Modeling and simulation of a vehicle with automatic transmission

7. Simulation results

There are 3 simulation scenarios (driving modes) which are going to be run:

  • full acceleration
  • acceleration followed by braking
  • hill climb

For each scenario we are going to observe the behaviour of the shift scheduler and the dynamic performance of the vehicle. All simulations are run for 50 s. The simulation time can be increased to whatever value as long as the accelerator/brake pedal and road slope profile are adjusted accordingly.

Save data - Xcos block diagram

Image: Save data – Xcos block diagram

Most relevant signals are saved into the Scilab workspace using Global GOTO blocks. The data is sampled at dt and further post-processed using Scilab instructions.

Driver and environment outputs

Input pedals - full acceleration

Image: Input pedals – full acceleration

Input pedals - braking

Image: Input pedals – braking

Input pedals - hill climb

Image: Input pedals – hill climb

The full acceleration scenario means pressing the acceleration pedal from 0 % to 100 % in very short time. In this scenario, the brake pedal is not pressed, 0 % and the road slope (gradient) is also 0 %. The purpose of this scenario is to check what is the acceleration time of the vehicle from standstill to 100 kph. Since the vehicle keeps accelerating, there will be only upshifts and no downshifts.

In the braking scenario we want to see if out transmission controller works properly and can downshift. In this scenario the accelerator pedal is pressed gradually to 60% to allow the vehicle to pickup speed. After 15 s, the accelerator pedal is released gradually and the brake pedal is pressed, again slowly, up to 35 %. After the braking event there is another small acceleration event, which will allow the vehicle to pickup speed again. The road slope is also kept to 0 % for the entire duration of the scenario.

In the hill climb scenario, the purpose is to see that a road load increase will slow down the vehicle and eventually will trigger a downshift. In this scenario the brake pedal is kept at 0 % for the entire duration of the simulation.

Vehicle speed

Vehicle speed - full acceleration

Image: Vehicle speed – full acceleration

Vehicle speed - braking

Image: Vehicle speed – braking

Vehicle speed - hill climb

Image: Vehicle speed – hill climb

From the full acceleration scenario speed profile we can see that it takes approx. 8 s for the vehicle to accelerate from standstill to 100 kph. The maximum speed is not reached in this scenario due to limited simulation time. To get the maximum speed value increase the simulation time to 100 s.

In the braking scenario we can see a steep decrease of the vehicle speed due to braking force. This will trigger a downshift, followed by an upshift when the driver starts to accelerate again.

In the hill climb scenario, the vehicle speed decreases gradually due to higher wheel resistances (road slope force) and lower engine torque (lower accelerator pedal position). Around 35 s there is a downshift event which increases the available traction torque at the wheel, which causes the vehicle to slow down at a lower rate.

Gear shift

Current gear - full acceleration

Image: Current gear – full acceleration

Current gear - braking

Image: Current gear – braking

Current gear - hill climb

Image: Current gear – hill climb

The gear shift pattern is meeting expectations. In the full acceleration scenario, we only have upshifts, since the vehicle speed keeps climbing and the accelerator pedal position is fully pressed. The final upshift recorded in the simulation is 4-5 upshift, at 30 s.

In the braking scenario, there is a 4-3 downshift at 37 s, due to vehicle speed drop and accelerator pedal position change.

In the hill climb scenario, due to higher resistive forces at the wheel, the transmission is forced to do a 4-3 downshift at 35 s, in order to increase the wheel traction torque and keep the vehicle from further decelerating.

Gear shift with dynamic corrections

Gear inhibits - full acceleration

Image: Gear inhibits – full acceleration

Gear inhibits - braking

Image: Gear inhibits – braking

Gear inhibits - hill climb

Image: Gear inhibits – hill climb

In the full acceleration scenario we have two gearshift dynamic corrections:

  • “Accelerator pedal tip-in” at 1 s, when the driver fully presses the accelerator pedal; this correction will inhibit a 1-2 upshift
  • “Minimum time in gear – upshift” at every shift; this correction will keep the current gear for minimum 2 s, even there is a shift map gear change active

In the braking scenario we have three additional gearshift dynamic corrections:

  • “Accelerator pedal tip-out” at 15 s, when the driver fully releases the accelerator pedal; this correction will inhibit a 3-4 upshift
  • “Engine brake inhibit” between 20 s and 40 s, triggered by the full release of the accelerator pedal; this correction will inhibit any upshift and keep the current gear for engine braking (overrun)
  • “Minimum time in gear – downshift” at 37 s; this correction will delay a potential 3-2 downshift

In the hill climb driving scenario we have three dynamic correction, for the same reason as explained above.

Gear shift speed limits

Speed shift limits - full acceleration

Image: Speed shift limits – full acceleration

Speed shift limits - braking

Speed shift limits – braking

Speed shift limits - hill climb

Image: Speed shift limits – hill climb

In all scenarios we can clearly see that when the vehicle speed is intersecting the upshift/downshift speed limits, the transmission changes gear. In some situations, the gearshift can be delayed due to the dynamic corrections being active.

Engine speed

Engine speed - full acceleration

Image: Engine speed – full acceleration

Engine speed - braking

Image: Engine speed – braking

Engine speed - hill climb

Image: Engine speed – hill climb

In the full acceleration scenario we can see that at every gear shift event, the engine speed drops. This is happening because higher gears have lower gear ratios. Also we can see that the engine acceleration takes more time in higher gears. This is due to lower traction torque at the wheel, since we have lower gear rations.

In the braking scenario, when the accelerator pedal is released, the engine speed drops around the idle speed value (1000 rpm). Since there is a connection between the engine and the gearbox, through the torque converter, the engine speed is still kept above the idle speed due to a drag torque.

In the hill climb scenario the engine speed is slowly decreasing, on the same path as the vehicle speed. Since in this scenario there is always positive torque on the engine side, the engine speed is not dropping into idle target. At 35 s we can see a small spike in the engine speed due to the 4-3 downshift.

Engine torque

Engine torque - full acceleration

Image: Engine torque – full acceleration

Engine torque - braking

Image: Engine torque – braking

Engine torque - hill climb

Image: Engine torque – hill climb

In the full acceleration scenario the engine torque reaches maximum value in first gear. During braking scenario, when the driver releases the accelerator pedal, the engine torque goes into negative territory. Due to the slip in the torque converter, the braking torque of the engine will decrease and keep at small negative values, around -5 Nm.

In the hill climb scenario, the engine torque is maintained around certain values, function of the accelerator pedal position. There are no massive spikes of the value because there are no sudden demands from the driver (through the accelerator pedal position).

Engine power

Engine power - full acceleration

Image: Engine power – full acceleration

Engine power - braking

Image: Engine power – braking

Engine power - hill climb

Image: Engine power – hill climb

Engine power has the same behaviour of engine torque, see above.

Turbine speed

Turbine speed - full acceleration

Image: Turbine speed – full acceleration

Turbine speed - braking

Image: Turbine speed – braking

Turbine speed - hill climb

Image: Turbine speed – hill climb

During vehicle acceleration, we can clearly see that the engine speed is bigger than the turbine speed. This means that there is positive traction torque going through the torque converter. During vehicle deceleration, due to accelerator pedal release, the engine speed drops below the turbine speed, the torque being in the opposite direction, from the wheels to the engine.

In the hill climb scenario we can see that there is a significant speed slip (difference) between the engine and the turbine. This means that there is a lot of friction in the torque converter which translates into low efficiency and thermal losses. All modern torque converter have a lock-up clutch, which has the role to mechanically link the impeller with the turbine in order to improve efficiency. In order to keep it simple, this example considers that the torque converter is always unlocked.

Turbine torque

Turbine torque - full acceleration

Image: Turbine torque – full acceleration

Turbine torque - braking

Image: Turbine torque – braking

Turbine torque - hill climb

Image: Turbine torque – hill climb

The turbine torque shows the benefit of the torque converter in terms of torque amplification. At standstill, where the speed ratio is 0, the torque coefficient of the torque converter is maximum, 2.163. This allows high torque to be applied at the wheels which benefits the acceleration performance of the vehicle.

The torque spikes in the simulation occur due to instant gear change and hence gear ratio change. In reality, the gearshift happens through clutch-to-clutch handover, the gear ratio ramps up/down linearly and the torque output is smooth.

Traction force at wheel

Traction force - full acceleration

Image: Traction force – full acceleration

Traction force - braking

Image: Traction force – braking

Traction force - hill climb

Image: Traction force – hill climb

In the full acceleration scenario, it is clear that the powertrain can generate more traction force than the wheel can apply on the road. In this example, for simplicity, we just limited the wheel traction force to the friction limit. In reality, the Electronic Stability Program (ESP), when detects a wheel slip during acceleration, reduces the engine torque to a sustainable value, hence reducing the wheel traction force.

Also, we can correlate the balance of traction force and road load with the acceleration of the vehicle. When the traction force at wheel is higher than the road load (resistive forces) the vehicle will accelerate. When the road load (resistive forces) is higher than the traction force, the vehicle will slow down (decelerate).

Vehicle acceleration

Vehicle acceleration - full acceleration

Image: Vehicle acceleration – full acceleration

Vehicle acceleration - braking

Image: Vehicle acceleration – braking

Vehicle acceleration - hill climb

Image: Vehicle acceleration – hill climb

The maximum vehicle acceleration is around 4.5 m/s2, obtained in the first gear during the full acceleration scenario. The acceleration if flat at maximum value for a couple of seconds, due the fact that the traction force is limited by the friction limit. The vehicle acceleration spikes happen because the gear change is instantaneous, which doesn’t happen in reality.

As expected, accelerator pedal lift-off or braking causes the vehicle to decelerate (negative values).

Vehicle offset

Vehicle offset - full acceleration

Image: Vehicle offset – full acceleration

Vehicle offset - braking

Image: Vehicle offset – braking

Vehicle offset - hill climb

Image: Vehicle offset – hill climb

Another way of measuring the dynamic performance of a vehicle is by looking at the time to travel 1000 m. In this case, during the full acceleration scenario, it takes around 28 s for the vehicle to reach 1000 m from standstill.


This model can be extended for fuel consumption studies, by adding a fuel map for the engine and also running it on type approval cycles like WLTP or FTP. Also, it can be used together with a wheel slip control model which properly controls the engine torque during the acceleration phases.

The model is highly flexible, different vehicle variants, with different engine and transmission configurations can be simulated, only by modifying the parameters.

The complete model can be recreated from the article, all the parameters being also available. If you want access to the source files, please support my Patreon page.


[1] Ioan Mircea Oprean, Transmisii Automate pentru Automobile, Editura Printech, Bucureşti, 1999.
[2] M.Untaru et al, Dinamica Autovehiculelor pe Roţi, Editura Didactică şi Pedagogică, Bucureşti, 1981.
[3] Harald Naunheimer et al, Automotive Transmissions – Fundamentals, Selection, Design and Application, 2nd edition, Springer.
[4] AUTOSAR_MOD_AISpecification_KeywordSet_Blueprint.xml

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