Drive Sizing Calculator
Size the drive of a linear or rotary axis: from the moving load, the gearbox and a trapezoidal motion profile the calculator determines the required motor speed, the peak torque during acceleration, the RMS torque over the cycle, the peak power and the inertia reflected to the motor shaft. These values are the basis for the manufacturer-specific motor or servo selection using the torque-speed curve, live with every input.
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Formulas and fundamentals
Motion profile and kinematics
The chain of calculation starts from the trapezoidal motion profile: during the acceleration phase the velocity rises linearly to its maximum, followed by constant travel and then deceleration. Within each phase the acceleration is constant, a = v/t. The output element converts the motor rotation into the useful motion via the travel constant K_VA (travel per revolution); the effective radius is r.
Hence at the output ω_out = v/r and α_out = a/r; through the gear ratio the motor speed and angular acceleration follow:
Reflected inertia and load torque
The total inertia reflected to the motor shaft combines motor, gearbox and load. Rotating loads and linear masses are reflected to the fast-running motor shaft with the square of the gear ratio, so a larger i strongly reduces the load inertia.
The stationary load torque at the output follows for a linear axis from the path force (gravity component, friction, process force); for a rotary axis it is given directly. Referred to the motor shaft and corrected for the drive-train losses:
Motor torques, RMS torque and power
The required motor torque combines a stationary load part and a dynamic acceleration part per phase; during deceleration it usually becomes negative and therefore regenerative.
For thermal sizing the RMS torque over the cycle governs; power follows from P = M·ω. The constant-travel power and the peak power during acceleration near maximum speed are decisive.
Worked example
A horizontal linear axis moves a mass of 200 kg via a pinion of 100 mm effective diameter (friction coefficient µ = 0.1, no process force). Gearbox i = 5 and efficiency η = 0.9, motor inertia J_motor = 0.001 kg·m². The trapezoidal profile runs v = 1 m/s with t_acc = 0.2 s acceleration, 1.0 s constant travel and t_dec = 0.2 s deceleration. From the pinion K_VA = π·0.1 = 0.314 m/rev and r = 0.05 m.
Kinematics: ω_mot = i·v/r = 5·1/0.05 = 100 rad/s, i.e. n_mot = 955 rpm. The motor angular acceleration is α_mot = i·(v/t_acc)/r = 5·5/0.05 = 500 rad/s². The friction force µ·m·g = 196.2 N gives M_out = F·r = 9.81 Nm at the output and M_load,mot = 9.81/(5·0.9) = 2.18 Nm at the motor. The reflected inertia is J_red = 0.001 + 200·0.05²/5² = 0.021 kg·m², the acceleration torque J_red·α_mot = 10.5 Nm.
The peak torque during acceleration is therefore M_mot = 2.18 + 10.5 = 12.68 Nm at 955 rpm, the peak power P = 12.68·100 ≈ 1268 W (about 1.27 kW). During constant travel only 2.18 Nm act (218 W); the RMS torque over the cycle is about 6.0 Nm. The task is thus to select a motor whose curve at 955 rpm provides a peak torque above 12.7 Nm and a continuous torque above 6.0 Nm - the final choice is manufacturer-specific.
Frequently asked questions
What is the difference between peak torque and RMS torque?
The peak torque occurs briefly during acceleration and must not exceed the motor's maximum torque per the torque-speed curve. The RMS torque is the root-mean-square over the whole cycle and governs the thermal continuous load; it must stay below the continuous rated torque. Both checks are independent - a motor may reach the peak torque yet still overheat.
Why is the load inertia divided by i²?
A gearbox with ratio i turns the load i times slower than the motor. When reflected to the fast-running motor shaft the load inertia therefore appears smaller by the factor 1/i². A higher ratio thus markedly lowers the motor's dynamic torque demand, but raises the required motor speed in the same proportion.
How does the efficiency enter the calculation?
The drive-train efficiency η corrects the stationary load torque at the motor shaft: M_load,mot = M_out/(i·η). It therefore penalises the driving operation (friction, gravity component, process force). The dynamic acceleration torque from the reflected inertia is applied here without η - the conservative approach for thermally relevant sizing.
Does the calculator select the motor?
No. The calculator supplies the required sizing values: speed, peak and RMS torque, power and reflected inertia. The actual motor or servo selection is manufacturer-specific, using the torque-speed curve that accounts for field weakening, thermal limits and the permissible inertia ratio.
What does the travel constant K_VA mean?
K_VA is the distance the axis travels per revolution of the output. For a lead screw K_VA equals the lead P (e.g. 10 mm/rev), for a wheel, pinion or roller it equals the circumference π·d. From K_VA follows the effective radius r = K_VA/(2·π), used to convert linear force and linear mass into torque and inertia.
Why is the deceleration torque often negative?
During braking the inertia opposes the motion and assists the drive. Once it exceeds the stationary load torque the motor torque turns negative: the motor operates as a generator and the braking energy must be dissipated via a braking resistor or fed back to the grid. In magnitude the braking load is smaller than the acceleration peak torque for a symmetric profile.
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