Safety Factor for a Large-Lead Ball Screw

Determining the safety factor for a large-lead ball screw requires more than dividing a single failure load by the normal working load. Static load capacity, fatigue life, shaft buckling, critical speed, ball-circulation speed and drive torque must be checked separately.

In this article, "large-lead screw" refers to a ball screw with a relatively large linear travel per revolution. DLY generally treats leads of 10 mm and above as high-lead options. The calculation method for a trapezoidal or ACME sliding lead screw is different and should not be mixed with the ball screw method below.

Why One Safety Factor Is Not Enough

Different failure modes use different load capacities and calculation methods. A ball screw may have sufficient static load capacity but still be unsuitable because its shaft can buckle, its rotational speed approaches the critical speed or its calculated fatigue life is too short.

Step 1: Calculate the Maximum Axial Load

The first step is to determine the highest axial force that the ball screw may experience. Do not use only the mass of the moving component.

Depending on the machine, the maximum axial load may include:

• Gravity on a vertical or inclined axis
• Acceleration and deceleration force
• Machining, pressing or process force
• Guide, seal and cable-chain resistance
• Counterweight or balancing force
• Emergency-stop deceleration
• Impact, collision or load uncertainty where applicable

Acceleration force can be estimated using:

F_a = m × a

where m is the moving mass in kilograms and a is the linear acceleration in metres per second squared.

For a vertical lifting axis, the approximate upward driving force before additional resistance is:

F = m × (g + a)

The load during downward movement, braking and emergency stopping should be calculated separately because the direction and magnitude may change.

Step 2: Check the Static Load Safety Factor

The basic static axial load rating, normally identified as C_0a, relates to permanent deformation at the ball-and-raceway contacts. It is not the same as an "ultimate breaking load."

A basic static safety factor can be expressed as:

f_s = C_0a ÷ F_max

where:

• f_s = static load safety factor
• C_0a = basic static axial load rating
• F_max = maximum equivalent axial load

The required minimum factor should follow the manufacturer's technical data and the machine's load condition. Smooth operation, vibration, impact, emergency stops and safety consequences require different margins. A universal value such as 1.2, 2 or 3 should not be applied without reference to the actual specification.

If the load is applied eccentrically, the ball screw should not be selected by simply increasing this factor. Side load and moment should be carried by the linear guides, while the screw and nut remain correctly aligned.

Step 3: Calculate the Equivalent Dynamic Load

Fatigue life is not calculated from the single highest load unless that load acts throughout the entire operating cycle. When the load changes during acceleration, constant-speed travel, processing and return motion, an equivalent dynamic load should be calculated.

For several constant-load stages, a simplified revolution-weighted equivalent load for a ball screw can be expressed as:

F_m = ∛[(F₁³N₁ + F₂³N₂ + …) ÷ (N₁ + N₂ + …)]

where F_m is the equivalent dynamic axial load and N represents the number of revolutions completed under each load.

Load direction, preload and operating sequence can affect the correct calculation. Use the selected manufacturer's life-calculation method when finalizing the design.

Step 4: Calculate the Nominal Fatigue Life

The nominal rating life of a ball screw is commonly calculated from the basic dynamic axial load rating C_a and equivalent dynamic axial load F_m:

L₁₀ = (C_a ÷ F_m)³ × 10⁶ revolutions

This is a statistical rolling-fatigue rating life, not a guarantee that every screw will run for exactly that number of revolutions. Contamination, poor lubrication, misalignment, shock and incorrect preload can cause earlier failure.

If the average rotational speed is known, revolutions can be converted into approximate operating hours:

Life in hours = L₁₀ ÷ (60 × average rpm)

An appropriate dynamic load rating should be selected from the required life-not by applying a general-purpose multiplier to the working load.

Step 5: Check Buckling Under Compression

A long ball screw under compressive load can become unstable and bend even when the ball nut's static load rating is sufficient. This is especially important on vertical lifting axes and long horizontal axes that push rather than pull the load.

The theoretical Euler buckling load is related to:

P_cr = π²EI ÷ (KL)²

where:

• E = elastic modulus of the screw material
• I = second moment of area based on the screw root diameter
• L = unsupported screw length
• K = effective-length factor determined by end support conditions

For a circular section:

I = πd_r⁴ ÷ 64

The root diameter-not only the nominal outside diameter-should be used. The actual permissible compressive load must include an appropriate margin below the theoretical buckling load and follow the manufacturer's calculation method.

Buckling resistance changes greatly with unsupported length because the critical load is inversely proportional to the square of that length.

Step 6: Check Critical Speed

A long rotating screw can vibrate or whip when its rotational speed approaches a natural frequency. Critical speed depends mainly on:

• Screw root diameter
• Distance between effective supports
• Fixed, supported or free end conditions
• Straightness and installation alignment

The operating speed must remain below the permissible speed calculated using the supplier's support-condition factor and recommended margin.

Large lead can reduce the required screw rpm for a given linear speed:

Required rpm = Linear speed ÷ Lead

For example, achieving 20,000 mm/min requires approximately 2,000 rpm with a 10 mm lead, but only 800 rpm with a 25 mm lead. This can help with critical-speed limitations, although other checks remain necessary.

Step 7: Check the DN Value and Ball-Circulation Limit

Even when the screw shaft remains below its critical speed, the ball nut may have its own rotational-speed limit. Ball circulation generates impact, friction and heat as the balls enter and leave the loaded raceway.

Manufacturers may specify a permissible speed or DN value based on screw diameter and rotational speed. The exact definition and allowable value should be taken from the selected product specification.

Do not assume that every large-lead nut is suitable for high speed. Return structure, ball size, lubrication, preload and assembly accuracy all affect the permissible operating speed.

Step 8: Calculate the Required Driving Torque

The approximate torque required to generate an axial force through a ball screw can be estimated as:

T = F × P ÷ (2πη)

where:

• T = driving torque
• F = axial force
• P = ball screw lead
• η = mechanical efficiency

For the same axial force, a larger lead generally requires greater driving torque, although it produces more linear travel per revolution.

The motor calculation must also include screw, coupling, pulley, motor and moving-load inertia. Peak acceleration torque, continuous torque, emergency-stop torque and motor-speed limits should be checked separately.

Step 9: Check End Machining and Support Bearings

Selecting a ball nut with sufficient load ratings does not guarantee that the complete assembly is safe. The machined screw ends and support bearings must transmit the same axial load and driving torque.

Check:

• Fixed-side bearing axial load rating
• Bearing preload and rigidity
• Bearing-seat diameter and shoulder strength
• Thread and locknut strength
• Keyway, flat or coupling connection
• Combined axial and torsional stress in the screw end

Small machined-end diameters may become the weakest section even when the main screw shaft and nut have sufficient capacity.

View DLY ball screw support units when checking the bearing and mounting arrangement.

Step 10: Add Safety Measures for Vertical Axes

Ball screws generally have high mechanical efficiency and can be back-driven. A vertical load may therefore descend and rotate the screw if motor torque is removed.

A vertical system should include an appropriate motor brake, counterbalance, mechanical holding device or other risk-control measure. Increasing the ball screw safety factor does not make the mechanism self-locking.

The safety design should consider power loss, coupling failure, brake failure, emergency stopping and maintenance conditions-not only normal motor operation.

Information Required for Selection

Prepare the following information before calculating a large-lead ball screw:

• Moving mass and mounting direction
• Maximum process and external forces
• Acceleration, deceleration and emergency-stop rate
• Required linear speed and screw lead
• Total screw length and support distance
• Fixed, supported or free end arrangement
• Load and speed during each part of the operating cycle
• Daily operating time and required service life
• Required accuracy, clearance or preload
• Lubrication, temperature and contamination conditions
• Motor, coupling and support-bearing information

Common Calculation Mistakes

• Using the normal load instead of maximum acceleration or emergency-stop load
• Treating the static load rating as an ultimate breaking load
• Using one safety factor for static load, fatigue and buckling
• Checking nut capacity but ignoring shaft buckling
• Using nominal diameter instead of root diameter
• Ignoring critical speed on a long rotating screw
• Ignoring the ball nut's permissible circulation speed
• Forgetting support-bearing and machined-end capacity
• Assuming a vertical ball screw is self-locking
• Mixing kilograms of mass with kilograms-force or newtons

Conclusion

The safety of a large-lead ball screw cannot be represented by one universal factor. Static contact safety, fatigue life, compressive buckling, critical speed, DN value, drive torque and support-bearing capacity must be verified separately.

Large lead reduces the rotational speed required for a given linear speed, but it generally increases the torque required for the same axial force. The final selection must balance speed, torque, load, rigidity, life and installation space.

View DLY ball screw products for available diameters, leads, nut types and accuracy options.

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