ME 466 PERFORMANCE OF ROAD VEHICLES 2016 Spring Homework 3 Assigned on Due date:

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1 PROBLEM 1 For the vehicle with the attached specifications and road test results a) Draw the tractive effort [N] versus velocity [kph] for each gear on the same plot. b) Draw the variation of total resistance [N] (on level road) on the same plot. c) Using the plots of tractive effort and total resistance curves, estimate the maximum speed [kph] and the corresponding engine speed in all gears. d) How do your results compare with th road test results? List possible reasons for any differences you may note. Note: i) Remember that the relation between vehicle speed and engine speed is given by: r V r w w V n (1) e i i s n i i s t d e t d In the vehicle specifications, the mph per 1000 rpm value is specified for each gear seperately. Thus if you use the specified mph per 1000 rpm values instead of approximate rolling tire radius and slip factor, you will avoid the uncertainities associated with the determination of rolling tire radius and slip factor. ii) You can take test weight as (kerb weight + 2*74+19) [kgf], to account for the driver and the test assistant, and instrumentation. Assume that the front and rear tire pressures are 2.0 and 1.9 kgf/cm 2. PROBLEM 2 Calculate the maximum vehicle velocity (for the vehicle of Problem 1) together with the corresponding engine speed, using the analytical expression obtained by setting the net tractive effort to zero. PROBLEM 3 For the same vehicle, estimate the time required to accelerate from 110 kph to 140 kph in 4 th gear. Note: You can take the same test weight given for Problem 1, and front and rear tire pressures as 2.0 and 1.8 kgf/cm 2, and consider wind at 7.5 m/s against motion. PROBLEM 4 The following data, including the partially open throttle characteristics of the engine, belongs to a small car. The driver depresses the accelerator pedal such that the throttle is 40% open and increases the engine speed to 3000 rpm, while the vehicle is stationary in first gear and takes his foot off the clutch pedal immediately. Estimate i) The time for the clutch to fully engage ii) The synchronization speed iii) The vehicle speed reached at the end of the engagement period Vehicle Specifications: Vehicle mass: 1175 kg Moment of inertia of parts: Rotating at engine speed: 0.25 kg.m 2 propeller shaft speed: 0.03kg.m 2 wheel speed: 6.40 kg.m 2

2 First gear ratio: 3.65 Differential ratio: 4.45 Rolling tire radius: Throttle Opening [%] Engine Torque (Nm) Engine Speed (rpm) PROBLEM 5 A simplified powertrain model is shown in Figure 1. The dynamic model includes a lumped engine inertia Ie, a torque converter, a gear box with input and output gear inertias It and I2 about their axes of rotation, and a vehicle with inertia Iv. Engine and vehicle damping are modeled by damper coefficients Be and Bv respectively. The following nomenclature and parameters are given.

3 Parameters Symbol Value Unit Engine inertia Ie kg.m 2 Engine speed e Variable rad/s Engine damping coefficient Be Nm/(rad/s) Input gear inertia It kg.m 2 Output gear inertia I kg.m 2 Input gear speed t Variable rad/s Output gear speed v Variable rad/s Gear ratio g g= 2/ 1= NA Vehicle speed Vveh v m/s Vehicle load TL Vveh 2 Nm Vehicle damping coefficient Bv 0.1 Nm/(rad/s) Vehicle inertia (lumped) Iv 170 kg.m 2 Torque converter characteristics are approximated by quadratic relationships, through simplified fluid dynamics equations. In the torque multiplication mode t 1 p 2 p t 3 t (2) p 4 p 5 p t 6 t In the coupling mode T T p t t 7 p 8 p t 9 t We have two sets of torque converter characteristics, given below: Converter 1 (N.m.s 2 ) Converter 2 (N.m.s 2 ) a a a a a a a a a a. Derive the dynamic equations describing the system. b. Implement the model using Simulink. Submit your Simulink model. Recommendation: When building Simulink block diagrams, use variables in the block diagrams instead of using numerical values directly. Assign numerical values to the variables using an m-file. c. Assuming a constant engine torque Te= Nm, run simulations with the two sets of given torque converter characteristics. Submit the following results for each of these cases: 1) e and t versus time. 2) Pump and turbine torques versus time (3)

4 3) Torque ratio (turbine torque/pump torque) versus speed ratio (turbine speed/pump speed) 4) K-factor (defined by p/tp 0.5 ) versus speed ratio 5) Efficiency versus speed ratio 6) Energy dissipated by the torque converter versus time 7) Vehicle speed versus time Comment on the differences between the two torque converters. d. In this exercise we wish to estimate pump and turbine torques based on measured engine and turbine speeds, used in conjunction with known torque converter characteristics. Since torque converter characteristics are commonly available in the form of K-factor versus speed ratio and Torque ratio versus speed ratio, we will use torque converter characteristics in this form. Since we generated torque converter characteristics in (c) above in this form, we will use these results. (1) Get the torque converter data below for the Torque Converter 1 in tabular form: K-factor versus speed ratio Torque ratio versus speed ratio Note: Take enough points to ensure that the characteristics can be reconstructed fairly accurately using linear interpolation. (2) Construct an Estimator block to (i) estimate Tp from the K-factor table and then (ii) estimate Tt from the torque ratio table. Attach your Simulink block diagram. (3) Run the simulation in (c) again for Torque Converter 1. Attach the following results: Estimated pump torque and the original pump torque, versus time Estimated turbine torque and the original turbine torque, versus time Comment on the comparison. (4) Comment on the usefulness of the technique proposed here, as a way to estimate pump and turbine torques on-line from measured pump and turbine speeds. PROBLEM 6 Two simple planetary gear sets that can be used in an automatic transmission are given in the links below, namely the Simpson three speed and the Ravigneaux four speed planetary gear-sets. Derive the input-output speed ratio for each gear for both gear sets. Find the errors in the given speed ratios underneath the video in the links, if there are any. Simpson compound planetary gear set: Ravigneaux compound planetary gear set: You need to refresh your 301 knowledge for this problem.

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