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More info on motor thermal qualities: R. Welch, Continuous, Dynamic, and Intermittent Thermal Operation in Electric Motors, S. Noodleman & B. Patel, Duty Cycle Characteristics for DC Servo Motors, paper TOD-73-30, IEEE/IAS Conference, Oct. 9-12, 1972, Philadelphia, Pa.
R. Welch, Why a Temperature Sensor Won’t Always Protect a Servomotor From Overheating, Machine Design Magazine, February 4, 2010, Motor-temperature switch placement, Motors spec’d with four-parameter thermal models, |

Motion-system designers frequently crank pretty hard on servomotors. To get the highest possible performance, they’ll often command the servomotor to put out the maximum peak torque that its maker allows. However, servomotor electrical windings can overheat rapidly and even burn up when this happens. Consequently, a servomotor needs a hot-spot temperature safety margin. This margin is defined as the difference between the winding maximum allowable hot-spot temperature and its maximum continuous winding temperature. Stated mathematically,

*T _{sm} = T_{hs} – T_{max}*

where *T _{sm}*= hot-spot temperature safety margin;

*T*= maximum hot-spot temperature; and

_{hs}*T*= maximum continuous-winding temperature, all in degrees.

_{max}Manufacturers normally publish values for each motor’s *T _{max}*, along with the corresponding maximum continuous current and torque output, plus the ambient conditions (drive electronics, ambient temperature, amount of forced cooling, heat-sinking method, and so forth). One needn’t worry about hot spots so long as the motor never exceeds its maximum continuous current value and ambient conditions don’t deviate from those the manufacturer specifies. However, that’s not the way a servomotor typically operates. Servomotors more often are commanded to produce a dynamic motion profile that contains one or more time intervals during which the motor must output peak torque exceeding its maximum continuous value. Hence, the manufacturer also specifies a peak-torque value for each servomotor. Depending on the motor model, the peak-to-continuous torque ratio typically ranges between 2:1 and 5:1, though one brand of brush dc servomotor carries a 7.2:1 ratio.

It’s normal for a servomotor to put out peak torque exceeding its maximum continuous value. But overheating can be a problem if it stays in this condition for too long. So during times of peak-torque output, the motor duty cycle must be less than 100%. The more the peak-torque value exceeds the maximum continuous value, the lower the allowable duty cycle.

For over 50 years, servomotors have been characterized thermally by what’s generally called the two-parameter thermal model. One generally finds manufacturers publishing one value for the motor winding-to-ambient thermal resistance, *R _{th}* (°C/W), plus the corresponding thermal time constant, τ (seconds). This information permits calculating the motor’s thermal capacitance,

*C*(J/°C), using the following equation:

_{th}*C _{th} τ/R_{th}*

This two-parameter thermal model lets motor manufacturers and users size and select the right motor. Many motor manufacturers have developed sizing programs employing this model that are publicly available. However, I have yet to find a single manufacturer willing to size a competitor’s motor. Hence, motor users generally must size and compare competing brands themselves to make valid comparisons.

Frequently, the first step in the sizing process is to completely specify the dynamic-motion profile, along with specifying the ambient conditions in which the motor will operate.

Next, in combination with the motor’s engineering specifications, one determines the peak torque and velocity the motor must exhibit during the most demanding time interval in the motion profile. This information becomes the peak operation point on the motor’s combined intermittent and continuous torque-speed curves, as shown in the accompanying figure.

A necessary requirement is that this peak operation point lies within the boundary of the intermittent torque-speed curve. Otherwise, the motor-drive combination in question will lack enough torque, velocity, and/or power for the application.

Finally, one calculates the root-mean-square (rms) torque and velocity for the entire motion profile from the two-parameter thermal model in combination with the time-averaged power dissipation technique. This rms-operation point goes onto the combined torque-speed curves visible in the accompanying figure. If the rms-operation point lies outside the boundary of the continuous torque-speed curve, then it is an absolute certainty the motor will overheat.

Conversely, the graph tells us that so long as the rms-operation point lies within the boundary of the continuous torque-speed curve, this particular motor will not overheat and it’s okay to use. However, extensive research has proven this last statement is NOT always true. In the real world of servomotors, it’s entirely possible the winding maximum allowable hot-spot temperature is actually exceeded in direct violation of UL 1446, despite operating in the safe part of the curve. Designers who depend on the two-parameter thermal model won’t realize this is happening.

This simple, two-parameter thermal model is still used extensively to calculate dynamic-winding temperature during all possible modes of servomotor operation. But experimental measurement shows it’s NOT particularly accurate in calculating dynamic-winding temperature when the motor uses more than its maximum continuous current. A much-more accurate four-parameter thermal model has been developed to overcome this inaccuracy. The basic problem with the two-parameter model is it assumes the entire motor, and every component in it including the windings, has the same dynamic operating temperature. Actual measurements show this isn’t true. In fact, measurements reveal that within the motor and even within the winding itself there can be temperature differences that the two-parameter model simply doesn’t account for.

Furthermore, there can be as much as a 50°C temperature difference between the motor winding and its outermost surface area, depending on motor size and operating temperature. This difference can’t be ignored. A higher order [i.e., 4, 6, 8,… parameter] thermal model allows for temperature gradients in the motor. The winding can have its own dynamic-operating temperature, thermal resistance, and thermal time constant. These can differ from those of the rest of the motor. Research has shown the four-parameter thermal model is accurate enough to explain all the measured temperature data. And it’s rather easy to obtain the four parameter values for the model.

As shown in the accompanying figure, the winding temperature calculated by the four-parameter model initially rises faster than in the two-parameter model. However, both curves converge at the rated 130°C maximum continuous-winding temperature. This feature is consistent between these two models with the continuous power-dissipation rating.

It is useful to compare the calculated temperature rise between the two-parameter and four-parameter models while the motor is producing 4× peak torque, corresponding to 16× power dissipation in the winding. (Torque developed by a servomotor rises linearly with current, while the power dissipation in its electrical winding rises as current squared, I2R.)

An accompanying figure depicts the case of 4× peak-torque output, specified for many servomotors, corresponding to 16× power dissipation. The four-parameter model shows that the winding temperature rises from its initial 25°C to its rated 130°C value in only 12 sec. The two-parameter model takes longer to respond. It predicts the winding temperature should be less than 55°C at 12 sec. Experiments show this winding temperature is in error. All in all, a significant temperature error that is clearly unacceptable accompanies the use of the two-parameter thermal model in calculating dynamic winding temperature when peak torque exceeds the 1× value.

Several motor manufacturers proudly claim their servomotors are recognized under the UL 1004 and/or CSA 22.2/100 standards by Underwriters Laboratories and the Canadian Standards Authority, respectively. As part of the UL/CSA recognition process, the insulation system for the motor’s electrical winding must comply with the UL 1446 Insulation System Standard. That standard says the class of the insulation on the winding determines the winding’s maximum allowable hot-spot temperature. To comply with UL 1446, the winding must have a hot-spot temperature rating at least equal to the maximum continuous-winding temperature. To ensure the motor complies with UL 1446 and to make sure the winding can’t possibly overheat, manufacturers often place a temperature sensor/switch inside the motor. The sole purpose of this temperature sensor/switch is to tell the drive when the winding approaches its maximum allowable hot-spot temperature. The drive responds by shutting off the power to the motor. However, there are at least three practical reasons why this overtemperature protection scenario doesn’t always work.

A point to note is that even the four-parameter model isn’t perfect. Though it allows the winding to have its own dynamic operating temperature, it still assumes the entire winding is at one temperature. Measurements at different points in the winding show this is not true. Nevertheless, the four-parameter model is accurate enough to show why a servomotor must have a hot-spot temperature safety margin while at peak-torque output.

Most servomotor manufacturers still perform all their motor-sizing and dynamic-winding-temperature calculations using the two-parameter thermal model. (I have found only one that uses the four-parameter model.) Thus motor users have no choice but to use the two-parameter model in calculating dynamic-winding temperature unless they measure the four parameter values themselves. These measurements are relatively straightforward.

Sizing the optimum motor for the application begins with the process of defining the dynamic-motion profile and the ambient conditions. Next, the designer determines the candidate motor’s rms-operation point and notes it on the continuous torque-speed curve. The motor will certainly overheat if this rms-operation point lies outside the boundary of the motor continuous torque-speed curve. The only way to use the particular motor under investigation would be to modify the motion profile and/or change the ambient conditions. Conversely, both motor manufacturers and conventional calculations will predict the motor won’t overheat if the rms-operation point lies within the boundary of the motor’s continuous torque-speed curve.

However, the four-parameter model predicts the winding heats more quickly and hits a higher temperature than the two-parameter model shows. In fact, the motor exceeds its maximum continuous-temperature value while at peak torque. Furthermore, the sensor/switch can’t always react fast enough to prevent this high temperature.

Thus, the electrical-winding insulation must have a maximum hot-spot temperature value exceeding the maximum continuous-winding temperature. The greater the safety margin for the hot-spot temperature, the better the protection. For example, all **Exlar** SLM servomotors have a 130°C maximum continuous-winding temperature. Their windings insulation system is rated Class H, which provides a 180°C maximum allowable hot-spot temperature. This gives a 180 – 130 = 50°C hot-spot safety margin.

In addition, all SLM servomotors have a 2:1 peak-to-continuous torque rating. This combined with their hot-spot safety margin gives excellent thermal protection during times of peak-torque output. In contrast, many other servomotors have a hot-spot safety margin of 15°C or less (some are zero). It is also common to find peak-to-continuous torque ratios ranging between 3:1 up to 5:1.

Over time, different authors have suggested varying figures of merit for selecting high-performance servomotors. But from a motor user’s perspective, the single-most important figure of merit is one that shows how much output to expect from a servomotor for the longest time period while remaining compliant with UL 1446. A hot-spot temperature safety margin provides this kind of feedback. So far, a 50°C margin is the highest value that I’ve been able to find.