complex MMR design might look, while a second prototype design focussed on manufacturing process efficiency. The second design was manufactured and assembled, ready for future rig testing A theoretical analysis of MMR operation was facilitated using Modelica computational modelling to model the MMR as a physical system. Where previous MMR models used an 'analogous electrical circuit approach' [3] [6], it is believed that this report is the first example of an MMR modelled as a mechanical system. Theoretical analysis:

Established the overall motion transfer function of an MMR. Finding the effect of Backlash on the Device to be largely negligible for high amplitude vibrations. Increasing frequency of input motion generates quasi-linear output motion, although instantaneous peak accelerations are high. The inertia of the MMR is constant when equivalent gear ratios for clockwise and anticlockwise motion are utilised, and the rotational inertia of the prototype was calculated as 0.00306757 kgm2.


Analysis of the Gear Meshing Forces in the Prototype allowed for an assessment of likely component failures.

Utilising a flywheel can increase energy generation, but reduces control over the vibrating mass. A concept rig for physical testing of the MMR prototype was established, and various potential future modifications to the prototype MMR were discussed. Finally an analysis of potential applications for the planetary-MMR established that a wave energy harvester might be a suitable system in which to implement a planetary-MMR. In this way, all of the aims and objectives of this project have been satisfied. Future research into the planetary-MMR should focus on physical testing of the prototype developed during this project, with the aim of producing a refined design suitable for installation into a real world device, such as a wave energy generator.


Appendix Appendix 1 - Gear Geometry Derivation The Equal Ratio Rule (Equation 1):

= = = =

ℎ ℎ : = . = , = ⇒ . = . ⇒ = ( . 1.1), = ( . 1.2) The Concentricity Rule (Equation 2):

2 + 2 + 2 = 2 ⇒ . + . + . = . ( . 1.3)

. 1.1, 1.2 ℎ . 1.3 : . + . = . − .

⇒ . 1 + 1 = . 1 − 1 ⇒ = − 1 + 1

1 − 1 ( . 1.4) . 1.1, . 1.4 ℎ . 1.3 :

. + . − 1 + 11 − 1 . =

⟹ = 1 + 1 − 1 + 11 − 1 ( . 1.5)


Appendix 2 - Supplier Provided Component Geometry Sun Gear:

Pitch Diameter - 60mm Inner Bore Diameter - 10mm Thickness - 8mm

P1 Gear: Pitch Diameter - 20mm Inner Bore Diameter - 8mm Thickness - 8mm P2 Gear:

Pitch Diameter - 40mm Inner Bore Diameter - 8mm Thickness - 8mm

Ring Gear: Pitch Diameter - 120mm Outer Diameter as supplied - 170mm Thickness - 11mm Inner Sprag:

Outer Diameter - 22mm Inner Diameter - 8mm Thickness - 9mm Part Number CSK8

Outer Sprag: Outer Diameter - 62mm Inner Diameter - 30mm Thickness - 16mm Part Number CSK30 Bearing:

Outer Diameter - 24mm Inner Diameter - 8mm Thickness - 8mm All gears are module 1 and 20o pressure angle.

Appendix 3 - Inertia Values for OpenModelica and Approximations Component Mass Moment of Inertia (kg.m^2)

Input Shaft 0.000000189 P1 0.000000961 P2 0.000015758

Sun 0.000079842 P-shaft Short 0.000000088

Ring Gear 0.002533808 Sun Shaft 0.000000453

Sun Sprag Shaft 0.000000101 Ring carrier 0.000293427

Large Sprag Outer 0.000028526 Large Sprag Inner 0.000014126 Small Sprag Outer 0.000000399 Small Sprag Inner 0.000000154

Output Shaft 0.000007767 Approximations: For components where the mass could not be uniquely measured, a density of 7850

kg/m3 for mild steel was used. The gears could be approximated as a cylinder with outer diameter equal to the pitch

diameter of the gear. Small features, such as fillets and bolt heads have a negligible effect on inertia. The inertia of a keyway is equivalent to two concentric circles. The Ring carrier flanges are equivalent to rectangular plate of similar dimensions. The mass of the sprag clutches considered 'attached to' the inner and outer races is found

by using the mean of the internal diameter and outer diameter to break the sprag clutch into two concentric cylinders.


Appendix 4 - Gear Meshing Force Analysis Matlab Script tau_in = 0:50; %Torque exerted on the input shaft [Nm] phi = pi/9; %Gear pressure angle = 20 degrees %Input Shaft Analysis r_P1 = 0.01; %Radius of P1 Gear [m] r_P2 = 0.02; %Radius of P2 Gear [m] Ft_P1 = -1*tau_in/r_P1; %Tangential Force Exerted on P1 [N] Ft_P2 = tau_in/r_P2; %Tangential Force Exerted on P2 [N] Fr_P1 = Ft_P1*tan(phi); %Radial Force Exerted on P1 [N] Fr_P2 = Ft_P2*tan(phi); %Radial Force Exerted on P2 [N] Fn_P1 = Ft_P1/cos(phi); %Normal Force on P1 [N] Fn_P2 = Ft_P2/cos(phi); %Normal Force on P2 [N] Fv_B1 = Fr_P2 + Fr_P1; %Vertical Force on Bearing B1 due to meshing(no weight) (Input Shaft Bearing) [N] Fh_B1 = Ft_P2 + Ft_P1; %Horizontal Force on Bearing B1 (Input Shaft Bearing) [N] x_P1 = 0.01; %Distance between the Centreline of Gear P1 and the Input Shaft Bearing [m] x_P2 = 0.02; %Distance between the Centreline of Gear P2 and the Input Shaft Bearing [m] Mv_B1 = (Fr_P2*x_P2) + (Fr_P1*x_P1); %Vertical Moment Exerted By Bearing B1 due to meshing (no weight) (Input shaft bearing) [Nm] Mh_B1 = (Fr_P2*x_P2) + (Fr_P1*x_P1); %Horizontal Moment Exerted By Bearing B1 (Input shaft bearing) [Nm] %Ring Gear Analysis Fr_ring = -Fr_P2; %Radial Force exerted on the ring gear [N] Ft_ring = -Ft_P2; %Tangential Force exerted on the ring gear [N] Fn_ring = -Fn_P2; %Normal Force Exerted on the ring gear [N] %Sun Gear Analysis Fr_sun = -Fr_P1; %Radial Force Exerted on the sun gear [N] Ft_sun = -Ft_P1; %Radial Force Exerted on the sun gear [N] Fn_sun = -Fn_P1; %Radial Force Exerted on the sun gear [N] %Outer Sprag Analysis Fv_OS = -Fr_ring; %Vertical Force Exerted On Outer Sprag by Ring Gear [N] Fh_OS = -Ft_ring; %Horizontal Force Exerted On Outer Sprag by Ring Gear [N] x_ringOS = 0.015; % Distance between centreline of ring gear mesh with P2 and the centreline of the outer sprag. [m] Mv_OS = -Fr_ring*x_ringOS; %Vertical Moment Exerted on Outer Sprag by the ring gear. [Nm] Mh_OS = -Ft_ring*x_ringOS; %Horizontal Moment Exerted on Outer Sprag by the ring gear. [Nm] %Output Shaft Analysis x_B2B3 = 0.049; % Distance between the Centreline of Bearing B2 (Sun Shaft Bearing) and that of the Bearing B3 (Output Shaft Bearing) [m] x_B2OS = 0.035; % Distance between the Centreline of Bearing B2 (Sun Shaft Bearing) and that of the Outer Sprag [m] x_B2sun = 0.01; % Distance between the Centreline of Bearing B2 (Sun Shaft Bearing) and that of the Sun Gear [m] Fv_B2 = (Fv_OS*(x_B2B3-x_B2OS) + Mv_OS + Fr_sun*(x_B2B3-x_B2OS))/x_B2B3; %Vertical Force Acting in Bearing B2 [N] Fv_B3 = Fv_B2-Fv_OS-Fr_sun; %Vertical Force Acting in Bearing B3 [N] Fh_B2 = (Fh_OS*(x_B2B3-x_B2OS)+ Mh_OS + Ft_sun*(x_B2B3-x_B2OS))/x_B2B3; %Horizontal Force Acting in Bearing B2 [N] Fh_B3 = Fh_B2-Fh_OS-Ft_sun; %Horizontal Force Acting in Bearing B3 [N]


%Plot Gear Forces figure plot (tau_in,Fn_P1,tau_in,Fr_P1,tau_in,Ft_P1,tau_in,Fn_P2,tau_in,Fr_P2,tau_in,Ft_P2) xlabel('Input Shaft Torque [Nm]') ylabel ('Force [N]') legend ('Normal Force on P1','Radial Force on P1','Tangential Force on P1',... 'Normal Force on P2','Radial Force on P2','Tangential Force on P2','Location','southwest') %Plot Bearing Forces figure plot (tau_in,Fv_B1,tau_in,Fh_B1,tau_in,Fv_B2,tau_in,Fh_B2,tau_in,Fv_B3,tau_in,Fh_B3) xlabel('Input Shaft Torque [Nm]') ylabel ('Force [N]') legend ('Vertical Force on Input Shaft Bearing','Horizontal Force on Input Shaft Bearing'... ,'Vertical Force on Sun Shaft Bearing','Horizontal Force on Sun Shaft Bearing',... 'Vertical Force on Output Shaft Bearing','Horizontal Force on Output Shaft Bearing','Location','southwest') %Assumptions %1. All forces can be approximated as point loads on the centreline of the %component. %2. Component Weight is not taken into account


Appendix A5 - Prototype Self-Manufacture and Assembly Photographs Left: Milling the Frame Joint to size. The milling machine could also be used to accurately position and cut the holes required for the frame tie bars. Below: Tapping an external thread onto the frame tie bars

Above Left: Using the Milling Machine to drill the grub screw hole in the P1 Gear. This hole would then have a 3mm thread cut into it. A similar operation was conducted on the P2 Gear. Above Right : The Front Housing with the sun gear pressed into position, ready to have the planetary input shaft fitted into its lower bearing


Appendix A7 - Prototype MMR Design Drawings


Appendix A8 - Getting Started with OpenModelica The purpose of this appendix is to provide a basic introduction into the OpenModelica software used for much of the modelling during this project, in particular the OMEdit graphical modelling tool. As a example pertinent to the modelling conducted within this report, a basic gear assembly will be modelled. A full user guide can be found here: https://openmodelica.org/doc/OpenModelicaUsersGuide/OpenModelicaUsersGuide-latest.pdf OpenModelica for Windows can be downloaded here, but is also available for Mac and Linux: https://openmodelica.org/download/download-windows Once OpenModelica has been installed on the computer, the OpenModelica Connection Editor can be opened on the PC, producing this screen:

A new model may then be started by clicking here:


Give the model a name. You cannot use spaces in the name. For this exercise, the model will be named 'Ideal_Gear_with_Inertia' .

The new model will be opened. Save the model now. Open models are shown in the tabs at the top (red), note also that the model now exists in the library browser:

The 'Libraries Browser' is used to locate models contained within the standard modelica libraries. To create the Ideal_Gear _With_Inertia, navigate through the Libraries Browser as follows: Modelica - Mechanics - Rotational - Components.


These components can then be dragged and dropped into the open model 'Ideal_Gear_With_Inertia'. Add two 'Inertia' models and an 'IdealGear' to the modelling space as shown:

These sub-models have now been inserted into the model. These models can now be re-parameterised with values specific to the 'Ideal_Gear_With_Inertia'. To bring up the model parameters, double click it's icon in the modelling space. Set the values of inertia to 0.0001 and the gear ratio to 2. The components can also be named by right clicking the model icon and clicking 'attributes'. OpenModelica Connection Editor is able to intelligently link these models together, matching the output parameters of one model, to the input parameters of another. (An error will be raised if the connection is incompatible). Connections are drawn by clicking and dragging the 'circles' on a component, and linking them to another connector:


In order to use the 'Ideal_Gear_With_Inertia' model in higher level models, such as a rig model, 'interface' component must be included to allow it to interact with other models. Libraries Browser - Modelica - Mechanics - Rotational - Interfaces Drag and drop a 'flange_a' and 'flange_b' model into 'Ideal_Gear_with_Inertia' model, and connect them as shown:

Note: there may be a bug in the software, and to draw connections to a flange model in the manner shown, click on the name of the component, not the grey/white circle. Save 'Ideal_Gear_With_Inertia'. To see the code this model has now generated, click here:

Note how the code efficiently references the models from the standard library, rather than writing all the defining all the parameters and equations for each component. These are compiled when each time a simulation is run. This allows models to be made very quickly from a set of standard components.

Completely new models, including declaring new parameters and equations could also be written in this window if necessary. Now start a new model, called 'gear_rig' and insert the following components: Modelica - Mechanics - Rotational - Source - Position Modelica - Blocks - Sources - Ramp Modelica - Blocks - Sources - Sine Modelica - Blocks - Math - Add Connect them up as shown:


This produces two signals, a ramp and a sine wave, adds them together and uses that as to define the position of a radial motion actuator. Then add the following parameters to the Ramp and Sine Models:

Note: Default values are shown in light grey, they do not need to be changed. Every standard modelica model has built in help documentation that can be access by right clicking on the model. Now, using the Libraries Browser, 'Ideal_Gear_With_Inertia', can be inserted into 'gear_rig':

Notice how the 'flange' interface components have propagated into the higher level model view and can be connected to the position control.


Save 'gear_rig'. To access the simulation setup click the icon highlighted in red:

Change the stop time to 3 seconds, and click the 'save simulation settings inside model' option, and click 'simulate', to run the 'gear_rig' model. Note the button highlighted in blue can be used to quickly simulate the model with the saved settings. The button highlighted in green is useful for checking the model for compilation errors, as it notes how many equations and variables exist within the model. The model will then compile and simulate. Any errors will be flagged in the pop-up box. If no errors have been made the following screen should be displayed:


The Variables browser (right) can then be used to produce plots of the system:

Here, the angle of displacement of 'flange_a' and 'flange_b' from 'Ideal_Gear_With_Inertia' have been plotted with time. The modelling and plotting workspaces can be navigated between by using: This appendix has now demonstrated how very basic models can be simulated in OpenModelica.


Appendix A9 - Risk Assessment for Prototype Manufacturing

RECORD OF RISK ASSESSMENT

Title of the risk assessment Mechanical Motion Rectifier Manufacture Risk Assessment

Date risk assessment carried out 09/02/2016

Describe the work being assessed Work to be carried out in the EDMC Student Workshop to contribute to the manufacture of an Individual

Project 'mechanical motion rectifier' design.

Describe the location at which the work is

being carried out

EDMC Student Workshop, Building 7

Where appropriate list the individuals doing the

work and the dates/times when the work will be

carried out

Geoffrey Moore, February 2016

EDMC Student Workshop Area Risk Assessment

Name and post of risk assessor Geoffrey Moore - Student

List the names and posts of those assisting in

compiling this risk assessment

Terry Webster - Student Workshop Manager, John Young - EDMC Deputy Manager

Name, post and where required, signature of

the responsible manager/supervisor approving

the risk assessment

Reference number and version number of risk

assessment

V1.0

List any other generic or specific risk

assessments or other documents that relate to

this assessment-use hyperlinks if possible

Page 1 of 4 HS/UOS/FR/038/04

ref Task/Aspect of work HazardHarm and how it could

arise

Who could be

affected?Existing measures to control risk

6 Use of Press Fit Machine Compressive

loads required to

press parts

together.

Injury through

improperly located parts

being forcibly ejected

from machine.

Anyone in close

proximity to the

operation.

Protective guards to be in place whenever

operating the press fit machine.

Ensure parts are properly located within the

machine, and all proper machine operation

practices are upheld.

1 4 4

5 Use of Press Fit Machine Compressive

loads required to

press parts

together.

Injury through

compressive forces

being exerted upon the

person.

Individual carrying

out the operation.


operating the press fit machine, preventing

any contact with the workpeice.

1 4 4

4 Metallic Dust Particles from

Machining.

Metal Dust Metal particles getting

in the eyes

Anyone in close

proximity to the

machining

operation.

Ensure anyone in close proximity to the

machining operation is wearing safety

glasses as PPE.

Washing hands after touching the

workpeice, avoiding metal shards being

transferred into the eyes from the hands.

1 3 3

Assessment

Overa

ll Lik

elih

ood

Overa

ll S

everity

Resid

ual R

isk s

core

Any c

hanges o

r extr

a c

ontr

ols

?

Risk Factors

Mechanical Motion Rectifier Manufacture Risk AssessmentTitle of risk assessment

Risk Acceptability

Risk to be reduced if readily possible4-6

Risk to be reduced if reasonably practicable7-14

Risk unacceptable15-25

Risk acceptable1-3

Risk Acceptability




Risk acceptable1-3

2520151055certainty

Lik

elih

ood

Severity

543211improbable

1086422less likely

15129633possible

201612844likely

54321

very

high

highmediumlowvery

lowRisk Matrix

2520151055certainty

Lik

elih

ood

Severity

543211improbable

1086422less likely

15129633possible

201612844likely

54321

very

high

highmediumlowvery

lowRisk Matrix


3 Use of Hand Tool, including

Saw

Sharp Tool Edges Minor Injury through

tool contact with

operator

Individual carrying

out the operation.

Use of a vice to avoid workpeice slipping

from hand.

Not leaving sharp tools loose on desk while

performing other work.

3 1 3

2 Milling Machine and Pillar Drill

Operation

Heat Generated

by machining

operation.

Burn (Hot) Individual carrying

out machine

operation.

Ensure sufficient time to cool workpeice

before accessing it.

Have heat resistant gloves available if

suspected hot parts must be handled.

1 3 3

1 Milling Machine and Pillar Drill

Operation

High speed

cutting

machinery.

Injury, including cutting,

most likely to the hand

or arm.

Individual carrying

out machine

operation.


milling machine or pillar drill is in operation.

Ensure the machines are isolated from its

power supply whenever access is required

to the workpeice.

Avoid clothing that may get caught in the

machine.

1 4 4

Risk Acceptability




Risk acceptable1-3

Risk Acceptability




Risk acceptable1-3

2520151055certainty

Lik

elih

ood

Severity

543211improbable

1086422less likely

15129633possible

201612844likely

54321

very

high

highmediumlowvery

lowRisk Matrix

2520151055certainty

Lik

elih

ood

Severity

543211improbable

1086422less likely

15129633possible

201612844likely

54321

very

high

highmediumlowvery

lowRisk Matrix


Have any of the specialist control measures listed below been identified as required during this risk assessment? -

indicate yes or no - if yes then include details on the post assessment action list below.

yes/no

is any exposure monitoring required? no

Is any occupational health monitoring required? no

Are there any hazards or other factors that could affect pregnant or nursing mothers? no

Is any specific training required before people can carry out this work? yes

EDMC Student Workshop Induction Completed - During Part 1.

Are any additional procedures or risk assessments required as a result of this assessment? no

Are any specialist disposal arrangements required? no

Are any special emergency arrangements required? no

ref action by whom by when

Post Risk Assessment Actions

Post Assessment actions

Title of risk assessment

Mechanical Motion Rectifier Manufacture Risk Assessment



References [1] L. Wang, “A Novel Energy Regenerative Shock Absorber,” 17 June 2015. [Online]. Available:

http://contest.techbriefs.com/2015/entries/automotive-transportation/5595. [Accessed 18 01 2016].

[2] Z. Jin-qui, P. Zhi-zhao, Z. Lei and Z. Yu, “A Review on Energy-Regenerative Suspension Systems for Vehicles,” in Proceedings of the World Congress on Engineering 2013 VolIII, London UK, 2013.

[3] Z. Li, L. Zuo, J. Kuang and G. Luhrs, “Energy Harvesting shock absorber with a mechanical motion rectifier,” Smart Materials and Structures, vol. 22, no. 025008, pp. 1-10, 2013.

[4] M. Moshrefi-Torbati, S. Sharkh, J. Vaughan, A. Newman, D. Martin, H. L. Williams, O. Hampden-Martin and A. Danos, “A Novel Hybrid Wave Energy Harvesting Device (GDP020),” University of Southampton, 2014 - 2015.

[5] E. D. Townsend, Dudley's Gear Design Handbook: The Design, Manufacture and Application of Gears, 2nd Edition, New York: McGraw Hill Education, 1992.

[6] T. Lin, J. Wang and L. Zuo, “Energy Harvesting from Rail Track for Transportation Safety and Monitoring,” State University of New York at Stony Brook, New York, 2014.

[7] Modelica Association, “Modelica and the Modelica Association,” [Online]. Available: https://www.modelica.org/. [Accessed 26 01 2016].

[8] R. Goldner, P. Zerigan and J. Hull, “A Preliminary Study of Energy Recovery in Vehicles Using Regenerative Magnetic Shock Absorbers,” SAE International, Washington D.C., 2001.

[9] M. Otter, H. Elmqvist and S. Mattsson, “The New Modelica Multibody Library,” in Proceedings of the Third International Modelica Conference, Linkoping, 2003.

[10] M. Tiller, “Modelica By Example,” Xogeny, [Online]. Available: http://book.xogeny.com/. [Accessed 20 2 2016].

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Image References Figure 1 - http://cdn1.greendiary.com/wp-content/uploads/2012/07/regenerative-shock-absorber_LaWe1_11446.jpg [Date Accessed: 4/11/15] Figure 2 - http://cdn.iopscience.com/images/0964-1726/22/2/025008/Full/sms425782f1_online.jpg [Date Accessed: 4/11/15] Figure 3 - Li et al , [3] Figure 5 - Edited using: http://img.directindustry.com/images_di/photo-g/7869-2615867.jpg [Date Accessed: 24/1/16] and https://c1.staticflickr.com/3/2619/3842006065_aa9e505c3f.jpg [Date Accessed: 24/1/16] Figure 7 - http://machinedesign.com/site-files/machinedesign.com/files/archive/ motionsystemdesign.com/images//Spur-gear-geometry.jpg [Date Accessed: 12/2/16] Figure 20 - Edited using: http://www.expertsmind.com/CMSImages/2318_Sprag%20Clutch.png [Date Accessed: 17/3/16] Figure 31 - http://www.hondogarage.com/image_assets/500px-Backlash.svg.png [Date Accessed: 14/2/16] Figure 37 - https://upload.wikimedia.org/wikipedia/commons/7/79/Gear_mesh_forces.PNG [Date Accessed: 4/4/16] Figure 46 - https://jagadees.files.wordpress.com/2010/04/6a00d8341c4fbe53ef0120a5e0eab9970b-800wi.png [Date Accessed: 12/4/16

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