*Duty Cycle and Peak Current both influence the operating life of brushless servo motors.*

In mechatronic designs, it is critical to manage motor heat dissipation as excess heat can affect the accuracy of a system’s mechanical components. A thorough understanding of motor thermal characteristics can ensure your brushless servomotors enhance overall system operation.

**By Richard Welch Jr., Consulting Engineer – Exlar Corporation**

The thermal characteristics of a brushless servo motor determine the length of time that the motor can operate in a peak range; a measurement many engineers and managers use to determine a motor’s productivity rating. This peak current range is defined as any current level between the motor’s continuous rating and its peak rating. The continuous ratings are often defined as the highest current a motor can draw while continuously dissipating the resulting motor heat in a 25°C ambient temperature.

There have long been “rules of thumb” in the brushless servo motor industry about what is acceptable to use as a duty cycle when operating in the peak or intermittent ranges. There have also been “rules of thumb” applied to how long any given motor can operate at peak current on an instantaneous basis.

Many times you will hear reference to numbers like one second or half a second as acceptable times to operate in the peak range, and it is believed that if you are in peak for one second, and then off for one second, you’ll have an acceptable duty cycle, in this case, 50%.

*The duty cycle curve shows the “peak” or intermittent operating range of a brushless motor. In this graph, the current corresponds to 100% duty cycle; the “1” being the motor’s maximum continuous current for a 130°C winding with a 25°C ambient. The “2“ on the curve corresponds to twice the continuous rated current.*

That is very far from the truth. We have conducted extensive thermal testing of many brushless motors, our own and others, and the following is true for virtually any brushless servo motor: When the motion profile of a brushless servo motor requires that it enter the “peak” or intermittent range during every cycle, the duty cycle is limited, somewhat exponentially, as the percentage peak current increases.

Below is the duty cycle curve for operating in the “peak” or intermittent range of a brushless motor. The current is “Normalized” such that 100% duty cycle corresponds to “1” being the motor’s maximum continuous current for a 130°C winding with a 25°C ambient. Hence “2” on this curve corresponds to twice the continuous rated current. The example motor, an Exlar SLM 115, was attached to a 12 in. by 12 in. by 1/2 in. heat sink.

The curve shows that operation at two times (2X) continuous current the acceptable duty cycle is 4%. Thus, if you are at 2X continuous current for one second, the motor will need to be without power for 24 seconds to achieve the acceptable duty cycle of 4%.

Another factor to consider when operating in an intermittent range is a motor’s thermal time constant. Powering the motor “on” with 2X current for 10 minutes and then turning it “off” for 240 minutes also corresponds to 4% duty cycle. Due to an inherently shorter thermal time constant a smaller (60 mm or 90 mm frame) motor will “overheat” in less than 10 minutes with 2X rated current. Hence, this curve is only a “guideline” and can not be applied blindly!

Another critical factor to consider is that use of a motor’s case temperature as a gage of allowable duty cycle is only acceptable when operating beneath the continuous rated current of the motor. The thermal time constant of the wire in the motor’s stator is far shorter than the thermal time constant of the motor’s case. Therefore, the wire in the stator will heat many times faster when subjected to currents in the “peak” or intermittent range.

For example, at 2X rated current, one tested motor’s stator increased from 25°C to 130°C in 90 seconds. In that same 90 seconds, the motor case temperature had increased only 10°C. Also in this example, due to the interrelationship between the components of the motor with different thermal time constants, and the flow of thermal energy in the motor, the motor’s case will continue to rise in temperature when the power is removed from the motor.

The thermal time constant of the wire in the stator is also less than that of temperature sensors and switches that are integrated into the stators. Therefore, when subjected to high peak currents, it is possible for the stator to demagnetize, or the stator to fail before the thermal switch or sensor indicates that the motor is in an overheated condition.

To determine how long a motor can operate in the peak range, you must also consider the starting temperature. The maximum allowable time “on” is going to be the time it takes before the motor’s stator reaches 130°C. This time is obviously longer if the starting temperature is 25°C than if it is 55°C.

Each brushless motor manufacturer selects the ambient temperature at which they rate their motors. The same is true for Exlar. A very common question we hear is: ‘What percentage do I need to de-rate the motor (or actuator) if my ambient temperature is X degrees?’

There is a de-rating equation that can be used to de-rate any brushless motor. This equation takes the difference between the maximum temperature rating of the motor and the ambient temperature of the motor’s operating environment, and divides it buy the difference between the maximum temperature rating of the motor and the rated ambient temperature of the motor.The square root of the result when multiplied by 100% gives the allowable percentage of the normal ratings at which the motor can operate in the elevated temperature environment.

What this equation is calculating is the ‘left over’ allowable temperature rise that the motor can produce when starting from an ambient temperature higher than that at which the motor is rated.

The standard operating temperature of the stator to which most brushless motor manufacturers limit their motors is 130°C. Assuming a catalog rated ambient temperature of 25°C, and an example operating ambient temperature of 55°C, the results of this equation would be: Remaining Continuous Current or Temperature Rise =

In this example, the given motor would have a de-rating to 84.5% of its catalog rated current, and thus of its output torque as well.

These two approaches to determining maximum allowable motor performance can be used in conjunction. For instance if an application required a motor de-rating due to an elevated ambient temperature but had a duty cycle that was less than 100%, the de-rated continuous current would first be obtained based on the maximum environmental temperature and the equation above, 84.5%. From there you could use the % Duty Cycle vs. Normalized Continuous Current curve to obtain a normalized continuous rating. Supposing the duty cycle was 22%, you could expect to operate said motor at 127% of its published continuous rating.

Exlar Corp.

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