Automatic Transmission Simulator

Automatic Transmission Simulator: How an Automatic Gearbox Works, in Interactive 3D Animation

An automatic transmission chooses and changes the gear by itself, so the driver only presses the accelerator and the brake. There are four ways to build one, and this simulator puts all of them in the same car:

• the classic torque converter automatic (AT), here as a 4-speed, a 6-speed and an 8-speed;
• the continuously variable transmission (CVT);
• the dual-clutch transmission (DCT);
• the automated manual transmission (AMT).

The animation is not drawn on a timeline. Each gear, shaft, clutch and brake is part of one rotational model that is solved a thousand times a second, so the virtual transmission shifts when its control unit decides to, a clutch slips for as long as the physics says it must, and the fuel figure comes from the engine's own fuel map. The page opens on an interactive 3D cutaway on a computer or tablet and on a 2D section on a phone.

Types of automatic transmission: AT vs CVT vs DCT vs AMT

The AT is smooth and strong at low speed because the converter multiplies torque, but the converter slips and the hydraulics cost power. The CVT can hold the engine at its most efficient speed, but it needs a high-pressure pump to clamp the belt. The DCT shifts fast with no loss of drive and no converter slip. The AMT is the cheapest and lightest, with the efficiency of a manual gearbox, but every shift interrupts the drive.

How a torque converter works

A torque converter is a sealed, oil-filled fluid coupling with three bladed wheels:

• the impeller (pump), bolted to the engine through the converter cover;
• the turbine, splined to the transmission's input shaft;
• the stator, between them, on a one-way clutch.

The impeller flings oil outward into the turbine, and the oil returns through the stator. While the turbine is slower than the impeller, the stator turns the returning oil so that it helps the impeller, and the turbine gets more torque than the engine gives. Two numbers describe the converter. The capacity factor K fixes how much torque the impeller absorbs at a given speed, T_p = (n_p/K)². The torque ratio TR falls from its stall value to 1 as the speed ratio SR = n_t/n_p rises:

TR = 2.0 − SR / 0.86   (SR < 0.86),   TR = 1 above

At SR = 0.86, the coupling point, the stator starts to freewheel and the converter becomes a plain fluid coupling. In the simulator K = 155 rpm/√(N·m). Held in D with full throttle and the brakes on, the engine settles at the stall speed, about 2,300 rpm, where it makes 221 N·m and the turbine receives 2.0 × 221 = 443 N·m.

A converter that is still slipping at a steady speed wastes fuel, so modern automatics close a lock-up clutch across it as soon as they can. In the simulator, cruising at 100 km/h with the lock-up clutch switched off uses 4 % more fuel in the 4-speed, 9 % more in the 6-speed and 14 % more in the 8-speed.

Planetary gear sets and the clutch apply chart

A planetary gear set has a sun gear, a ring gear and a carrier with planet gears. It gives a ratio only when one member is held or two are driven, so a stepped automatic is a few planetary sets with hydraulic clutches (which join two turning members) and brakes (which hold a member to the case). Each gear is a different set of applied elements, and the table of them is the clutch apply chart. The Planetary Gear Simulator works through the ratios of a single set with the Willis equation.

The ZF 8HP has four simple planetary sets and five shift elements: brakes A and B and clutches C, D and E. Three are applied in every gear:

Every shift between neighbouring gears releases exactly one element and applies exactly one. That is what makes a clutch-to-clutch shift possible. In the torque phase the load passes from the releasing element to the applying one at constant speeds. In the inertia phase the applying element slips the engine down to its new speed, while the engine's torque is briefly reduced so the shift does not jolt. The 4L60-E does its 1–2 shift a simpler way: its 1st gear is held by a roller one-way clutch, so applying the 2–4 band is enough and the roller clutch simply overruns.

Gear ratios of the six transmissions

These are the published ratios, and the simulator reproduces each one from its own planetary sets or gear pairs. Every car has the same overall 1st-gear ratio, 14.26:1 (3.462 × 70/17), so the final drive differs and the six transmissions launch on equal terms.

The DCT's 5th gear (0.914) is numerically higher than its 4th (0.902) because the two output shafts have their own final drives: 4.118 for gears 1 to 4 and 3.043 for 5, 6 and reverse. Overall, 5th is 2.782 and 4th is 3.714. The spread is the overall 1st-gear ratio divided by the overall top-gear ratio; the CVT's is 2.349/0.394 = 5.96.

How a CVT works

A CVT replaces the gears with two V-shaped pulleys and a push belt: several hundred thin steel elements threaded on two packs of steel bands. One half of each pulley slides on its shaft. Pushing the primary halves together moves the belt outward on the primary and inward on the secondary, which raises the gear, and the belt's length never changes:

L = 2√(a² − (R_s − R_p)²) + R_p(π − 2β) + R_s(π + 2β),   sin β = (R_s − R_p)/a

In the simulator the pulleys are 155 mm apart and the belt is 636.7 mm long, so the primary radius runs from 30.0 mm at the low ratio (2.349) to 71.8 mm at the high ratio (0.394). The belt carries torque by friction, so the pulleys must squeeze it hard enough not to slip: F = S·T·cos λ / (2μR_p), with a flank half-angle λ of 11°, a friction coefficient μ of 0.09 and a safety factor S of 1.3. At the low ratio 200 N·m needs a clamping force of 47.2 kN, which is why a CVT's pump runs at high pressure all the time. Without steps, the control unit can hold the engine on its ideal operating line, the speed at which each power is made for the least fuel, and the belt moves to keep it there.

How a dual-clutch transmission (DCT) works

A DCT is two manual gearboxes sharing one housing. Clutch K1 drives a solid inner input shaft carrying 1st, 3rd, 5th and reverse; clutch K2 drives a hollow outer shaft carrying 2nd, 4th and 6th. While the car accelerates in 1st on K1, the synchroniser for 2nd is already engaged on the other shaft. The shift is a hand-over: K2 takes the load as K1 releases, then K2 slips the engine down to the new speed. The drive to the wheels never stops. In the simulator a full-throttle 1–2 shift takes 0.42 s from command to the new clutch locking, about the same as the 8-speed automatic's 0.38 s, but with no torque converter slipping before or after it.

How an automated manual transmission (AMT) works

An AMT keeps a manual gearbox and a single dry clutch, and adds two actuators: one opens and closes the clutch and the other moves the gear selector. Every shift has three steps. The clutch opens, the synchroniser brings the next gear to speed and its sleeve moves across, then the clutch closes again. For that time no drive reaches the wheels, so the car's acceleration drops to zero: the torque gap. A full-throttle 1–2 shift in the simulator takes 0.95 s, and the strip chart shows the gap clearly. The Gearbox Simulator shows the synchromesh and the gear selection of a manual box in detail.

The shift schedule, kick-down and lock-up

A stepped automatic picks its gear from road speed and accelerator position. In the simulator the up-shift happens when the engine reaches

n_up = 1500 + 4700·a² rpm

where a is the accelerator position from 0 to 1, capped at 96 % of the 6,500 rpm red line. The down-shift line is lower, 1150 + 2300·a² rpm, so the box does not hunt between two gears. Push the pedal past 95 % and the transmission kicks down to the lowest gear that keeps the engine safely below its up-shift line, about 5,800 rpm with the pedal on the floor. The lock-up clutch closes from 2nd gear above 25 km/h in the 8-speed, from 3rd above 45 km/h in the 6-speed and from 3rd above 60 km/h in the 4-speed.

Results from the simulation: acceleration and fuel economy

Same car, same 2.5 L engine, six transmissions. The city drive is three runs of: accelerate at 35 % throttle to 50 km/h, hold it for 12 seconds, brake to a stop and wait 8 seconds.

More gears let the engine turn more slowly at cruising speed, which is where the 8-speed's advantage comes from. The AMT is the most economical in town, because it has no converter slip and no high-pressure pump, but it is the slowest from 0 to 100 km/h because each shift interrupts the drive. The DCT comes closest to having both. The CVT loses on economy because of its pump and belt losses. These are figures for this simulated car, so use them to compare the transmissions, not to predict a real vehicle's numbers.

Who uses this automatic transmission simulation?

• Automotive technician students learning how automatic transmissions work and how to read a clutch apply chart, for example for the ASE A2 (Automatic Transmission/Transaxle) test.
• Engineering students studying planetary gear trains, torque converters and vehicle performance.
• Teachers and instructors who need a working cutaway in the classroom instead of a still diagram.
• Drivers and enthusiasts who want to know what is happening inside an AT, CVT, DCT or AMT when it shifts.

Frequently asked questions

How does an automatic transmission work?

A torque converter automatic couples the engine to the gearbox through fluid: the engine turns an impeller, the oil drives a turbine, and a stator multiplies torque at low speed. Behind it, planetary gear sets give each gear when hydraulic clutches and brakes hold or join their members. A control unit picks the gear from road speed and pedal position and swaps one clutch for another to shift without interrupting the drive.

What is the difference between AT, CVT, DCT and AMT?

An AT uses a torque converter and planetary gears and shifts by swapping clutches. A CVT uses a steel belt between two variable pulleys, so it has no fixed gears and can hold the engine at its most efficient speed. A DCT has two clutches, one for the odd and one for the even gears, and pre-selects the next gear so shifts take a fraction of a second. An AMT is a manual gearbox with actuators that work the clutch and the gear lever, so the drive is interrupted during every shift.

What does a torque converter's stall speed mean?

Stall speed is the engine speed reached when the turbine is held still, for example with the brakes on in Drive and full throttle. It is where the converter absorbs all the engine's torque, so it is set by the converter's capacity factor K: stall speed = K × √(engine torque). In this simulator K is 155, so a 2.5 L engine stalls the converter at about 2,300 rpm and the torque is multiplied 2.0 times.

What is a clutch apply chart?

It is the table that shows which clutches and brakes are applied in each gear. In the ZF 8HP, for example, three of five shift elements are applied in every gear and each shift between neighbouring gears swaps exactly one of them, which is what makes a smooth clutch-to-clutch shift possible.

Why does an AMT feel jerky compared with a DCT?

An AMT has one clutch. To change gear it must open the clutch, move the gear lever and close the clutch again, and for that time, about a second, no drive reaches the wheels. A DCT changes gear by handing the drive from one clutch to the other with both gears already engaged, so the drive is never interrupted.

Explore Related Simulators

• Gearbox Simulator: a manual gearbox with synchromesh, gear selection and an interactive 3D car around it.
• Planetary Gear Simulator: one planetary set, the Willis equation, the Simpson set and the Prius power split.
• Car Differential Simulator: the final drive and differential after the transmission, open, limited-slip, Torsen and locking.
• Clutch System Simulator: plate, multi-plate, cone and centrifugal clutches, torque capacity and take-up heat.
• Gear Trains Simulator: simple, compound and worm gear trains and their ratios.
• Belt Drive Simulator: open and crossed belts, belt tensions and the power a belt can carry.
• Four-Stroke Engine Simulator: the cycle, torque and fuel use of the engine that drives the transmission.
• Hydraulic Brake System Simulator: the brakes that stop the same kind of car.
• Hydraulic Circuit Simulator: the valves and cylinders that apply clutches in a real valve body.

Updated 26 October 2026