Maxon BLDC Operation Fundamentals
This page discusses some of the operational fundamentals of BLDC motors. BLDC and regular brushed DC motors share very similar torque/speed/current characteristics, thus most of the listed information also applies to brushed DC motors. Majority of information was sourced from Maxon resources which will be linked in various sections of this page.
DC Motor Constants
DC motors have three fundamental operating characteristics:
1: Speed is directly proportional to operating voltage
- n - speed in rpm
- kn - speed constant of the motor, given in rpm/V
- Uind - voltage induced in the windings of the motor
Note: Some motor manufacturers will provide a "Kv" rating of the motor. This "Kv" is actually the speed constant of the motor, and is the same is kn in the equation above.
2: Torque is directly proportional to the motor current
- M - motor torque
- km - torque constant
- Imot - current drawn by motor
3: Speed is approximately inversely proportional to torque at a constant operating voltage
- At a constant voltage, all brushed DC motors experience a linear decrease in speed with increasing torque
- Brushless DC motors can sometimes deviate slightly from this linear relationship depending on the number of pole pairs. Motors with a higher number of pole pairs (such as maxon ec-flats) experience higher amounts of deviation due to a lack of current development in short commutation intervals. However, when operating these motors in their recommended continuous operation ranges, the torque speed can be approximated with a straight line.
The constant relating torque and speed is referred to as the speed-torque gradient. Speed-torque gradients are given by:
- n0 - no load speed
- Mh - stall torque
- This value is typically given as a constant in a data sheet
Torque Speed Curves
As mentioned above, both brushed and brushless DC motors experience approximately an inversely linear relationship between speed and torque. However, to actually plot a torque-speed curve, there are two additional points of interested - stall torque and no load speed.
- Stall torque refers to the torque the motor can produce when the shaft is not rotating. In general, you almost never want to design a motor to operate at stall torque, as it is very dangerous to the operation of the motor. Motors need to spin to dissipate heat, thus if operated at stall for an extended period of time the motor will burnout and die. If you look in the operating range section, you will see that stall torque is never in the continuous operation range of the motor. Stall torque is also the MAXIMUM torque that the motor is capable of producing. (See point 1).
- Torque is directly proportional to current, thus at stall torque there will also be a stall current, which is the maximum current that the motor is capable of drawing.
- No load speed refers to the MAXIMUM speed that the motor can achieve. However, at no load speed the torque production on the output of the motor shaft is zero. If you look at a torque speed curve, you will notice that the no load speed is not actually the y-intercept of the torque/speed axis. This is because all motors have an internal torque that the shaft has to overcome to rotate, due to internal friction. Thus, at no load speed the NET torque output of the motor is zero. Mr will refer to the internal motor torque that needs to be exceeded any time the motor wants to spin. (See point 2).
- Note: You will notice that if you multiple the speed constant of the motor by the rated operating voltage, the RPM will be slightly higher than the no load speed. This is where the speed/torque curve should intercept the y axis, but it is not a real operating RPM that can be achieved.
Sorry for the german, but y axis is RPM, x axis is torque and below that is an axis for current. Torque and current are interchangeable on the x axis as they are directly linear proportional, so either work.
Efficiency and Thermal Performance
No motor performs at 100% efficiency. In other words, not all of the electrical power input to the motor will be 100% converted into useful mechanical power. Often times, losses in power occur in the form of frictional and heat losses. The maximum efficiency of the motor is usually supplied in the data sheet, but can also be approximated via a function of the no load and stall current. 
The efficiency at a specific operating point can be given as a function of RPM, motor voltage and current, torque output and no load torque.
DC motors do not have a linear efficiency. Maximum power output and maximum efficiency do not occur at the same torque.
Motors do not necessarily have to run at peak efficiency. However, an important key consideration that limits the operation of the motor is it's thermal performance. Current is directly proportional to the torque of a motor. However, if you draw more current, your windings will experience a greater rise in temperature. If the motor cannot dissipate this heat, the windings can rise in temperature, exceed their rated maximum temperatures, then melt or fry out. This thermal performance creates recommended operating ranges for the motors.
Operating Ranges
If the motor operates anywhere within the continuous operation range, it can be continuously operated without any concerns of thermal performance.
The continuous operation with reduced thermal resistance zone refers to an updated "continuous operation" range when the motor has sufficient heat dissipation facilities. There is some math where you can calculate the thermal resistance between the motor mount and related interface to see if you fit within this range.
The motor can still be operated within the short term operation range for a limited amount of time. Supposedly you can approximate 2.5x the nominal torque rating can be operated as long as at the thermal time constant of the winding, but this depends on a number of conditions. Watch the video below for a better explanation.
IMPORTANT NOTE: OPERATIONG RANGES ARE SHOWN FOR ROOM TEMPERATURE.
Rated Power and Rated Operating Points
Motors are given a power rating and rated operating points. The nominal torque refers to the maximum torque available within the continuous operation range - aka the max current that can be drawn where it's generated heat is passively dissipated at room temp.
The rated power is the power at a specific operationg point - the maximum torque available at max operating speed. However, your actual power output changes depending on your operating point in the torque speed curve. This value is not a constant by any means, its just the torque, power and speed at this given max continuous current. In applications, this value does not seem that useful.
- Mn - nominal torque
- In - nominal current
- nn - nominal speed
Speed Control
All of the DC motors listed on the maxon website (or wherever) are assigned a rated operating voltage. For example, a 48V motor is rated for operation at 48V power supply. However, all DC motors can be operated at voltages higher or lower than the rated voltage. When you change the operating voltage of the motor, the speed-torque gradient will remain the same - however the no load speed and stall torque will change. The new no load speed can be approximated using the speed constant of the motor. This means that at a specific torque, if you vary the voltage into the motor the speed will increase with higher voltage, and decrease with lower voltage.
For example, look at the constant torque vertical green line. When operating at a higher voltage, the RPM of the motor will be higher. However, when doing so you must keep in mind where you are in the operating range of the motor. Likewise, if you decrease the voltage via duty cycle, you will see a lower speed of the motor.
In our applications, we will likely be varying the voltage into the 48V motor using a duty cycle. This begs the question - why use a 48V motor at all? See the example below:
Say we are looking at at a 60mm diameter maxon EC-flat motor, 200W brushless. There are variants of this motor for rated operation at 12V, 24V and 48V. However, the motors rated for lower volt operations have different internal windings. As a result, these three motors have different speed/torque gradients, as shown below.
The motor rated for 48V operation has the lowest speed/torque gradient (and thus when inverted, the highest torque/speed gradient). This means that when these three motors operate at the same speed, the 48V motor will have the same torque. The speed torque gradient of a motor is independent of it's operating voltage, thus the 48V motor will always see the most torque at the same speed.
Resources
https://support.maxongroup.com/hc/en-us/articles/360013761160-Motor-data-and-simulation