Power transmission calculator
Angular Acceleration & Motor Calculator
Calculate acceleration torque, output speed, power, time to speed, and motor reduction from rotational inertia and angular acceleration.
Input → stages → output
Edit any value and the drivetrain, target, and motor curves update immediately.
Motor input
Gear stages
14.6667:1 totalMotion target and results
- Acceleration torque
- 7.38 lbf·ft
- Time to speed
- 3.14 s
- Rotation to speed
- 7.85 rev
Derived output target: 300 rpm · 7.38 lbf·ft · 314 W peak at target speed
- Entered ratio
- 14.6667:1
- Predicted speed
- 310.28 rpm
- Speed vs. target
- +3.4%
- Efficient ratio
- 15.399:1
- Motor at target
- 4,619.61 rpm · 34.9 A
- Required power / motor
- 334 W · 70.9% peak
Drivetrain and Custom motor performance
RPM and torque through each shaft, followed by the interpreted motor curves.
Motor input
4,550.71 rpm
0.53 lbf·ft
Shaft 1
1,137.68 rpm
2.07 lbf·ft
Mechanism output
310.28 rpm
7.38 lbf·ft
Most efficient solution for the required power
The movement needs 314 W at the output. With 94.1% drivetrain efficiency, each motor must deliver 334 W at its shaft. The calculator selects the higher-efficiency of the two motor-curve points that produce this power.
- Motor speed
- 4,619.61 rpm · 77%
- Current per motor
- 34.9 A
- Motor efficiency
- 79.7% · 91.9% of max
- Required shaft power
- 334 W · 70.9% peak
- Ratio for desired speed
- 15.399:1
Estimated electrical input at this point is 419 W per motor · 419 W total at nominal voltage. This is the steady-state power for the entered speed and torque; acceleration requires additional power.
The curves are an engineering estimate, not a thermal or controller simulation. A breaker rating is not a motor-current cap; brief current can exceed that rating before a time-dependent trip. Battery or supply sag, configured controller limits, commutation, temperature, friction, and manufacturing variation change real performance.
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Quick answer
How this angular acceleration calculator works
Angular acceleration torque equals rotational inertia multiplied by angular acceleration, plus any resisting torque. Target angular speed then determines peak mechanical power and the motor reduction needed to reach the motion target.
How to use the calculator
- 1Enter the mechanism’s rotational inertia about the driven axis and the desired angular acceleration.
- 2Enter the target angular speed and any constant resisting torque from friction or the process load.
- 3Enter motor specifications, motor count, gear stages, and estimated mesh efficiency.
- 4Compare acceleration torque, time to speed, peak power, motor curve position, and recommended ratio.
Worked example
Accelerating a rotating assembly
- Inputs
- A 1 kg·m² assembly accelerates at 10 rad/s² to 300 rpm with no additional resisting torque.
- Result
- Acceleration torque = 10 N·m, time to speed ≈ 3.14 s, and peak power ≈ 314 W.
Torque follows inertia times angular acceleration. Peak power occurs at the target speed for this constant-torque acceleration model.
Common questions
What to know before using the result
- What is rotational inertia?
- Rotational inertia describes how strongly a body resists angular acceleration about a selected axis. Mass farther from the axis contributes disproportionately more inertia.
- How do I include friction or process torque?
- Enter it as resisting torque. The calculator adds that load to the inertia-based acceleration torque throughout the modeled movement.
- Does the calculator include reflected motor and gearbox inertia?
- Not automatically. Add meaningful rotating inertia to the load model or verify it separately when the motor, gearbox, couplings, or shafts are a significant part of the system.
Formula
F = ma + Fᵣ · T = Fr · P = Fv · GR = ∏(N driven ÷ N driver)
Linear mode uses F = ma and drive radius; angular mode uses τ = Iα plus resisting torque. Multiply each gear-stage ratio for total reduction; required motor-shaft power also includes drivetrain losses.
Engineering references
Assumptions and limits
- Each listed row represents one external gear mesh between a driver and a driven gear.
- Gears on the same compound shaft rotate at the same speed and do not add another mesh.
- Torque excludes bearing, windage, lubrication, and other losses beyond the entered mesh efficiency.
- Required power is the steady-state power at the entered speed and torque; acceleration requires additional power and energy.
- Linear acceleration mode assumes constant acceleration from rest, constant drive radius, no wheel slip, and the entered resistance force. Its displayed power is the instantaneous mechanical output required at target speed.
- Angular acceleration mode assumes constant acceleration from rest, fixed rotational inertia, and the entered resisting torque.
- Motor curves are ideal constant-voltage approximations from entered or published free-speed, free-current, stall-torque, and stall-current endpoints.
- No current cap is applied by default. The optional cap represents a configured motor-controller setting, not a branch-breaker rating.
- Breaker trips are time- and temperature-dependent; battery sag, controller mode, current limiting, temperature, and manufacturing variation change real motor performance.
- Pitch, pressure angle, tooth form, center distance, and interference must be checked separately.
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