# Understanding Pull-Out and Pull-In Torque Curves of Stepper MotorsUnderstanding Pull-Out and Pull-In Torque Curves of Stepper Motors

Which stepper motor torque curve is right for your application?

Valentin Raschke, Application Engineer

September 13, 2022

Image of motors courtesy of Portescap

When it’s time to specify a high-performance motor that offers both precise positioning and cost efficiency, stepper motors offer many advantages over DC motors thanks to their brushless technology. While selecting a stepper motor involves many considerations, designers should both understand and account for pull-out and pull-in torque curves, which describe the motor’s speed and torque characteristics when it is driven. This article will provide an overview of pull-out and pull-in torque concepts to consider when implementing stepper motors with a motion system.

## BLDC Motors and Stepper Motors: A Comparison

Figure 1 below shows the torque produced by a three-phase brushless DC (BLDC) motor with six-step commutation. Hall sensors are integrated into the motor to track the rotor position. This information allows commutation of the three phases at the right moment in order to maintain an angle of 90°± 30° between the magnetic field of the rotor and the stator. There is a small current ripple, but the torque developed by the motor is relatively stable and somewhat dependent on the rotor position. A high-resolution encoder can provide more-precise rotor position feedback and reduce the torque ripple to nearly zero.

Figure 2 below shows a simple version of a stepper motor: a magnet with one pole pair serving as a rotor and two separate phases located in the stator. This design provides four full steps over one mechanical revolution. The resulting torque curves indicating a continuous current being applied to each phase are shown in Figure 3, represented by blue and orange graphs. If the motor is driven in full step enabling only a single phase at a time, a current will be applied in the following order: A, B, -A, and -B.

The green graphs below in Figures 3a and 3b illustrate the resulting torque at the motor shaft. Unlike a BLDC motor, the motor torque of a stepper motor will significantly depend on the rotor position. To achieve a cost-efficient and simple design, the stepper motor is typically driven in open-loop mode without rotor position feedback. The commutation thus occurs with an external signal—in steps per second—without an established current rotor position. An “ideal” commutation would enable the current in the phase when the rotor is positioned exactly between two phases. However, in an open loop—without rotor position feedback—the rotor may not always be in the ideal position. When sizing a stepper motor, the designer must take this uncertainty into account by applying a safety factor on the pull-out torque.

## Stepper Motor Pull-Out Torque

### Measure Pull-Out Torque

To better understand how the maximum pull-out torque is defined, it’s important to review how it is measured. Typically, the pull-out torque is measured under the following conditions:

• No load on the motor.

• Open loop mode.

• With one specific driver.

Figure 4 below shows the measurement setup for the pull-out torque. The motor will be connected to a driver, which defines the direction of rotation and the velocity of the motor via a pulsed signal. The motor shaft is connected to a variable brake system, such as an eddy current brake, which allows a variable load to be applied to the motor.

The measurement is performed as follows:

1. The motor is started with no load and brought to a given, rather low speed of 100 pulses per second (pps).

2. An increasing load is applied on the motor shaft using the brake system until the motor loses synchronization.

3. The maximum load under which the motor can rotate at 100 pps without losing synchronization is stored.

4. Steps 1 to 3 are repeated but at higher speeds — 200 pps, for example.

The maximum load values for each velocity measured during Step 3 represent the pull-out torque curve of the motor, as shown above in Figure 5. Due to resonance, certain velocities can cause the motor to behave erratically and should be avoided. This condition can be shown in the pull-out torque diagram.

## Pull-Out Torque, in Practice

In practice, pull-out torque is used to define a torque and speed range for safely driving the motors in open loop. For the maximum load torque, a safety factor of typically 30 percent is considered (represented in Figures 6a and 6b by the dotted blue line), as compared with the maximum available pull-out torque (represented below in Figures 6a and 6b by the solid blue line).

Additionally, the pull-out torque is used to determine the optimal acceleration profile for the motor. The motor should achieve a working point, which is indicated by the red cross in the Figure 6a example. There are two ways to accelerate the motor to the required speed:

1. If only the maximum available pull-out torque at the desired working point is considered, the motor accelerates linearly with a constant torque. A minimum range of the available pull-out torque is used, indicated by the blue bar on the torque-versus-speed graph.

2. Adapt the acceleration torque based on the available pull-out torque. At low speed, a higher pull-out torque enables faster acceleration. This leads to a non-linear acceleration, thus reaching the entire speed faster. The entire range of the available pull-out torque is used, as indicated by the orange bars in the torque-versus-speed graph.

## Stepper Motor Pull-In Torque

### Measure Pull-In Torque

The pull-in torque can, for example, be measured using the setup in Figure 7 below. A disk is mounted on the motor shaft, and a cord is wrapped around it. The tension forces F1 and F2 in the cord are measured, and the difference between the forces creates a load torque on the motor, which is dependent on the diameter of the disk. The resulting load on the motor shaft consists of pure friction torque with negligible load inertia. The only inertia present during the measurement will therefore be the rotor inertia of the motor. The motor is connected to a driver in open-loop mode, and the entire measurement is done without an acceleration ramp.

The measurement is typically conducted as follows:

1. A low load is applied on the motor.

2. The driver is set to a low velocity and enabled. If the motor can start, the same step is repeated at a higher velocity.

3. When the motor is unable to start, the maximum start-up frequency for the given load has been found.

4. Steps 1-3 are then repeated with a higher load.

The maximum velocity values captured during Step 3 represent the pull-in torque curve shown above in Figure 8. Typically, motor suppliers like Portescap will provide the pull-in torque curve of the unloaded motor and measure it with one specific driver. In the actual application, the inertia of the load also must be considered because this additional inertia acting on the motor shaft will decrease the available pull-in torque of the motor. To summarize, the factors that influence the pull-in torque of a stepper motor are:

• The motor’s characteristics — for example, the rotor inertia.

• The inertia of the disk attached to the motor shaft.

• The total load torque on the motor.

## Pull-In Torque in Practice

In practice, there are two key situations in which the pull-in torque is used when sizing a stepper motor:

• For slow motions where no motor acceleration is required, the motor will be started directly with the desired speed using a fixed number of steps per second.

• In certain cases, the natural resonance frequency of a stepper motor can be avoided by starting it at a speed above this resonance frequency. Here, the pull-in torque needs to be known.

## Select a Stepper Motor With the Right Torque and Speed Characteristics

When selecting a stepper motor, understanding the pull-out and pull-in torque curve of the motor is critical to ensuring good performance and reliability in the intended application. Portescap offers a broad range of standard and custom stepper motors along with engineering support.

We will help you select a stepper motor with the speed and torque characteristics that will best meet your requirements and ensure trouble-free performance.