KEVOS® 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. |
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
