BIZOMAT MAKEOS · Power Transmission
Linear Guide Selection (Carriage Loads, Life and Static Safety)
What load does the most heavily loaded carriage of this linear guide carry, including the offset and acceleration, and how long will the guide last?
Selection check of a profile-rail linear guide with four carriages on two rails: the static load on each carriage from a load offset along and across the rails, the extra load on the leading and trailing carriages from acceleration at the load’s height, the cubic mean load over constant-speed and accelerating travel, nominal life in kilometres on the 50 km basis with a load factor, life in hours from stroke and cycle rate, and the static safety factor.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Moving mass | kg | Mass carried by the four carriages. |
| Carriage spacing along the rail | mm | Distance between the two carriages on each rail. |
| Rail spacing | mm | Distance between the two rails. |
| Load offset along the rail | mm | Distance of the load’s centre of mass from the carriage pattern centre, along the rails. |
| Load offset across the rails | mm | Distance of the load’s centre of mass from the centre, across the rails. |
| Height of the load centre above the carriages | mm | Height of the load’s centre of mass above the carriage mounting faces. |
| Acceleration | m/s² | Acceleration and deceleration of the axis. |
| Share of travel spent accelerating | % | Share of each stroke spent accelerating or decelerating. |
| Dynamic load rating per carriage | kN | Dynamic load rating of one carriage on the 50 km basis (from the maker). |
| Static load rating per carriage | kN | Static load rating of one carriage (from the maker). |
| Load factor (shock and vibration) | Load factor for shock and vibration (about 1.0–1.5 smooth, 1.5–2 with shock). | |
| Stroke | mm | Length of the stroke. |
| Cycles per minute (out and back) | Number of out-and-back cycles per minute. | |
| Life required | h | Life the machine needs. |
| Least static safety factor | Least static safety factor you require. |
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: Moving mass
- What it is
- The total mass moving on the four carriages: table, fixtures, workpiece and anything else carried.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0.000001 kg to 100000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- All carriage loads rise in proportion, so life falls with the cube of the mass.
What this means: Carriage spacing along the rail
- What it is
- The centre-to-centre distance between the two carriages on the same rail.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Wider carriage spacing reduces the extra load from offsets along the rail and from acceleration.
What this means: Rail spacing
- What it is
- The centre-to-centre distance between the two parallel rails.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 400 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Wider rail spacing reduces the extra load from offsets across the rails.
What this means: Load offset along the rail
- What it is
- How far the load’s centre of mass sits from the centre of the carriage pattern, measured along the rails.
- Units and format
- Enter a number in mm: millimetres. The form accepts -5000 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The sign does not matter; the tool uses the size of the offset and checks the worst carriage.
What this means: Load offset across the rails
- What it is
- How far the load’s centre of mass sits from the centre of the carriage pattern, measured across the rails.
- Units and format
- Enter a number in mm: millimetres. The form accepts -5000 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The sign does not matter; the tool uses the size of the offset.
What this means: Height of the load centre above the carriages
- What it is
- The height of the moving load’s centre of mass above the carriage mounting faces. Acceleration acting at this height tips load onto the leading or trailing carriages.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The extra carriage load during acceleration rises in proportion to height.
What this means: Acceleration
- What it is
- The rate at which the axis speeds up and slows down, from the motion profile.
- Units and format
- Enter a number in m/s²: metres per second squared. The form accepts 0 m/s² to 100 m/s². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 m/s² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The extra carriage load while accelerating rises in proportion.
- Get it right
- m/s², not a multiple of g (1 g = 9.80665 m/s²).
What this means: Share of travel spent accelerating
- What it is
- The share of each stroke spent accelerating or decelerating, used to weight the higher accelerating load in the mean load.
- 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.
- Get it right
- Type a percentage (20 for 20 %), not a fraction.
What this means: Dynamic load rating per carriage
- What it is
- The dynamic load rating of one carriage, from the guide maker’s catalogue, stated on the 50 km rated life basis.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 10000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 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 rating.
- Get it right
- If the maker quotes a 100 km basis, multiply that rating by the cube root of 2 to get the 50 km value.
What this means: Static load rating per carriage
- What it is
- The static load rating of one carriage, from the guide maker’s catalogue. The most loaded carriage while accelerating is compared with it.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 10000 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
- Enter it in kN, not N: divide a catalogue value given in newtons by 1000.
What this means: Load factor (shock and vibration)
- What it is
- A multiplier on the carriage load for shock and vibration in service, from the guide maker’s catalogue.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 3.5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 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: Stroke
- What it is
- The length of travel in one direction for each move.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 500 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Life in hours falls in proportion to stroke, since each cycle covers more distance.
What this means: Cycles per minute (out and back)
- What it is
- The number of complete out-and-back moves the axis makes each minute while running.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 to 1000. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Life in hours falls in proportion.
- Get it right
- One cycle is out and back, two strokes.
What this means: Life required
- What it is
- The running hours the guide must last, from the machine’s design life or service interval.
- Units and format
- Enter a number in h: hours. The form accepts 0.000001 h to 1000000 h. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20000 h as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Least static safety factor
- What it is
- The smallest ratio of static rating to the highest carriage load you require, from the guide maker’s guidance or your practice.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 20. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Carriage at (±L₀/2, ±W₀/2): P = W ÷ 4 ± W x ÷ (2L₀) ± W y ÷ (2W₀) for weight W = m g.
- Acceleration adds ± m a h ÷ (2L₀) to the leading and trailing carriages.
- Mean load P_m = ³√(s P_acc³ + (1 − s) P_run³) for the most loaded carriage, s = share accelerating.
- Life L = 50 km × [C ÷ (f_w P_m)]³; hours = L ÷ (2 × stroke × cycles per minute × 60); static factor = C₀ ÷ P_acc.
- Example: the worst carriage carries 388.18 N running and 471.51 N accelerating; life is about 45,549 h.
Limitations
- Rigid table and equal carriage stiffness; real load sharing depends on mounting accuracy.
- Lift-off and side loads on the carriages are not included.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Choose a linear guide size for a gantry or slide
- Check life when the load is off-centre
- See how acceleration loads the carriages
Who it is for
- Machine designers
- Automation engineers
- Design engineers
What you get
- Load on each carriage at constant speed
- Peak load during acceleration and the mean load
- Life in km and hours, static safety factor
Interpreting the result
- Centring the load and spreading the carriages cut the worst carriage load the most.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2365–2416. Topic reference; no source tables or recommended settings are reproduced.
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Open the Linear Guide Selection (Carriage Loads, Life and Static Safety) calculator