Question: How do I calculate RMS (Root Mean Square) Torque for a given axis motion profile in my application?

Answer:  Let’s take a look at the Root Mean Square (RMS) Torque and why it is important. Typically an axes’ motion profile is broken up into multiple segments, each segment is found to require a specific torque for a specific amount of time to complete the desired motion.  For example, this can include torque required to accelerate, traverse (against an external force and/or friction),  decelerate, and dwell.  Each of these segments affects the amount of heating the motor experiences and thus the equivalent steady state continuous requirement utilized to select the correct motor.  The RMS Torque calculation  considers not only the amount of torque, but also the duration of that torque (by segment).  Our example below illustrates how to calculate Trms of your motion profile.

The below motion profile would be broken up into eight (8) different segments, each with a required torque T_x and time t_x.

To calculate Trms, use this equation:

 

Where T₁ = torque required by and during segment 1, and t₁ = time duration (t₁-t₀) of segment 1, etc..  Note the additional torque required by the motor to over come some external/thrust force (greater than friction alone) during segment 2, and the lack of this required torque  during the dwell segment 4 and 8.

Going back to the example motion profile above and the chart of that motion profile:

Therefore, if you do the math – and we will spare you writing this into a very long equation, the result is:

Trms =     = 2.74 lb-ft or 3.715_Nm (1.35582_Nm/lb-ft.)

Conclusion:  We hope that this tutorial has helped you!  If you have questions about this or other calculations,  or any automation related problem you may be having, please contact the motion control and programming experts at CMA/Flodyne/Hydradyne.

CMA/Flodyne/Hydradyne is an authorized  Kollmorgen distributor in Illinois, Wisconsin, Iowa and Northern Indiana.

In addition to distribution, we design and fabricate complete engineered systems, including hydraulic power units, electrical control panels, pneumatic panels & aluminum framing. Our advanced components and system solutions are found in a wide variety of industrial applications such as wind energy, solar energy, process control and more.