Calculator Inputs
Formula Used
Screw mass: ms = π × r² × L × ρ
Screw inertia: Js = 0.5 × ms × r²
Reflected load inertia: JL = mmoving × (lead ÷ 2π)²
Linear acceleration: a = stroke ÷ [ta × (t - ta)]
Angular acceleration: α = 2π × a ÷ lead
Force torque: TF = F × lead ÷ (2π × η)
Peak torque: Tpeak = (Jtotal × α + TF) × service factor
How to Use This Calculator
- Enter the actual moving load, including fixtures and carried materials.
- Add screw geometry, lead, material density, and rotating attachments.
- Enter process force, guide friction, axis angle, efficiency, and stroke data.
- Press the calculate button and review inertia, speed, torque, power, and ratio values.
- Use the export buttons to save the result for review or job records.
Example Data Table
| Case | Load kg | Lead mm | Stroke mm | Move time s | Use note |
|---|---|---|---|---|---|
| Light positioning gate | 120 | 8 | 400 | 3.5 | Low speed site actuator |
| Concrete form lift | 450 | 10 | 650 | 4.0 | Medium duty vertical planning |
| Heavy sliding carriage | 950 | 20 | 1200 | 6.5 | Check ratio and screw speed |
Ball Screw Inertia Guide
Why Inertia Matters
Ball screw drives appear in jacks, gantries, forming tables, shuttering lifts, and automated site equipment. A drive may look strong at rest. It can still fail during fast motion. Inertia is the reason. The motor must spin the screw and also move the linear load. The screw lead converts linear mass into reflected rotary inertia at the shaft. A small lead gives high force. It also raises motor speed. A large lead lowers speed demand. It can raise torque demand from load forces.
Inputs That Change Torque
Good sizing starts with real mass. Include the carriage, fixture, payload, nut, and any moving guard. Then add external axial force. That force may come from slope, cutting pressure, seal drag, or pressing work. Friction is added as a steady load. Efficiency reduces useful torque. A conservative service factor covers dirt, shock, misalignment, and field wear.
Motor Ratio and Control
The screw itself is a rotating part. Its inertia depends on diameter, length, and density. Long steel screws can dominate the total. Couplings, pulleys, brakes, and gear hubs also add inertia. Motor inertia is listed by the maker. The load to motor inertia ratio helps judge control quality. A lower ratio is easier to tune. A high ratio may need a larger motor, gear reduction, slower acceleration, or a different lead.
Motion Profile Review
Motion time also matters. Short moves create high acceleration. The calculator uses a trapezoid move. It estimates acceleration from stroke, move time, and acceleration share. It then converts linear acceleration into angular acceleration. Peak torque combines acceleration torque and force torque. The result is multiplied by the service factor. The output also shows peak speed, screw mass, reflected load inertia, total inertia, and power.
Safe Engineering Checks
Use these values as an early engineering check. They do not replace a machine design review. Ball screw buckling, critical speed, bearing life, column support, lubrication, backlash, and mounting stiffness must also be checked. Construction equipment often sees impact and poor alignment. Use stronger margins when loads are lifted over workers or valuable materials. Verify final motor selection with supplier data. Test the finished axis at low speed first. Increase speed only after temperature, noise, vibration, and following error look safe under load.
Record the final inputs with the job file. Future maintenance crews can compare changes, diagnose wear, and avoid unsafe replacement choices onsite later.
Frequently Asked Questions
What is reflected load inertia in a ball screw?
It is the linear moving mass converted into rotary inertia at the motor shaft. The lead controls the conversion. Larger moving mass and larger lead increase the reflected inertia.
Does screw diameter affect inertia?
Yes. Screw inertia rises strongly with radius. A larger diameter can improve stiffness and buckling resistance, but it can also increase acceleration torque and motor size.
Why is motor inertia included?
The motor rotor must accelerate with the screw and load. Including it gives a closer peak torque estimate and helps compare external inertia against motor inertia.
What load ratio is usually acceptable?
Many servo axes work well below 5:1. Ratios up to 10:1 can be usable with tuning. Higher ratios may need gearing, a different lead, or a larger motor.
Should efficiency change inertia?
Efficiency mainly changes torque needed to overcome force. The calculator keeps reflected inertia as a motion property, then applies efficiency to axial force torque.
How does a vertical axis change the result?
A vertical axis adds gravity force to the working axial force. This raises holding torque, moving torque, and peak torque. Brakes and safety devices may be required.
What is acceleration time share?
It is the part of the total move spent accelerating. A small share creates higher acceleration. A larger share gives smoother motion but may reduce constant speed time.
Can this calculator size the final motor?
It gives an early sizing estimate. Final selection should also check thermal limits, duty cycle, drive voltage, critical screw speed, bearing life, and machine stiffness.
Why add a service factor?
Construction equipment often faces shock, dust, misalignment, and changing loads. A service factor adds margin so the estimate is not based on perfect conditions.
What units should rotating inertia use?
The input fields use kg·cm² for motor, coupling, brake, and pulley inertia. The calculator converts them into kg·m² for the final equations.
What checks are still needed after calculation?
Check buckling, critical speed, lubrication, support bearing capacity, backlash, control tuning, brake holding force, guarding, and local safety rules before equipment use.