CVT, AMT and dual-clutch transmissions

Why it matters

Most new two-wheelers and a large share of new cars now use something other than a conventional manual or torque-converter automatic. A continuously variable transmission (CVT) keeps the engine at its best speed, an automated manual transmission (AMT) gives two-pedal driving at low cost, and a dual-clutch transmission (DCT) shifts without interrupting drive. Engineers must know how each works, what limits it and why a manufacturer would choose one over another.

Key ideas

Continuously variable transmission (CVT)

• The common type is the variable-pulley (V-belt) CVT: two pulleys, each made of a fixed and an axially movable conical sheave, connected by a steel push belt (many thin steel elements on steel bands) or a chain in cars, or a rubber V-belt in scooters.
• Moving the sheaves apart lets the belt drop to a smaller running radius; moving them together forces it outward. Because the belt length is fixed, when one pulley's radius increases the other's decreases, so the ratio changes continuously and steplessly between its limits.
• Ratio = driven-pulley radius ÷ driving-pulley radius. Low (starting) ratio: small radius on the driving pulley, large on the driven. Overdrive: the reverse. Typical car ratio spreads are about 5–7.
• The belt transmits torque by friction on the pulley flanks, so a large axial clamping force (tens of kilonewtons in cars), supplied hydraulically, is needed to prevent slip; too much clamping wastes pump power and adds friction. This limits CVT torque capacity and efficiency (roughly 85–90%, below a good manual).
• A CVT still needs a launch device – a torque converter, a wet clutch, or a centrifugal clutch in scooters – and usually a planetary set for reverse.
• Control: the TCU (or, in scooters, centrifugal roller weights in the driving pulley and a torque-sensing spring/cam on the driven pulley) holds the engine near its best-efficiency or maximum-power speed while road speed changes.
• Power-split "e-CVT" in many hybrids is a different device: a planetary gear set linking engine and two electric machines, giving continuously variable ratio without a belt.

Automated manual transmission (AMT)

• A conventional manual gearbox and dry clutch, with electro-hydraulic or electro-mechanical actuators for the clutch, gear selection and shifting, commanded by a TCU using engine speed, road speed, throttle and selector inputs.
• Advantages: low cost, high mechanical efficiency close to a manual, low weight, and easy adaptation of an existing gearbox – which is why it is popular in small, price-sensitive cars and in heavy trucks.
• Drawback: drive is interrupted during each shift (clutch must open), which feels like a pause or a forward "nod" in hard acceleration. Shift strategy and engine torque cut-back are tuned to soften this.

Dual-clutch transmission (DCT)

• Effectively two gearboxes in one casing: one sub-gearbox carries the odd gears (and often reverse), the other the even gears. Their input shafts are concentric – a solid inner shaft and a hollow outer shaft – each driven by its own clutch (a double clutch, dry for lower torques, wet multi-plate for higher).
• While one clutch drives through the current gear, the TCU preselects the next gear on the other shaft with ordinary synchronisers. The shift is a crossover: one clutch is released as the other is applied, so torque flow to the wheels continues and shifts take only a few tens of milliseconds (actual times depend on design and calibration).
• Advantages: no torque interruption, efficiency close to a manual, fast shifts, good economy. Drawbacks: complexity and cost, heat in dry clutches during slow crawling or hill starts, low-speed judder, and a delay if the TCU preselected the wrong next gear.

Choosing between them: CVT – smoothness and engine-speed optimisation for low-to-medium torque. AMT – lowest cost, good efficiency, but shift interruption. DCT – performance and efficiency at higher cost. Conventional automatics with torque converters remain strongest for high torque and towing.

Formulas

i = r₂ / r₁ = N₁ / N₂

• i: CVT ratio (input speed ÷ output speed, –); r₁, r₂: belt running radii on the driving (input) and driven (output) pulleys (m); N₁, N₂: their speeds (rev/min). Assumes no belt slip.

S_R = i_max / i_min

• S_R: ratio spread (–).

v = 2π · r_w · N_e / (60 · i · i_f)

• v: vehicle speed (m/s); r_w: wheel radius (m); N_e: engine speed (rev/min); i_f: final-drive ratio.

T = 2 · μ · F_a · r / cos β, so F_a = S · T · cos β / (2 · μ · r)

• T: torque the belt can transmit on a pulley (N·m); μ: belt–sheave friction coefficient (–, of order 0.09 for a push belt in oil; take from the maker's data); F_a: axial clamping force on the movable sheave (N); r: belt running radius on that pulley (m); β: sheave half-angle (about 11° for push-belt CVTs); S: safety factor against slip. The two flanks each carry a normal force F_a / cos β.

T_out = T_in · i · η

• Output torque of any of these transmissions (N·m); η is the transmission efficiency in that ratio.

Worked examples

Example 1 (standard). A car CVT has a lowest ratio of 2.5 and a highest (overdrive) ratio of 0.4. Final drive 5.5, wheel radius 0.30 m. With the engine held at 2500 rev/min, find the ratio spread and the vehicle-speed range.

1. Spread: S_R = 2.5 / 0.4 = 6.25.
2. Low ratio: v = 2π × 0.30 × 2500 / (60 × 2.5 × 5.5) = 5.712 m/s = 20.6 km/h.
3. Overdrive: v = 2π × 0.30 × 2500 / (60 × 0.4 × 5.5) = 35.70 m/s = 128.5 km/h.

Answer: spread 6.25; vehicle speed from about 20.6 km/h to 128.5 km/h without any change in engine speed.

Example 2 (GATE level). In launch ratio, the push belt runs at a radius of 40 mm on the driving pulley, which receives 150 N·m. Belt–sheave friction coefficient is 0.09, sheave half-angle 11°, and a safety factor of 1.3 against slip is required. Find the axial clamping force on the driving pulley.

1. F_a = S · T · cos β / (2 · μ · r).
2. cos 11° = 0.9816.
3. F_a = 1.3 × 150 × 0.9816 / (2 × 0.09 × 0.040) = 191.4 / 0.0072 = 26 586 N.

Answer: F_a ≈ 26.6 kN (20.5 kN without the safety factor). Clamping forces of this size are why CVTs need a high-pressure pump, and why the clamping is reduced whenever torque demand is low.

Common mistakes

• Defining CVT ratio as driving diameter ÷ driven diameter. Ratio is input speed ÷ output speed, which equals driven radius ÷ driving radius.
• Saying a CVT has "infinite ratios" without limits; it is stepless only between i_min and i_max.
• Forgetting that a CVT still needs a launch device and a reverse mechanism.
• Saying a DCT engages the next gear "while the current gear is still driving" without explaining that the next gear sits on the other, unclutched shaft; only the clutches cross over.
• Describing an AMT as a torque-converter automatic: it has a dry clutch and a manual gearbox and does interrupt torque during shifts.
• Treating the hybrid power-split e-CVT as a belt CVT.

For GATE ME

This topic mainly supports descriptive and comparison questions: working of belt CVTs, AMTs and DCTs, their efficiency and shift-quality trade-offs. Numericals are of the ratio and speed type – CVT ratio from running radii, vehicle speed at fixed engine speed, ratio spread – and occasionally belt clamping force from friction. Practise the speed-ratio convention until it is automatic.

Quick check

1. Driving-pulley running radius 60 mm, driven 30 mm: what is the CVT ratio, and is it a reduction or overdrive?
2. Why does a DCT not lose drive during an upshift?
3. What causes the "nod" felt in an AMT during hard acceleration?
4. A CVT has i_max = 2.4 and i_min = 0.4. What is its spread?
5. Why does a belt CVT need a high-pressure hydraulic supply?

Answers: 1. i = 30/60 = 0.5, an overdrive. 2. The next gear is preselected on the other shaft and the clutches cross over, so one is always transmitting torque. 3. The clutch must open during the shift, interrupting torque. 4. 6. 5. To clamp the belt between the sheaves with enough axial force to prevent slip.