Motor constants

This article describes the relationship between the different motor constants (e.g. speed and torque constant).

Generally, motor constants result from the construction details of a given motor. Such as

• active length and diameter
• winding geometry, winding resistance and winding number
• magnetic flux densities, permanent magnets

Torque constant k_M

• relates the produced torque to the motor current
• maxon unit: mNm / A
• SI unit: Nm / A

Speed constant k_n

• relates the motor speed to the back EMF voltage
• maxon unit: rpm / V
• SI unit: rad/s / V

Relationship between k_n and k_M

• k_n is basically the inverse of k_M
• in maxon units
  
• in SI units
  

Generator constant k_G

• relates the generated back EMF voltage to the motor speed
• the inverse of the speed constant: k_G = 1/ k_n
• unit: V / rpm
• often also in V / 1000rpm

Motor constant k

• used to express the strength of the motortype (size)
• independent of the winding details, such as resistance R
• relation:
  
  with:

• • M = torque
  • P_J = Joule power loss (= R * I²)
    
    
• The maxon speed-torque-gradient is proportional to 1 / k².