Two-Speed Transmission vs Single-Speed for an Electric Car

The problem

Most EVs use one fixed ratio, but some high-performance and commercial EVs use two speeds to combine strong launch with high top speed and better motor efficiency. Whether the added mass, cost and shift complexity pay back depends on the motor, the cycle and the shift strategy. This study quantifies that trade-off.

Objectives

• Build single-speed and two-speed driveline models with clutches in Simscape Driveline.
• Design an efficiency-based shift schedule with hysteresis in Stateflow.
• Model torque-fill during shifts and quantify shift jerk.
• Compare energy, performance and shift metrics against the single-speed baseline.
• Study sensitivity to transmission efficiency and added mass.

What you need

Key concepts

Ratio spread

The ratio between first and second gear. A larger spread gives more launch torque and higher top speed but a bigger speed change at each shift.

Efficiency-optimal shift map

For each vehicle speed and wheel torque demand, the gear in which the motor's operating point has higher efficiency. Hysteresis is added so the gearbox does not hunt between gears.

Torque-fill

During a clutch-to-clutch shift the motor torque is controlled to keep wheel torque near the demand, reducing the torque hole that passengers feel.

Jerk

The rate of change of vehicle acceleration, in m/s³. It is a common objective measure of shift comfort.

Step-by-step guide

1. 1

   Requirements and baseline

   Use an example car of 1800 kg with a 150 kW motor of 15,000 rpm maximum. Define the baseline as a single-speed ratio chosen for 180 km/h top speed. Choose example two-speed ratios, for example 14:1 and 8:1 overall. Targets: 0–100 km/h time, top speed, Wh/km on MIDC and WLTP, and maximum jerk during shifts below a stated limit such as 10 m/s³. Note the added mass and efficiency loss assumed for the two-speed box.

   Checkpoint: A requirements and assumptions table including mass and efficiency penalties for the two-speed box.

2. 2

   Build the single-speed driveline

   In Simscape Driveline, connect an ideal torque source for the motor with rotor Inertia, a Simple Gear with an efficiency setting, a differential represented by another gear, and Tire (Magic Formula or simple) plus Vehicle Body blocks. Add a Solver Configuration and use daessc or ode23t. Drive the torque source from the motor envelope and a PI driver. Keep this model as the baseline throughout and change only the transmission subsystem later.

   Checkpoint: The single-speed model follows WLTP within ±2 km/h and its Wh/km matches a simpler road-load model within a few per cent.

3. 3

   Build the two-speed transmission

   Model two gear paths, each a Simple Gear with a Disk Friction Clutch, joined on the output shaft, so that engaging one clutch and releasing the other changes ratio. Set clutch friction coefficients, normal-force actuator dynamics and engagement thresholds. Start with a simple test: hold first gear, then command a shift at constant motor torque and observe the speed change across the clutches.

   Checkpoint: A shift test shows the motor speed moving from the first-gear to the second-gear value while the vehicle speed stays continuous.

4. 4

   Compute the shift map

   In MATLAB, for a grid of vehicle speed and wheel torque, compute motor speed and torque in each gear, look up the efficiency and mark the better gear where both are feasible. Smooth the boundary, then define upshift and downshift lines separated by hysteresis in speed (for example 5 km/h). Plot the map with the motor's feasible regions. Repeat the calculation for regenerating torque so downshifts during braking are handled sensibly.

   Checkpoint: A shift map plot with upshift and downshift lines and no region where neither gear is feasible.

5. 5

   Implement the shift logic in Stateflow

   Create a chart with states Gear1, ShiftUp, Gear2 and ShiftDown. Transitions use the map lines, with inhibits for minimum time in gear and no shift during heavy braking. Inside the shift states, sequence the clutch pressures (off-going release, on-coming apply) with timed ramps. Export the gear and clutch commands to the Simscape clutches. Use Stateflow's animation and the Simulation Data Inspector to step through a few shifts and confirm the state sequence is correct.

   Checkpoint: On WLTP the gear changes only at the map boundaries and does not hunt; the number of shifts is logged.

6. 6

   Add torque-fill and measure jerk

   During the torque phase of the shift, reduce motor torque in proportion to the transfer between clutches; during the inertia phase, adjust motor torque to bring motor speed to the new synchronous speed. Compute jerk by differentiating filtered acceleration. Tune ramp times and the torque-fill gain to keep jerk below the limit with a short shift time. Filter acceleration before differentiating so noise does not dominate the jerk value.

   Checkpoint: Shift duration and peak jerk for a full-throttle upshift, with jerk below the stated limit.

7. 7

   Verify the subsystems

   Check clutch behaviour with a locked output (clutch slip and heat as expected), confirm that wheel torque during a steady gear equals motor torque times ratio times efficiency, and close the energy balance including clutch slip losses. Compare a fixed-step discrete approximation if you plan code generation; otherwise keep the variable-step Simscape solver. Record each check in a verification table with the expected value, the simulated value and the pass or fail result.

   Checkpoint: Energy balance closes within 1 per cent, including clutch losses.

8. 8

   Run the comparison

   Run the baseline and two-speed models on MIDC, WLTP and a highway cycle, plus launch and top-speed tests, using a script that collects results into a table. Include the assumed mass penalty and gearbox loss. Plot operating points on the efficiency map for both designs to explain any energy difference. Use identical driver gains, cycles and solver settings for both designs so that differences come only from the transmission and its control.

   Checkpoint: A comparison table of Wh/km, 0–100 time, top speed, shift count and peak jerk for both designs.

9. 9

   Sensitivity and ratio tuning

   Sweep the two ratios and the hysteresis width, and vary the gearbox efficiency penalty and added mass. Find the break-even efficiency penalty at which the two-speed design no longer saves energy on each cycle. If you have Optimization Toolbox, use fmincon on the ratios with sweep results as a starting point. Report how much of the saving comes from the motor operating more efficiently and how much is lost to added mass.

   Checkpoint: A break-even plot of energy saving against gearbox efficiency penalty for each cycle.

10. 10

    Report

    Present the models, shift map, Stateflow logic, verification, comparison and sensitivity. Discuss when a two-speed box makes sense (high top speed, heavy vehicles, motors with narrow efficient regions) and when it does not. State the limits of the clutch and efficiency models and the example nature of all parameters. Include the Stateflow chart, shift map data and comparison scripts so another student can rerun the study with a different motor map or vehicle.

    Checkpoint: A report with quantified conditions under which the two-speed design is beneficial.

Testing & validation

• Baseline model consumption agrees with a simple road-load model.
• Shift test shows correct synchronous speeds before and after the shift.
• Energy balance closes including clutch losses.
• Shift map produces no hunting on any cycle.
• Peak jerk is below the stated limit.

Expected results

A Simscape Driveline comparison of single-speed and two-speed EV transmissions with a Stateflow shift controller, showing energy, performance and shift quality, and the gearbox efficiency penalty at which the two-speed advantage disappears.

Take it further

• Use a planetary gearset with a brake and clutch instead of two parallel gears.
• Optimise the shift map with dynamic programming as a benchmark.
• Add a motor thermal model and study continuous power on long climbs.
• Generate code for the shift controller and run it in software-in-the-loop.

Viva and review questions

Learn it at DIYguru

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