Lowell Christensen VP Engineering TruTech Specialty Motors

Magnetics 2012 Orlando Florida Mar 13 & 14 2012

This presentation will discuss the design issues of designing a permanent magnet motor to be used in low voltage applications. The major issue in these applications is the low inductance of these motors and the high currents required. This presentation will talk about these issues and discuss some ways to deal with these issues. The applications discussed will be remote type low voltage applications that are powered off the power grid. These offline applications will be powered by such sources as solar panel or wind generators. These are usually run off a battery type storage system and would range in a battery voltage of 12 to 48 volts. These applications could also run directly on the power system or use a battery system to store the power. The battery type system will give a fairly constant voltage source but the direct type of system can have a large variation in the voltage available. The problems with the low inductance and high currents will be present in both types of the remote applications. The speed of systems discussed here will be in the 4 to 5 thousand RPM range. The problem with low inductance will increase with higher speed motors run on low voltages but it is easier to show the effects of the low inductance in the 4 to 5 thousand RPM range. Also these higher speeds will require a lot lower Motor Voltage Constant, Ke, and just magnify the problem of low inductance. These types of very high speed applications are best met by using higher voltages. This will allow a higher Ke to be used and this will result in a higher winding inductance.

Motor Ke is the quotient of voltage divided by the speed in radians per second. This value for Ke will be low since this paper is discussing low voltage high speed applications. The equation for motor speed is derived from the voltage equation for a motor, (V=I*R + Ke*S + L*di/dt). The inductive term for the voltage is usually a small number and can usually be ignored when using this equation to determine a starting value for the Ke needed. Even in Low voltage situations the turns count will be small allowing it to be ignored in most cases since the inductance is a function of the turns and is also very low. This term in a very low voltage case does need to be checked because if the current ripple di/dt is large the voltage loss can still be large when compared to the very low input voltage. Motor Ke is the quotient of voltage divided by the speed in radians per second. The motor torque constant can be shown to be equal to the motor voltage constant in the MKS set of units and is expressed as N-M/amp, ( Ke = V/S = B*L*N = T/I = Kt). This means that the torque constant will also be low and the motor will require large currents to produce the torque required in most applications. The other factors in the above equation are winding length L in meters and air gap Flux density B in Tesla. The N in the above equation is the number of conductors in the winding. The length is optional since the motor in these types of applications are not a typical application issue in most cases. A shorter length would give a lower resistance and inductance. The longer length would have a higher resistance and inductance but will give higher rotational losses. Since the torque constant is equal to the Ke and will also be low, the current required in these applications can be a very high number. This high current will give a high I*R voltage drop and leave less voltage available to generate the speed desired. This means that an even lower Ke will be needed. This requires more current and a runaway condition can develop. This lower Kt will also require more current which will drop the voltage even lower because of the increasing I*R voltage. This could lead into a runaway condition. Failure to consider this would give lower speeds than desired. Another problem with the low Kt is that a higher amount of current is needed to overcome the torque losses due to friction and the rotational losses. This adds to the voltage lost in the I*R drop and makes the Ke needed a little lower than expected. The current capacity of the wires in the motor winding will also need to be considered since they could go into a fuse condition if they cannot carry the current needed.

The Permanent Magnet Motor can take several design configurations. The most common type of design is a cylindrical type of motor. This motor has a long length when compared to the motor diameter. Due to the small diameter the number of poles will be limited. This will result in a trend to a higher value of the resistance and inductance. This style motor will tend to be a high speed type of motor and are commonly used in geared type applications. Another style of motor is commonly called a pancake motor. These motors tend to be large in diameter and the length is significantly shorter than the diameter. These motors tend to have a large number of magnetic poles and will have very low inductances and resistance. This will mean that these motors will be low speed motors and can be used in direct drive type applications. The pancake motor can also easily be made into on outer rotation type of motor with the magnets in the outer rotating cup. This style motor will have a high inertia and would be used on directly coupled high inertia loads. When the smaller pancake motors are used, the high pole counts will give a low inductance and can give problems due to the high ripple currents. Another class of motors would be the axial flux style motors. These motor would also mainly be a pancake style motor but would use powdered metal instead of laminations. These motors can be made with either rotating iron or rotating coils and will have a large variation in inductance in these different construction styles. Inductance will vary inversely with the number of magnetic poles of the motor. This function of increasing inductance with increasing pole count is proportional with the square of the number of poles. Another benefit of the pole count is that the higher pole counts will also give a lower resistance. Fig 1 shows the effect of the number of poles on inductance and resistance in a 3 inch diameter 1 inch long stator with 36 slots where the motor design parameters are kept constant except for the pole counts. The Ke was kept constant a 8 v/krpm. This allows more turns for the comparison and would give the speed needed at the higher voltages. This curve will show that the low pole count will have a high inductance but also a high resistance. Since a higher inductance and a low resistance are ideal, the best pole count is one in the mid-range. The higher pole counts have flattened out for the resistance and inductance so these pole counts would need to be determined for other design reasons. Another effect of the higher pole count is the commutation frequency. The higher the speed of the motor the higher the frequency of the commutation switching of the motor phases will be required. The lower inductance and resistance will give a lower electrical time constant which allows a faster rise time of the current in the PWM switching. The higher pole counts will require a higher PWM frequency to get several current pulses in each commutation cycle. The higher frequency gives a benefit in that it will minimize the current ripple amplitude and lower the resistive heating in the stator. The negative effect of the higher frequency required for higher pole counts is that the eddy current losses and the hysteresis losses increase with frequency so these losses will be higher. These factors will result in a higher motor temperature and lower motor efficiency.

Another way to change the motor inductance is to change the magnet material used in the motor. The motor voltage constant required, Ke, is defined by the speed needed and the voltage available for the application. Since the Ke and the motor torque constant, Kt, are dependent on the Flux density of the air gap, the flux density in the airgap will affect the resistance and inductance. A 4 inch motor design was used to check the effects of the magnet material. The Ke was used in this comparison was 8 v/krpm.

The stator lamination was varied in both the tooth width and the back iron width to keep the Flux density of the lamination tooth at 14 KG and the back iron flux density at 13 KG. This will allow the slot area to change for each magnet material and then the number of winding turns was changed for each material to keep the Ke constant. Figure 2 shows the effect of the changes in the lamination needed for the two largest variations of magnet materials. The plot on the left is a ceramic M8a magnet and the plot on the right is for a sintered neo 40/23 grade of neo. There is a large variation in the area for the winding when keeping the flux density constant in the teeth and back iron. This will make the lower energy magnet material more attractive in the low voltage applications and a material between these two variations would be a good choice in many applications when size and weight is not a major requirement. Figure 3 shows the change in resistance and inductance for this change in magnet material. Since the inductance will increase with the number of turns squared, the lower grade material will have a significantly higher inductance. The downside of this is that the higher number of turns will give a higher resistance. This increase in resistance is partially offset due to the fact that the lower flux density in the air gap allows less iron in the magnetic circuit and gives more area for the wire allowing larger wire sizes to reduce the resistance. The lower energy magnet materials will give the highest inductance but will also give a higher resistance and the higher resistive heat losses and reduce the efficiency. Here also a mid range of the magnetic energy will give the best result for inductance and the actual material used needs to be picked using other application requirements. Since each of the magnet material designs used had the same pole angle size and same Ke and was run on the same voltage and current, the only difference was in the resistance and inductance of the motor. These differences would have the effect to change the thermal characteristics of the motor and the efficiency of the motor. The lower energy magnet would run hotter than the High energy magnet material and this factor will also need to be considered.

**Magnet Material**

The magnet thickness is less for the high energy material so the actual volume of the magnet will change. The lower energy magnet material will usually cost less so this will offset the increase of the volume of the low energy material.

Current ripple is the major system level problem due to the low inductance. The low inductance will give a higher rise times and fall times of the current ripple due to the PWM frequency switching the phase currents. This will result in a higher peak to peak value of the ripple current. Since the positive side of the average current will produced a positive torque ripple and the negative side of the average of the current will give a negative torque ripple, they will balance out with no net torque change. This ripple produces heating in the winding and reduces motor performance due to the added copper losses and magnetic losses. Increasing the frequency of the PWM is a common way to try to reduce these losses. The increase in frequency will result in a shorter time for the rise and fall of the current ripple and reduce the current ripple amplitude in this way. This does reduce the copper losses but will increase the iron losses. Both the eddy current losses and the hysteresis losses increase with the switching frequency so these losses will be higher. The lamination thickness and material can be changed to minimize these losses but this can also affect the lamination cost.

One trend that has become common is to shop for motors and drives thru a catalog. If the components chosen do not meet the requirements the system will run hot and become inefficient and give premature system failures. If the system is oversized to allow all components to exceed the minimum requirements, then the cost will be high and the system components will also become inefficient and be larger than needed. This type of system will also tend to need to be degraded in the voltage and current from the levels available. Any of these motor drives are now digital type drives that can easily be programmed to match more applications. This will help in getting a drive that better matches the application requirements. These drives can have the same basic hardware and be programmed to match the parameters of the motor requirements to meet the application requirement. These programmable drives can also react very fast to feedback from the motor and the load to define the optimum inputs to the motor. The real time response of these systems will allow the system to operate at a higher efficiency level and at a lower power level to meet the real time requirements of the total system. Since everything is in real time the system can be programmed to react to issues due to low inductance and minimize the negative effects of low inductance and low resistance. Also since the drives are digital in nature, various algorisms can be used to minimize the effects of inductance and current ripple.

The systems using programmable drives can be taken one step further by designing a motor and a drive specifically to meet the requirements of the application. If the actual application can be defined a motor and drive system can be designed to meet the application and give a more efficient and less costly solution to the problem. This would allow the motor to be designed using the best magnet materials and magnetic design that can be used for the application. This drive system can then be programmed to give the best voltage and current to the motor by modifying the input voltage and current provided to the system. This would be monitored with feedback from all components to the drive to match the most efficient output of the system using the input power that is available at real time. The voltage delivered to the motor can also be varied by using digital voltage level shifting to get the best available power to the motor and the best available power to the load. Since this is all done in real time, these changes can be made to match the real time requirements. This system could also change the frequency in real time to minimize current ripple when it can be allowed. Knowing the real time condition of the input power and the output power allows many reactions to this in the programmable portion of the drive. This system would only be limited by the amount of feedback from the input and output of the system. This type of system can use a varying type of input power directly or run off batteries and match the input power to the output power. This system can change system parameters to meet the needs of the motor used. A motor then can be designed with any available magnet material and any pole count that will work best for the total application. This would greatly diminish the effects of the inductance and maximize the efficiency of the motor.

**Summary and Conclusions**

The low voltages along with high speeds will require a low motor Ke. As has been discussed, this will also give a low inductance value. This low inductance gives a high current ripple and high current ripple gives high motor losses. The low Ke also gives a low Kt which will require high currents and high resistive losses. These low inductance effects will give high losses and a poor efficiency for the system. One of the ways to increase the inductance value is the use a low pole count in the motor. The inductance will start very high with the low pole counts and then flatten out as the pole count increases. Another way to increase the inductance in the motor design is to use a lower energy magnet material. Figure 3 shows that the inductance will start high with the lower energy products and then flatten out as the magnet energy is increased. Wire area can increase for the lower energy magnet materials allowing larger wire to be used to offset some of the increase in resistance with the higher number of turns required. Increasing the frequency has been a common way to lower the current ripple losses but this also has limits in how high the frequency can go. The digital programmable drives have made several ways to address the low inductance at the system level. The lowering of the cost in digital drives has allowed the drives to be programmed to best meet the applications. The best solution to get the best performance and efficiency is to design all of the components to meet the requirement of the drive. This design will then be able to match the input power to the output power on a real time basis giving the most efficient type of solution to an application. Since this type of system allows software define how the power is handled, it can react easily to real time changes and give the most efficient type of total system.