An Example on Choosing a Servo Motor
Suppose that a designer requires to move a load inertia of 0.1 kg m2 from 0 speed to 1,000 rpm at maximum of 500 ms. At this rotating speed a torque of 10 N m is applied to the motor which could, for example, be an equivalent of a cutting force in a machine tool. Following the procedure set out in the previous section;
1. The load inertia is 0.1 kg m2.
2. Maximum velocity variation ωc-105 rad/s. The maximum required settling time is ta: = 0.5 s.
3. The minimum power requirement is
P: = Te.ωc
P: = 10.105, which is approximately 1 kW.
Therefore, the first choice will be a motor with 1 kW power rating providing it satisfies the required speed of response.
4(a). Calculation of total settling time for AC motors
From Figs. 9.5, 9.6, 9.7, and 9.8 for a 1 kW power rating motor, the following settling time can be obtained,
Comparing ta with the required settling time of 0.5 s, it is obvious that the 1 kW AC motor does not provide the required speed of response.
If the above calculation is repeated for 2, 3 kW or higher power AC motor it can be found that the 5 kW AC motor with total settling time of 0.49 s provide the required speed of response. This is because the load inertia is very large for smaller AC motors.
The dynamic velocity drop for the torque of 10 N m for this motor using eq. (9.4) and Figs. 9.9 and 9.10 can be calculated as
4(b). Total settling time from DC motors
From a similar analysis for DC servo motors it is found that that the following mo- tors will provide a satisfactory performance:
One kilowatt ceramic DC motor controlled with 150 Hz Thyristor Bridge with total of settling time of 0.45 s and dynamic velocity drop of 39 rpm.
One kilowatt ceramic magnet DC motor with pulse width modulated controller with total settling time of 0.41 s and dynamic velocity drop of 28 rpm.
One kilowatt rare earth magnet DC motor with total settling time of 0.27 s and dynamic velocity drop of 19 rpm.
One kilowatt brushless DC motor with total settling time of 0.49 s and dynamic velocity drop of 16 rpm.
Because of large dynamic settling time other types of motors are not suitable for this application.
If the dynamic response is the only criterion, a 5 kW AC or a 1 kW DC with ceramic or rare earth magnet might be selected. The final decision obviously depends on the capital cost, size, and reliability.
Conclusion
In this chapter, the dynamic response of a number of types of servo motors commonly used in industry have been considered. To obtain the best performance, one must optimize the forward loop gain, and the integral gain and the feedback gains and the gains of compensation network in the controller. The dynamic performance in each case was represented by a step input settling time and dynamic velocity drop when an external torque is applied. The settling time was divided into a saturated region where the motor operates in a torque limited condition and a dynamic region behaves according to the linear mathematical model. A series of simulations were carried out on different types and sizes of motors and the settling times plotted in a series of graphs in such a way that the designer can predict the settling time and dynamic velocity drop to be expected for a particular motor and applications, or alternatively the motor to choose for a specific dynamic requirements.
As one might expect, no motor excels in all circumstances and the suitability of a servo motor depends on its application. The following general comments can be made as follows:
1. Low load inertia and low power motor: For these types of applications hydraulic motors provide the fastest speed of response. The rare earth magnet and brush- less DC motors are competitive with hydraulic motors. The effect of external torque on the velocity of a hydraulic motor is somewhat higher than electrical motors. The ceramic magnet DC, AC, and stepping motors have the lower speed of response than the hydraulic and rare earth magnet DC motors.
2. High load inertia, low power motor: Under these conditions, the DC motors pro- vide the best speed of response, followed by AC, hydraulic, and stepping motors. The effect of external torque becomes less significant on hydraulic motors than electrical motors.
3. Low load inertia, high power motor: Here, the hydraulic motors provide the fast- est speed of response, followed by electrical DC and AC and stepping motors. AC motors at high power ratings become competitive with conventional DC motors. The effect of external torque on electrical motors is less than hydraulic motors.
4. High load inertia, high power rating: For this condition, electrical motors pro- duce a faster speed of response than the hydraulic motor and the AC motors became competitive with conventional DC motors. External torque has less effect on hydraulic motors.
5. Using acceleration feedback: Acceleration feedback improves the performance of all types of servo motors. The improvement is greater for hydraulic and AC motors, but the difference in dynamic performance between all types of motors reduces. In this case, the saturated performance of servo motors influence the final decision more than the dynamic characteristic, so that the maximum avail- able torque is important. It should be noted when using acceleration feedback that the velocity feedback must be differentiated. Therefore, high quality veloc- ity transducer must be used so that there is not much noise in the acceleration feedback. A filter must be used to minimize the noise in the acceleration feed- back. Some manufacturers provide a current feedback instead of acceleration feedback.
If, for a particular application, a number of servo motors satisfy for the dynamic requirements, the final decision depends on capital cost, reliability, and availability.
In this chapter, a selection procedure has been outlined and it is only a guidance for selection. The reader is encouraged to study the dynamic behavior by solving the mathematical model of different complexities to ensure that the right motor has been selected.