A toroidal traction variator places tiltable power rollers between opposed input and output discs. Tilting changes the two contact-circle radii and therefore the ideal rolling speed ratio.
Toroidal CVT Interactive Calculator
Enter relative input- and output-disc contact radii. Results are ideal no-slip and lossless comparison quantities, not a transmission design or rating.
Equation Used
- Entered radii are positive relative contact-circle radii measured from the common disc axis.
- Ideal rolling is imposed at both roller contacts with no creep, spin or gross slip.
- The displayed torque multiplier is a magnitude ratio under ideal lossless power conservation.
- The signed radius-asymmetry index is arithmetic and is not a control signal or efficiency measure.
- Geometry closure, roller tilt, contact ellipse, normal force, traction coefficient, lubricant behavior, stress, temperature, efficiency, capacity, dynamics and safety are omitted.
Opposed Discs and Tiltable Power Rollers
Toroidal CVT patents describe input and output discs arranged face to face with power rollers between their toroidal working surfaces. Tilting a roller increases one disc contact-circle radius while decreasing the other, continuously varying the rotational-speed ratio.
The two discs rotate in opposite directions in the basic variator arrangement. The calculator reports speed and torque magnitudes and does not model a reversing or combining gear train.
What This Calculator Does
The tool evaluates the ideal input-speed/output-speed ratio from entered contact radii, its reciprocal output-speed/input-speed magnitude, the corresponding ideal lossless torque magnitude ratio and a signed normalized radius-asymmetry index.
It does not infer roller tilt, package geometry, trunnion control, traction capacity, efficiency or durability.
Ideal Rolling Radius Ratios
|omegaout/omegain| = rin/rout
|Tout/Tin|ideal = rout/rin
B = 100(rout-rin)/(rout+rin)
The torque relation additionally assumes equal input and output power. Real variators have traction, spin, creep and other losses.
Worked Ideal Example
For entered input radius 1.0 and output radius 1.0, both speed-ratio magnitudes and the ideal torque magnitude ratio are 1.00, and the asymmetry index is 0.0%. For 0.5 input and 1.5 output, input/output speed ratio is 3.00, output/input speed magnitude is 0.33, ideal torque magnitude ratio is 3.00 and the index is +50.0%.
Model Boundary
- Mechanical arrangement: opposed input/output toroidal discs, intervening power rollers and ratio change through roller tilt and changed contact radii.
- Calculated: ideal radius ratios, reciprocal speed magnitude, lossless torque magnitude and a normalized arithmetic index.
- Not calculated: actual torus and roller geometry, tilt angle, contact ellipse, spin, creep, slip, traction coefficient, fluid rheology, clamping force, loading cam, trunnion control, torque capacity, Hertz stress, fatigue, heat, efficiency, bearing and seal losses, ratio limits, dynamics, noise, life, ratings, integration or safe use.
Frequently Asked Questions
Why are there two speed-ratio outputs?
One is input speed divided by output speed; the other is its reciprocal magnitude. Ratio conventions must always be stated.
Do the input and output discs rotate in the same direction?
No. The basic opposed-disc variator reverses direction; the calculator displays magnitudes.
Is the torque multiplier a measured result?
No. It follows only from ideal lossless power conservation.
Does radius asymmetry equal roller tilt?
No. Geometry is required to relate contact radii to a specific tilt angle.
Does no-slip mean a real traction contact has zero creep or spin?
No. Those real contact effects are omitted.
Can this size or rate a toroidal CVT?
No. Use validated manufacturer or engineering analysis for the complete system.
References
- NASA Technical Note, Fatigue Life Analysis for Traction Drives with Application to a Toroidal Type Geometry: input/output traction discs, intermediate rollers, preload and tilt-dependent drive ratio.
- EP 0 930 448 B1, Toroidal type continuously variable transmission: opposed discs, tiltable power rollers and explicit output-speed relation r_in/r_out.
- WO 2013/104731, Continuously variable toroidal transmission: contact-radius definition, opposite disc directions and variator ratio convention.
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