TW32 UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING BENG (HONS) AUTOMOTIVE PERFORMANCE ENGINEERING and BSC (HONS) MOTORSPORT TECHNOLOGY EXAMINATION SEMESTER 2-2015/2016 VEHICLE DYNAMICS AND ADVANCED ELECTRONICS MODULE NO: MSP6001 Date: Monday 16 May 2016 Time: 10.00 1.00 INSTRUCTIONS TO CANDIDATES: This paper is split into two parts. Part A and Part B. Answer ALL questions. All questions carry equal marks. Marks for parts of questions are shown in brackets. CANDIDATES REQUIRE: Electronic calculators may be used provided that data and program storage memory is cleared prior to the examination. i) Formula Booklet Provided. ii) Matlab Tutorial (booklet) iii) PC, Matlab software
Page 2 of 7 Part A Question 1 Two racing cars have a corner sprung mass of 115kg and an un-sprung mass of 22kg. One car runs soft springs, the other hard springs. The soft springs are marked 750 lbs/in and the hard springs 1000 lbs/in. The motion ratio is 1.3. The vertical stiffness of the tyre is unknown, but some experimental results are available. (a) Use the experimental data in the table below to plot a graph on graph paper and calculate the vertical tyre stiffness in N/mm. Displacement (mm) 0 1 2 3 4 5 6 7 8 9 10 Load (kg) 0 13 33 48 66 91 104 114 147 170 198 (b) Modify the equation for springs in series so that the wheel rate, KW, term can be replaced by the spring rate and motion ratio. (c) Convert the spring rates given into suitable metric units. (d) Calculate the ride rate, KR, for each car. (e) Determine the sprung and un-sprung natural frequencies for each car. (3 marks) (2 marks) (10 marks) (Total: 25 marks)
Page 3 of 7 Question 2 A racing car has a wheelbase of 3200mm, a track of 1525mm (front and rear) and a mass of 800kg. The centre of mass is located 1975mm from the front axle centreline, 330mm above ground level along the centreline of the car. (a) Describe the method by which the static wheel loads of the car can be calculated and calculate for each wheel to 1 decimal place. (b) Determine the maximum lateral load transfer that occurs during cornering given a coefficient of friction between the tyre and the road of 1.2. (c) Estimate the velocity that the car can travel around a 125m radius. State one reason why this value is an estimate. (3 marks) (d) Calculate the increase in required cornering force for the car to travel around the same corner 5 km/h faster. (3 marks) (e) Sketch a diagram showing the forces on a tyre under cornering. The diagram should be a plan view and orientated such that the direction of travel is vertical. Include: direction of travel, slip angle, force from axle, rolling resistance, grip force from road, pneumatic trail and induced drag. (f) With reference to the sketch above, explain the term self-aligning torque (4 marks) (Total: 25 marks)
Page 4 of 7 PART B Question 1 Determine the Transfer Functions: (a) H 1 (s) = C R [13 marks] and (b) H 2 (s) = C D [12 marks] for the feedback loop of Figure 1 given that: G c (s) = s+1 s 2 +s+4, G(s) = 2 0.25s+1 and H = 1 Figure 1 Note that: i) The Transfer Functions H 1 (s) and H 2 (s) have to be determined both analytically and using Matlab. The analytic results for each Transfer Function should be compared with the results obtained through Matlab.
Page 5 of 7 ii) In your answer, the Matlab code developed for obtaining H 1 (s) and H 2 (s) as well as the corresponding outputs should be included. [25 marks] Question 2 a) Find the poles and zeros of the system: G1(s) = (s+1.5) (s2 s+1) (s+2) (s 2 +0.1s+4) Comment on the stability of the system G1(s). b) The Transfer Function of a closed-loop system is: [10 marks] s+1 G2(s) = s 4 +10s 3 +35s 2 +50s+124 Use the Routh Hurwitz stability criterion to determine whether G2(s) is a stable system. [15 marks] [Total marks: 25] End of Questions
Page 6 of 7 Formula Sheet 1kg = 9.81N = 2.205 lbs 1in = 25.4mm g = 9.81 N/kg Equation for Springs in Series: 1 = 1 + 1 K R K W K T Relationship between spring rate and wheel rate: K S = K W x (motion ratio) 2 Sprung Natural Frequency: Un-sprung Natural Frequency: f s = 1 2π K R m s f u = 1 2π K W + K T m U Load Transfer: W X = ± Fh m L W Y = ± Fh m T where h m is the height of the centre of mass above ground level Maximum corning force = W μ Centripetal Force: F = mv2 R
Page 7 of 7 Roots of Quadratic Equations ax 2 + bx + c = 0 x = b ± b2 4ac 2a Routh-Hurwitz Characteristic equation: q(s) = a n s n + a n 1 s n 1 + + a 1 s + a 0 = 0 Routh table: s n a n a n 2 a n 4 a n 6... s n 1 a n 1 a n 3 a n 5 a n 7... s n 2 b n 1 b n 3 b n 5... s n 3 c n 1 c n 3 c n 5............... s 0 g n 1 where b n 1 = 1 a n a n 1 a n 1 a n 2 a = 1 (a n 3 a n a n 3 a n 1 a n 2 ) n 1 b n 3 = 1 a n a n 4 a n 1 a n 1 a n 5 c n 1 = 1 a n 1 b n 1 b n 1 a n 3 b n 3