Understanding Back-EMF and Torque/Force Constants for 3-Phase Brushless Motors
This video defines and explains the Kt and Ke motor constants used in sizing an amplifier for a Linear Brushless Motor but also applies to for a rotary brushless motor.
Can Varedan help me size an amplifier?
Absolutely! We are here to help.
The process all starts with filling out our new Application Information Form and a Linear Amplifier Sizing Spreadsheet as best you can for each axis that requires an amplifier. Send that information to Varedan Engineering along with any questions and we will get right back to determine what else we need to do to size, select, and tune an amplifier that will meet all your requirements.
If you are not familiar with how to develop your motion profile, or would just like to offload the work, Varedan can provide engineering support for a fee to assist you in all or part of the design and selection of your high-performance motion control system. For engineering assistance, please fill out & submit Varedan’s Application Assistance Request Form.
Is peak power dissipation simply current x voltage?
Peak-power dissipation in the amplifier does not always equal Current x Voltage.
Power dissipation in Linear Amplifiers is actually quite non-intuitive. Do you know when the power demands are typically highest on a linear amplifier? It’s at the start of deceleration. The backEMF voltage from the motor combines with the commanded voltage causing it to essentially double at the same time that the current demands are highest. That can be a lot of power. You can have confidence in the advanced SOA protection features of the Varedan Linear Amplifiers, but under-sizing the amplifier due to misjudging the peak-power demands can result in fault conditions and machine down time. Using the most aggressive motion profile numbers from your application requirements, the Varedan Linear Amplifier Sizing Spreadsheets will tell you if you can use a smaller LA-200 Series or if you need something like the LA-1555 Series with 4 parallel power devices to handle that peak power event.
Is one motor as good as any other motor?
Maybe, maybe not. Motors with lower resistance put more power dissipation demands on the amplifier (think power in series resistors). Motors with higher inductance require higher Bus voltage to get to max speed (reactance gets ya every time). Lower Torque Constant trades higher current for lower voltage, which might be attractive if the voltage gets too high. If it’s an option, selecting the right motor that matches with the right Linear Amplifier can result in the best system that can meet all your requirements. That’s something else we can help with.
One more thing about motors and current loop bandwidth tuning. In order to provide the high bandwidth and ultra-low noise, the Varedan Linear Amplifiers have an all analog power signal path. This means that the control loops are analog as well and are factory tuned with Rs and Cs on the board. We have developed a system of equations, simulations, and bench testing that allow us to tune an amplifier with the bandwidth and response you request based on your motor parameters, specifically inductance. The thing that may not be obvious is that for a given tuning the current loop bandwidth linearly scales with motor inductance. A given tuning for a given motor will change if a different motor with a different inductance is used. This may not be an issue if the inductances are similar or if the motors fall in the range of the four bandwidth options of the LA Series Linear Amplifier, but in some cases it can cause issues such as:
a) A specific target bandwidth or response is required for the application.
b) A very low inductance motor is used with a tuning set up for very high inductance. This can lead to instability.
If multiple different motors are planned to be used for a given application, discuss this with the Varedan Engineering Team to come up with a plan to support all of your requirements.
There are separate Varedan Linear Amplifier Sizing Spreadsheets and Application Notes for Linear Brushless, Rotary Brushless, Rotary Brush-Type, and Voice coil applications. These spreadsheets cover most basic direct drive type system configurations. If you have something more complex like gearboxes, rollers, multiple linkages, etc. then the numbers need to be pre-calculated to get the reflected inertia/forces at-the-motor to be entered in the spreadsheets. We understand this can be quite the job, so we have resources to help here as well such as “The Motion Control Cheat Sheet”. Contact Varedan Engineering and we can see what we can do!
How hot will things get and how much air flow do I really need?
Well that all depends on the continuous power dissipation, and that depends on your motion profile and duty cycle. Everyone wants to increase the max velocity to reduce cycle times, but how does that effect the amplifier and how hard can you push it before it gets too hot? You don’t have to guess. That’s what the Varedan Linear Amplifier Sizing Spreadsheets do! Adjust the motion profile numbers in the spreadsheet to get real time feedback on amplifier continuous power dissipation and how much airflow you will need to handle it. We have amplifier heatsinks with up to 3in fins for maximum efficiency and offer high power system baseplate packages with tested fan and airflow ducting configurations so you don’t have to worry about it.
What are the most common pitfalls in sizing and tuning a linear amplifier?
Here is a list of common issues with selecting and tuning linear amplifiers and how the Varedan Technologies design resources can help simplify the process and give you confidence in your amplifier selection:
1) More Bus Voltage isn’t always better, unless you want more heat (which you don’t!).
Configuring the correct Bus voltage can mean the difference between optimal performance and a hot system. A common trap is sizing the amplifier Bus based on the maximum motor voltage from the motor data sheet. This might work for PWM amplifiers, but finding the minimum Bus for Linear Amps require some additional calculations based on the motor backEMF (Ke), torque constant (Kt), resistance, inductance, moving mass/inertia, and maximum application velocity. This may sound complicated but that is what the Varedan Linear Amplifier Sizing Spreadsheets are for. Plug in the numbers and we give you the value to use for the Bus supply. You can even add in some bus voltage overhead and see how that effects the power dissipation. Once the optimal Bus voltage is selected we can match that to one of the many VPS Series Varedan Power Supply models designed to run our amplifiers.
2) Peak-Power dissipation in the amplifier does not always equal Current x Voltage.
Power dissipation in Linear Amplifiers is actually quite non-intuitive. Do you know when the power demands are typically highest on a linear amplifier? It’s at the start of deceleration. The backEMF voltage from the motor combines with the commanded voltage causing it to essentially double at the same time that the current demands are highest. That can be a lot of power. You can have confidence in the advanced SOA protection features of the Varedan Linear Amplifiers, but under-sizing the amplifier due to misjudging the peak-power demands can result in fault conditions and machine down time. Using the most aggressive motion profile numbers from your application requirements, the Varedan Linear Amplifier Sizing Spreadsheets will tell you if you can use a smaller LA-200 Series or if you need something like the LA-1555 Series with 4 parallel power devices to handle that peak power event.
3) How hot will things get and how much airflow do you really need?
Well that all depends on the continuous power dissipation, and that depends on your motion profile and duty cycle. Everyone wants to increase the max velocity to reduce cycle times, but how does that effect the amplifier and how hard can you push it before it gets too hot? You don’t have to guess. That’s what the Varedan Linear Amplifier Sizing Spreadsheets do! Adjust the motion profile numbers in the spreadsheet to get real time feedback on amplifier continuous power dissipation and how much airflow you will need to handle it. We have amplifier heatsinks with up to 3in fins for maximum efficiency and offer high power system baseplate packages with tested fan and airflow ducting configurations so you don’t have to worry about it.
4) Some motor is just as good as any other motor, right?
Maybe, maybe not. Motors with lower resistance put more power dissipation demands on the amplifier (think power in series resistors). Motors with higher inductance require higher Bus voltage to get to max speed (reactance gets ya every time). Lower Torque Constant trades higher current for lower voltage, which might be attractive if the voltage gets too high. If it’s an option, selecting the right motor that matches with the right Linear Amplifier can result in the best system that can meet all your requirements. That’s something else we can help with.
One more thing about motors and current loop bandwidth tuning. In order to provide the high bandwidth and ultra-low noise, the Varedan Linear Amplifiers have an all analog power signal path. This means that the control loops are analog as well and are factory tuned with Rs and Cs on the board. We have developed a system of equations, simulations, and bench testing that allow us to tune an amplifier with the bandwidth and response you request based on your motor parameters, specifically inductance. The thing that may not be obvious is that for a given tuning the current loop bandwidth linearly scales with motor inductance. A given tuning for a given motor will change if a different motor with a different inductance is used. This may not be an issue if the inductances are similar or if the motors fall in the range of the four bandwidth options of the LA Series Linear Amplifier, but in some cases it can cause issues such as:
a) A specific target bandwidth or response is required for the application.
b) A very low inductance motor is used with a tuning set up for very high inductance. This can lead to instability.
If multiple different motors are planned to be used for a given application, discuss this with the Varedan Engineering Team to come up with a plan to support all of your requirements.
Should I use a PWM or linear amplifier?
Many of our customers ask us whether to use a PWM or linear amplifier for their application. Below is an overview of the differences between PWM and linear servo amplifiers.
Pulse Width Modulation (PWM) Amplifiers
PWM servo amplifiers are the most popular because they operate at energy efficiencies of greater than 90%. The output devices in a PWM amplifier operate in either cut-off (turned off) or saturated mode (turned on). Varedan’s PWM amplifiers have switching frequencies from 20 to 100 KHZ. Under normal operation the output of the amplifier is switched on and off once during each cycle of the switching frequency. The ratio of the off to on time determines the net voltage delivered to the load. As higher outputs are commanded, the ratio of on to off time is increased which increases the net output voltage. Protection of a PWM amplifier is as simple as restricting the peak and continuous current.
Linear Amplifiers
Linear servo amplifiers are less energy efficient than PWM amplifiers. The output devices in a linear amplifier always have a small quiescent current flowing through them, which enables them to operate in a linear mode. Therefore, the energy efficiencies of a linear amplifier can be below 50% – this lack of efficiency typically means that for a given power level a linear amplifier will weigh more, be larger and generate more heat than a PWM amplifier. Protection of a linear amplifier from abnormal conditions is much more complex than with a PWM amplifier. Varedan’s linear amplifiers incorporate a high speed DSP that provides Safe-Operating-Area (SOA) protection. The DSP measures the voltage across and the current through each output device. The heat sink temperature is also measured from which we can determine the die temperature of the output device. With this data we check to make sure that the maximum power level of the output device is not being exceeded. If the data shows that the maximum power level of the output device is being exceeded the amplifier shuts down protecting the output devices.