The force calculation is only one contribution
A horizontal carriage carries 20 kg and accelerates at 2000 mm/s². Convert acceleration to 2 m/s² before multiplying: translational force is 40 N. With a 10 mm screw and assumed efficiency 0.9, that force contributes about 0.0707 N·m at the screw.
That small number is not the required motor rating. Add screw, coupling and motor rotational inertia, friction, external process forces and gearbox effects. A vertical mechanism also needs gravity and a suitable load-retention arrangement. The bench calculates horizontal load torque only and deliberately states those omissions.
Speed and torque must fit the whole cycle
A direct 10 mm screw at 500 mm/s needs 3000 rpm. Check available motor torque at that speed, not only the catalogue's stall or peak figure. Include acceleration, constant-speed process load, deceleration and dwell in the duty cycle.
An RMS torque estimate is:
T_rms = sqrt(sum(T_segment² * time_segment) / total_cycle_time)It relates to heating under the assumptions of the selection method. Peak torque, its permitted duration, drive current limits, cooling, ambient conditions and repetition rate still need independent checks. Regenerative deceleration can require sufficient bus-energy handling or braking equipment.
Reflected load inertia through an ideal ratio scales with the square of the speed ratio. Define the ratio convention before applying the formula. A gearbox can reduce reflected inertia and motor torque while increasing required motor speed and adding efficiency losses or backlash.
Following error points to several possible causes
Command position minus actual position gives following error in a compatible coordinate/time frame. Large error during acceleration can indicate torque saturation, excessive acceleration, incorrect tuning or mechanical resistance. Oscillation can indicate resonance, poor gain choices, compliance or feedback problems.
If motor feedback tracks well while the load is misplaced, inspect lost motion after the encoder. Increasing position gain cannot repair a slipping belt. If error spikes with fieldbus events, inspect timing and communication before changing mechanical parameters.
Tuning under an approved procedure
Start with mechanically sound equipment, verified scaling, permitted low dynamics and the vendor's commissioning process. Tune the relevant loops in their documented order. Record the load state and parameters so results are reproducible. A tuning result on an empty carriage may be unsuitable with the heaviest permitted workpiece.
Use traces for command/actual position, velocity, current or torque and relevant status events. Compare the beginning of saturation with the beginning of following error. A single maximum-error number loses the timing that helps identify the cause.
Do not defeat following-error protection or increase limits merely to hide trips. Determine whether the demand is attainable and the protection settings correspond to the machine design.
Bench investigation
Set moving mass to 20 kg, acceleration to 2000 mm/s², external force to zero and screw efficiency to 90%. Verify 40 N and approximately 0.0707 N·m. Add 100 N of resisting force; thrust becomes 140 N and the load-torque contribution becomes about 0.2476 N·m.
Double mass while keeping acceleration and external force unchanged. Then double acceleration with the original mass. Compare the contributions instead of assuming every quantity doubles together. The model does not include actual motor or screw inertia and cannot select a part number.
Exercises
A cycle uses 1 N·m for 0.5 s, 0.2 N·m for 2 s and 0.8 N·m for 0.5 s. Calculate RMS torque over three seconds: sqrt((0.5 + 0.08 + 0.32)/3), approximately 0.548 N·m. Explain why the peak-duration and speed checks remain necessary.
For a vertical lift, list the extra mechanical, thermal and safety questions before applying the horizontal worksheet. Include gravity, brake capability, power loss, regenerative travel and validation of load retention.
References
Beckhoff motor selection guidance includes torque, speed, inertia and effective torque. Use the chosen motor, drive and transmission manuals for actual selection and commissioning limits.