﻿ Dialog: Servo-Gearbox Sizing-Torque-Speed

# Dialog: Servo and Gearbox Sizing

## Kinetostatic Motor Torque and Speed dialog-box - MD14.2

Note: This topic has been updated to describe the new functionality in MD14.2

Note: The options for a Linear Motor with a Slide-Joint will become available in a later release.

 To Open the Kinetostatic Torque and Speed dialog-box

Make sure:

 • Force toolbar > Calculate Force is active
 • Visibility toolbar > Forces Vectors is active (MD14.2+

You will see the Motor-Symbol at a joint - see image below.

If you want the Motor and Gearbox to be at a different joint, then use:

 • Force toolbar > Configure Power Source to move the motor to the correct joint.

To see the Motor-Symbol, you must use: Force toolbar > Show Force

 1 Click the Motor-Symbol in the graphic-area

The Pin-Joint shows in the Selection-Window

 2 Right-Click the Pin-Joint
 3 Click Edit element in the contextual-menu

- or -

The Kinematic Torque and Speed dialog-box opens.

 Application (Load) Torque vs Speed plot

FOUR QUADRANT: TORQUE(LOAD) vs SPEED

When you open the Kinetostatic Torque-Speed dialog, you will see a plot of the Application (or Load) Torque vs Speed in all Four-Quadrants.

Four-Quadrant - Why 4 Quadrants

Many mechanism applications, when inertia is a significant or dominant load, require the servo-motor to apply:

 • Positive Torque - when accelerating in the positive direction and also decelerating in the reverse-direction
 • Negative Torque - when decelerating in the positive direction and also accelerating in the reverse-direction.
 • Positive angular velocity  - when advancing the mechanism
 • Negative angular velocity  - when returning the mechanism

 STEP 1: Auto-Filter and Range-Factor
 1 Auto-Filter check-box

The Auto-Filter check-box is at the Top and Right of the dialog.

 ❑ Auto-Filter OFF

When Auto-Filter is off, you can select from 1000s of Gearboxes.

 ☑ Auto-Filter ON

Click the check-box to make the Auto-Filter active. We recommend you select Auto-Filter.

Auto-Filter ON, : MechDesigner offers for selection only those Gearboxes that have, as a Lower-Limit, the Torque and Speed capacity to drive the Application Load.

The Upper-Limit of Gearboxes that MechDesigner presents for selection is determined with the Range-Factor.

 2 Range-Factor

The Range-Factor is bottom and left of the dialog.

Auto-Filter ON pre-filters Gearboxes to those that have as a minimum capacity the Torque and Speed capacity to drive the Application (Load)

Range-Factor pre-filters Gearboxes to those do not exceed Application-Load × Range-Factor.

Example: Auto-Filter ON, Range-Factor: 1.3

Lower Gearbox Torque Capacity = Equivalent Application (Load) Torque (21.495 N.m.)

Upper Gearbox Torque Capacity = Range Factor × Equivalent Application (Load) Torque (1.3 × 21.495 = 27.944 N.m.)

 STEP 2: Select a Gearbox Manufacturer

#### Select a Gearbox Manufacturer

There are four Gearbox manufacturers from which you can choose: APEX, Neugart, Vogel, and Wittenstein

Note: If you need us to list a different Gearbox Manufacturer, then please email us.

 STEP 3: Select a Gearbox Model

#### Select a Gearbox Model

When you select a Gearbox Manufacturer, and Auto-Filter is ON, and you have entered a Range-Factor, the list of Gearboxes is limited to those whose capacity can satisfy these in-equalities:

 Manufacturer The Selected Manufacturer Model The Selected the Model. Each manufacturer has a different model format. Series Series - from the selected Model i # Gearbox Ratio from the Model T2N Nm Rated Torque referred to Output Shaft - data sheet - T2max Nm Max. Torque referred to Output Shaft - data sheet - n2N RPM Rated Speed referred to Output Shaft - data sheet / i - m2MAX RPM Max Speed referred to Output Shaft - data sheet / i -

T2max T2MAX RF × T2max

Maximum Application (Load) Torque Maximum Output Torque of the Gearbox Range-Factor × Maximum Application (Load) Torque

T2m T2N RF × T2m

Equivalent  Application (Load) Torque Rated Output Torque Capacity of the Gearbox Range-Factor × Equivalent  Application (Load) Torque

n2max× i n1MAX

Maximum Application (Load) Speed × Gearbox Ratio (i) Maximum Input Speed of the Gearbox

n2n × i n1N

Average Application (Load) Speed (or Equivalent, Mean) × Gearbox Ratio (i) Rated Input Speed of the Gearbox

 Gearbox Parameters Check List.

When you select a Gearbox model, its Gearbox Parameters Summary Sheet will show. This form is read only.

There should be 4 × to indicate that the Gearbox has the capacity to drive the Application Load and satisfies those 4 × requirements.

Peak Torque ≥ Maximum Application (Load)

Rated Torque ≥ Equivalent Application (Load) Torque

(Max Output Speed) ≥ Maximum Application (Load) Speed

(Rated Output Speed) ≥ Equivalent Application (Load) Speed

Notes: Parameters in ( ) are referred to the output-shaft from the Gear-Ratio and the listed data-sheet information.

Other Parameters include:

 • Backlash
 • Stiffness
 • Efficiency
 • Shaft Diameter - the input shaft diameter, which is not in the list until you select a Servomotor.
 • Inertia - referred to the input, which is not in the list until you select a Servomotor.
 Gearbox Output Torque vs Speed plot

When you select a Gearbox, the Torque (N.m.) vs Speed (RPM) plot changes to indicate whether the Gearbox has the  Capacity to drive the Application Load or not.

The colour code is :

 • Green : Torque AND Speed of the Load ≤ Rated Gearbox Capacity
 • Amber : Torque OR Speed of the Load ≥ Rated Gearbox Capacity ≤ Maximum Gearbox Capacity
 • Red : Torque OR Speed of the Load ≥  Maximum Gearbox Capacity

Gearbox Torque and Speed Limits.

The Show Gearbox Limits check-list box is above the Gearbox selection box.

 ❑ Show Gearbox Limits OFF

The axes are auto-scaled to the Maximum Application Torque and Speed, at the output of the Gearbox.

 ☑ Show Gearbox Limits ON

The axes are auto-scaled to the Maximum Torque and Speed Capacity, referred to the output of the Gearbox.

This helps you compare the Torque and Speed Capacity of the Gearbox with the Application Load.

The Limits of Torque and Speed are shown as boxes.

Before you select a servomotor, the limit boxes and their colour codes indicate the:

 • Dark Blue : Maximum Torque and Speed capacity of the Gearbox
 • Light-Blue : Rated (or Nominal) Torque and Speed capacity of the Gearbox
 • Light-Brown : Equivalent Torque and Speed of the Application Load
 STEP 4: Select a Servomotor Manufacturer

#### Select a Servomotor Manufacturer

There are four many Servomotor manufacturers from which you can choose one.

When you select a Servomotor Manufacturer, MechDesigner finds those that have the Torque and Speed Capacity required by the Application Load.

Note: If you need us to list a different Servomotor Manufacturer, then please email us.

 STEP 5: Select a Servomotor Model

#### Select a Servomotor Model

When you select a Servomotor Manufacturer, and Auto-Filter is ON, and you have entered a Range-Factor, the list of Servomotor is limited to those whose capacity can satisfy these in-equalities:

 Manufacturer The Selected Manufacturer Model The Selected the Model. Each manufacturer has a different model format. Series Series - from the Selected Model d1 mm Motor Shaft Diameter - data sheet - Tn Nm Rated Torque - data sheet - Tmax Nm Max. Torque - data sheet - Nn RPM Rated Speed - data sheet - Nmax RPM Max Speed - data sheet -

d1max D   d1min

The Servomotor Shaft Diameter, D, must fit directly into the Gearbox, d1.

Note: Most Precision Planetary Gearboxes can accept a range of shaft diameters at their input. The Gearbox inertia is referred to the input shaft, and is different for each shaft diameter.

Tmax Tmotmax RF × Tmax

Maximum Application Load Torque referred to the Gearbox input-shaft

Maximum Servomotor Torque Capacity

Range-Factor × Maximum Application Load Torque referred to the Gearbox input shaft

Tm TN RF × Tm

Equivalent Application (Load) Torque referred to the Gearbox input-shaft

Rated Servomotor Torque Capacity

Range-Factor × Equivalent  Application (Load) Torque referred to the Gearbox input shaft

Tmax Tmotmax RF × Tmax

Maximum Application (Load) Torque referred to the Gearbox input-shaft

Rated Servomotor Torque Capacity

Range-Factor × Equivalent  Application (Load) Torque referred to the Gearbox input shaft

n1max Nmax

Maximum Application Speed referred to the Gearbox input-shaft Maximum Servomotor Speed

nN NN

Average Application (Load) Speed (or Equivalent, Mean) Rated Servomotor Speed

 Servomotor Parameters Check List.

When you select a Gearbox model, its Gearbox Parameters Summary Sheet will show. This form is read only.

There should be 4 × to indicate that the Gearbox has the capacity to drive the Application Load and satisfies those 4 × requirements.

Peak Servomotor Torque ≥ Maximum Application (Load) ÷ i

Rated Servomotor Torque ≥ Equivalent Application (Load) Torque ÷ i

Max Servomotor Speed ≥ Maximum Application (Load) Speed × i

Continuous Servomotor Speed ≥ Equivalent Application (Load) Speed × i

Rated Power > Nominal Load Power.

Other Parameters include:

 • Vdc - Bus Voltage for Drive
 • Jm - Servomotor Inertia
 • D - Servomotor shaft diameters.
 Servomotor Torque vs Speed plot

When you select a Gearbox, colours of the dots for the Torque (N.m.) vs Speed (RPM) plot changes to indicate whether the Gearbox has the Capacity to drive the Application Load or not.

The colour code is :

 • Green : Torque AND Speed of the Load ≤ Rated Servomotor Capacity
 • Amber : Torque OR Speed of the Load ≥ Rated Servomotor Capacity ≤ Maximum Servomotor Capacity
 • Red : Torque OR Speed of the Load ≥  Maximum Servomotor Capacity

Motor Torque and Speed Limits.

The Show Motor Limits check-list box is above the Motor selection box.

 ❑ Show Motor Limits OFF

The axes are auto-scaled to the Maximum Torque and Speed, at the Servomotor Drive Shaft.

 ☑ Show Motor Limits ON

The axes are auto-scaled to the Maximum Torque and Speed Capacity of the Selected Servomotor

This helps you compare the Torque and Speed Capacity of the Servomotor with the Application Load referred to its input-shaft.

The Limits of Torque and Speed are shown as boxes.

 • Purple  : Maximum Torque and Speed capacity of the Servomotor
 • Pink : Rated (or Nominal) Torque and Speed capacity of the Servomotor
 • Light-Brown : Equivalent Torque and Speed of the Application Load

 The Torque we show in the graphic-area when we Display Force Vectors is the torque to move the mechanism only. It does not include the Torque to move the motor and gearbox. It is necessary to add the Torque to accelerate the motor and the gearbox to Torque in the graphic-area. Clearly, the Torque to move motor depends on the ....inertia of the motor and gearbox as well as the gearbox ratio. The higher the gear ratio, the less Torque the motor 'sees'. But the motor must run faster and accelerate more. This influences the overall power, as well as system efficiency.

#### More on Torque vs Speed Curves

 The performance characteristics of a brushless servo motor (motor/drive combination) are described by a torque/speed operating envelope. As shown below, the coloured areas of the curve identify the Exceeded Duty, Continuous Duty and Intermittent Duty zones of the system. Exceeded Duty To move the mechanical system, the gearbox and itself, the servomotor must exceeds its maximum speed or the maximum torque, or both. Continuous Duty Zone (S1) The continuous duty zone is bordered by the maximum continuous stall torque up to the intersection with the intermittent duty line. The continuous torque line is set by either the motor’s maximum rated temperature, or the drive's rated continuous current output, whichever is less. The system maximum continuous or 'voltage line' is set by the voltage rating of the drives, the line voltage supplied, and the motor winding. The system can operate on a continuous basis anywhere within this area, assuming the ambient temperature is 40°C or less. Intermittent Duty Zone (S5) The intermittent duty zone is bordered by the peak stall torque and the system voltage line. The peak torque line is set by either the drives’ peak current rating, which the drive can give for a limited time, or the maximum rated peak current for the motor, whichever is less. Higher torque levels may be achievable at higher power levels. Typical Torque / Speed Duty Capability of a Brushless Servomotor. Peak Torque: (ԎPS ) The Peak Torque the Motor and Gearbox at Stall Speed Continuous Stall Torque: (ԎCS ). The Continuous Torque the Motor and Gearbox can give Continuously at Stall Speed. Maximum Speed: (ωMAX ) Maximum possible speed of the Motor and Gearbox. Not attainable when the voltage is limited by the drive. Knee Speed: (ωK ) The Speed at 'knee' in peak envelope that is the intersection of the Peak Torque with the Voltage Torque/Speed Limit Line. Motor Providers also give a Rated Power - this is dependent on the Drive. Continuous Rated Torque:(ԎCR ). The Continuous Torque at the Speed of the Rated Power. Rated Speed: (ωR ) The Rated Speed or Speed at Rated Power. The motor can operate at this speed with the supply voltage.

#### How we calculate the Motor Torque and Motor Speed

 The Reflected Inertia at the Motor shaft usually continuously changes in a machine-cycle. With Constant Inertia Mechanical Systems it is easy to calculate Inertia Torque. With mechanisms, the Torque is dependent on reflected inertia that is a function of Acceleration, Velocity, and Position. PSMotion has developed algorithms to calculate these, which give a true indication of the reflected inertia at a motor shaft for even the most complex mechanisms. The equations below, are calculated at every instant in a machine-cycle. Typically, you aim to make the Reflected Load Inertia = (Motor + Gearbox) Inertia. However, when the Load Inertia is not constant, it is more difficult to select the Motor and Gearbox. Speed: ωm = N × ωL αm = N . αL Torque Tm = - αm (JG + JM) + sign(TVD) TL = (TMD  ∕  N )  ∕  η TT = Tm +  TL N    = Gear Ratio ωm = Motor Angular Velocity ωL  = Load Angular Velocity TT   = Total Torque Tm  = Motor Torque TL  = Load referred to Motor Shaft TVD = Viscous 'Drag' Torque. It is always opposite to the direction of motion TMD = Torque derived by MechDesigner at Motor Shaft ( f{PL , ωL, αL } ) JG   = Inertia of Gearbox JM   = Inertia of Motor αm  = Motor Acceleration αL = Load Acceleration η    = Gearbox Efficiency

Tutorials and Reference Help Files for MechDesigner and MotionDesigner 14.2 + © Machine, Cam, Mechanism, and Motion Design Software by PSMotion Ltd