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Robotics Engineering DISCUSSION
I am choosing two DC gearmotors for a 10 kg robot with 100 mm drive wheels. It should reach 1 m/s, accelerate at about 0.5 m/s² and climb a 10° ramp. Motor listings give no-load speed, stall torque, free current and stall current, and I do not know how to match those figures to my requirements.
How do I get from the robot's mass and speed to a required torque and rpm, and how much of the stall torque is it sensible to use?
Work out the force at the wheels first. On the ramp, gravity along the slope is m × g × sin(10°) = 10 × 9.81 × 0.174 = 17.0 N. Acceleration needs m × a = 5 N. Rolling resistance with a coefficient of about 0.03 adds roughly 2.9 N. Total is about 25 N.
With a wheel radius of 0.05 m that is 25 × 0.05 = 1.25 N·m, or about 0.62 N·m per motor with two driven wheels. Wheel speed for 1 m/s is v / r = 20 rad/s, which is 191 rpm. Mechanical power is 25 N × 1 m/s = 25 W, so 12.5 W per motor at the wheel.
A brushed DC motor has a straight-line torque-speed curve at a fixed voltage: no-load speed at zero torque, stall torque at zero speed. The speed under load is n = n_noload × (1 - T / T_stall). Peak mechanical power is at half the stall torque, but efficiency and heating are poor there. A common target is to run continuously at about 20 to 30 percent of stall torque.
For your numbers a gearmotor with roughly 3 N·m stall torque and 250 rpm no-load speed fits: at 0.62 N·m it runs at 250 × (1 - 0.62 / 3), about 198 rpm, just above the 191 rpm you need.
Current follows torque in the same linear way. Free current is what the motor draws spinning with no load, and stall current is the supply voltage divided by the winding resistance, drawn when the shaft is not turning. In between, I = I_free + (I_stall - I_free) × T / T_stall. If the motor lists 0.2 A free and 5 A stall, then at 0.62 N·m out of 3 N·m you draw about 0.2 + 4.8 × 0.21 = 1.2 A.
The motor driver and the battery must still handle stall current, because every start from rest and every reversal begins at or near stall. Size the driver for 5 A per channel here, not 1.2 A.
Check traction as well, since it caps the force you can use. With all 10 kg on the driven wheels and a friction coefficient of about 0.7, the most the tyres can push is 0.7 × 98 N, about 69 N. Two motors at 3 N·m stall could produce 2 × 3 / 0.05 = 120 N, so the wheels will spin before the motors stall. That is useful protection for the gears and the driver, but if casters carry part of the weight, the available traction drops in proportion.
Two practical cautions about listings. Stall torque and stall current are quoted at a stated voltage; at a lower battery voltage both fall in proportion, and so does the no-load speed. And the gearbox is not lossless: spur gearboxes lose a few percent per stage, and a quoted output torque may or may not include that, depending on the supplier.
Leave margin for it, and do not hold a motor at stall for more than a moment, because all of the electrical input becomes heat in the winding.
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