No-Load Speed and Stall Torque

The parameter values for a certain motor are
$K_{T} = K_{b} = 0.05 N · m/A$

$c = 10^{−4} N · m ·s/rad R_{a} = 0.5 Ω$
The manufacturer’s data states that the motor’s maximum speed is 3000 rpm, and the maximum armature current it can withstand without demagnetizing is 30 A.

Compute the no-load speed, the no-load current, and the stall torque. Determine whether the motor can be used with an applied voltage of $v_{a} = 10 V$ .

Question

No-Load Speed and Stall Torque

The parameter values for a certain motor are

[latex]K_{T} = K_{b} = 0.05 N · m/A [/latex]

[latex]c = 10^{−4} N · m ·s/rad R_{a} = 0.5 Ω[/latex]

The manufacturer’s data states that the motor’s maximum speed is 3000 rpm, and the maximum armature current it can withstand without demagnetizing is 30 A.

Compute the no-load speed, the no-load current, and the stall torque. Determine whether the motor can be used with an applied voltage of [latex]v_{a} = 10 V[/latex].

Accepted Answer

For [latex]v_{a} = 10 V[/latex], (6.5.5) and (6.5.6) give

[latex]i_{a} = \frac{c V_{a} + K_{b} T_{L}}{c R_{a} + K_{b}K_{T}} [/latex]          (6.5.5)
[latex]ω = \frac{K_{T} V_{a} − R_{a} T_{L}}{c R_{a} + K_{b} K_{T}} [/latex]      (6.5.6)
[latex]i_{a} = 0.392 + 19.61 T_{L} A    ω = 196.1 − 196.1 T_{L} rad/s [/latex]
The no-load speed is found from the second equation with [latex]T_{L} = 0[/latex]. It is 196.1 rad/s, or 1872 rpm, which is less than the maximum speed of 3000 rpm. The corresponding no-load current is [latex]i_{a} = 0.392 A[/latex], which is less than the maximum allowable current of 30 A. The no-load current is required to provide a motor torque [latex]K_{T} i_{a} [/latex] to cancel the damping torque cω.
The stall torque is found by setting ω = 0. It is [latex]T_{L} = 1 N · m.[/latex] The corresponding stall current is [latex]i_{a} = 20 A[/latex], which is less than the maximum allowable current.

Question 6.5.1: No-Load Speed and Stall Torque The parameter values for a ce...

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