High-performance motion control demands compact and economical servomotors. Fortunately, because most servo applications only intermittently demand maximum continuous-torque motor output, a smaller motor that occasionally outputs peak torque is usually sufficient.

In fact, Underwriter Laboratories (UL) now recognizes that both servo and stepper motors typically output peak torque intermittently ¡ª and recently issued its revised UL1004 electric motor standard. As shown in Section 45 of UL1004-6, both servo and stepper motor manufacturers are now required to publish both a continuous safe operating area (SOAC) plus an intermittent torque-speed curve for each motor.

Why change models?

Banking on a certain operation profile is not without risk. As we'll explore further in this third and final Course Audit installment, using four-parameter models to calculate dynamic winding temperatures allows designers to extract the most performance from a given servomotor, while preventing windings from overheating. In contrast, using two-parameter models for dynamic temperature calculations increases the likelihood of improper motor selection ¡ª and leaves engineers in the dark about the true causes of failure when it occurs.

In Parts I and II of this series, we discovered that peak current in excess of the motor's 1¡Á maximum continuous value supplied for too long causes motor windings to overheat. In other words, the windings exceed maximum rated temperature T_R ¡ª or just burn up completely.

To prevent overheating failures, designers must accurately calculate the motor's safe duty cycle for each specific application. Commonly used for this purpose are duty-cycle calculations first published by Noodleman and Patel in 1973. This two-parameter model oversimplifies motors by assuming one dynamic operating temperature for the entire motor.

In fact, real motors exhibit measurable temperature gradients, as electrical windings heat much more quickly than, say, the motor case. In short, two-parameter models grossly overestimate how long a servomotor can safely output peak torque in excess of 1¡Á maximum continuous value.

Let us now compare the differences between the duty cycle calculated by both the two-parameter and four-parameter thermal models.

Under cyclical operation

Calculating realtime motor temperatures is useful, but beyond the scope of this paper. Instead, let us explore how to consistently prevent windings from exceeding T_R during repetitive power-dissipation cycles.

Combining the two-parameter heat-up and cool-down equations gives the expression for the peak power that a motor can safely dissipate:

Where P_r = Maximum continuous or rated power dissipation

t_on = Ontime

t_cy = Cycle time, and

¦Ó = Motor thermal time constant

Solving for maximum t^on (during which the motor can safely dissipate repetitive power pulses P_d) gives:

Where P_d/P_r = Power ratio

t_off = Off time

How do we apply this equation? Here is an example: Assume 1.5¡Á power is repetitively dissipated inside the motor. We must determine how much ontime can occur before applied power must be shut off to allow the motor to cool to T_C. Assume that this period of zero power dissipation occurs for one thermal time constant before 1.5¡Á power dissipation is reapplied.

Solving for P_d/P_r = 1.5 and t_off = ¦Ó the maximum ontime is:

In fact, the motor can repeatedly dissipate 1.5¡Á power pulses for 81.7% of a thermal time constant, but after each pulse, power must completely be turned off and the motor allowed to cool for one thermal time constant. This gives total cycle time t_cy = 1.817 ¦Ó. Therefore, for this intermittent operation with a 1.5¡Á power cycle:

Percent duty cycle (1.5¡Á power)
= 0.817¦Ó/ 1.817¦Ó
= 45%

Various P_d/P_r ratios (obtained from the t_on equation) and percent duty cycles (as a function of repetitive, intermittent power dissipation) are shown in this article's table. Power dissipation in the motor's winding corresponds to P_d = I²R, so percent duty cycle is also a function of current greater than the motor's 1¡Ámaximum continuous current value.