• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar
  • Skip to footer

Motion Control Tips

Automation • Motion Control • Power Transmission

  • News
    • Industry News
    • Editor Blogs
    • Video
  • Controls
    • HMIs
    • PC-Based Controllers
    • PLCs + PACs
    • Stand-Alone Controllers
    • Software
  • Drives
    • Servo Drives
    • Stepper Drives
  • Encoders
    • Absolute Encoders
    • Incremental Encoders
    • Rotary Encoders
  • Mechanical
    • Bearings
    • Brakes + Clutches
    • Belt + chain
    • Couplings
    • Gears + Gearing
    • Lubrication
    • Shock + Vibration Mitigation
    • Springs + Rings + Seals
  • Linear
    • Actuators
    • Linear Motors
    • Linear Encoders
  • Motors
    • AC Motors
    • DC Motors
    • Brushless Motors
    • Gearmotors
    • Piezo Motors
    • Servo Motors
    • Stepper Motors
  • Systems
    • Conveyors + linear transport systems
    • Gantries + Stages
    • Rotary Tables
    • Grippers + End Effectors
    • Robotics
  • Networks
    • Connections + Sliprings
    • Fieldbuses
    • I/O
    • Sensors + Vision
  • FAQs
    • Motion Casebook
    • Motion Selection Guides
  • Suppliers
You are here: Home / FAQs + basics / Why is the electrical time constant important for stepper motors?

Why is the electrical time constant important for stepper motors?

April 26, 2017 By Danielle Collins Leave a Comment

Motor windings have a property referred to as inductance, which is a resistance to any change in the electrical current through the winding. The result of inductance is the production of back EMF to oppose the change in current.

Time Constant

Where:

Eb = back EMF (volts)

L = inductance (H, or Ohm-s)

dI/dt = rate of change of current

Note that the magnitude of dI/dt is expressed as frequency times current (ω x I). The value of frequency is given by:

Time Constant

Where:

ω = frequency (rad/s)

S = motor speed (rpm)

N = number of magnetic cycles per shaft rotation

The windings also have a resistance to the current flowing in them. This resistance is proportional to the square of the number of turns in the winding. According to Ohm’s Law, voltage equals current times resistance: V = I x R. Ohm’s law expressed in terms of resistance shows:

Time Constant

Where:

R = resistance (ohms)

V = voltage (volts)

I = current (amps)


While resistance and inductance are similar properties, resistance determines the maximum current in the winding, whereas inductance determines the maximum rate of change of current in the winding.


The electrical time constant is the amount of time it takes the current in the winding to reach 63 percent of its rated value. The time constant found by dividing inductance by resistance.

Electrical Time Constant

Where:

τe = electrical time constant (s)

Electrical Time Constant
The time constant, τ, is the time it takes the current in the winding to reach 63 percent of its maximum rated value.
Image credit: NJR Co., Ltd.

Q: Why does the electrical time constant represent 63 percent of the maximum rated current (and not, say 50 percent or 85 percent)? 

A: Because the time constant of an increasing system is the time that it takes the system’s step response (the resulting output when the input changes from zero to one very quickly) to reach 1 – 1/e of its final value. The value of 1 – 1/e is 0.632, or approximately 63 percent. 


A lower time constant is usually desirable, because it means that current flows more quickly into the windings. This allows the motor to reach its rated torque before current is switched to the next phase. When the motor speed is high (high stepping frequency), there’s not enough time for the winding to receive sufficient current to produce the rated torque.

There are two ways to achieve high speed from a stepper motor: increase the rate of current flow, or decrease the time constant by keeping the inductance low. The first option, increasing the rate of current flow, requires increasing the voltage to the motor. While stepper motors can be run at higher than rated voltage, the higher voltage also means higher maximum current, which could cause the motor to overheat or the rotor to be demagnetized. So in this solution, some form of current limiting must be employed.

The second solution, using a motor with low induction (and therefore, a lower time constant), is a matter of motor selection. However, low induction means higher current, and a stepper drive with a higher current rating—and therefore, higher cost—will be required.

You may also like:


  • FAQ: What features need to be compatible for a stepper…

  • FAQ: How to set a stepper motor’s current limit and…

  • FAQ: What are the requirements for stepper motor acceleration?

  • FAQ: What kind of torque can I get out of…

  • FAQ: How do stepper drives and motors get smooth motion…

Filed Under: FAQs + basics, Featured, Stepper Drives, Stepper Motors

Reader Interactions

Leave a Reply

You must be logged in to post a comment.

Primary Sidebar

POWER TRANSMISSION REFERENCE GUIDE

DESIGN GUIDE LIBRARY

“motion
Subscribe Today

RSS Featured White Papers

  • Specifying electric rodless actuators: Ten tips for maximizing actuator life and system performance
  • The truth about actuator life: Screw drive survival
  • Top Ten Tips: How to specify electric rod-style actuators for optimal performance, reliability and efficiency

Footer

Motion Control Tips

DESIGN WORLD NETWORK

Design World Online
The Robot Report
Coupling Tips
Linear Motion Tips
Bearing Tips
Fastener Engineering.

MOTION CONTROL TIPS

Subscribe to our newsletter
Advertise with us
Contact us
About us
Follow us on TwitterAdd us on FacebookAdd us on LinkedInAdd us on YouTubeAdd us on Instagram

Copyright © 2022 · WTWH Media LLC and its licensors. All rights reserved.
The material on this site may not be reproduced, distributed, transmitted, cached or otherwise used, except with the prior written permission of WTWH Media.

Privacy Policy | RSS