A ball differential transfers drive from a ball carrier to two output rings while allowing the outputs to rotate at different speeds. Axial preload maintains traction at the ball-ring contacts. Follow the carrier and ring motion, then compare an ideal combined input-torque capacity with a selected torque demand. The estimate does not predict vehicle handling or the speed of a slipping differential.
Ball Differential Interactive Calculator
Compare ideal traction capacity for a driven ball carrier between two output rings. The animation distinguishes carrier rotation from the two output speeds.
Equation Used
The model adds equal traction limits from two interfaces at the same track radius to estimate combined input capacity. A positive margin places the entered input torque below this ideal estimate; it is not a measured slip threshold or a guarantee of operation.
- Constant effective traction-coefficient approximation; lubricant behavior is not calculated.
- Clamp force is total axial preload through the diff stack.
- Two effective friction interfaces act at the same ball track radius.
- Friction coefficient is constant; wear, heat, and surface damage are not modeled.
The gear drives the ball carrier; each ring connects to an output. The 2μFr estimate is combined input capacity for equal traction on both faces. Above that estimate the no-slip motion is only a reference, not a predicted slipping speed.
Rolling between two output rings
The gear or pulley drives the carrier that locates the balls. Each opposing ring connects to one output. An axial clamping arrangement presses the rings against the balls so that tangential contact forces can transmit torque.
When the two output rings turn at the same speed, the assembly moves without differential motion between them. When their speeds differ, the balls can roll between the rings. Differential action does not inherently require gross sliding across the ring faces.
For the symmetric ideal rolling geometry shown, carrier speed equals the average of the two output speeds: ωc = (ω1 + ω2)/2. For example, outputs at 800 and 1200 rpm have a 1000 rpm average. Their actual speeds depend on the connected system; the animation illustrates the relationship rather than calculating wheel traction.
Parts and load paths
- Carrier: receives input rotation and positions the balls.
- Two drive rings: connect to separate output members.
- Balls: carry normal contact load and transmit tangential traction.
- Spring, adjuster and thrust bearing: provide preload while accommodating the required relative rotation.
Above the available traction, contacts can slip. The calculator does not model the resulting heat, damage, friction changes or output speed. A ball differential should not be treated as a separate slipper clutch simply because excessive torque can make it slip.
Application and adjustment
Radio-controlled vehicle ball differentials are a documented application. Team Associated’s RC10B6.2 manual, for example, shows a differential gear, balls, drive rings, outdrives and an adjustable thrust assembly. Use the specific vehicle manual for compatible parts, lubrication and adjustment.
The educational model explains how one input can serve two outputs through rolling contacts. It does not establish that every touring car uses a ball differential, that one material pairing is universally required, or that a particular preload gives the fastest lap time.
Torque capacity, differential resistance and wheel traction are related but different questions. This calculator addresses only a simple contact-traction capacity estimate and equal sharing of axial preload.
Total preload, two traction interfaces
Let F be total axial preload in newtons, μ the selected effective traction coefficient and r the ball-track radius in millimetres. Under equal traction on both faces, combined input capacity Tcap = 2μFr, in N·mm. This is the quantity labeled Slip Torque.
Each ring’s ideal traction contribution is μFr. The factor two adds the two output-side contributions to the input capacity. It does not mean that either single output can deliver the full 2μFr.
With n equally loaded balls, the normal load per ball at each face is F/n. Summing μ(F/n)r across n balls gives μFr for one face: the ball count cancels. Multiplying μFr by n again would count the total preload repeatedly.
Torque Margin = Tcap − Tdrive. Capacity Used = 100Tdrive/Tcap for positive capacity. At zero capacity the implementation displays zero percent; this undefined ratio must not be read as spare capacity. The torque margin still shows a deficit for positive demand.
The coefficient is a chosen constant, not a prediction of lubricated contact behavior. The formula excludes unequal load sharing, contact stresses, thrust-bearing drag, changing temperature, wear and losses. Divide N·mm by 1000 to obtain N·m.
Worked example: avoid counting preload twice
Use hypothetical values F = 50 N, μ = 0.05, r = 10.5 mm and n = 12 balls. The equal-share load is 50/12 = 4.167 N per ball at each face. Combined input capacity is 2 × 0.05 × 50 × 10.5 = 52.5 N·mm, or 0.0525 N·m.
With input torque demand 40 N·mm, Capacity Used is 76.19% and Torque Margin is 12.5 N·mm. Increasing demand to 60 N·mm gives 114.29% and a −7.5 N·mm margin. The latter exceeds the ideal estimate; the motion shown is then only a rolling reference.
At 20 N preload the same model gives 21 N·mm combined capacity; at 80 N it gives 84 N·mm. These values vary linearly with preload. They do not identify a vehicle setup as too loose, locked or suitable for a racing class.
Changing from 12 to 10 balls at the same total preload changes equal-share load from 4.167 to 5 N per ball, while calculated total capacity remains 52.5 N·mm. Actual contact stress and durability would need separate analysis.
Ball differential, gear differential and spool
| Arrangement | How it permits output motion | Practical distinction |
|---|---|---|
| Ball differential | Balls roll between clamped output rings. | Depends on contact traction, condition and the specified preload arrangement. |
| Gear differential | Meshing gears allow output speed differences. | Gear geometry and any fluid or friction elements determine its behavior. |
| Spool | Outputs are mechanically coupled at one speed. | No differential action; tire and driveline behavior must accommodate turning. |
Weights, cost, service intervals and appropriate driving conditions depend on the actual product. The ball-differential capacity estimate does not rank these arrangements for a particular vehicle.
Ball-differential questions
No. In the ideal symmetric arrangement, rolling between the two rings permits different output speeds while their mean follows the carrier.
Total clamp force is held fixed. More balls share that preload, so individual normal loads decrease. In this simplified sum the count cancels; real contact stress and load sharing still matter.
The displayed 2μFr is combined input capacity for equal traction on both faces. Each output-side contribution in that ideal model is μFr.
Only with the actual spring, thread, stack geometry and loading behavior. This page does not specify force per turn or a universal adjustment.
Not in the ideal rolling equations. Increased preload raises the selected traction estimate, while real drag and handling can also change. A mechanically locked spool is a different arrangement.
Use a combination approved for the specific differential. Different hardness scales cannot be compared by simply dividing their numerical readings, and a blanket compatibility rule is inappropriate.
Contact damage, preload, lubrication, adjustment and other conditions can matter. This static estimate does not diagnose them. Inspect and service according to the manufacturer’s instructions.
Manufacturer references
- Team Associated RC10B6.2 instruction manual: a specific ball-differential assembly and its service instructions.
- Team Associated caged thrust-bearing differential kit: the distinct thrust-bearing assembly in a ball differential.
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