Calculator Inputs
Enter screw geometry, speed ramp, torque, moving masses, resisting load, and rotational inertia. Results appear above this form after submission.
Example Data Table
| Item | Example Value |
|---|---|
| Lead | 10 mm/rev |
| Start Speed | 0 rpm |
| Target Speed | 3000 rpm |
| Ramp Time | 0.40 s |
| Available Torque | 2.50 N·m |
| Efficiency | 90% |
| Payload + Carriage Mass | 25 kg |
| Total Rotational Inertia | 0.000015 kg·m² |
| Resisting Force | 150 N |
| Desired Linear Acceleration | 1.2500 m/s² |
| Required Ramp Torque | 0.3335 N·m |
| Maximum Acceleration from Available Torque | 40.8700 m/s² |
Formulas Used
1) Linear speed from rotational speed
v = (rpm × lead) / 60
2) Desired linear acceleration for a speed ramp
a = (lead × Δrpm) / (60 × ramp time)
3) Angular acceleration
α = (2π × Δrpm) / (60 × ramp time)
4) Drive force from screw torque
F = (2π × η × T) / lead
5) Reflected mass from rotational inertia
mref = J × (2π / lead)2
6) Equivalent moving mass
meq = payload mass + carriage mass + reflected mass
7) Maximum acceleration from available torque
amax = (F - resisting force) / meq
8) Torque required for the requested ramp
Treq = ((meq × a) + resisting force) × lead / (2π × η)
These equations estimate axial motion from screw lead, torque, efficiency, and inertia reflection. Real machines may also be limited by motor current, servo tuning, stiffness, preload, friction change, and thermal effects.
How to Use This Calculator
- Enter the screw lead in millimeters per revolution.
- Set the start and target motor speeds in rpm.
- Enter the ramp time for the requested speed change.
- Provide available drive torque and mechanical efficiency.
- Add payload mass, carriage mass, and resisting axial force.
- Enter screw, motor, and extra rotational inertias.
- Add a travel distance if you want a move time estimate.
- Press the calculate button and review the results above the form.
- Use the CSV or PDF buttons to export your output.
- Compare required torque with available torque before final sizing.
FAQs
1) What does this calculator actually solve?
It estimates linear acceleration, drive force, reflected mass, required ramp torque, and whether your selected torque can achieve the requested ball screw speed ramp.
2) Why is lead so important?
Lead controls the distance moved per revolution. A larger lead raises linear speed for a given rpm, but it usually demands more torque for the same axial force.
3) What is reflected mass?
Reflected mass converts rotational inertia into an equivalent linear mass at the screw output. It can become large when the lead is small, making acceleration harder than expected.
4) Why can available torque differ from required torque?
Available torque comes from the motor and drive system. Required torque depends on ramp rate, mass, resisting force, efficiency, and screw lead. The system works only when available torque stays above demand.
5) Does this include gravity?
Yes, if gravity acts along the screw axis, include it inside the resisting force input. For a vertical axis, the load weight often dominates the required torque.
6) Can I use this for deceleration?
This page is arranged for acceleration ramps where target rpm is at least the start rpm. For deceleration studies, the same relationships apply, but sign handling must be adjusted carefully.
7) Why might the real machine accelerate slower?
Real systems may have torque rolloff at speed, controller limits, friction changes, backlash, compliance, and mechanical losses not fully captured in a simple first pass sizing model.
8) When should I add a safety margin?
Use a safety margin during final design whenever duty cycle, contamination, lubrication changes, temperature, or uncertainty in mass and load values could raise torque demand.