computer aided design of multi-stage...

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Computer Aided Design of Multi-Stage GearboxesProf. Dr. M. A. Nasser Prof. Dr. F. R. Gomaa

Department of Production Engineering & Mech. design Department of Production Engineering & Mech. designUniversity of Menoufia University of Menoufia

Shebin El-kom, Menoufia, Egypt Shebin El-kom, Menoufia, Egypt

[email protected] [email protected]

Dr. M. A. Asy Ahmed DeabsDepartment of Production Engineering & Mech. design Department of Production Engineering & Mech. design

University of Menoufia University of MenoufiaShebin El-kom, Menoufia, Egypt Shebin El-kom, Menoufia, Egypt

[email protected] [email protected]

Abstract - Gearboxes are the most important and complicatedpart of machine tools, there are a great lack of an integratedmanual and/or computerized design of gearbox, this problemmotivate to made a solution. The developed software called(GearBox LAB) for design and simulate multi-stage gearboxes, itis created by using Visual Basic6 (VB6) programming language.The software considers optimum structural diagram, speedsdesign (theoretical, actual and their errors), speed chart,kinematic diagram, design of gears, shafts, keys and spline,bearing selection, shafts axis layout, gear box dimensions, fixingbolts and foundation studs, gear meshing and bearing frequenciesas well as the Campbell diagram. The program is helpful formechanical designers, researchers, students, troubleshooters aswell as quality control and vibration engineers.

Index Terms — Computer aided design, design techniques,simulation, software design, machine tools.

1. INTRODUCTION

Machine tools use a gear box driven by electric motorsallowing the operator to select suitable cutting speeds andfeeds entirely through the gearboxes. Gearboxes also allow theinput shaft and the output shaft to be in different directions.Gearboxes save money, time and power consumption in metalcutting. References [1-6] concern the design of machine toolgear boxes, while [7-9] concern the design of machineelements. Computer-aided design (CAD) is the use ofcomputer systems to assist in the creation, modification,analysis, or optimization of a design [10]. CAD software isused to increase the productivity of the designer, improve thequality of design, improve communications throughdocumentation, and to create a database for manufacturing.CAD is the technology concerned with the use of digitalcomputers to perform certain functions in design. Thistechnology is moving in the direction of greater integration ofdesign and manufacturing activities. These activities havetraditionally been treated as distinct and separate functions in aproduction firm. Ultimately, CAD will provide the technologybase for the computer-integrated factories of the future. Some

programs are used for designing gears and gear boxes such asKISSsoft [11], Program 580 [12], MD design [13] and Amtecsoftware [14]. KISSsoft is a program for sizing, optimizingand recalculating designs for machine components such asgears, shafts and bearings, screws, springs, joining elementsand belts. Program 580 is used to design a gearbox for theminimum weight. It is also useful in estimating the cost of agearbox before it is manufactured. MD design software is usedto generate a gear model and subsequent recalculation of thekinematics and single stage spur gears described how to checkthis construction. Amtec software is used to determine thegears dimensions for single stage, it is very useful for checkingtooth profile, reasoning, noise reduction, bearing load andflash temperature. The design and calculations software formulti stages gear boxes are limited to only one step or outputrotating speed, [20].From the literature review it is clear that there is a great lack inthe specific design applications such as machine tool gearboxes, like those concerned with machine elements [15, 16]. Inthis paper the design of machine tool gear boxes iscomputerized using visual basic 6 (VB-6) [17] considering theselection of electric motor, stepped diagram, finding the gearmodule, gear ratios, calculates the number of teeth ofindividual and cluster gears, limitations in the choice of thenumber of teeth in the gear trains, used in the gear boxes, andcomputing torque regulation of speed, Laws of steppedregulation, progression, No. of speed steps, break up of speedsteps, structural formulae, structural diagram, selection of beststructural diagram, speed chart, kinematic and shaft sizes, aswell as gearbox gears and bearings noise and vibrationfrequencies as well as Campbell diagram is achieved.Campbell diagram is a mathematically constructed diagramused to check for coincidence of vibration sources with naturalresonances.The gear box size is estimated and can be minimized. Designcase study of speed gear box for lathe machine is solvedmanually and by using the written program. Good agreementbetween both methods is achieved. The program is essentialfor professional mechanical designers, researchers, students,

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n3

n2

n1

I II

Speed chart.

n3

n1

n2

I II

Flow diagram.

troubleshooters as well as quality control and vibrationengineers. It enables them in analyzing, simulation, redesign ofmulti stage gear boxes. Moreover, it helps them in both design,production and operation stages.

1.2 HELPFUL HINTS

Subscripts:

2. Theoretical Design Procedure:In this section, it indicate to all calculation processes that

software consider in programming.

2.1 Gearbox speeds regulations:In machine tools, stepped speed regulation obtained by

more than one way using different progression as geometric,harmonic, logarithmic and differential progression.Differential progression is the best one to achieve speedproximity. However geometric progression is widely used inmachine tools as an international standard. Speeds ingeometric progression are estimated as the following form:First Speed

Second Speed

Third speed

Generally

2.2 Flow Diagram and Speed Chart:Flow Diagram and Speed Chart are defined as chart thatdescribe speeds distribution in gearbox and how to choosesuitable reduction ratios in required speed, speed distributionis depend on this equation [3, 4, 8]:

Figure (1) Speed Chart, Flow diagram & Kinematic diagram of 3 SpeedsGear Box.

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Flow Diagram and Speed Chart are very similar to eachother except speed charts are constrained with reduction ratiovalues however flow diagrams doesn't have any abidance tonumbers, it only gives a general distribution of speed. Shaftare expressed as (I, II, III, …. ) and also speeds as horizontallines (n1, n2, n3, ……. ) as shown in figure (1):

2.3 Kinematic Diagram:It is considered as a graphical solution chart or structural

diagram to design gearbox depend mainly on speedsdistributions, their mission is give gears and speedsdistribution in simple charts that aid mechanical designersthrough designing of gearbox, kinematic diagram give andrawn description to gears, its location, fixation and movementin gear box, number and types of shafts and layout of gearbox.

2.4 Gears details and reduction ratios:Theoretical speeds are determined according to standard

geometric base (f) (1.06, 1.12, 1.26, 1.41, 1.58, 1.78, and 2).Once theoretical speed is determined, then reduction ratioscalculated from equation:

Gears details include module, gears dimensions andnumber of teeth. The number of teeth is mainly determinedfrom reduction ratios of meshed gears groups [1, 2, 3, 5] asshown from the kinematic diagram of three meshed reductionratios (six gears):

2.5 Theoretical speed, Actual speeds and Speed error:Theoretical speeds means design speeds or ideal speeds

but sometimes it is not real speeds due to some approximationor standardizations in design processes or availability inpractical side. Actual speeds are the real speeds which arereally produced in spindle of machines due to the movement inmechanical parts [3,8], Deviation of speeds (theoretical)produce speed error that must be less than maximum errors.For the kinematic diagram shown in figure (1) theoretical,actual speeds and speed errors are calculated from followingequations:

2.6 Gear Meshing Frequency:Frequency is defined as Hertz (Hz) [cycles / sec.]. For the

gear meshing it can be calculated by (number of teeth *rotational speed [rpm]) / 60. Gear meshing frequency is aharmonic phenomenon. Its harmonics can be found bymultiplying fundamental meshing frequency by the numbers 1,2, 3, ……etc.

2.7 Bearing Frequencies:

Different bearing frequencies are calculated from theinner geometry of the bearings using formulas with number ofcontacts in possible place of defect [18].

2.8 Gearbox Dimensions:Gear box dimensions are estimated for Fig. (2) From

equations given in reference [19]. As shown in table (1), Gear

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Box Casing wall thickness can be determined as a function ofmaterial and hardened condition

Figure (2) Gear box casing sketch.

TABLE (1) GEAR BOX CASING WALL THICKNESS.

2.9 Campbell Diagram:The Campbell diagram represents the natural frequency

versus the rotation speed of the shaft: the evolution of thenatural frequencies corresponding to a mode are drawn as afunction of the rotation speed of the shaft.

Figure (3) Campbell diagram

3. THE SOFTWARE:The software is produces to design multi-stage gearboxes

with (2, 4,6,8,9,12,16,18 & 24) speed. The design includegears design, speeds regulation, shafts design, keys design, andkinematic diagram also bearing and gear meshing frequenciesare determined, gear box casing and top cover dimensions.

3.1 General Design Flow Diagram:The mainframe of both manual and CAD solution of

designing multi- stage gear boxes is given in Figure (4). Inputdata are defined as (A), (B) and (C), where:Input (A): speed input data for motor and gearbox.Input (B): gear, shaft and casing input data.Input (C): bearing, pulley and belt input data.

The software is used to design 16 speed gearbox withmotor power 3.5 HP and 1000 rpm, maximum speed = 770rpm, minimum speed = 31.5 rpm, gear permissible bendingstress = 1580 kg/cm2, gear pressure angle = 21 o, driver pulleydiameter = 14.6 cm, distance between pulley axis = 55 cm, beltreduction ratio = 0.49, bearing efficiency = 0.95, gearefficiency=0.95, pulley efficiency = 0.95, Driven Pulley Width= 15 cm, initial bearing width = 2 cm, shaft yield strength =4920 kg/cm2, shaft diameter safety factor =1.5. The CADresults were compared with manual solution of this gear box.

3.2 Coding:The software written in Visual Basic language. The

software working as graphic user interface (GUI) to be userfriendly. The software is converted to an executable file toenable starting the program by just one click.

MaterialNon-Case Hardened

GearsCase Hardened

Gears

CI Castings 0.007L+6 mm 0.010L+6 mm

Steel Castings 0.005L+4 mm 0.007L+4 mm

Welded Construction 0.004L+4 mm 0.005L+4 mm

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Figure (4-a) Gear Box Design Flow Diagram Figure (4-b) Data Input Sequence

A

Choose Gearbox Speed

Input (Motor Speed, MotorPower, Max Speed, Min.

Speed)

Input (MotorSpeed, Motor

Power, Max Speed,Geometry Base)

Input Speed 1

Check data Completion &Standard value of Base

Geometry

B

C

Input (No. of Teeth, BendingStress, Pressure angle,

Gears Efficiency)

Check dataCompletion

No. of Teeth Correction

Input (Bearing & BeltEfficiency, Belt Reduction

Ratio)

Check dataCompletion

Speeds C Speeds Correction

Output Design processes

Start

End

Input Speed Data (A)

Input Gear Data (B)

Input Shaft Data (C)

Gears Dimension

Gearbox Speeds

Flow and Speed Chart

Campbell Diagram for

Each Reduction Ratio

Campbell Diagram for All

Reduction Ratios

Proximity Diagram for

Each Reduction Ratios

Gearbox Arrangement

Shaft Design

Kinematic Diagram and (Bearing

frequencies & Gear Meshing Frequencies)

Calculation Design Process

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3.3 Software (GUI) windows:In this part, it discuss the (GUI) windows that users can

deal.3.3.1 Welcome Screen:

The screen Shot of the welcome screen is shown inFigure (5). It shows the name of software (GEARBOX Lab),author and supervisors. This part of GEARBOX Lab isconcerned with multi-stage gear boxes (MSGB) design.

Figure (5) Screen shot of welcoming screen.

3.3.2 Main Menu:The main menu shown in figure (6) is divided into three

steps, choosing number of speeds and input motor, maximumand minimum speed, motor power and progression ratio inFirst Step. Entering minimum number of teeth, pressure angle,efficiency, width factor and stresses of gears, also shaftstresses and casing data in second step. Third step used toenter width and efficiency of bearing, inclined angles andreduction ratio of belt, pulley diameter and width and distancebetween pulleys axis.

Figure (6) Screen shot of the main input data.

3.3.3 Designed Gear Data Window:

Screen shot shown in figure (7) gives a designed geardata such as number of teeth, module, outer diameter, pitchdiameter, inner diameter, width of gears and reduction ratiosof gears groups.

Figure (7) Screen shot of gears number of teeth, modules & dimensions.

3.3.4 Actual and Theoretical Speeds and speeds errors:Screen shot given in figure (8) gives theoretical and

actual speeds, speed error and maximum speed error for eachspeed.

Figure (8) Screen shot of theoretical, actual speeds and percentageerrors between them.

3.3.5 Speed and Flow diagram:Screen shot Shown in figure (9) gives a plotting chart for

the optimum probability for gear box speeds (Flow diagram)and actual speed chart according to input data.

Figure (9) Screen shot of speed chart & flow diagram.3.3.6 Gearbox Arrangement Window:

Figure (10) presents gear box shafts axis layout as sideview of the designed gear box. The user can easily minimizethe size of the gear box by choosing the shafts arrangementaccording to the inclined angle of each shaft to the others byusing scroll bars or digital vales of inclined angles betweenshafts axes.

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Figure (10) Interactive gear box shafts layout(horizontal, vertical or arbitrary).

3.3.7 Gearbox Shaft Design Window:

Gear box shafts design window given in figure (11)gives shafts with their dimensions. The user can design bothkeyed and splined shafts and easily change the number ofsplines. Bearing information has to be entered to thesoftware.

Figure (11) Screen shot of gear box shafts design.

3.3.8 Gearbox Casing Dimensions Window:It gives designed dimension of gears with neat sketch

according to previous designed data.

Figure (12) Screen shot of gear box casing dimensions.

3.3.9 Frequencies of Gearbox Components Window:Figure (13) gives a kinematic diagram of gear box,

bearings frequencies and gear meshing frequencies forselected speed, the user can select the required speed andkinematic diagram using speed scroll bar.

Figure (13) Screen shot of the gear box componentsfrequencies.

3.3.10 Gear Meshing Frequencies Window:Figure (14) gives gear meshing frequencies for each gear

group at each speed.

Figure (14) Screen shot of gear meshing frequencies at allrotating speeds.

3.3.11 Campbell Diagram for Gear Meshing FrequenciesWindows:

Campbell diagram is used to illustrate interferencesbetween natural frequencies and common exciting forces.Excitation can be stationary, rotating, static, dynamic andsynchronous. Campbell Diagrams investigates the dynamicbehavior of the system, For gear box, eigenfrequencies are afunction of shafts speed, critical speeds are the intersectionpoints of natural frequency curves with 1x n line, naturalfrequencies depend on shaft speed, critical speeds do not. Inthe case of a gear box, gear meshing frequency is plottedagainst spindle running speed. Three windows are given tocheck for coincidence of vibration sources with naturalresonances. Figure (15) presents the screen shot of Campbelldiagram for each gear mesh and its harmonic frequencies atdifferent speeds. It gives a plot of Campbell Diagram betweenrotating speed and gear meshing Frequencies for each geargroup and its harmonic frequencies at each speed. The windowcontains four parts namely; arbitrary input data (Speed

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3

4

1

2

number, Reduction Ration Number), Speed cursorcorresponding to probable frequencies, frequency cursorcorresponding to probable rotating speeds, digital values ofrpm according to excited frequency.

Figure (15) Screen shot of Campbell diagram for each gearmesh and its harmonic frequencies at different speeds.

Figure (16) gives a plot of Campbell Diagram betweenrotating speed and all gear meshing Frequencies for each gearat each speed. The user can choose the required speed and thesoftware will give five probable frequencies. The user can alsochoose required frequency and the software will give fiveprobable speeds. Beside the Campbell chart four main parts ofthe menu are namely; speed step number, speed cursorcorresponding to probable frequencies, frequency cursorcorresponding to probable rotating speeds and digital values ofrpm according to excited frequency.

Figure (16) Campbell diagram between speed and all gearmeshing frequencies for each gear at each speed

There is uncertainty in both design and operation stages,this may cause changes in both rotating speed and frequencies

of the system. For this reason the use of proximity diagram isessential. Figure (17) gives the software menu of Campbelldiagram considering its two proximity ratios at each speed.Beside the chart there are four major parts in the windownamely; arbitrary input data (Speed step number, ReductionRation Number, Proximity Ratio), speed cursor correspondingto probable frequencies, frequency cursor corresponding toprobable rotating speeds, digital values of rpm according toexcited frequency.

Figure (17) Campbell diagram between speed and gearmeshing frequencies for each gear group and its two proximity

Value (Design Margin)

4. RESULTS & DISCUSSION:

Comparison between Manual and CAD Solutions:

Validation of Gear box Lab software is obtained bycomparing the obtained results with manually solved problemsas given in the tables (2:6).

Gear Number ofTeeth

Gears Module(cm)

Gears AddendumDiameter (cm)

Manual CAD Manual CAD Manual CADz1 44 44 0.15 0.15 6.9 6.9z2 56 56 0.15 0.15 8.7 8.7z3 39 39 0.15 0.15 6.15 6.15z4 61 61 0.15 0.15 9.45 9.45z5 50 50 0.15 0.15 7.8 7.8z6 50 50 0.15 0.15 7.8 7.8z7 39 39 0.15 0.15 6.15 6.15z8 61 61 0.15 0.15 9.45 9.45z9 56 56 0.2 0.2 11.6 11.6

z10 44 44 0.2 0.2 9.2 9.2z11 33 33 0.2 0.2 7 7z12 67 67 0.2 0.2 13.8 13.8z13 61 61 0.4 0.4 25.2 25.2z14 39 39 0.4 0.4 16.4 16.4z15 20 20 0.4 0.4 8.8 8.8z16 80 80 0.4 0.4 32.8 32.8

Table (2-a) Gear Number of Teeth, Gears Module (cm),Gears Addendum Diameter (cm).

3

2

1

4

4

1

2

3

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Theoretical Speeds(rpm)

Actual Speeds(rpm)

Speeds Errors (%)

Manual CAD Manual CAD Manual CAD

nth1 770 770 758.75 758.75 1.46 1.46

nth2 616 616 617.4 617.4 -0.23 -0.23

nth3 485.1 485.1 485.1 485.1 0.02 0.02

nth4 385 385 394.73 394.73 -2.53 -2.53

nth5 308 308 293.63 293.63 4.67 4.67

nth6 242.55 242.55 238.93 238.93 1.49 1.49

nth7 192.5 192.5 187.73 187.73 2.48 2.48

nth8 154 154 152.76 152.76 0.81 0.81

nth9 123.2 123.2 121.28 121.28 1.56 1.56

nth10 96.25 96.25 98.68 98.68 -2.52 -2.52

nth11 77 77 77.54 77.54 -0.7 -0.7

nth12 61.6 61.6 63.09 63.09 -2.42 -2.42

nth13 48.5 48.5 46.93 46.93 3.26 3.26

nth14 38.5 38.5 38.19 38.19 0.81 0.81

nth15 30.8 30.8 30.01 30.01 2.56 2.56

nth16 24.26 24.26 24.42 24.42 -0.68 -0.68

Table (3) Theoretical Speeds (rpm), Actual Speeds (rpm)& Speeds Errors (%).

Gearbox Dimensions Manual Solution CAD Solutionk1 0.87 0.87k2 0.79 0.79kc 0.7 0.7kf 1.74 1.74dcb 1.3 1.3bs 7.8 7.8dfb 2.7 2.7kff 4.1 4.1Wf 6.8 6.8

Table (4) Gearbox Dimensions (cm) in both Manual & CADSolutions.

Gear Meshing Frequency Manual Solution CAD Solution

Gear Group1 355.7 355.72 323.4 323.43 362.2 362.24 497.1 497.1

Table (5) Gear Meshing Frequency (Hz) in both Manual& CAD Solutions at 770 rpm.

Gears PitchDiameter (cm)

Gears DedendumDiameter (cm)

Gears Width (cm)

Manual CAD Manual CAD Manual CAD

z1 6.6 6.6 6.23 6.23 1.2 1.2

z2 8.4 8.4 8.03 8.03 1.2 1.2

z3 5.85 5.85 5.48 5.48 1.2 1.2

z4 9.15 9.15 8.78 8.78 1.2 1.2

z5 7.5 7.5 7.13 7.13 1.2 1.2

z6 7.5 7.5 7.13 7.13 1.2 1.2

z7 5.85 5.85 5.48 5.48 1.2 1.2

z8 9.15 9.15 8.78 8.78 1.2 1.2

z9 11.2 11.2 10.70 10.70 1.75 1.75

z10 8.8 8.8 8.30 8.30 1.75 1.75

z11 6.6 6.6 6.10 6.10 1.75 1.75

z12 13.4 13.4 12.90 12.90 1.75 1.75

z13 24.4 24.4 23.40 23.40 3.2 3.2

z14 15.6 15.6 14.60 14.60 3.2 3.2

z15 8 8 7.00 7.00 3.2 3.2

z16 32 32 31.00 31.00 3.2 3.2

Table (2-b) Gears Pitch Diameter (cm), Gears DedendumDiameter (cm) & Gears Width (cm).

Bearings Frequencies Manual Solution (MSGB)Solution

Shaft No. 1

FTF1 3.2 3.2BPFI1 39.2 39.2BPFO1 25.4 25.4BSF1 30.2 30.2FTF2 3.2 3.2BPFI2 39.2 39.2BPFO2 25.4 25.4BSF2 30.2 30.2

Shaft No. 2

FTF1 2.5 2.5BPFI1 31.1 31.1BPFO1 20.2 20.2BSF1 24 24FTF2 2.5 2.5BPFI2 31.1 31.1BPFO2 20.2 20.2BSF2 24 24

Shaft No. 3


Shaft No. 4


Shaft No. 5


Table (6) Bearings Frequencies (Hz) in both Manual &CAD Solutions at 770 rpm.

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Potential Benefits That Result from Implementing CAD.Improved mechanical engineering designers productivity andMinimize manual process errors in designs, Shorter designtimes, Reduced engineering personnel requirements, Customermodifications are easier to make, Faster response to requestsfor quotations, Improved accuracy of designs, Provides betterfunctional analysis to reduce prototype testing, Assistance inpreparation of design documentation, Designs have morestandardization, Better designs provided, Improvedproductivity in machine tool design, Helps ensure designs areappropriate to existing manufacturing techniques, Savesmaterials and machining time by optimization algorithms,Provides operational results on the status of work in progress,Makes the management of design personnel on projects moreeffective, Assistance in inspection of complicated designs,Better communication interfaces and greater understandingamong engineers, designers, drafters, management, anddifferent project groups.

5. CONCLUSION:1. A reliable, user friendly, integrated, accurate, faster

software and in a good agreement with the manualdesign of machine tools gear boxes is achieved.

2. The given software is an integrated tool that bridges thegap exist in the design of machine tools multi stage gearboxes.

3. The program helps in the design, modification andanalysis of machine tool gear boxes.

4. The program is fruitful for professional mechanicaldesigners, researchers, students, troubleshooters as wellas quality control and vibration engineers in severalengineering fields such as machine tools, vehicles andmechanical power transmission.

REFERENCES:

[1] Mehta N.K., "Machine Tool Design", Third Edition, 2012.[2] JOSHI P. H., "Machine Tools Handbook", Fourth Edition, 2013.[3] Sharma P.C., "Principles of Machine Tools".[4] Basu S. K., "Design of Machine Tools", Fifth Edition, 2011.[5] Nasser A., "Machine Tool Design (Power Transmission)", Faculty of

Engineering, Menoufia University, Egypt, 1979.[6] SEN G.C., Bhattacharyya A., "Principles of Machine Tools", Second

Edition, 2009.[7] Andrew D. Dimarogonas, "Machine Design: A CAD Approach", Second

Edition, 2001.[8] Bhandari V.B., "Design of Machine Elements", Third Edition, 2010.[9] Gupta J.K., Khurmi R.S., "Textbook of Machine Desig n", SI Edition,

2005.[10] Narayan, K. Lalit (2008), "Computer Aided Design and

Manufacturing", New Delhi: Prentice Hall of India. p.3. ISBN812033342X.

[11] ins-304-Frequencies," Calculation of the gear and bearing frequencies", Available fromhttp://www.kisssoft.ch/english/downloads/KISSsys/Templates/ins-304-Frequencies.pdf

[12] IGSProgram580, "Program 580—Minimum Weight TransmissionSystem", Available fromhttp://www.uts.com/ResourceCenter/TutorialsandExamples/IntegratedGearSoftware/IGSProgram580.pdf

[13] Tutorial_gearbox_2012_en," Tutorial for gear design and calculationwith MDESIGN gearbox", Available fromhttp://www.driveconcepts.com/info/tutorial_gearbox_2012_en.pdf

[14] Sigma-sh(Eng), "[1] involuteΣ(Spur and Helical Gear Design)",Available from http://www.amtecinc.co.jp/sigma-sh(Eng).pdf

[15] Adeyeri Michael Kanisuru, Adeyemi Michael Bolaji, Ajayi OlumuyiwaBamidele & Abadariki Samson Olaniran, “Computer Aided Design ofCouplings”, International Journal of Engineering (IJE), Volume (5) :Issue (5) : 2011

[16] A.P. Azodo, B.Eng, S.B. Adejuyigbe, Ph.D. M.A. Waheed, Ph.D. andO.U. Dairo, Ph.D. “Computer Aided Design of Mechanical Clutch.”,The Pacific Journal of Science and Technology , Volume 13. Number 2.November 2012 (Fall).

[17] Richard J. Simon, Richard Peasley, "Using Visual Basic 6.0", 1998.[18] Calculation of the gear and bearing frequencies, 2007, www.kisssoft.ag[19] Gearbox Design Lecture 17, Available from

http://nptel.iitm.ac.in/courses.[20] MDESIGN gearbox 2010, design and calculation software for

multi stage gearboxes. Drive Concepts GmbH, 2010

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