BIZOMAT MAKEOS · Power Transmission
Friction Wheel Drive Check (Tangential Force, Normal Force Needed, Contact Stress, Speed Ratio)
For a friction wheel (traction) drive between two rollers, how hard must they be pressed together to carry the power without slipping, and is the contact stress within limits?
Check of a friction (traction) drive of two cylinders pressed together: the input torque and the tangential force at the driver, the normal force needed to carry it without slip from the friction coefficient and a slip factor, the contact half-width and peak contact pressure of the two cylinders (as the Hertz contact stress tool for line contact), the output speed and the load on the shaft bearings, against the allowable contact pressure.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Power | kW | Power transmitted. |
| Driver speed | rpm | Speed of the driving roller. |
| Driver roller radius | mm | Radius of the driving roller. |
| Driven roller radius | mm | Radius of the driven roller. |
| Friction coefficient at the contact | Friction coefficient between the rollers (dry steel on steel about 0.15; traction fluids less). | |
| Slip safety factor | Factor on the normal force against slip. | |
| Contact | ||
| Contact width | mm | Width of the contact along the roller axes. |
| Modulus of the driver | GPa | Elastic modulus of the driver. |
| Poisson’s ratio of the driver | Poisson’s ratio of the driver. | |
| Modulus of the driven roller | GPa | Elastic modulus of the driven roller. |
| Poisson’s ratio of the driven roller | Poisson’s ratio of the driven roller. | |
| Allowable contact pressure | MPa | Allowable peak contact pressure for the roller materials and life. |
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: Power
- What it is
- The mechanical power the friction drive must transmit from the driving roller to the driven roller.
- Units and format
- Enter a number in kW: kilowatts. The form accepts 0.000001 kW to 10000 kW. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 kW as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The tangential force, normal force needed and contact pressure rise with it.
- Get it right
- Enter kilowatts; use the power the driven machine needs, not just the motor nameplate rating.
What this means: Driver speed
- What it is
- The rotational speed of the driving roller, used with the power to find the input torque.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A faster driver needs less torque and less normal force for the same power.
- Get it right
- Use the speed of the driving roller itself, after any gearbox or belt between it and the motor.
What this means: Driver roller radius
- What it is
- The radius of the driving roller at the contact, from its axis to the rolling surface.
- 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 50 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 driver radius lowers the tangential and normal forces and raises the output speed.
- Get it right
- Enter the radius, which is half the measured diameter.
What this means: Driven roller radius
- What it is
- The radius of the driven roller at the contact, from its axis to the rolling surface.
- 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 100 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 driven radius lowers the output speed and raises the output torque.
- Get it right
- Enter the radius, which is half the measured diameter.
What this means: Friction coefficient at the contact
- What it is
- The friction or traction coefficient between the two rolling surfaces, which limits how much tangential force the contact can pass before slipping.
- Units and format
- Enter a plain number with no unit. The form accepts 0.01 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.15 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A lower coefficient needs a higher normal force, which raises the contact pressure and bearing load.
- Get it right
- Use a value for the actual materials, surface condition and any lubricant or traction fluid, from supplier data or a test.
What this means: Slip safety factor
- What it is
- A margin on the normal force against slip, multiplying the force that would just carry the tangential load at the friction coefficient.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 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
- The normal force rises in proportion to it.
- Get it right
- It multiplies the normal force, so it also raises the contact pressure and the bearing loads.
Contact
What this means: Contact width
- What it is
- The length of the line of contact between the two rollers, measured along their axes: the narrower of the two roller faces.
- 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 20 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A wider contact lowers the peak contact pressure, roughly with the square root of the width.
- Get it right
- Use the face width that actually touches, allowing for edge chamfers or crowning.
What this means: Modulus of the driver
- What it is
- The elastic (Young’s) modulus of the driving roller’s rim material at the contact.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1000 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.
- Effect on the result
- A stiffer material raises the peak contact pressure.
- Get it right
- Enter it in GPa, not MPa; take it from the material supplier’s data sheet, especially for polymer or rubber rims.
What this means: Poisson’s ratio of the driver
- What it is
- Poisson’s ratio of the driving roller’s rim material: the sideways contraction relative to the stretch under load.
- Units and format
- Enter a plain number with no unit. The form accepts 0 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.
- Get it right
- Take it from the material data sheet; it is a ratio, not a percentage.
What this means: Modulus of the driven roller
- What it is
- The elastic (Young’s) modulus of the driven roller’s rim material at the contact.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1000 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.
- Effect on the result
- A stiffer material raises the peak contact pressure.
- Get it right
- Enter it in GPa, not MPa; take it from the material supplier’s data sheet.
What this means: Poisson’s ratio of the driven roller
- What it is
- Poisson’s ratio of the driven roller’s rim material: the sideways contraction relative to the stretch under load.
- Units and format
- Enter a plain number with no unit. The form accepts 0 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.
- Get it right
- Take it from the material data sheet; it is a ratio, not a percentage.
What this means: Allowable contact pressure
- What it is
- The highest peak contact (Hertz) pressure the roller materials can carry for the required life, checked against the calculated peak pressure.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 600 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the pass or fail line; the calculated contact pressure does not change.
- Get it right
- Take it from the roller material supplier or a contact fatigue standard for your life requirement.
Method and formulas
- Driver torque = 9549 P ÷ n; tangential force = torque ÷ R₁.
- Normal force = SF × tangential force ÷ μ.
- Line contact of two cylinders: half-width b = √(4 F R ÷ (π L E*)), peak pressure 2F ÷ (π b L) (as the Hertz contact stress tool); output speed = n₁ R₁ ÷ R₂.
- Example: 318.31 N tangential needs 3,183.1 N pressing force; contact pressure 418.76 MPa.
Limitations
- Rigid rollers with a uniform line contact; misalignment concentrates the load at one end.
- Creep of about 1–2% lowers the output speed slightly.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a friction wheel drive for a feeder or turntable
- Check rollers on a friction-driven conveyor
- Find the spring force for a roller drive
Who it is for
- Machine designers
- Design engineers
- Automation engineers
What you get
- Torque and tangential force
- Normal force needed and contact stress
- Output speed and bearing load
Interpreting the result
- Friction drives need a pressing force many times the transmitted force, which loads the bearings heavily.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2301–2309, 165–168. Topic reference; no source tables or recommended settings are reproduced.
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