Mechanical Sizing and Verification
Lifetime and Safety Checks for a Motion Axis
See how screw life and overall engineering limits are verified.
You are applying “Lifetime and Safety Checks for a Motion Axis” to a real system and need the concept, assumptions and verification boundary to stay clear.
Turn ball-screw load ratings into a traceable life estimate, then verify static capacity, buckling, critical speed, guides, motor duty, lubrication, environment and machine safety as separate engineering gates.
- Select or check first
- 1. Freeze the configuration. Record screw and nut code, preload or clearance class, lead, diameter, accuracy, support bearings, seals, lubricant, covers and mounting orientation.
- Controlling assumption
- Load, motion profile, geometry, alignment, duty, lubrication and environment match the selected mechanism and ratings.
- Top risk
- Never use the life equation as a buckling or overload check. A slender screw in compression can buckle or a raceway can be permanently indented long before a fatigue-life number appears concerning.
- Proof
- 7. Recalculate after change. Payload, recipe, acceleration, software limits, mounting, lubricant, environment or replacement-part changes can invalidate the original evidence.
Start with the basics Optional foundation before “Lifetime and Safety Checks for a Motion Axis”
Mechanical-design basics
Mechanical parts must carry loads, guide motion and remain aligned; similar-looking components can behave very differently under real force and duty.
- Force and torque
- Force pushes or pulls along a line. Torque is a turning effect equal to force multiplied by its perpendicular lever arm.
- Speed and acceleration
- Speed describes how fast position changes. Acceleration describes how fast speed changes and often creates the highest inertial load.
- Strength and stiffness
- Strength concerns permanent damage or failure. Stiffness concerns elastic deflection under load; a part can be strong enough yet too flexible for accurate motion.
- Load path
- The load path is the complete route by which force travels through shafts, bearings, fasteners, frames and foundations. Every interface on that route must be checked.
- Tolerance, clearance and alignment
- Tolerance permits controlled variation, clearance provides intentional space, and alignment keeps interacting axes or surfaces in the required relationship.
How to use this article: Sketch the load path and motion direction first, then attach units, worst-case loads, duty and acceptance limits to every calculation.
On this page
A motion axis can meet its force and speed target on paper yet fail early because its screw is overloaded, its support arrangement permits whipping, its lubricant never reaches the loaded contacts or its emergency stop drives the carriage into an unverified end condition. Reliable design separates these failure modes, calculates each one with the selected manufacturer's method, and records evidence for the complete installed system.
Read L10 as a statistical fatigue rating
Diagram description
A conceptual curve falls steeply as equivalent dynamic load increases. Beside it, an illustrative calculation uses a 12,000-newton dynamic rating and a 3,000-newton equivalent load in L10 equals C over P cubed times one million revolutions, producing 64 million revolutions.
For a ball screw, basic rating life L10 is commonly expressed as the number of revolutions that 90% of a sufficiently large group of identical screws can reach without rolling-contact fatigue under the stated conditions. That definition describes probability across a population. It neither predicts the exact failure time of one screw nor includes every mechanism that can remove an axis from service.
Basic ball-screw rating life
L10 = (Ca ÷ Pm)³ × 10⁶ rev
Ca is the selected screw's basic dynamic axial load rating. Pm is the manufacturer-defined equivalent or average dynamic axial load for the duty profile. Use the exact catalogue convention, modification factors and direction rules for the product; do not substitute a peak force or a simple arithmetic average without justification.
- L10
- basic rating life, screw revolutions
- Ca
- basic dynamic axial load rating for the exact screw and nut, N
- Pm
- equivalent dynamic axial load under the applicable catalogue method, N
For the teaching values Ca = 12,000 N and Pm = 3,000 N, L10 = (4)³ × 10⁶ = 64 × 10⁶ revolutions. Halving Pm while everything else remains valid would increase this calculated life by eight; doubling Pm would reduce it to one eighth.
Build equivalent load from the real duty profile
A reciprocating axis rarely sees one constant load. Acceleration, deceleration, gravity, process force, friction and preload change across the cycle. Because fatigue damage is nonlinear, a short high-load segment can matter much more than its time share suggests. Divide the cycle into intervals, calculate axial load with direction for each interval, and weight it by screw revolutions or travel according to the catalogue procedure.
Illustrative cubic equivalent-load form
Pm = ³√[(Σ |Pi|³ Ni) ÷ (Σ Ni)]
This compact form illustrates the cubic weighting for ball-screw fatigue when the selected manufacturer permits it. Pi is the axial load magnitude in interval i and Ni is the screw revolutions in that interval. Reversing-load rules, preload, shock or vibration factors and modification factors are product-specific; THK, for example, instructs users to evaluate positive and negative directions separately when the sign changes.
- Pm
- equivalent dynamic axial load, N
- Pi
- axial load magnitude in interval i, N
- Ni
- screw revolutions or catalogue-approved travel weighting in interval i
Retain the original interval table so the result can be recalculated when acceleration, payload or process force changes. A single unlabeled 'average load' cell hides the very transient that may dominate life.
| Input | What must be represented | Common omission |
|---|---|---|
| Axial forces | Acceleration, friction, gravity, process force, seals, preload and external disturbances | Using payload weight alone |
| Direction | Positive and negative load intervals handled by the selected maker's reversal rule | Cubing signed values so opposing directions cancel |
| Exposure | Travel or screw revolutions at each load and speed, including return strokes | Weighting only by elapsed time when the screw does not rotate throughout |
| Duty variation | Normal mix, credible overloads, setup cycles and changed products | Sizing only the easiest recipe |
| Uncertainty | Measured friction range, load tolerance, shock or vibration and data confidence | Adding an unexplained universal factor after the calculation |
| Preload | Internal preload effect where the nut construction and catalogue method require it | Assuming preload affects accuracy but not life or heat |
Translate revolutions into a service target carefully
Travel represented by screw revolutions
D = L10 × lead
Use compatible units. If L10 is in revolutions and lead is in metres per revolution, D is total linear travel in metres. Hours require a representative speed and duty history; cycles require the total outbound and return travel per cycle. Dwell contributes calendar time and may affect lubrication or corrosion even though it adds no screw revolutions.
- D
- calculated total linear travel corresponding to L10
- L10
- basic rating life, rev
- lead
- linear travel per screw revolution
With the image's 64 million revolutions and an illustrative 10 mm/rev lead, the mathematical travel is 640 km. That conversion still inherits every L10 assumption and does not promise 640 km in a contaminated, misaligned or poorly lubricated machine.
| Question | Required evidence | Why it matters |
|---|---|---|
| How much production is required? | Cycles per shift, travel per cycle, operating days and product mix | Converts business demand into revolutions, distance and calendar exposure |
| What probability and consequence are acceptable? | Risk, downtime and redundancy review | L10 is a population statistic; critical applications may need a different reliability strategy |
| What ends useful life? | Accuracy, backlash, noise, torque, wear, corrosion and fatigue criteria | Performance may become unacceptable before visible flaking |
| How will condition be observed? | Inspection points, trend limits and measurement interval | Turns deterioration into planned action rather than surprise failure |
| How will lubrication be delivered? | Lubricant specification, amount, path, interval and access | Catalogue life commonly assumes effective lubrication |
| What will be retained? | Baseline data, calculations, supplier revisions and maintenance history | Allows assumptions to be compared with the real machine |
Verify independent mechanical and operating limits
Diagram description
Six panels surround a screw-driven linear axis. They identify screw critical speed, compression buckling, screw life, guide static and dynamic loading, peak motor torque and RMS motor thermal capacity, with empty requirement and capability fields marked not checked.
| Gate | Question to answer | Inputs that control it |
|---|---|---|
| Static screw capacity | Does the maximum credible axial load stay inside the catalogue static-selection rule? | Static rating, peak and shock load, preload, contact condition and required static factor |
| Buckling | Can the screw carry maximum compression without instability? | Unsupported length, root diameter, end restraint, alignment, compression direction and maker factor |
| Tensile/compressive strength | Is shaft stress acceptable even if Euler buckling is not governing? | Shaft section, material, threads or shoulders, load and catalogue limit |
| Critical speed | Is operating and overspeed sufficiently below the permitted rotational-speed limit? | Unsupported length, shaft diameter, support arrangement, straightness and chosen margin |
| Speed-related product limits | Do nut recirculation, DN value, seals and lubricant permit the motion? | Screw diameter, rpm, nut design, stroke, acceleration and temperature |
| Guide capacity and life | Do rail blocks carry all forces and moments in static and dynamic cases? | Fx, Fy, Fz, Mx, My, Mz, block spacing, preload and mounting accuracy |
| Bearings and coupling | Can supports and coupling carry thrust, speed, torque and residual misalignment? | Exact arrangement, fits, preload, thermal growth and simultaneous loads |
| Motor and drive | Do peak torque at speed and cycle-equivalent thermal demand pass? | Torque-speed envelope, overload duration, RMS method, supply, regeneration and ambient |
| Stops and safety | Can the machine reach a safe state for faults and foreseeable misuse? | Stopping distance, stored energy, brake or holding needs, guards and validated safety functions |
Protect the assumptions after the component is selected
Catalogue calculations commonly assume good lubrication and suitable mounting. Offset or angular error between screw supports and nut can concentrate contact load and sharply reduce life. Chips, abrasive dust, coolant, water or corrosive material can damage raceways or seals. Temperature changes lubricant consistency, internal clearance, preload and thermal growth. Small oscillating strokes may not spread an oil film over the raceway. These are design inputs, not maintenance details to decide after commissioning.
Turn catalogue assumptions into controlled evidence
- 1. Freeze the configuration.Record screw and nut code, preload or clearance class, lead, diameter, accuracy, support bearings, seals, lubricant, covers and mounting orientation.
- 2. Preserve every load case.Store the motion profile, direction, forces, travel weighting, factors, units and source revisions behind life, static, buckling and speed checks.
- 3. Define installation acceptance.Measure support and nut alignment, free or running torque, axial behavior and full-stroke condition using the supplier's procedure.
- 4. Commission progressively.Begin at reduced energy, then increase load, speed, acceleration and duty while recording torque or current, temperature, vibration, noise and positioning behavior.
- 5. Establish a warm baseline.Retain measurements after thermal stabilization so later inspections can detect drift, contamination, lubrication loss or joint movement.
- 6. Set service triggers.Define inspection and lubrication intervals plus action limits for backlash, torque, temperature, vibration, noise, seal damage and lubricant condition.
- 7. Recalculate after change.Payload, recipe, acceleration, software limits, mounting, lubricant, environment or replacement-part changes can invalidate the original evidence.
Why a single generic safety factor is not enough
Different checks address different physics and uncertainties. A static safety factor cannot be inserted into the life equation and assumed to cover buckling; a motor torque margin cannot protect against screw critical speed; extra dynamic capacity cannot repair poor lubrication. The relevant product standard, manufacturer method, load confidence and consequence of failure determine each margin.
Record factors next to the limit they modify and explain their basis. When uncertainty is large, improve the input with measurement, redesign for lower demand, choose a more capable component or consult the manufacturer rather than hiding uncertainty inside an undocumented multiplier.
Start with the traceable workflow in Sizing a Motor and Screw as One System. Use Supporting and Protecting a Long Screw for support and contamination context, Linear Guides and Their Load Ratings for force-and-moment verification, and How Assembly Errors Damage Motion Systems for installation evidence. Release the axis only when every applicable gate has an identified requirement, verified capability, margin basis and test record.
One-minute questions
Questions to answer before you apply this lesson
What should I select or check first for Lifetime and Safety Checks for a Motion Axis?
1. Freeze the configuration. Record screw and nut code, preload or clearance class, lead, diameter, accuracy, support bearings, seals, lubricant, covers and mounting orientation.
Which assumption can change the conclusion?
Load, motion profile, geometry, alignment, duty, lubrication and environment match the selected mechanism and ratings.
What can go wrong if I copy the example directly?
Never use the life equation as a buckling or overload check. A slender screw in compression can buckle or a raceway can be permanently indented long before a fatigue-life number appears concerning.
How do I verify the result in the real system?
7. Recalculate after change. Payload, recipe, acceleration, software limits, mounting, lubricant, environment or replacement-part changes can invalidate the original evidence.
Sources and further reading
- Studying the Service Life — Ball Screw Selection CriteriaTHK · 2026-10-12Primary manufacturer guidance reviewed for L10 definition, dynamic rating, cubic life relationship, modified life, fluctuating-load treatment and load-direction rules.
- Method for Mounting the Ball Screw Shaft — Selection CriteriaTHK · 2026-10-12Primary selection guidance reviewed for mounting-condition effects on permissible axial load, buckling and screw-shaft critical speed.
- Permissible Axial Load — Ball Screw Selection CriteriaTHK · 2026-10-12Primary manufacturer material reviewed for treating buckling and permissible tensile/compressive load as checks separate from fatigue life.
- Ball Screw Handling PrecautionsTHK · 2026-10-12Primary product guidance reviewed for misalignment, contamination protection, special environments, lubrication, short-stroke fretting and field-set maintenance intervals.
- Precision Rolled Ball Screws — Recommendations for SelectionSKF · 2026-10-12Primary manufacturer handbook reviewed independently for equivalent dynamic load, basic dynamic rating, nominal fatigue life and cases governed by static capacity rather than life.