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MTU EE 5295 - Introduction_to_Propulsion_Systems_HW_2_Drive_Cycle_Ft_Simulink_2013 (1)

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Michigan Tech MEEM/EE 4295: Introduction to Propulsion Systems for Hybrid Electric Drive Vehicles HW_2 Topics: Power Requirement, Introduction to Matlab and Model Based Design (Simulink) Modeling and Matlab Exercise Using the Matlab code from HW-1 as a starting point, add the following. Part I: Matlab 1) Using the Matlab code from HW-1 a) Put the time, velocity and road slope (seconds, MPH, degrees) in arrays. They will appear in the Workspace once you execute the .m file b) List the variables needed, writes to the Workspace. c) Enter the conversion factors you need. d) Add the Simulink “Callbacks” to execute the Matlab file that loads the initial values into the workspace. Part II: Introduction to Simulink Implement the same vehicle model from above using Simulink. The acceleration tables (arrays) from Part I may be used in Part II. This should save significant time in entering the data. If the model in Part I has been validated, it can be used to compare the results in Part II, but not the only validation. 1) Using the Simulink code, MTU_Basic_Drive_Cycle_1.mdl1 shown in class, develop a Simulink model to the tractive force (think “required torque) for the drive cycle. Remember we have rolling resistance, wind drag and road slope. 2) Use your Simulink model to: a) Determine the tractive force needed to maintain the given speed. b) Determine the power needed as a function of time. c) Determine the power lost from aerodynamic drag. d) Determine the increase/decrease in Ft for the change in slope 3) Plot the results for tractive forces versus time. 1 The Simulink model is posted on the web, you may “cut and paste” or use any portion you want.4) Plot the power gained during regeneration. 5) If the power gained during regeneration was lost to heat, put the heat loss in terms of something a potential customer would grasp2. Code/Solution Validation In homework 1, we asked for various plots of force and power given a specific drive cycle. Since the answers were not in the back of the book, you needed a method to validate your code or at least determine if the solution is reasonable. Using what we know about energy expended for portions of a drive cycle, determine if your CALCULATED external forces acting on the vehicle are reasonable. Do this for rolling resistance, wind drag, tractive force and losses due to slope. Also check the power required for at least one of the above forces. The information below is repeated from HW-1. Figure 1 shown below is the velocity versus time of our drive cycle. The cycle is as follows 1) WOT from 0-60 2) Steady state at 60 3) Apply brakes and decelerate to 40 (now behind a slow driver) 4) Steady state at 40 5) WOT from 40-70 to pass 6) Steady state at 70 to complete the pass 7) Decelerate to 55 8) Steady state at 55 9) Maintain 55 while going uphill, the elevation curve (road slope) is shown in Figure 2. i) As we crest the hill, we maintain 55 to the bottom of the hill ii) Steady state at 55 to almost the end of the drive cycle, apply the brakes and stop the vehicle. The drive cycle is being used to demonstrate basic math modeling methods and how to formulate those in Matlab. It is NOT representative of “reasonable” driving. 2 The amount to toast bread, dry hair, etc.During deceleration, we may recover 80% of the energy normally lost due to braking. 0 50 100 150 200250 300 350 400 450 500010203040506070Time, secondsVelocity, mph12345678 9 Figure 1: Vehicle velocity versus time for the drive cycle Figure 2 shown below is the grade of road over our drive cycle. You may notice we are driving on level ground most of the time. At a time of 300 seconds, we start up an incline of 4.0 degrees. Once we reach the top of the hill the slope is now a -4.5 degrees. We maintain the 55 mph speed down the hill and by good use of our brakes and our magic regeneration system. Once we meet the bottom of the hill we maintain a constant speed for the remainder of the drive cycle until braking at the end. The entire drive cycle has taken 500 seconds. For the given system we first model the vehicle. Figure 3 is our standard 2-D car model3. The forces acting on the vehicle are summed in the X-direction, our direction of motion. For most of the cycle the direction of travel is horizontal. 3 Fundamentals of Vehicle Dynamics, T. D. Gillespie, SAE Publication, 1992.Figure 2: Road slope for the drive cycle. For this problem include rolling resistance and wind drag, but neglect other power losses. The Cd for this model is 0.40. You may assume a constant temperature of 72o F. Time Velocity, mph Slope, degrees 0 0 0 13.0 60 0 145.0 60 0 148.0 40 0 160.0 40 0 165.5 70 0 180.0 70 0 183.0 55 0 300.0 55 Starts up the hill, slope of 4 degrees 350.0 55 Apex or top of hill, starts down 390.0 55 Bottom of hill, slope returns to zero 493.6 55 0, Start to brake 500.0 0.0 0, vehicle at rest Table 1: Data use to generate Figure 1. 050100150200250300350400450500-5-4-3-2-101234Time, secondsSlope, degreesWe are working this problem in SAE units, you may convert them if you choose. Table 2: Item Value Units Weight 4,100 Lbf ρ 0.00236 Lbf-sec2/Ft4 g 32.17 Ft/sec2 Cd 0.4 Unit less A 2.7 meters2 θ Given in table and figures degrees Symbol Definition Units Wf Front wheel load Wr real wheel load ha distance to location of drag forces h distance to cg L wheelbase b distance to front wheels from cg c distance to rear wheels from cg Rxf rolling resistance, front wheels Da Fxf Wr Wf Rxf Rxr Fxf Figure 3: Basic model of the vehicle and the external forces.Rxr rolling resistance, rear wheels Fxf tractive force, front wheels Fxr tractive force, rear wheels θ Road slope When we sum the forces in the X-direction we get the following equation. sin( )atXfF mx F R D mgθ==−−−∑ Rolling resistance may be approximated as follows if we use a function that approximates the friction losses as a linear function of speed. It is commonly written as: 1100fVfWR= + f=0.01 and W is the weight in Lbf, V is in mph. Since all of the calculations are in Ft and Lbf., convert the equation to the form 1fvfXfWKR= + and determine the appropriate value of Kfv for the velocity in Ft/sec. The variable Kfv is the conversion to allow you to use Ft/sec. Wind drag may be approximated by the following. 212adD C AXρ= The variables are ρ=density


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