A dual-clutch transmission has separate clutch-driven paths for odd and even gears. One path can carry torque while the next gear is already selected in the other. During an upshift, torque passes to the incoming clutch, and the engine speed then falls to the new ratio.
This cutaway shows two representative preselected gear pairs, the concentric input shafts, their clutch packs and a common output shaft. The calculator uses a defined two-stage upshift with explicit clutch slip and engine-side inertia. It does not lock two different ratios to the engine at once.
Dual-clutch Transmission Interactive Calculator
Explore one adjacent upshift with separate clutch torque paths, controlled slip and engine-side inertia. Output speed is held constant. The diagram uses representative gears and slowed playback.
Equation Used
- Six illustrative gear ratios; only the two selected pairs are shown.
- Torque transfer occupies 40% of shift; speed synchronization occupies 60%.
- Cubic smoothstep torque and speed transitions.
- No gear losses, output acceleration, clutch limit or engine-controller model.
Representative gear pairs and prescribed two-stage shift. No simultaneous locking of unequal ratios. Animation repeats a slowed inspection of one upshift.
Transfer torque, then synchronize speed
During the first 40% of the modeled shift, the outgoing clutch stays at its original locked speed. Its torque falls as the incoming clutch torque rises. The incoming clutch slips because its gear path is turning more slowly than the engine.
During the remaining 60%, the outgoing clutch is open. Engine speed falls smoothly to the incoming shaft speed, and the incoming clutch carries the engine torque plus the torque released by the slowing engine-side inertia. At the endpoint, that clutch reaches zero slip.
Both gear pairs remain meshed with the output. Their input shafts therefore rotate at different speeds throughout. The cutaway omits the other four gear pairs and shows the two selected dogs as engaged; selection hardware is not being actuated during this example.
A representative six-speed upshift model
The six illustrative gear pairs use input tooth counts 20,25,30,35,40 and 44, with each mating output gear chosen so the tooth counts sum to 100. All pairs therefore share the same center distance at a common module. These are teaching ratios, not specifications for a Volkswagen or other production transmission.
Choose a starting gear from 1 through 5; the incoming gear is always the next one. Odd gears use the blue inner input shaft and clutch K1, while even gears use the gold hollow input shaft and clutch K2. The lower shaft is the common output.
The animation is slowed for inspection and repeats one upshift. The selected duration is used in the calculations; screen playback is eight seconds. Each replay restarts the speed schedule. Shaft angles remain continuous, and the displayed stage identifies the handover.
Speed, torque and slip-energy balance
Let G1 and G2 be the old and new input/output speed ratios, ωo the held output speed, Te the constant engine torque, J the lumped engine-side inertia and T the total shift time. For a gear pair, G=Noutput/Ninput. Define Δω=(G1−G2)ωo and s(u)=3u²−2u³.
For 0≤t≤0.4T, set u=t/(0.4T): Toutgoing=Te[1−s(u)], Tincoming=Te s(u), and ωengine=G1ωo.
For 0.4T<t≤T, set u=(t−0.4T)/(0.6T): ωengine=G1ωo−Δω s(u), α=−Δω · 6u(1−u)/(0.6T), Toutgoing=0 and Tincoming=Te−Jα.
Toutput=G1 Toutgoing+G2 Tincoming
Slip heat rate is the sum of each clutch torque times its engine-to-input-shaft speed difference. This is nonnegative for the specified upshift. Integrating the complete schedule gives:
Eslip=0.5 Te Δω T+0.5 J(Δω)²
The energy balance is engine work equals output work plus slip heat plus the change in engine-side kinetic energy. Gear losses, shaft inertia, vehicle acceleration, clutch capacity and thermal limits are not included.
Try a third-to-fourth upshift
The default uses third gear 30/70 and fourth gear 35/65. At 400 output rpm, the old engine speed is 933.33 rpm and the new speed is 742.86 rpm. Both input paths remain at those respective speeds while the engine synchronizes between them.
With 200 N·m engine torque, the steady output torque changes from 466.67 N·m to 371.43 N·m. The transition also depends on the entered inertia and shift duration. The clutch’s temporary torque can exceed engine torque because the engine-side inertia is slowing.
Changing the duration changes the transient peak and slip energy. It does not change the gear ratios or endpoint speeds. The model separates the effects of shift time and engine-side inertia on clutch loading.
What the model does and does not predict
Volkswagen’s manufacturer description establishes the odd/even clutch-path principle. The ratios, dimensions, torque-transfer law and inertia law here are explicit educational choices, not a recovered production controller or measured shift.
The output speed is externally held constant, as on an ideal test stand. The resulting output torque is not wheel torque unless a final-drive model is added. The model does not predict vehicle acceleration or engine-control intervention.
No clutch capacity or thermal limit is inferred from the diagram. The calculated slip energy is an energy quantity, not a clutch temperature or durability rating. Shift time and torque delivery depend on the specified control schedule and operating conditions.
Dual-clutch questions
Why are both gear pairs turning?
Both are preselected and meshed with the same output shaft. Only their engine-side clutches determine how much torque enters each path.
Are both clutches locked during the handover?
No. The incoming clutch slips during torque transfer. Two unequal selected ratios cannot both be rigidly locked to one engine at a nonzero output speed.
Why can incoming clutch torque exceed engine torque?
The engine-side inertia releases kinetic energy as its speed falls. Its deceleration adds to the torque transmitted by the incoming clutch.
Why is there no sixth-to-seventh choice?
This representative transmission has six forward ratios. The starting-gear input ends at fifth.
What does zero output speed show?
The shafts stop and slip energy is zero. The displayed torque schedule is a static idealization, not a launch simulation.
Manufacturer reference
Volkswagen, The New Polo: Engines and transmissions, describes separate clutches for odd-numbered and even-numbered gear paths. The specific ratios and two-stage control schedule on this page are independently defined model assumptions.
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