BIZOMAT MAKEOS · Mechanics
Crane or Trolley Wheel on Rail (Contact Stress, Wheel Pressure, Travel Force)
Is this crane or trolley wheel big enough for its load on the rail, and what force and power does it take to roll the machine along?
Check of a steel wheel on a flat-headed rail: Hertz line-contact half-width, peak contact pressure and the depth of the largest shear stress for a cylinder on a flat (as the Hertz contact tool), the mean wheel pressure W ÷ (D b) against your limit, rolling resistance per wheel from the coefficient of rolling friction (as the rolling resistance tool), the total travel force and power for all wheels, and checks of contact pressure and wheel pressure.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Load on one wheel | kN | Largest load on one wheel (with the trolley at the end of its travel). |
| Number of wheels | Number of wheels carrying the machine. | |
| Wheel diameter | mm | Rolling diameter of the wheel. |
| Effective rail head width (contact length) | mm | Usable width of the rail head (flat contact length). |
| Wheel modulus | GPa | Elastic modulus of the wheel. |
| Wheel Poisson’s ratio | Poisson’s ratio of the wheel. | |
| Rail modulus | GPa | Elastic modulus of the rail. |
| Rail Poisson’s ratio | Poisson’s ratio of the rail. | |
| Largest contact pressure | MPa | Largest peak contact pressure for the wheel and rail hardness (your value). |
| Largest mean wheel pressure W ÷ (D b) | MPa | Largest mean pressure W ÷ (D b) for the wheel material and speed (your value from the crane standard). |
| Coefficient of rolling friction | mm | Coefficient of rolling friction (lever arm; about 0.5 mm steel on steel). |
| Travel speed | m/s | Travel speed. |
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: Load on one wheel
- What it is
- The largest load carried by one wheel, normally with the loaded trolley at the end of its travel nearest that wheel.
- 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.
- Get it right
- The load on one wheel, not the whole crane.
What this means: Number of wheels
- What it is
- The number of wheels carrying the crane or trolley, used for the total travel force.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 64. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Wheel diameter
- What it is
- The rolling diameter of the wheel tread on the rail.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 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
- A larger wheel lowers contact pressure, mean wheel pressure and rolling resistance.
What this means: Effective rail head width (contact length)
- What it is
- The width of rail head in flat contact with the wheel tread, excluding the rounded corners of the rail head.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 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.
What this means: Wheel modulus
- What it is
- Young’s modulus of the wheel material, from the material data.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 400 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 210 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter it in GPa, not MPa: 1 GPa = 1000 MPa, so divide a data-sheet value given in MPa by 1000.
What this means: Wheel Poisson’s ratio
- What it is
- Poisson’s ratio of the wheel material, from the material data, used for the combined contact modulus.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 0.5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Rail modulus
- What it is
- Young’s modulus of the rail material, from the material data.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 400 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 210 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Rail Poisson’s ratio
- What it is
- Poisson’s ratio of the rail material, from the material data, used for the combined contact modulus.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 0.5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Largest contact pressure
- What it is
- The largest peak Hertz contact pressure you accept for the wheel and rail hardness, from your design standard or material data.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 5000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Largest mean wheel pressure W ÷ (D b)
- What it is
- The largest mean wheel pressure, load ÷ (diameter × rail width), allowed by your crane standard for the wheel material and speed.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 50 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Coefficient of rolling friction
- What it is
- The coefficient of rolling friction expressed as a lever arm: how far ahead of the wheel centre the rail reaction acts.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 20 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Rolling resistance and travel power rise in direct proportion.
- Get it right
- A length in mm, not a dimensionless friction coefficient.
What this means: Travel speed
- What it is
- The travel speed of the crane or trolley along the rail, used for the travel power.
- Units and format
- Enter a number in m/s: metres per second. The form accepts 0.000001 m/s to 20 m/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 m/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Combined modulus 1 ÷ E* = (1 − ν₁²) ÷ E₁ + (1 − ν₂²) ÷ E₂; half-width b = √(4 W R ÷ π L E*); p₀ = 2W ÷ (π b L); largest shear about 0.30 p₀ at 0.786 b (as the Hertz contact tool).
- Mean wheel pressure = W ÷ (D b).
- Rolling resistance per wheel = W f ÷ r (as the rolling resistance tool); travel force = per wheel × wheels; power = force × speed.
- Example: 50 kN on a 400 mm wheel gives 428.53 MPa peak contact and 2.5 MPa mean; rolling the machine takes 500 N.
Limitations
- Line contact on a flat head; crowned wheels and rail wear change the contact.
- Travel force excludes wind, slope, flange friction and acceleration.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size crane or trolley wheels
- Check wheels for a heavier load
- Estimate travel resistance for a drive
Who it is for
- Crane engineers
- Design engineers
- Maintenance engineers
What you get
- Contact half-width, peak pressure and shear depth
- Mean wheel pressure
- Rolling resistance, travel force and power
Interpreting the result
- A larger wheel lowers both contact stress and rolling resistance.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2301–2309, 165–167. Topic reference; no source tables or recommended settings are reproduced.
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Open the Crane or Trolley Wheel on Rail (Contact Stress, Wheel Pressure, Travel Force) calculator