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Dynamic Torque & Step Motor Sizing

by Jeff Kordik

In the posts What Do NEMA Sizes Mean? and What is Step Motor Stack Length? we discussed factors affecting holding torque in step motors, such as frame size and stack length.  Holding torque is a measure of how much rotating force is required to force a stationary step motor shaft out of position. Holding torque (T) is the product of a motor’s torque constant (KT) and the current (i) applied to the stator windings.


In most applications, step motors are controlled by electronic drivers that employ pulse width modulation (PWM) technology to monitor the stator current and apply the proper voltage (V) to achieve the desired current (i) and torque.  When a motor is stationary, the driver only need apply enough voltage to overcome the resistance (R) of the stator coils (also known as motor phases).  This is described by Ohm’s law:


Since most high performance step motors have low phase resistance, not much power supply voltage is needed by the driver to hold the motor in position. For real applications, the motor does not remain forever stationary, but rather is used to move a load.  As a colleague once said “if all you need is holding torque, buy a bolt”.  To move something at a particular speed, you are concerned with the dynamic torque available at that speed.  Step motors do not instantly change from standstill to a given speed; they have to be accelerated, just as your car gradually increases its speed when you step on the gas pedal.  If you want to accelerate faster, you give the car more gas. Step motors are similar, following Newton’s famous law F=ma.  In rotational terms, Newton’s law is expressed as


Torque (T) is proportional to rotor and load inertia (J) and angular acceleration (A).  If you have a heavier load or want to accelerate faster, you need more torque.  Problem is, the dynamic torque of a step motor decreases as speed increases.  Why?  Because when a motor starts moving, it becomes a generator.  As the rotor’s magnetic field moves among the stator coils, a voltage appears on the motor terminals.  The driver must apply extra voltage to the motor to overcome this voltage, known as back EMF, which is a product of motor speed (w) and the voltage constant (KE).  Also, the stator coils, like all coils, have inductance that resists the change of current.  But the stator current must change in order to keep the rotor turning, so more voltage must be used to overcome inductance (L).  The voltage equation for a motor in motion is

A PWM driver will increase the voltage applied to the motor to keep the current and torque constant, but at some speed there will not enough voltage available from the power supply and the motor current will begin to fall.  The torque drops with the current.  If a higher voltage power supply is used, the dynamic torque curve will remain flat to a higher speed, as shown in the chart below for a popular NEMA 23 integrated step motor.


The process of “sizing an application” involves calculating the required torque and speed range necessary to move the load.   For example, if we needed 80 ounce-inches of torque up to 10 revolutions/second, we could use this motor and a 24 volt power supply.


If we needed to go farther, faster, I might need 80 oz-in at 20 rps.  For that we need a 48 volt power supply.


Hopefully this post will give you a feel for the dynamics of step motor motion and some insight into application sizing.  We’ll try to revisit this topic in future posts.

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