Introduction to stepper motor specifications and voltage mode drive

Nesh Basnet,  Shiraz Macuff,  Subash Shrestha,  Lhakpa Dhondup,  Lobsang Lekshey,

Anil Rajpatei,  Francisco Santos,  Adrian Serrano

Abstract

This application note gives a brief introduction to stepper motor specification and voltage mode drive method. We look at drive requirements once the motor has been chosen and give several application examples. A method for increasing the stepping speed is also examined. Motor selection based on mechanical requirements is not included.

Introduction

Designing any complex system requires an iterative process. Top down design where requirements are defined and then solved is most favored by seasoned engineers because it reduces the probability of rework later in the design process. However to leverage the benefits of top down design, the design engineer has to be aware of the state of art of and non-ideal characteristics of these subsystem.

Torque produced by a stepper motor

The torque produced by a stepper motor is a function of the current through the winding and the position of the rotor. This torque is known as the static torque and is supplied by the motor’s manufacturer. A simplified graph is shown in Figure 1.0 [1]. The graph shows the torque produced on the vertical axis as a function of the rotor position on the horizontal axis. Looking at the horizontal axis, one complete step is from zero to C in clockwise direction. The center of the horizontal axis labeled C, is when the rotor tooth and stator pole are completely aligned. The points labeled A and B, is when the rotor tooth is exactly between two of the stator poles. So we see that maximum torque is developed when the rotor tooth is at half of the step angle. Each winding or phase has a resistance and inductance associated with it. The specifications of the motor are normally given in amp per phase and maximum torque. Also, the resistance and inductance of the motor coils are provided.

Fig. 1.0

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Methods of driving the phase of a stepper motor

There are two ways to drive the phase of a stepper motor. One is by controlling the current in the winding and the other is by applying the correct voltage across the winding. The latter (voltage mode) is the simplest and most cost effective way. Using the winding resistance, the steady state current can be controlled by carefully selecting the appropriate voltage. If the appropriate voltage is unavailable, resistors can be placed in series to reduce the steady state current. That is to use the winding resistance and the maximum winding current to determine the applied voltage. The disadvantage of the voltage mode is that stepping speed and resolution are compromised. Another disadvantage is the vibration produced by the motor. With the voltage mode, the maximum stepping speed is determined by the inductance of the coil. The maximum stepping resolution is half stepping. Current mode drives have the advantage of higher stepping speeds, and if provided by the driver, higher resolution by micro stepping. With micro stepping, vibration can also be reduced to a point where it’s unnoticeable. The disadvantage is higher cost when compared to voltage mode motor driver.

Voltage mode example

The mechanical requirements of the motor allows us to select a motor with required torque and stepping resolution. Once the motor is selected, the drive method has to be selected so that it meets the performance and cost requirement. For systems that would require micro stepping, the voltage mode driver cannot be used.

Calculating the voltage requirements

The voltage requirement is determined by the amp per phase rating and the winding resistance. The voltage requirement is simply V=I*R . That is the maximum current supplied to the coil at steady state.

Calculating the maximum stepping speed in voltage mode

The maximum stepping speed at the maximum torque requires that at each step, the maximum current is reached. This is determined by the transient response of the system. When a step pulse is applied to the winding, the current in the winding will gradually increase at a rate determined by the resistance and inductance. The complete response is given by

Eq.1.0

    \[ i(t)=\frac{V}{R}+(I_0-\frac{V}{R})e^{\frac{-t}{\tau}}\]

Where  is \tau=\frac{L}{R},I_0=0,

    \[ i(t)=\frac{V}{R}-(\frac{V}{R})e^{\frac{-t}{\frac{L}{R}}}\]

Eq.1.1

    \[ i(t)=\frac{V}{R}*(1-e^{\frac{-t}{\frac{L}{R}}})\]

From the equation above we see that the transient part will eventually go to zero and be left with the steady state current \frac{V}{R} .

Fig.2.0

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Note that V was determined previously , R and  L are determined by the motor that was selected based on the mechanical requirements. Based on all this information, the equation above can be solved for  t. However, setting i(t) equal to maximum current which is \frac{V}{R} would result in the transient part e^{-x}=0. Solving this would result in an infinite step length x=\infty. The industry standard is to set the maximum current to 0.632 of its steady state value. That is I_{max}=0.632 \frac{V}{R}. Adjusting the maximum current and substituting the values into the equation above results in 0.632*\frac{V}{R}=\frac{V}{R}(1-e^{\frac{-tR}{L}}).
solving for t.

Eq.2.0

    \[ t=\frac{.9996723408*L}{R}$ \]

Fig. 3.0

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Equation 2 gives us the time it would take for the current to reach 63% of its stead state value when the step pulse is applied to the coil. When the step pulse is removed, the current in the stator coil decays at a rate determined by the inductance and resistance of the coil. A complete cycle requires 2*0.9996723408*\frac{L}{R}=1.9934\frac{L}{R}\approx 2*\frac{L}{R}.

Example 1

The mechanical requirements have been determined and the two most relevant requirements are listed below.

  • 1.8 deg full step. No micro stepping needed due to lead screw pitch.
  • holding torque min =20 oz-in

Two motors have been selected so they meet the mechanical requirements and their specifications are listed below.

 Motor A  Motor B
  • maximum current :0.14 Amp/phase
  • resistance : 240 ohms/phase
  • inductance : 420 mH/phase
  • maximum current :1 Amp/phase
  • resistance :4.3 ohms/phase
  • inductance : 5.5 mH/phase
steady state voltage requirements  is I*R=0.14*240=33 Volts. Solving for the maximum stepping speed results in t=2*\frac{420*10^{-3}}{240}=3.5*10^{-3} s resulting in \frac{1}{3.5*10^{-3}}=285 steps per second steady state voltage requirements  is I*R=0.14*4.3=0.602 Volts. Solving for the maximum stepping speed results in t=2*\frac{5.5*10^{-3}}{4.3}=2.55*10^{-3} s  resulting in 392 steps per second