BIZOMAT MAKEOS · Power Transmission
Ball Screw Life over a Duty Cycle (Mean Load, Mean Speed, Life)
Over my machine’s duty cycle of different loads and speeds, what mean load and speed does the ball screw see, and how long will it last?
Life of a ball screw working through a duty cycle of up to four load–speed steps: the time-weighted mean speed and the cubic mean load (as the bearing duty cycle tool, ball exponent), the rated life in revolutions and hours at that mean load with the load factor, and the travel in kilometres (as the ball screw life tool), against the life you need.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Dynamic load rating Ca | kN | Dynamic load rating of the ball screw nut from the maker. |
| Load factor fw | Load factor for shock and vibration (1.0–1.2 smooth, up to 2 or more with shock). | |
| Lead | mm | Lead of the screw. |
| Required life | h | Life the screw must reach. |
| Step 1 | ||
| Axial load | kN | Axial load in step 1 (including preload effect). |
| Speed | rpm | Screw speed in step 1. |
| Share of time | % | Share of operating time in step 1. |
| Step 2 | ||
| Axial load | kN | Axial load in step 2. |
| Speed | rpm | Speed in step 2. |
| Share of time | % | Share of time in step 2. |
| Step 3 | ||
| Axial load | kN | Axial load in step 3. |
| Speed | rpm | Speed in step 3. |
| Share of time | % | Share of time in step 3. |
| Step 4 | ||
| Axial load | kN | Axial load in step 4 (0 if unused). |
| Speed | rpm | Speed in step 4. |
| Share of time | % | Share of time in step 4. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Dynamic load rating Ca
- What it is
- The basic dynamic load rating of the ball screw nut from the maker’s catalogue: the axial load for a rated life of one million revolutions.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 100000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Life rises with the cube of the load rating.
- Get it right
- Enter kN; catalogues sometimes give the rating in N, so divide by 1000.
What this means: Load factor fw
- What it is
- A multiplier on the mean load for shock and vibration in service, from the ball screw maker’s guidance.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 3. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Life falls with the cube of the load factor.
What this means: Lead
- What it is
- The axial travel of the nut for each revolution of the screw, used to convert life in revolutions into travel distance.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Only the travel result uses it; the life in hours comes from the speeds and loads.
What this means: Required life
- What it is
- The operating life in hours the ball screw must reach, from the machine’s design life.
- Units and format
- Enter a number in h: hours. The form accepts 0 h to 10000000 h. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8000 h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Step 1
What this means: Axial load
- What it is
- The axial load on the screw during this step of the duty cycle, including the effect of preload where the maker says to add it.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0 kN to 100000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use kN, the same unit as the dynamic load rating Ca.
What this means: Speed
- What it is
- The screw speed during this step of the duty cycle; a step with zero speed or zero time is left out.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0 rpm to 1000000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1500 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Share of time
- What it is
- The share of total operating time spent in this step; shares that do not add up to 100 are normalised and flagged.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Step 2
What this means: Axial load
- What it is
- The axial load on the screw during this step of the duty cycle, including the effect of preload where the maker says to add it.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0 kN to 100000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use kN, the same unit as the dynamic load rating Ca.
What this means: Speed
- What it is
- The screw speed during this step of the duty cycle; a step with zero speed or zero time is left out.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0 rpm to 1000000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 750 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Share of time
- What it is
- The share of total operating time spent in this step; shares that do not add up to 100 are normalised and flagged.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Step 3
What this means: Axial load
- What it is
- The axial load on the screw during this step of the duty cycle, including the effect of preload where the maker says to add it.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0 kN to 100000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use kN, the same unit as the dynamic load rating Ca.
What this means: Speed
- What it is
- The screw speed during this step of the duty cycle; a step with zero speed or zero time is left out.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0 rpm to 1000000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3000 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Share of time
- What it is
- The share of total operating time spent in this step; shares that do not add up to 100 are normalised and flagged.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Step 4
What this means: Axial load
- What it is
- The axial load on the screw during this step of the duty cycle, including the effect of preload where the maker says to add it.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0 kN to 100000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Leave the speed or time of this step at 0 if the duty cycle has only three steps.
What this means: Speed
- What it is
- The screw speed during this step of the duty cycle; a step with zero speed or zero time is left out.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0 rpm to 1000000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Share of time
- What it is
- The share of total operating time spent in this step; shares that do not add up to 100 are normalised and flagged.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Mean speed n_m = Σ nᵢ tᵢ ÷ Σ tᵢ; mean load F_m = [Σ Fᵢ³ nᵢ tᵢ ÷ Σ nᵢ tᵢ]^(1/3) (as the bearing duty cycle tool with exponent 3).
- Life L = (C_a ÷ f_w F_m)³ × 10⁶ revolutions; hours = L ÷ (60 n_m); travel = L × lead (as the ball screw life tool).
- Example: the screw runs at a mean 1,800 rpm and 4.1857 kN, giving 9,133.6 h (9,864.3 km of travel).
Limitations
- Basic rating life at 90% reliability; poor lubrication or contamination shortens it.
- Preload must be included in the step loads.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a ball screw for a machine’s real duty cycle
- Compare screws for a new axis
- Estimate replacement intervals
Who it is for
- Design engineers
- Machine builders
- Maintenance engineers
What you get
- Mean speed and cubic mean load
- Life in revolutions, hours and travel
- Check against the required life
Interpreting the result
- Life varies with the cube of load: a step with double the load uses up life eight times as fast.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2400–2420, 2561–2568. Topic reference; no source tables or recommended settings are reproduced.
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Open the Ball Screw Life over a Duty Cycle (Mean Load, Mean Speed, Life) calculator