positioner selection and motor sizing...positioner selection criteria positioner selection and motor...

Positioner Selection and Motor Sizing

Jim WileyProduct Manager

Parker Hannifin

Overview

Positioner Selection

Motor & Drive Sizing

Positioner Selection Criteria

Precision

Loading

Environment

Geometry

Motion

Positioner Selection Criteria

Positioner Selection and motor sizing is not a strictly linear process.

One set of criteria might restrict another, for example travel distance v. precision or load v. motion profile.

Selection often requires compromise and reassessment of needs based on budget, size constraints and other goals.

In many cases there is more than one right answer

Precision

Loading

EnvironmentGeometry

Motion

Application Categories

Making

• Transform

• Welding, Cutting, Etching, Dispensing, Bending

Moving

• Transfer

• Pick & Place, Storage & retrieval, palletize, Shuttle

Measuring

• Test

• Inspection, Vision, Gauging, Sampling

Positioner Selection : Precision

Accuracy is “more expensive” than repeatability so be sure to understand the difference and machine requirements

Making

Moving

Measuring

Precision

Accuracy

Repeatability

Accuracy

Positioner Selection : Geometry

Rod Style

• Electric Cylinder

• Rodded Actuator

• PistonRodless Actuator

• Electric Actuator

• Linear Actuator

Linear Positioner

• Linear Table

• Linear Stage


Rod StyleDefining characteristics:

Non-constant support geometry

Packaged drivetrain, guidance and moving rod

Similar functionality to pneumatic and hydraulic

cylinders

Applications:

Push/pull

Push to force

Pressing

Forming

Clamping

Vertical axis in gantry

Good for-

High thrust force applications

Vertical applications

Fluid power conversion

Reach in and retract applications


Rodless Actuator

Defining characteristics:

Constant support geometry

Packaged drivetrain, guidance and moving

carriage assembly

Single linear guide

Applications:

Pick and place

Push to force

Indexing

Cutting/feeding

Material Handling

Good for-

Low Cost

Flexibility- drive trains/guides

Scalability- multiple frame sizes

Long stroke

Moderate payloads

Industrial applications


Linear Positioner

Defining characteristics:

Constant support geometry

Packaged drivetrain, guidance and moving

carriage assembly

Dual linear guides

Applications:

High precision positioning

Dynamic control

Multi-axis

Scanning

Metrology

Electronics mfg

Good for-

Precision positioning

High moment loading

Multi-Axis Stacking

Straightness/flatness

Positioner Selection : Travel

Determine Overall Travel Distance/StrokeDrive TrainGuidance SystemMounting Considerations

Review how the overall length of the positioner impacts the machine constraints


Positioner Specifications will typically call out a repeatability as a +/-value.

Positional Accuracy, straightness is generally travel length dependent.


Straightness and Flatness are generally travel length dependent.


Errors can occur in 6 different ways in a linear positioning device:

Guidance system, drive train, machined surfaces, assembly techniques all contribute the accuracy specification.

XZ Y

YAW

PITCH

Positioner Selection : Motion Profile

Review Motion profile requirements to determine maximum speed and acceleration

Motion


Trapezoidal Move Profile: 𝑽𝒆𝒍𝒐𝒄𝒊𝒕𝒚𝑴𝒂𝒙𝒊𝒎𝒖𝒎 =1.5∗𝐷

𝑡

𝑨𝒄𝒄𝒆𝒍𝒆𝒓𝒂𝒕𝒊𝒐𝒏𝑴𝒂𝒙𝒊𝒎𝒖𝒎 =4.5∗𝐷

𝑡2

17


Positioner Specifications will typically rate a maximum allowable velocity and acceleration based on the drive train and guidance system limits.

Maximum velocity will vary based on overall travel distance and in the case of ballscrew, the lead (or pitch of the screw.

Load Selection Criteria

Select Positioner based on

Normal Load capacity

Moment load capacity

Axial load capacity


Consider

Mounting Orientation

Load Center of gravity

Axial load capacity


Moment Load Capacity


Maximum Load Rating

Load/Life Charts based in cumulative travel distance

Environmental

Environmental conditions may lead to additional design considerations

Dust/Dirt/Debris>>>> Sealing/Bellows

Clean room/Vacuum/Explosion>>>Special preparation

Overview

Positioner Selection

Motor & Drive Sizing

Motor Sizing

Speed

Peak Torque

AmplifierInertia

Continuous Torque

Motor Sizing

Convert required linear speed to rotational speed

Simple rotational velocity equation for a screw device:

𝜔 =𝑉 ∗ 𝑅

𝐿

𝜔 = rotational velocity required (RPM, RPS)

𝑉 = linear velocity (in/s, m/s)

𝑅 = any gear reduction ratio

𝐿 = Lead of the screw (mm, in)

Example: 𝑉 = 300 𝑚𝑚/sec𝐿 = 12 mm screw

𝜔 =300 𝑚𝑚/𝑠

12𝑚𝑚𝑟𝑒𝑣

= 25RPS

or 1500 RPM

Motor Sizing

Convert required linear acceleration to rotational acceleration

Simple rotational acceleration equation for a screw device:

𝛼 =𝐴 ∗ 𝑅

𝐿

𝛼 = rotational acceleration required (RPS)

𝐴 = linear acceleration (in/s2, m/s2)

𝑅 = any gear reduction ratio

𝐿 = Lead of the screw (mm, in)

Example: 𝐴 = 3 m/sec2

𝐿 = 12 mm screw

𝛼 =3 m/sec2

12𝑚𝑚𝑟𝑒𝑣

= 250 𝑟𝑒𝑣/𝑠𝑒𝑐2

α = 2𝜋 ∙ 𝑟𝑎𝑑/ rev ×250 𝑟𝑒𝑣/𝑠𝑒𝑐2

α = 1570 𝑟𝑎𝑑/𝑠𝑒𝑐2

Motor Sizing

Peak Torque

The total torque required from the motor to move itself and the load

𝑻𝒕 = 𝑻𝒂 +𝑻𝒇 + 𝑻𝒐𝒕𝒉𝒆𝒓

𝑇𝑡 = 𝑡𝑜𝑡𝑎𝑙 𝑝𝑒𝑎𝑘𝑇𝑎 = 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑡𝑜𝑟𝑞𝑢𝑒𝑇𝑓 = 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝑡𝑜𝑟𝑞𝑢𝑒 𝑖𝑛 𝑁 −𝑚

𝑇𝑜𝑡ℎ𝑒𝑟= 𝑡𝑜𝑟𝑞𝑢𝑒 𝑓𝑟𝑜𝑚 𝑔𝑟𝑎𝑣𝑖𝑡𝑦, 𝑝𝑟𝑒𝑙𝑜𝑎𝑑𝑠, 𝑝𝑢𝑠ℎ/𝑝𝑢𝑙𝑙 𝑓𝑜𝑟𝑐𝑒𝑠𝑇𝑔 = 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 𝑡𝑜𝑟𝑞𝑢𝑒 𝑖𝑛 𝑁 −𝑚

Motor Sizing

Acceleration Torque

𝑇𝑎 = 𝐽𝑡𝑜𝑡𝑎𝑙 × 𝛼

𝐽𝑡𝑜𝑡𝑎𝑙 = 𝐽𝑚 + 𝐽𝐿 + 𝐽𝑝

𝑇𝑎 = acceleration torque

α = angular acceleration, rad/sec2

𝐽𝑚 = inertia of motor

𝐽𝐿 = reflected inertia of load thru mechanics

𝐽𝑝 = inertia of positioner mechanics

𝛼 = angular acceleration, rad/sec2

Motor Sizing : Inertia

Determine the reflected inertia of the load back to the motor

For ballscrew:

𝐽𝐿 =𝑚𝑙𝑜𝑎𝑑 ∗ (𝐿

2𝜋)2

JL = reflected inertia of loadthru mechanics𝑚𝑙𝑜𝑎𝑑= payload in kgL= Lead of screw (mm, in)

Example: 𝑚𝑙𝑜𝑎𝑑 = 50𝑘𝑔𝐿 = 12𝑚𝑚/𝑟𝑒𝑣

𝐽𝐿 = 50𝑘𝑔 ∗ (0.012𝑚

2𝜋)2

𝐽𝐿 =0.00018 𝑘𝑔 ∙ 𝑚2

Motor Sizing : Torque

Use reflected inertia to approximate acceleration torque

𝑇𝑎 = (𝐽𝐿 + 𝐽𝑝) × 𝛼

Example: 𝑚𝑙𝑜𝑎𝑑 = 50𝑘𝑔𝐿 = 12𝑚𝑚/𝑟𝑒𝑣

𝐽𝐿 = 50𝑘𝑔 ∗ (0.012𝑚

2𝜋)2

𝐽𝐿 =0.00018 𝑘𝑔 ∙ 𝑚2

α = 1570 𝑟𝑎𝑑/𝑠𝑒𝑐2

𝐽𝐿 = 0.000182 𝑘𝑔 ∙ 𝑚2

𝐽𝑝 = 0.0000042 𝑘𝑔 ∙ 𝑚2

𝑇𝑎 = 0.000186 𝑘𝑔 ∙ 𝑚2 ×1570 𝑟𝑎𝑑/𝑠𝑒𝑐2

𝑇𝑎 = 0.34𝑁𝑚

𝐽𝑝


Total Torque

𝑻𝒕 = 𝑻𝒂 +𝑻𝒇 + 𝑻𝒐𝒕𝒉𝒆𝒓

𝑇𝑡 = 0.34 + 0.2 = 0.54𝑁𝑚


Peak Torque Required = 0.55Nm @ 1500rpm

Peak Versus Continuous

Determining and RMS or effective torque is pertinent for determining a number of itemsAppropriately sizing a system (actuator, motor, and drive)

Accurately modeling the life of a system

Be sure to include dwells or periods of rest

38

Calculating RMS Torque

Once forces are modeled by unit of time the following equation can then be applied:

𝑇𝑜𝑟𝑞𝑢𝑒𝑅𝑀𝑆 = 𝑖=1𝑖=𝑛𝑇𝑖

2 ∗ 𝑡𝑖

𝑖=1𝑖=𝑛 𝑡𝑖

Where:

T = is the Torque require per time segment (ti)

ti = is the time segment a force is seen, include dwells if being used for motor sizing

n = the total number of segments in a motion profile.

39

Calculating RMS Torque

𝑇𝑜𝑟𝑞𝑢𝑒𝑅𝑀𝑆 = 𝑖=1𝑖=𝑛𝑇𝑖

2 ∗ 𝑡𝑖

𝑖=1𝑖=𝑛 𝑡𝑖

40

t T T^2 T^2*t0.15 0.55 0.3025 0.166375

1 0.2 0.04 0.0080.15 0.55 0.3025 0.166375

1 0.2 0.04 0.0080.15 0.55 0.3025 0.166375

tsum 2.45 0.515125 0.2102550.458536


Peak Torque Required = 0.55Nm @ 1500rpm

Continuous Torque Required = 0.45Nm @ 1500rpm

Motor Sizing : Inertia Ratio

reflected inertia of the load compared to motor inertia

𝐽𝐿 =𝑚𝑙𝑜𝑎𝑑 ∗ (𝐿

2𝜋)2

𝐽𝐿 =0.00018 𝑘𝑔 ∙ 𝑚2

𝐽𝑚 =0.000009 𝑘𝑔 ∙ 𝑚2

𝐽𝐿/𝐽𝑚= 19.9

Motor Sizing : Inertia Ratio

reflected inertia of the load compared to motor inertia

𝐽𝐿/𝐽𝑚= 10.5

𝑱𝑳/𝑱𝒎= 7.8

Motor Sizing

Screw Lead Motor Speed Inertia Ratio Motor Torque Torque Margin

5 3600 1.34 0.12 10.9

12 1500 7.70 0.29 4.5

16 1125 13.68 0.38 3.4

25 720 33.40 0.60 2.2

Linear Speed 300mm/sec

Acceleration 3000mm/sec2

Load 50kg

Motor Inertia 2.37 e-5 kg-m^2

Motor Torque 1.3Nm

Motor Sizing

Motor Sizing

Convert required linear speed to rotational speed

Rotational speed for belt and pulley :

𝜔 =𝑉 ∗ 𝑅

2𝜋𝑟

V = required linear velocity (in/s, m/s)

R = any additional gear reduction

r = radius of the drive pulley

Example: V = 800 mm/secr = 45 mm pulley

𝜔 =800 𝑚𝑚/𝑠

2𝜋 ∗ 45 𝑚𝑚= 2.83RPS

or 170 RPM

Example: V = 800 mm/secr = 45 mm pulley R=10: 1 gear

𝜔 =800

𝑚𝑚𝑠∗ 10

2𝜋 ∗ 45 𝑚𝑚= 28.3RPS

or 1700 RPM

Motor Sizing

Gear ratioMotor Speed, rpm Inertia Ratio Motor Torque Torque Margin

1 170 2136 :1 3.38 0.4

5 849 85:1 0.68 1.9

10 1698 21 :1 0.34 3.9

20 3395 5:1 0.17 7.7

Linear Speed 800mm/sec

Acceleration 3000mm/sec2

Load 25kg

Motor Inertia 2.37 e-5kg-m^2

Motor Torque 1.3Nm

Motor Sizing

Speed

Peak Torque

AmplifierInertia

Continuous Torque

Jim WileyProduct Manager

Parker Hannifin Corporation

Electromechanical & Drives

5500 Business Park Drive

Rohnert Park, CA 94928

Telephone: 707-584-2541

Email: [email protected]

www.parker.com/emn

positioner selection and motor sizing...positioner selection criteria positioner selection and motor...

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