Question 1:

A car is turning (cornering) on a road, the speed of the car is 250 kph and the turning radius is 250m with a banking angle of 7 ° ,  as shown in Figure Q1-1.  The car parameters are as follows:

•    m = 900 (kg) (56% of the weight is on the rear axle);

•    Air density =  1.225 (kg/m3);

•    Aerodynamic frontal area =  1.41 (m2);

•    Slip angle of the front tyres = +2.3 (°);

•    Slip angle of rear tyres = +1.2 (°);

•    Steering angle of front wheels = −5.5 (°);

•    Engine power at 250 kph = 250kW;

•    The efficiency of the drivetrain from the engine to the contact patch of tyres is 100%.

- 5 . 5    →

R=250 m

m9

*2

αR  = ＋1 . 2 

Figure Q1-1 Motion of the vehicle and the angles

a)   Calculate the percentage of the engine power delivered to tyres to overcome the total induced drag due to lateral forces. [8 marks]

b)   A tyre is specified as 230/60R17. Explain the meaning of the 3 values in   this specification (230, 60 and 17) and use them to calculate the radius of the tyre. (1inch = 25.4 mm) [2 marks]

c)   From the graph of Lateral Force versus Slip Angle in Figure Q1-2, calculate the lateral stiffness of the tyre.

Figure Q1-2 Lateral Force versus Slip Angle

Sketch a curve of Lateral Force versus Slip Angle for an increase in vehicle mass. [3 marks]

d)   Using a sketch of the lateral force profile on a contact patch that is

slipping with slip angle “, explain what aligning torque is and how it helps the driver control the vehicle steering. [3 marks]

e)   Using a sketch of the variation of traction force versus slip ratio, explain how a traction controller can maximise the acceleration. [4 marks]

Question 2:

Carry out an evaluation of under-steer or over-steer analysis for the following vehicle:

.    m = 1200 (kg) (40% of weight is on rear axle);

.    Cornering stiffness of front tyres = 一40 (kN/rad);

.    Cornering stiffness of rear tyres = 一40 (kN/rad);

.    Wheel base is 2.8 m.

a)  The vehicle travels at speed of v = 50 kph and driver turns steering wheel such that the front wheel steering angle is δ. Assume that the moment of   inertia of the vehicle around axis z is Iz  = 1650 kg m2 .

Calculate all values of Yβ , Nβ , Yr , Nr , Yδ  and Nδ  to construct the following transient equations for r and β. Then calculate the time constant of r if   side slip angle and its variation are zero.

l] = lYr/m(Nr)v(/)Iz   1

Yβ(N)/m(β/I)v(z)| lβ(r)] + lYδ(N)/(δ)m(/I)v(z)| δ [10 marks]

b)  Calculate the stability factor K and explain if the car is over-steered or under-steered. [4 marks]

c)  Plot the curvature response of the car to the steering angle δ for the speeds of [0, 20, 50, 90] kph and add the neutral steer curve. [6 marks]

Question 3:

This question is related to specification of a powertrain for a parallel hybrid

electric powertrain for a front-wheel-drive car with the following parameters:

•   Vehicle mass: 1160 (kg) (35% of the weight is on rear axle);

•   Aerodynamic frontal area: 1.2 (m2);

•   Aerodynamic drag coefficient Cd: 0.25 (−);

•   The effective radius of tyres: 0.35 (m);

•   Topspeed vmax  = 200 (kph);

•    Maximum engine speed: 4,500 rpm;

•   Air density: 1.225 (kg/m3);

•    Fuel density: 0.832 (kg/litre).

•   The efficiency of the final drive (differential) and gearbox can be assumed 100%.

a)  The designer of the powertrain has chosen the 4-stroke internal

combustion engine of Figure Q3-1, which shows the BSFC map and

power contours of the engine. Write down the maximum power of the

engine and use this to calculate the swept volume of the required internal combustion engine. [4 marks]

Figure Q3-1 BSFC map of the engine with the curve of the maximum BMEP and contours of the constant powers

b)  If the gear ratio of the final drive (differential) of the powertrain is 3.95 (-), what is your suggestion for the ratio of the highest gear? [2 marks]

c)  The engine at its maximum power must provide 100% of the required

power to run the car longitudinally at the constant 120kph on a road with a grade of 5。. Calculate the free-rolling resistance coefficient f0  (assumerolling resistance is not a function of velocity) and the fuel consumption rate of this car in litre/100km at this condition? [4 marks]

d)  When running in hybrid mode, the engine operating point is moved to the point of lowest BSFC. Calculate the power required from the motor to

maintain 120 kph on a grade of 5。and the fuel consumption in this

condition. The battery is sized to provide this assistance for 20km,

calculate the size of the battery in kWh, assuming the vehicle can use the battery between 20% and 80% state of charge. [6 marks]

e)  State one advantage and one disadvantage of Parallel versus Series   hybrid electric powertrains and discuss why there are not many Series hybrid vehicles in production. [4 marks]

Question 4

a)  Using the following equations, calculate the sprung (fn,m ) and unsprung (fn,um ) frequencies for the quarter car model which is modelled in

Figure Q4-1.

The wheel mass (i.e. unsprung mass) is mus   =  15 kg and the spring stiffness of the suspension system is k  =  15 kN/m.

fn,m ~    

fn,um ~  [2 marks]

Figure Q4-1 Simplified quarter-car model

b)  Explain the meaning and importance of the sprung and unsprung masses of a suspension system. [2 marks]

c)  Sketch the response gain for the quarter car model assuming the

response gain magnitudes are approximately 2 for the sprung mass and 0.2 for the unsprung mass. [4 marks]