CVT

Continuously variable transmissions provide infinite ratios between limits. Learn push-belt/chain CVTs with variable pulleys, ratio spread, clamping force and slip, engine operating-line control, efficiency trade-offs, toroidal CVTs and hybrid e-CVTs.

Instead of fixed gears, a CVT squeezes a steel belt or chain between two pulleys whose widths change — so the effective diameters, and the ratio, vary smoothly. The engine can stay at its most efficient or most powerful speed while the car accelerates.

Hybrids use 'e-CVTs' — planetary power-split devices — to achieve the same effect electrically.

An analogy

A CVT is like a bicycle with infinitely many gears that shift themselves — you keep pedalling at the perfect cadence while the bike speeds up.

How a belt CVT works

Each pulley has two conical halves; hydraulic pressure moves one half, changing where the belt rides. Small drive radius + large driven radius = low ratio (launch); the reverse = overdrive (cruise). Ratio changes continuously without steps.

Engine operating line

The controller chooses the ratio so the engine runs on its best-efficiency line at light load, or at peak power when flooring the throttle — producing the characteristic constant engine note ('rubber-band' feel). Stepped 'virtual gears' are often programmed for drivers who prefer shift feel.

Clamping and efficiency

The belt transmits torque by friction, so clamping force must exceed what's needed to avoid slip — but too much wastes pump energy and adds belt losses. CVT mechanical efficiency ≈ 85–92 %, offset by keeping the engine at efficient points.

Toroidal and e-CVTs

Toroidal CVTs transmit torque through traction oil between rollers and discs (high torque capacity). Power-split e-CVTs in hybrids (e.g. Toyota THS) use a planetary set with two motor-generators — no belt, highly reliable, engine speed decoupled from vehicle speed.

Formulas

• Ratio: i = r_driven / r_drive
• Ratio spread: spread = i_low / i_od
• Clamp force (no slip): F ≥ T cos α / (2 μ r)
• Ratio for target engine speed: i = N_engine · 2πr_tyre / (60 · v · i_f)

Worked example: Ratio spread

Given: Lowest ratio 2.5, overdrive 0.4

Find: Spread.

• 2.5/0.4 = 6.25

Answer: 6.25 (comparable to a 6–7-speed AT)

Worked example: Clamping force

Given: Torque 200 N·m at drive pulley, r = 30 mm; α = 11°, μ = 0.09

Find: Minimum clamp force.

• F = 200 × cos 11°/(2 × 0.09 × 0.03) = 36 400 N

Answer: ≈ 36 kN (plus safety margin ≈ 1.3)

Common mistakes

• Wrong: Over-clamping 'to be safe'. — Right: Excess clamp force costs efficiency; use torque-dependent clamping with margin.
• Wrong: Assuming CVTs suit high-torque engines. — Right: Belt friction limits torque; toroidal or other designs are needed for high torque.

Applications

• Small & mid-size cars: Belt/chain CVTs for fuel economy (Nissan, Honda, Subaru).
• Hybrids: Power-split e-CVTs in Toyota and Ford hybrids.
• Scooters & ATVs: Rubber-belt centrifugal CVTs.

Key takeaways

• Infinite ratios between i_low and i_od.
• Keeps the engine on its best line.
• Clamp force F = T cos α/(2μr).
• e-CVTs (power split) dominate hybrids.

Going further

• Push-belt design: Hundreds of steel elements on steel bands transmit force in compression.
• Ratio-change dynamics: Shifting speed limited by hydraulics and belt mechanics (Ide model).
• Traction fluids: Toroidal CVTs use fluids that become glassy under pressure to transmit shear.