A Toroidal CVT is a continuously variable transmission that transmits torque between two opposed toroidally-shaped discs through tilting power rollers riding in the cavity between them. The rollers transfer torque via shear in a thin film of traction fluid — there is no gear mesh and no belt. Tilting the rollers changes the contact radii on the input and output discs, smoothly varying the ratio without steps. You get stepless ratio change at high torque density, used in cars like the Nissan Cedric/Gloria Extroid and in aerospace constant-speed drives.
Toroidal CVT Interactive Calculator
Vary the normalized input and output contact radii to see the stepless ratio, speed change, torque multiplication, and roller tilt bias.
Equation Used
The toroidal CVT ratio is set by the output contact radius divided by the input contact radius. At r1 = r2 the variator is at 1:1; increasing r2 relative to r1 increases torque multiplication and reduces output speed.
- Contact radii are normalized to the neutral 1:1 position.
- Ideal traction drive with no slip or spin losses.
- Speed ratio is based on equal rolling surface speed at the contacts.
Operating Principle of the Toroidal CVT
The mechanism lives or dies on a single contact: a hardened steel power roller pressed between two concave discs whose facing surfaces form a torus. The input disc spins, the output disc spins, and the rollers in the cavity transmit torque from one to the other. Critically, the rollers do not contact the discs metal-to-metal. A film of specialised traction fluid roughly 0.1 to 0.5 µm thick sits in the contact patch and goes briefly glassy under the enormous Hertzian pressure — typically 3 to 4 GPa. That elastohydrodynamic lubrication (EHL) film is what actually carries the shear load. Get the fluid wrong and the rollers slip; get the clamp force wrong and you either burn the fluid or tear up the discs.
Ratio change happens by tilting each power roller around an axis perpendicular to its spin axis. Tilt the roller one way and it contacts the input disc near the rim and the output disc near the centre — a high reduction. Tilt it the other way and you flip the contact radii, giving overdrive. Because the contact moves smoothly across the toroidal surface, the ratio sweep is genuinely stepless. Half-toroidal designs (Nissan Extroid, NSK) use shallow cavities and lower spin losses; full-toroidal designs (Torotrak) use deeper cavities and accept higher spin losses in exchange for better torque-handling geometry.
What goes wrong? Three things, mostly. If the clamp-force loading cam is sized wrong, contact pressure drops below the fluid's traction limit and the rollers slip — you'll see a sudden RPM flare with no acceleration. If the traction fluid degrades or gets contaminated with regular engine oil, the coefficient of traction drops from around 0.09 down to 0.04, and the variator can't transmit rated torque. And if a roller bearing develops play above about 20 µm, the roller skews under load, the contact ellipse migrates off-centre, and you get accelerated micropitting along one edge of the toroidal surface.
Key Components
- Input Disc: The driving disc, machined with a concave toroidal surface to a profile tolerance typically held within ±5 µm. Surface hardness runs 60-62 HRC and the working face is finished to Ra 0.05 µm or better — anything rougher punches through the EHL film and starts micropitting within hours.
- Output Disc: The mirror image of the input disc, mounted back-to-back so the two cavities share a common roller set. Both discs are typically through-hardened bearing steel (SUJ2 or M50) because the rolling contact stresses approach 4 GPa under peak load.
- Power Roller: The tilting torque-transfer element, usually 60-80 mm in diameter for an automotive variator. It rides on a precision angular-contact bearing and tilts around its trunnion axis to vary the ratio. Roller crown profile is held to within 1-2 µm to keep the contact ellipse stable across the full tilt range.
- Trunnion and Tilt Actuator: Carries the power roller and rotates it about the perpendicular axis to change ratio. Most modern designs use hydraulic pistons on the trunnion ends, with position feedback to a control valve. Response time runs 50-150 ms for full ratio sweep.
- Loading Cam (Clamp Mechanism): A ramped cam pack that converts input torque into axial clamp force on the discs. More torque, more clamp — exactly what you need to keep the EHL film from slipping. Ramp angle typically 20-30°; get it wrong by 2° and either the variator slips at high torque or it cooks the fluid at low torque.
- Traction Fluid: Synthetic cycloaliphatic hydrocarbon — Santotrac 50 or equivalent — engineered to give a high coefficient of traction (≈0.09) under EHL conditions. This is not engine oil. Mix the two and traction drops by half overnight.
Where the Toroidal CVT Is Used
Toroidal CVTs show up wherever you need stepless ratio change combined with high torque density — situations a belt or chain CVT can't survive. The traction drive principle predates automotive use by decades; it ran in early-1900s machine-tool spindles long before Nissan put it in a luxury sedan. You see them anywhere a designer needs to decouple input speed from output speed under serious torque without the steps of a planetary or the elasticity of a belt. The half-toroidal variator dominates the surviving production examples because spin losses scale with cavity depth, and half-toroidal geometry trims those losses by roughly 30% versus full-toroidal at the same torque rating.
- Automotive: Nissan Cedric and Gloria Y34 Extroid CVT (1999-2004), the only mass-production passenger-car toroidal CVT, paired with the VQ30DET twin-turbo V6 at 280 PS
- Aerospace: Constant-speed drives (CSDs) on aircraft generators — Sundstrand and Allison developed traction-drive CSDs in the 1960s for B-52 and DC-8 alternator drives
- Heavy Equipment: Torotrak Infinitely Variable Transmission (IVT) prototypes used on JCB Fastrac and Allison commercial bus drivelines for fuel-economy testing
- Industrial Machinery: Kopp Variator and Beier traction drives used as adjustable-speed drives on textile spinning machines and printing presses through the mid-20th century
- Motorsport: Torotrak full-toroidal flywheel KERS systems used in Volvo Flywheel KERS development cars, storing kinetic energy at flywheel speeds up to 60,000 RPM
- Wind Turbines: Torotrak/Artemis variable-ratio drives evaluated for synchronous-generator wind turbines to eliminate power electronics
The Formula Behind the Toroidal CVT
The ratio of a toroidal CVT depends entirely on where the power roller contacts each disc, which is set by the roller tilt angle. At the low end of the tilt range — say θ = -30° — the variator is in deep reduction, useful for launch and hill-climb. At nominal θ = 0° the roller sits at equal radii on both discs and ratio is 1:1, where spin losses are minimum and efficiency peaks around 92%. At the high end — θ = +30° — you're in overdrive, dropping engine RPM at cruise. The geometric ratio formula below tells you the mechanical ratio at any tilt angle, before you account for creep (typically 1-2% under load).
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| i | Speed ratio (input speed / output speed) | dimensionless | dimensionless |
| r1 | Contact radius on the input disc | mm | in |
| r2 | Contact radius on the output disc | mm | in |
| R | Toroidal cavity radius (centre of torus to disc axis) | mm | in |
| e | Roller crown radius (distance from trunnion axis to contact point) | mm | in |
| θ | Roller tilt angle (zero at 1:1 ratio) | deg | deg |
Worked Example: Toroidal CVT in a regenerative flywheel test rig
You are commissioning a half-toroidal variator on a 60,000 RPM regenerative flywheel test rig at a university powertrain lab in Loughborough, England. The variator couples a 200 kW electric dyno to a carbon-composite flywheel and must sweep from deep reduction during spin-up to overdrive during energy recovery. Cavity radius R is 65 mm, roller crown radius e is 35 mm, and the tilt mechanism allows θ between -28° and +28°. The dyno runs at a fixed 6000 RPM and you need to know the flywheel speed at the low, nominal, and high ends of the tilt sweep.
Given
- R = 65 mm
- e = 35 mm
- θlow = -28 deg
- θnom = 0 deg
- θhigh = +28 deg
- Ninput = 6000 RPM
Solution
Step 1 — at nominal θ = 0°, sin θ = 0 so the contact radii on both discs are equal at R = 65 mm. The ratio collapses to:
Output speed equals input speed: 6000 RPM at the flywheel. This is the high-efficiency sweet spot for the variator — spin losses minimise here because the rollers are not skewed, and traction-fluid shear heating is at its lowest. You'd run cruise-equivalent steady-state testing at this point.
Step 2 — at the low end of the tilt range, θ = -28°, sin(-28°) = -0.469. Plug in:
Output speed is 6000 / 1.675 = 3582 RPM. This is the spin-up regime — the dyno cranks the flywheel slowly while applying high torque. You'd feel this on the rig as a heavy bog-down note from the dyno as it loads up.
Step 3 — at the high end, θ = +28°, sin(+28°) = +0.469:
Output speed is 6000 / 0.597 = 10,050 RPM at the flywheel. This is energy-recovery overdrive — the flywheel is dumping stored kinetic energy back through the variator into the dyno. In theory you can push tilt closer to ±30° for slightly more range, but the contact ellipse starts crowding the edge of the toroidal surface and edge-stress concentration accelerates micropitting. Most production half-toroidal variators clamp the tilt envelope at ±28° for exactly this reason.
Result
At nominal θ = 0° the flywheel spins at 6000 RPM (1:1). The variator is at peak efficiency here — about 92% — and steady-state losses on the rig run roughly 16 kW of heat into the cooler. At θ = -28° the flywheel drops to 3582 RPM (1.675:1 reduction) for spin-up; at θ = +28° it climbs to 10,050 RPM (0.597:1 overdrive) for energy recovery — that's a 2.8x total ratio sweep, which is what you'd expect from a single-stage half-toroidal variator. If your measured output is more than 2-3% below predicted at high torque, suspect creep slip from inadequate clamp force first — check the loading-cam ramp angle and the disc clamp-force telemetry. If output drifts unpredictably across the tilt range with no torque change, the trunnion bearing has likely developed axial play above 20 µm, letting the roller skew. And if you see ratio collapse only when fluid temperature exceeds 110°C, the traction fluid has been contaminated with mineral oil — drain, flush, and refill with virgin Santotrac or equivalent.
When to Use a Toroidal CVT and When Not To
A toroidal CVT is one of three serious choices for stepless ratio change in a torque-dense application. Belt CVTs (Van Doorne push-belt) are cheaper and dominate light-vehicle production. Hydrostatic transmissions handle infinite ratio sweep at heavy torque but bleed efficiency. Toroidal sits in the middle — better efficiency than hydrostatic, better torque density than belt, but more expensive and finickier than either. Pick on torque rating, efficiency at the operating point, and whether you can tolerate the cost.
| Property | Toroidal CVT | Push-Belt CVT (Van Doorne) | Hydrostatic Transmission |
|---|---|---|---|
| Peak efficiency | 90-93% at 1:1 | 86-88% at mid-ratio | 78-85% at design point |
| Maximum input torque | 350-450 Nm production, 800+ Nm prototype | 250-350 Nm typical | Effectively unlimited with displacement scaling |
| Ratio spread | ~5-6:1 single stage | ~6-7:1 with planetary | Infinite (includes reverse and zero) |
| Unit cost (relative) | High — precision discs and traction fluid | Low — mass production scale | Medium-high |
| Service life under rated torque | ~250,000 km in Extroid fleet data | ~200,000 km typical | 10,000-20,000 hours industrial |
| Response time (full ratio sweep) | 50-150 ms hydraulic | 300-800 ms hydraulic | 100-300 ms |
| Best application fit | High-torque passenger cars, KERS, aerospace CSDs | Mass-market passenger cars, scooters | Off-highway equipment, harvesters, skid-steers |
Frequently Asked Questions About Toroidal CVT
Sudden slip under high torque almost always points at the loading cam, not the fluid. The cam converts input torque into axial clamp force on the discs — if the ramp angle has worn flat by even 1-2°, clamp force lags behind the torque demand and the rollers break traction. You'll feel it as a momentary RPM flare with no corresponding acceleration.
Pull the cam pack and check the ramp profile against the service spec. Anything more than 50 µm of ramp wear at the contact band, and the cam is finished — these aren't field-serviceable surfaces.
No, and the reason is fundamental. Traction fluids like Santotrac 50 are cycloaliphatic hydrocarbons engineered to go briefly glassy under the 3-4 GPa contact pressure inside the torus. That solid-like behaviour is what carries shear and gives the fluid a traction coefficient around 0.09. ATF and engine oil are designed to do the opposite — stay fluid and reduce friction — so their traction coefficient sits around 0.04.
Run engine oil in a toroidal variator and it will lose roughly half its torque capacity overnight. The discs will start slipping under loads they handled yesterday. Drain it, flush twice with fresh traction fluid, and refill.
Traction coefficient drops with temperature even within the fluid's rated range. Santotrac 50 holds about 0.092 at 80°C but falls to roughly 0.078 at 120°C — a 15% loss that shows up as creep slip under high torque. Creep slip dissipates power as heat, which raises temperature further, which drops traction further. Classic positive feedback loop.
If you're running steady-state at 110°C+, the cooler is undersized for your duty cycle or the cooler bypass valve is stuck open. Fit a larger cooler core or check the thermostat — production Extroids target 85-95°C sump temperature for a reason.
Full-toroidal wins for high-torque-density energy-recovery duty, which is why Torotrak and Volvo went that route on flywheel KERS. The deeper cavity puts the contact ellipse in a more favourable orientation for transmitting peak torque, and the geometry better tolerates the torque reversals you see in regen events.
Half-toroidal beats full-toroidal on steady-state efficiency by 2-3 points because spin losses scale with cavity depth. So if your application is steady-state cruise (an Extroid passenger car, an aerospace CSD), half-toroidal is the right pick. If it's transient, high-torque, bidirectional (KERS, motorsport hybrid), go full-toroidal.
Cost and supply chain, not engineering. The toroidal discs need bearing-grade steel held to ±5 µm profile tolerance with sub-0.1 µm surface finish. That's grinding-and-superfinishing time, and it doesn't scale down in cost the way a stamped steel push-belt does. The Extroid variator cost Nissan roughly 3x what a Jatco belt CVT cost to build at the same volume.
The traction fluid supply is also fragile — only a handful of suppliers worldwide make qualified traction fluids in production volume, and the OEM can't accept that as a single-source risk on a passenger car platform. Belt CVTs use ordinary CVT fluid that any major lubricant maker can supply.
Listen and look at the telemetry. Roller skew from worn trunnion bearings produces a low-frequency whine that varies with ratio — loudest at extreme tilt angles, quietest near 1:1 — because skew angle is amplified at the tilt limits. The ratio control loop will also hunt by ±0.5° around the commanded tilt, which shows up as a 1-2 Hz oscillation on output speed.
Disc surface damage (micropitting, spalling) produces a higher-frequency rumble that's roughly constant across ratios, plus iron particles in the fluid. Pull a fluid sample and run particle count — anything over 100 mg/kg of ferrous debris means the disc surfaces are coming apart and you're past the point of fluid change as a fix.
References & Further Reading
- Wikipedia contributors. Continuously variable transmission. Wikipedia
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