

Motor constant Km is the most convenient figure of merit for comparing or sizing dc motors for any motion control application. Physically, Km represents the available torque T per squareroot watt of input power W; that is, Km = T/P ^{0.5 }. Because the load torque and power supply are normally specified before selecting the motor, the torque constant Kt is calculated first; Kt = T/I, where I = input current (A), and T = torque (Nm). Km is found by substituting P = I ^{2 }R into Km = T/P ^{0.5 }, where R = armature resistance, Ω This yields Km = Kt /R ^{0.5 }.
For a motor with specified magnets and physical size, the maximum value of Km is a constant, regardless of armature wire diameter or number of turns. For example, increasing the number of armature turns raises torque constant, but it also increases the winding resistance. Similarly, decreasing winding resistance with a large diameter conductor lowers the torque constant because the armature slot accommodates fewer turns.
The relationship between torque constant and armature resistance is a function of the root of the resistance. Choosing a value for Kt yields the minimum armature resistance for the motor size. At the indicated torque constant, resistance greater than this value may also be specified. Choosing a value for R, on the other hand, yields the maximum torque constant possible, though a lower torque constant may be specified.
With load torque and speed defined, the motor can be specified. The available voltage and current fix the required torque constant and winding resistance. Motor vendors' literature generally contain winding parameters for a number of motors at nominal voltages. But the likelihood of finding a motor that exactly matches the required parameters is slim. The minimum value of Km required is found by dividing Kt by R ^{0.5 }. Motor constant is then computed for a variety of possible motors. A motor is finally selected with a Km equal to or greater than that required. Because specifications are usually published for full armature slots, values computed are close to the maximum available for the given size motor.
If volume is a constraint, select a motor that meets size requirements, calculate Km, and plot Kt versus R. From the graph, work in reverse to trade off torque for speed and specify the voltage.
Though the motor constant alone does not completely specify a motor for an application, it does provide a solid starting point based on size. In general, motors selected in this manner will be capable of driving the specified load. However, ensure that the allowable winding temperature is not exceeded during operation.
Candidate motors  
Motor  #1  #2  #3  
Voltage, V  V  1.5  3  6 
Noload speed, ω  rpm  13,400  5,400  4,700 
Stall torque, Ts  Nm  0.0003  0.0016  0.007 
Noload current, I  A  0.02  0.016  0.01 
Terminal resistance, R  Ω  5  9.5  10 
Torque constant, Kt  Nm/A  0.001  0.005  0.012 
Length  mm  17  21  31 
Diameter  mm  8  16  23 