Basic theory of Stepping Motors
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Friction torque

Friction torque is the load implemented on the shaft through mechanical tolerances in the application.

Figure 14 illustrates how that for a given loadthe friction torque also needs to be considered if accurate positioning is required.


This phenomenon can also be explained using the mountain model (fig 13). Although the ball tries to find it's natural place of rest, friction on the surface prevents it from doing so.




Figure 15 The mountain model

Systematic angle tolerance

'Systematic angle tolerance' is the deviation from the theoretically correct position of any angle stepped. Also know as 'absolute accuracy', it can either be expressed as a percentage of a full step or as an angular measure. It is also non-cumulative as it remains constant for any angle stepped.

'Systematic angle tolerance' is caused by manufacturing tolerances in the motor (i.e. differing winding resistances or turns, unequally magnetized magnets, air gaps etc.) and drive electronics. Although with modern manufacturing techniques these tolerances are negligible, for extreme accuracy they may need to be considered.


Static and dynamic load angle.

The 'static load angle curve' (fig. 14) illustrated what happens to a stationary stepping motor under load. Therefore, if it is producing torque the motor must be lagging behind the stator field under dynamic conditions i.e. motor running. Similarly there will be a lead situation during deceleration.
From the static torque curve, it is clear that the lag or lead can not exceed the maximum holding torque if the motor is to maintain it's synchronism. Therefore, for a Hybrid (50 pole pair) stepping motor the maximum lead or lag angle is 3.6 or, depending on the number of phases 2, 3 or 5 full steps. Figure 16 illustrates the maximum lag which occurs under dynamic load conditions.


Figure 16 Dynamic load curve

Resonance

The phenomenon of 'resonance' is suffered by all stepping motors, to some degree or other. Resonance is the term used for the effect which occurs when a stepping motor is stepped at it's natural oscillating frequency. Stepping at this natural frequency can result in the stepping motor desynchronizing or even stalling.

For a Hybrid stepping motor under no load conditions this resonance occurs between 80 and 200 Hz i.e. 80 to 200 steps per second. A stepping motor's resonance can be calculated using the formula:

For ease of use and so that the values can be used directly from SIG Positec' 'Complete Catalogue', the formula can be altered as follows:

Calculate the following:

Using the resonance formula, calculate the natural oscillating frequency for the SIG Positec motor types VRDM 31117/50LW and VRDM 397 LW shown on page 22 of the 'Complete Catalogue'.



Resonance can be overcome by operating outside the resonance range, through half-step or micro-stepping, shifting the resonance frequency through changes in the system's inertia or electrical or mechanical friction. Increasing the systems inertia or friction generally known as damping.

Torque ripple

If, a motor is driven close to it's maximum run torque, torque ripple can have a resonance effect. Torque ripple is illustrated on 'dynamic torque diagrams' (figs. 17 & 18) and the improvements gained through higher resolution and micro stepping are clearly visible.



Figure 17 Dynamic torque diagram for a 2-phase stepping motor



Figure 18 Dynamic torque diagram for a 5-phase stepping motor

As previously discussed, the phase currents of the 3-phase motor are controlled with a sine wave. Although this switching technique is more demanding than the straight forward block commutation used for 2- and 5-phase stepping motors, it does offer considerable benefits in the operating characteristics.

The higher the resolution, the lower the current change per step, i.e. the greater the approximation to a sine function. This ensures the motor has a lower current ripple and subsequently a lower torque ripple. As only the fundamental component of the wave form generates torque, any ripple only has a heating effect on the motor. Which is easily dissipated through the motor body.

This lower tendency to ripple also has a positive effect in reducing acoustic noise.



Figure 19 Sine wave commutation of a 3-phase stepping motor

Defining the start / stop frequency

For the simplest of positioning requirements, driving a stepping motor in it's start / stop mode is the least time consuming method. The maximum no load starting frequency (f_Aom) is always given by manufacturers and it will obviously be reduced when the motor is subjected to a load M_L and it's subsequent load inertia J_L.

The starting frequency's load dependence is also illustrated on two logarithmic curves (fig. 20).


Figure 20

These curves are used as follows:

1. Starting with the inertia curve, the load inertia (J_L) is plotted and transposed to the torque curve.


2. From this point, and parallel to the maximum no load start frequency curve (f_Aom), a new start frequency curve which accounts for the load inertia is drawn.

3. From the known load torque and the new start frequency curve, the maximum start / stop frequency can be found .

Calculate the following:

Using the performance curve (fig 21) from SIG Positec's 'Complete Catalogue', find the maximum start / stop frequency of the motor for an application where:

Inertia 13.5 kgcm²
Torque 210 Ncm



Figure 21

Written by Steve Jennings , Edited for the World Wide Web by Jim Huntley, alterations for the UK by Richard Massara

Version 1.0 Nov. 96