Shaft Power and Drive Sizing

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Tool · Drives · Power transmission

Size a motor and gearbox from the load, or check what a motor delivers at the output. Solve power, torque or speed in any units, add a gear stage with its efficiency, include the torque needed to accelerate the load inertia, and check the shaft in torsion. The gear pair animates through a start and run cycle, and the charts show the torque, speed and motion profile.

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Running

Motor speed-

Motor torque-

Load speed-

Load torque-

Inputs

Load (output shaft)

Calculate Power, from torque and speedTorque, from power and speedSpeed, from power and torque

Power

Unit

Torque

Unit

Speed

Unit

Gearbox

Ratio i (motor : load)

Efficiency (%)

Ratio 1 and 100 % means a direct drive. For a reduction, i is motor speed divided by load speed.

Acceleration (optional)

Ramp time, 0 to speed

Unit

Inertia unit

Load inertia J_L

Motor inertia J_m

J_L is at the load shaft. Add the gearbox input inertia from its datasheet to J_m. Leave the ramp time at 0 to skip this section.

Shaft torsion check (optional)

ShaftLoad shaftMotor shaft

Length unit

Outside dia. d

Bore d_i

Twist length L

Stress unit

Shear modulus G

Unit

Allowable shear

G defaults to 79.3 GPa for carbon steel (Shigley Table A-5). Enter the allowable shear stress from your own design basis to get a safety factor and the minimum diameter. Leave d at 0 to skip this section.

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Motor and load

Checks

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Charts

Motor torque vs speed

Lay this over your motor's torque-speed curve: every point must sit below it.

Motion profile at the motor

Details

Unit conversions

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Equations, assumptions and limits

Power, torque and speed

P = T · ω    ω = 2πn / 60

P in watts, T in newton meters, ω in rad/s and n in rpm. The familiar shorthand forms follow directly: P[kW] = T[N·m] × n[rpm] / 9549.3 and P[hp] = T[lbf·ft] × n[rpm] / 5252.1, where 9549.3 = 60 000/2π and 5252.1 = 33 000/2π.

Gearbox

n_load = n_motor / i    T_load = T_motor · i · η    P_load = P_motor · η

The efficiency η covers the gear stage only. The loss P_motor − P_load becomes heat in the gearbox.

Acceleration

α_m = ω_m / t    J_ref = J_L / i²    T_acc = J_mα_m + J_refα_m / η    T_peak = T_run + T_acc

• Newton's second law for rotation, T = Jα, with a linear speed ramp from rest to full speed in time t.
• The load inertia is reflected to the motor shaft by dividing by i², so that both sides carry the same kinetic energy. The load's share of the acceleration torque passes through the gearbox, so it is divided by η.
• The ratio J_ref / J_m is shown for comparison with your motor maker's recommended inertia ratio. Limits differ between makers and motor types, so this tool does not set one.

Shaft torsion

τ = T · (d/2) / J    J = π(d⁴ − d_i⁴) / 32    θ = T L / (G J)

• Elastic torsion of a round shaft. The peak torque is used when acceleration data is given, otherwise the running torque.
• The minimum diameter solves τ = allowable for the same bore-to-diameter ratio.
• G = 79.3 GPa (11.5 Mpsi) for carbon steel, from Shigley's Mechanical Engineering Design, Table A-5.

Units

Exact definitions from NIST SP 811: 1 hp = 550 ft·lbf/s = 745.70 W, 1 PS = 75 kgf·m/s = 735.50 W, 1 lbf = 4.4482216 N, 1 kgf = 9.80665 N.

Validity

The torque, speed and power relations are exact. The drive model assumes steady load torque, a rigid gearbox without backlash or compliance, and a linear acceleration ramp. It does not include motor bearing friction, gearbox inertia (add it to J_m), duty cycle and RMS torque, or motor thermal limits. The shaft check covers torsion only. Bending, keyway and shoulder stress concentrations, and fatigue are not included; for a full shaft design see Shigley Chapter 7.

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