Michigan Tech MEEM/EE 4295: Introduction to Propulsion Systems for Hybrid Electric Drive Vehicles HW-3 Topics: Driver Input (WOT), Torque and Traction Limits, Numerical Integration, Gear Ratio Influence on Performance In HW: 1-2, the tractive force necessary to meet a specific drive cycle was calculated WITHOUT consideration of the tractive force and powertrain limits. In HW 4-6, a linear vehicle dynamics subsystem, an e-drive and IC engine subsystem, transmission and differential subsystem and driver subsystem will added to the Simulink model from HW-2. In this problem, both available torque and traction limits will be considered (we are now moving into the real world) and you are given an engine torque curve for a 1939 Ford Flat Head V-8 as a starting point. For those interested in a modern IC Engine, use the torque curves from the four cylinder engines, Ford ZeTec or GM ECOTec1. As part of your analysis you will want to show the performance that is demanded of a vehicle when entering an interstate highway from the approach ramp of 600 feet in length when the traffic is moving at an average speed of 65 mph and the difficulty in reaching those speeds with minimal power and WITHOUT the e-motor assist. Start the vehicle in first gear at zero speed, shift to the next highest gear when the tractive force in the “upshift” gear is higher than current gear. You may assume the time to shift is infinitely fast. Model the torque as a 2nd order polynomial, TICE=C0+C1ω+C2ω2 For the initial test case using an IC Engine with a maximum of 75 Hp ( or 55.95 kW) and the gear ratios given below, determine the elapsed time to travel 600 Ft. and the speed at the end of 600 Ft of WOT. Use either Matlab or excel to curve fit the data, once you have the coefficients for a specific engine, you may scale them to fit a different max power. Note that peak power and peak torque DO NOT occur at the same rpm when an engine torque curve is represented by a 2nd order polynomial. The curve may be a separate program. Use Matlab and Euler’s integration method to integrate the acceleration equation. Include the rolling resistance, wind drag and road slope. Assume two road slopes, 0.0 and 5 degrees. A suggested time step is 0.01 seconds or less. 1 While both are less than 3 liters, they can “hot-rodded” to 1,400 Hp.Use a road friction of µ=0.8 and fr=0.015. The power, gear and differential ratios, plus the overall size of the vehicles will probably result in an under performing vehicle. Gear ratios (Labeled as Nt(i) in the lectures) 1st=2.5/1 2nd=2.0/1 3rd=1.0/1 ND=2.3/1 Compare the performance with a CVT with the same vehicle parameters. Once you are satisfied with the model, design a five speed (or greater) transmission to increase the performance (approach the CVT). You may increase the power for this portion. Your last name starts with Differential Ratio A-G 3.73/1 H-L 3.55/1 M-P 3.82/1 Q-Z 3.25/1 Table 1: Transmission and final drive (differential) ratios. Your last name starts with Weight, Newton Area, meters2 Tire Radius, meters Cd Wheelbase, Meters L=variable Front/Rear Weight Ratio L/H Ratio H=height to cg. A-G 18,680 2.40 0.318 0.44 2.89 52.0 3.71 H-L 18,680 2.45 0.318 0.44 2.89 52.0 3.71 M-P 13,400 2.10 0.303 0.38 2.61 51.5 3.93 Q-Z 18,460 2.37 0.355 0.42 2.91 52.1 3.69 In the discussion of the results, include plots of Ft versus velocity, be sure to include the CVT. Include plots of velocity versus distance. Remember the validation.Da Fxf Wr Wf Rxf Rxr Fxf Figure 1: Basic model of the vehicle and the external forces.Figure 2: A classical torque curve from the "state of the art" engine of that time
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