How to Calculate Ball Screw Motor Torque: Horizontal and Vertical Axis Examples

Calculating ball screw motor torque requires more than converting the moving load into an axial force. A reliable estimate should also consider acceleration, process force, guide resistance, ball screw efficiency, rotating inertia, preload and the required safety margin.

The calculation method also changes with the mounting orientation. A horizontal axis mainly needs torque to accelerate the moving mass and overcome resistance, while a vertical axis must continuously work against gravity during upward movement.

This guide explains the main formulas and provides two practical examples for preliminary motor sizing. The final motor selection should still be checked against the actual motion profile, ball screw specifications and motor performance curve.

1. Information Required Before Calculating Torque

Collect the following operating data before calculating ball screw driving torque:

• Moving mass, including the table, fixture, workpiece and other moving components
• Horizontal or vertical mounting orientation
• Maximum linear speed
• Required acceleration and deceleration
• Ball screw lead
• Ball screw transmission efficiency
• Guide resistance, seal resistance and other friction forces
• External process force, such as cutting, pressing or clamping force
• Ball screw and coupling rotational inertia
• Ball screw preload or starting torque, when available
• Required duty cycle and safety factor

The dynamic and static load ratings in a ball screw catalogue are not motor torque values. They are primarily used to evaluate ball screw load capacity and service life.

2. Basic Ball Screw Torque Formula

After determining the total axial force acting on the ball screw, the torque required to convert rotary motion into linear motion can be estimated using:

Lead must be converted from millimetres to metres before using this formula. For example, a 10 mm lead is entered as 0.010 m/rev.

Ball screws generally have high mechanical efficiency, but the actual value depends on the nut design, preload, lubrication, seals, alignment and operating condition. Use the efficiency supplied by the ball screw manufacturer whenever available instead of assuming a universal value.

3. Calculating Axial Force for a Horizontal Axis

For a horizontal axis, gravity is normally supported by the linear guides or machine structure rather than acting directly along the ball screw. The axial force is therefore mainly determined by acceleration, guide resistance and the external working force.

Where:

• m = total moving mass, kg
• a = linear acceleration, m/s²
• F_resistance = guide, seal and mechanical resistance, N
• F_process = external force acting against movement, N

If the guide manufacturer provides running resistance, use that value. Estimating resistance only from a generic friction coefficient may be inaccurate because guide preload, seals, lubrication and mounting alignment can substantially change the actual resistance.

4. Horizontal Axis Calculation Example

Consider a horizontal automation axis with the following conditions:

Moving mass	100 kg
Maximum acceleration	1.0 m/s²
Guide and seal resistance	40 N
External process force	200 N
Ball screw lead	10 mm
Assumed driving efficiency	0.90

Step 1: Calculate the acceleration force

Step 2: Calculate the total axial force

Step 3: Convert the ball screw lead

Step 4: Calculate the torque for axial force

This 0.60 N·m value only represents the torque required to generate the calculated axial force. It does not yet include the torque required to accelerate the ball screw, coupling and other rotating components.

5. Add the Rotational Inertia Torque

The motor must accelerate both the moving table and the rotating components. Although the table acceleration is already included in the axial-force calculation, the rotational inertia of the ball screw, coupling and other rotating parts must be calculated separately.

Assume the combined inertia of the ball screw and coupling in the horizontal-axis example is 0.0008 kg·m².

If an additional 0.15 N·m is allowed for ball screw preload, seals and other unmodelled resistance:

Using a preliminary service factor of 1.5:

For this example, the motor and transmission system should be able to provide at least approximately 1.88 N·m under the required acceleration condition. The available torque must be checked at the actual operating speed, not only at zero speed.

6. Calculating Axial Force for a Vertical Axis

A vertical axis must overcome the weight of the moving assembly during upward acceleration. The worst upward force can be estimated as:

Where g is gravitational acceleration, normally taken as 9.81 m/s².

The force condition changes during upward travel, downward travel, acceleration, deceleration and emergency stopping. For initial motor sizing, upward acceleration is commonly checked as one of the highest driving-torque conditions. The complete motion cycle must still be evaluated separately.

7. Vertical Axis Calculation Example

Consider a vertical lifting axis with these operating conditions:

Moving mass	120 kg
Upward acceleration	0.5 m/s²
Mechanical resistance	60 N
Ball screw lead	10 mm
Assumed driving efficiency	0.90
Combined rotating inertia	0.0005 kg·m²

Step 1: Calculate the gravity force

Step 2: Calculate the acceleration force

Step 3: Calculate the total upward axial force

Step 4: Calculate the torque for vertical movement

Step 5: Add rotational inertia torque

Allowing another 0.15 N·m for preload, seals and additional resistance:

Applying a preliminary service factor of 1.5:

The selected motor should therefore be able to provide approximately 3.90 N·m at the required acceleration and speed in this example. Because this is a vertical axis, a holding brake, counterbalance or other mechanical safety device may also be necessary.

8. Calculate the Required Motor Speed

Torque must always be evaluated together with speed. Motor rotational speed is calculated from linear speed and ball screw lead:

Where:

• n = ball screw rotational speed, rpm
• v = linear speed, m/s
• p = ball screw lead, m/rev

For example, if the horizontal axis requires a linear speed of 0.5 m/s with a 10 mm lead:

The motor must therefore provide the required torque at 3,000 rpm. A motor may have sufficient low-speed or peak torque but insufficient continuous torque at this speed.

The calculated rotational speed must also remain below the allowable ball screw speed determined by the screw diameter, unsupported length, support arrangement and internal circulation design.

9. Rated Torque, Peak Torque and RMS Torque

Motor selection should not be based on only one torque value. Three conditions should be checked:

• Peak torque: required during acceleration, deceleration or a short process-force peak
• Continuous or rated torque: torque the motor can provide continuously at the operating speed
• RMS torque: thermal-equivalent torque calculated from the complete operating cycle

A motor may meet the calculated peak torque but still overheat if its RMS torque exceeds the continuous rating. Applications with frequent acceleration, short dwell time or continuous production therefore require a complete duty-cycle calculation.

10. Why a Vertical Axis Needs a Brake

Ball screws are efficient and can normally be back-driven. When motor torque is removed, the weight of a vertical load may rotate the screw and cause the axis to descend.

Servo holding torque alone should not be treated as the only safety measure. Depending on the application and risk level, a vertical axis may require:

• A motor holding brake
• A counterweight or pneumatic counterbalance
• A safety nut or mechanical locking mechanism
• An emergency stopping device
• A load-holding brake or redundant restraint

Read more about vertical-axis safety in Can a Ball Screw Hold a Vertical Load?

11. Common Ball Screw Torque Calculation Mistakes

Using only the moving weight

Mass in kilograms cannot be entered directly into the torque formula. It must first be converted into force, and the force calculation depends on whether the axis is horizontal or vertical.

Ignoring acceleration

A fast-moving but gradually accelerating axis may require less peak torque than a slower axis with very rapid acceleration. Both speed and acceleration must be defined.

Ignoring ball screw inertia

The rotational inertia of a long or large-diameter ball screw can be significant. This is especially important in high-acceleration applications.

Using motor holding torque as running torque

Motor torque normally decreases as speed rises. The required torque must be checked against the motor torque-speed curve at the actual operating speed.

Selecting lead only from the speed requirement

A larger lead reduces the screw rpm required for a given linear speed, but it also requires more driving torque for the same axial force. Lead selection should balance speed, torque, positioning resolution and critical-speed limits.

Applying an arbitrary safety factor

A service factor helps cover calculation uncertainty but does not replace correct engineering data. A larger safety factor cannot correct an underestimated process force, unsuitable motor inertia ratio or inadequate vertical-axis brake.

12. Practical Motor Sizing Procedure

1. Define the moving mass, axis orientation and external process force.
2. Define maximum speed, acceleration, deceleration and duty cycle.
3. Select a preliminary ball screw diameter and lead.
4. Calculate the maximum axial force for each motion condition.
5. Convert axial force into ball screw driving torque.
6. Add ball screw, coupling and other rotating inertia torque.
7. Add verified preload, seal and mechanical resistance.
8. Apply an appropriate design margin.
9. Calculate the required ball screw rpm.
10. Check peak torque, continuous torque and RMS torque against the motor curve.
11. Check critical speed, buckling load and ball screw service life.
12. Add a suitable holding and safety system for vertical axes.

Conclusion

Ball screw motor torque is determined by the complete motion system rather than the moving mass alone. A horizontal axis mainly requires torque for acceleration, process force and mechanical resistance. A vertical axis must also overcome gravity and normally requires additional load-holding protection.

The basic axial-force torque formula provides a useful starting point, but rotating inertia, ball screw preload, motor speed, duty cycle and safety requirements must also be evaluated before selecting the final motor.

DLY supplies ball screws in multiple diameters, leads, accuracy grades and nut configurations. Standard and custom end machining can also be provided to match motor couplings and BK/BF, FK/FF or EK/EF support arrangements.

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