Increasingly, equipment designers who use dc servomotors find that they need customized motor windings to match specific applications. For example, in a retrofit use, the motor’s envelope and footprint might already exist, but the performance characteristics no longer fit. Or, because of hardware economies, an OEM designer of short-run or single-unit customized machinery may prefer not to change motor physical characteristics, but needs to change performance characteristics to suit individual applications.

An armature-winding change affects many parameters, including the torque constant K_t, voltage constant K_e, armature resistance Ra, and armature inductance L_a.

It would help motor users much to have a way to quickly calculate new motor parameters and assess their effects on the servo system. A winding change is nothing more than a new combination of number of coil turns and magnet wire gage. The procedure is simple once you define the “load points.” On the basis of the applications, each load point is defined by the torque and speed the servomotor needs to do its tasks.

Motor power

We must revisit some of the figures of merit that dominate dc motor design; the definition of motor parameters affected by winding changes; and their intrinsic relationship. To begin, let us define motor power output as the product of torque and speed measured at the motor shaft for a specific load point, that is:

P_out = Ts (1)

where

P_out = Output power, W

T = Torque, Nm

s = Shaft speed, rad/sec

or

P_out = Tn/7.04 (1a)

where

P_out = Output power, W

T = Torque, lb-ft

n = Shaft speed, rpm

Equation (1) shows that, to get the same continuous power output at a higher torque, you need only a proportional reduction in speed. Conversely, a higher speed at the same power output means a torque change inversely proportional to the speed increase.

Due to inefficiency, not all of the power input, P_in, to a motor becomes power output. The difference between P_in and P_out constitutes the motor losses. DC motor ratings depend on the motor’s ability to dissipate the heat created by the losses without exceeding its maximum operating temperature. There are limitations in power output capability in terms of torque, or speed, or both.

The new winding must not compromise the maximum safe temperature for the given motor size. Because the initial heat rise usually comes from armature current, this automatically sets a maximum current permissible in the armature windings for a given time. The maximum current also limits the amount of output-shaft torque the motor can produce. The designer also designates a maximum safe speed for the motor, usually depending on its rotor diameter or, if it is a brush-type motor, on number of commutator segments. In other words, there will be limits to the motor’s ability to meet the desired load points.

Motor constants

Motor torque is directly proportional to the developed current in the armature windings thus:

T = K_tI (2)

where

T = Torque, Nm

K_t = Motor torque constant, Nm/A

I = Armature winding current, A or

T = [2.254310^-7(zΦp/a)]I (2a)

where

T = Torque, oz-in.

z = Effective number of series conductors per coil

Φ = Magnetic flux in webers, wb

p = Number of poles

a = Shaft speed, rpm

I = Current, A

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