A friction gear transmits torque through contact between pressed-together wheels rather than meshing teeth. This calculator estimates a driven-wheel torque limit from normal force, contact friction and radius, then compares it with an entered load torque.
Friction Gear Interactive Calculator
Compare the estimated friction-force and torque limits with a steady load. Capacity/Demand and Torque Difference describe that comparison; they do not certify a drive or predict how it behaves while slipping.
Equation Used
The estimated force limit is mu times F_N, and its driven-wheel torque is that force times R. A load above the threshold cannot be transmitted without exceeding the model limit. Sliding torque, acceleration and heat require additional information.
- Static rolling contact with no slip below torque capacity
- Driven wheel radius is measured at the contact patch
- Coefficient of friction is the available traction coefficient
- Load torque is compared directly to available friction torque
Normal load and tangential force
The loading mechanism presses the wheels together along the contact normal. A separate tangential contact force transmits torque as the driver turns against the driven load. In the simplified static-friction model, this force can rise with demand up to μF_N; it is not always equal to that maximum.
The driven wheel's moment arm is its contact radius. Shafts and bearings react to both normal and tangential contact forces, with individual bearing loads depending on support spacing and wheel position. The contact preload is not automatically the load on every bearing.
For ideal external rolling contact, the wheels turn in opposite directions and their angular-speed magnitudes obey ω₂/ω₁ = r₁/r₂. The numerical outputs concern torque and force rather than speed. The animation uses an illustrative 50 mm driver and the entered driven radius, keeping their rims in contact and their sizes in proportion. Within the estimated static threshold, their surface speeds match. Above it, the driven wheel turns more slowly than ideal rolling to illustrate relative motion; that rate is prescribed, not calculated from the load. The spring and arrow indicate normal loading without calculating spring compression. The colored contact marker compares demand with capacity; it does not show temperature.
Friction wheels and traction drives
Rolling-contact transmission can be used where tooth engagement is undesirable. More elaborate traction drives use several rollers, tailored loading systems and sometimes specialized fluids. Those designs require their own contact and performance data; their ratings cannot be inferred from a simple pair of dry friction wheels.
A variable ratio needs a geometry that changes the effective contact radii, such as a suitable disc or cone arrangement. Merely changing preload on two fixed-radius wheels changes this model's torque threshold, not their ideal speed ratio.
Torque limit and load comparison
Force Limit = μF_N. Torque Capacity = μF_N R, with R converted from millimeters to meters to obtain N·m. Capacity/Demand divides the capacity by the entered load torque. Torque Difference subtracts the load torque from capacity.
A ratio of 1 means the ideal threshold equals demand. Above 1 there is a positive modeled difference; below 1 there is a shortfall. These quantities are not an independently selected design factor or a guarantee of harmless slipping. The model omits shock, acceleration, changing traction, creep, contact pressure and thermal limits.
The coefficient must represent the actual contact conditions. Surface material alone does not supply a universal coefficient. Likewise, an entered normal force needs a real loading system capable of maintaining it. The calculator cannot derive allowable preload, service life or operating temperature.
Example: comparing capacity with demand
At the defaults, μ = 0.60, F_N = 250 N and R = 50 mm. The force limit is 150 N and the torque capacity is 150 × 0.050 = 7.5 N·m. Against a 5 N·m demand, Capacity/Demand is 1.5 and Torque Difference is 2.5 N·m.
As a separate hypothetical comparison, μ = 0.40, R = 40 mm and F_N = 375 N give a 6 N·m capacity. For 4 N·m demand the ratio is again 1.5. At 250 N normal force, capacity is 4 N·m; at 600 N it is 9.6 N·m. These changes do not establish wear rates or a recommended setting for a pottery wheel.
Across the input range, force limits span 1–1,200 N and capacities span 0.01–240 N·m. Combining these with loads of 0.1–50 N·m gives ratios from 0.0002 to 2,400. The two-decimal ratio readout can round a very small positive ratio to zero; it remains a shortfall, not a zero-force calculation.
Contact drive tradeoffs
A friction wheel has no clearance between meshing teeth, but contact deformation, creep and slip can still affect position and speed. A toothed gear relies on geometric engagement; a belt drive has its own tension, bending and contact limits. Noise, efficiency, service life and usable power depend on the specific design.
Slip dissipates energy and can damage the contacting surfaces. Treat overload protection as a separate engineered function, not an automatic benefit of any friction drive. Lubrication and adjustment must follow the actual drive's design; a traction-fluid drive and a dry friction wheel are not interchangeable.
Frequently asked questions
Is Force Limit the actual force at all times?
No. It is μF_N, the modeled maximum. Actual tangential force depends on transmitted torque and operating conditions.
What does Capacity/Demand 1.5 mean?
Calculated torque capacity is 1.5 times the entered steady load. The calculator has not established that 1.5 is an appropriate design target.
Why does a larger driven radius increase capacity?
The same tangential contact force acts through a longer moment arm. The calculator uses radius, not diameter.
Does increasing preload change wheel speed?
Not for ideal rolling between fixed-radius wheels. It changes the force threshold here; speeds are not calculated.
Does the red animation calculate slip speed or heat?
No. The contact marker identifies demand above capacity. The slower driven-wheel motion illustrates relative sliding without calculating its rate or temperature.
Will the drive protect itself by slipping?
That is not guaranteed. Slip can generate heat and damage surfaces or connected equipment.
Can I choose bearings using only the entered normal force?
No. Include tangential force, other shaft loads, support geometry and the bearing manufacturer’s rating method.
Can the tool prescribe a repair for chatter or lost torque?
No. It has no thermal, vibration or component-condition model. Diagnosis needs the actual equipment and operating information.
Contact-force and rolling references
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