PRIUS动力系统sinmulink建模.doc

2 IntroductionFor this project, we examined the transmission described in Patent No. 6837816 for use in a hybrid Toyota Prius. Specifically, we looked at modifying the number of gear teeth, the shift sequence, and the shift time in order to optimize the time to accelerate from 0 to 60 mph using the transmission shown in Figure 2.1. Figure 2.1: Diagram of TransmissionThe transmission is driven by an internal combustion engine (20) and an electric motor (30) with shaft 50 as the output. There are two planetary gear trains and four clutches (61, 62, 63, and 64). We are given sixteen different operating modes, which involve various clutch configurations. Table 2.1 shows all of the possible operational modes. Table 2.1: Operational ModesClutches EngagedMotor OperatingNo.Operational Mode61626364Condition1Motor-OnlyXMotor2Power 1XXMotor3Power 2XXMotor4Power 3XXMotor5Engine Charge 1XXGenerator6Engine Charge 2XXGenerator7Engine Charge 3XXGenerator8Continuous Variable Transmission/ChargingXGenerator9Engine-Only 1XXFree Wheeling10Engine-Only 2XXFree Wheeling11Engine-Only 3XXFree Wheeling12Engine-Only 4XXStationary13Regenerative Breaking 0XGenerator14Regenerative Breaking 1XXGenerator15Regenerative Breaking 2XXGenerator16Regenerative Breaking 3XXGenerator3 Problem StatementThe project objective was to optimize the time required for a Toyota Prius to accelerate from 0 to 60 mph using the transmission described. There are three parameters used for the optimization: the number of teeth of each gear, the shift sequence, and the shift timing. Table 3.1 lists the pertinent parameters as assigned by the Rose-Hulman Mechanical Engineering Department for this project. Table 3.1: Known ParametersParameterGiven ValuesProjected Cross-Sectional AreaVehicle WeightDrag CoefficientEngine Torque Relationship(600 to 5000 rpm)Motor Torque Relationship(0 to 6000 rpm)Wheel RadiusFinal Gear ReductionRolling Resistance CoefficientAir DensityIn order for the transmission to fit the size of the Prius, constraints were imposed on the number of gear teeth to limit the sizes of the gears. The number of teeth on the ring gear was no more than 150 teeth. As a minimum, the number of teeth on either the planet gear or the sun gear was no less than 14 teeth. Using the guidelines for gear train design, the ratios of gear teeth were no greater than 10:1. For the purpose of this project, we made a few additional assumptions. For simplicity, we assumed the clutching changes to be instantaneous. We also assumed that the car wheels were rolling without slip. 4 Design Calculations In order to analyze the problem, we created a free-body diagram of the Toyota Prius. We made the assumption that the car could be treated as a point mass. The free-body diagram is shown in Figure 4.1. y xfrollFDragWNFDriveDirection of motionFigure 4.1: Free-Body Diagram of CarFrom this diagram, we applied conservation of linear momentum, that is, in the y-direction to obtain: (1)where is the normal force in and is the weight in . When simplified, the equation becomes.(2)We also applied conservation of linear momentum, that is , in the x-direction to obtain: (3)where is the driving force of the car in , is the drag force in , and is the rolling resistance force in . For this project, we assumed that the drag force could be modeled as follows: (4)where is the unitless drag coefficient, is the density in , is the velocity in , and is the projected cross-sectional area in . We modeled the rolling resistance with the following equation:(5)where is the unitless coefficient of rolling resistance and is the weight of the car in . This assumes that the vehicle is rolling without slip. To find the driving force, we created a free-body diagram of the wheel. The free-body diagram of the wheel is shown in Figure 4.2. FDriveNTDriveWFigure 4.2: Free-Body Diagram of Car WheelWe then applied conservation of angular momentum, that is , to the system above to get(6)where is the driving force in , is the radius of the car wheel in , and is the drive torque in . In this case, we assumed that was negligible since the mass of the wheel is significantly less than the mass of the entire car. Thus, we simplified the equation to .(7)Further simplification leads to the equation.(8)The driving torque is governed by the torque of the motor and the gear reductions according to the following equation: (9)where is the gear reduction of the engine, is the gear reduction of the motor, and is the final gear reduction. Substituting equation (9) into equation (8) we get.(10)In order to find , we applied conservation of energy and simplified to get:(11)Using all of these equations, we derived a single equation for the motion of the car: .(12)In order to limit the possible clutch configurations, we chose to analyze the first four modes only. Motor-only, Power 1, Power 2, and Power 3 are the modes where the torque of the motor is added to the torque of the engine. For other modes, the transmission acts as a generator or braking mechanism or remains stationary. These modes do not provide optimal acceleration capabilities, so we chose to neglect them. For the four modes we analyzed, we calculated the planetary gear ratios using the tables shown in Appendix A. The resulting ratios are shown in Table 4.1. Table 4.1: Planetary Gear AnalysisModesMotor SpeedEngine Speed1: Motor Only2: Power 13: Power 24: Power 35 Final DesignThe equations derived in the calculations section were modeled using MATLAB and Simulink (see Appendix B) in order to numerically evaluate the performance of the transmission. This enabled us to vary each of the inputs to test different states and configurations of the transmission. By graphically examining each output, we were able to arrive at certain conclusions based on the resulting outcome. This method of guess and check in fact helped us realize certain fundamental properties of the engine, which we may not have otherwise observed. For instance when Power Mode 2 was engaged, it was observed that for whatever shift period it was engaged for, we were getting less performance than with Power Mode 3. This led us to try using a gear shift sequence that actually omitted Power Mode 2 from the sequence. In the end, we were able to get desirable results for our 0 to 60 mph time.After analyzing many different configurations, we arrived at one particular setup, which seemed to be our best option. Although there was no way to test every possible combination by the methods we used, the configuration below seemed to be best we could achieve based on our judgments.Table 5.1: Gear Teeth and Clutch SequenceN10165 teethN102125 teethN10330 teethN201120 teethN202150 teethN20315 teethMotor-Only Time0.30 secPower 1 Time2.68 secPower 2 Time0.00 secPower 3 Time5.20 sec6 ResultsBy implementing the values in Table 5.1 in the Simulink model, the optimal 0 to 60 mph time was 8.18 seconds. A graphical representation for the performance of our car during this acceleration period can be seen in Figure 6.1. Table 6.1 lists the initial and final velocities of the car for each clutch sequence.Figure 6.1: Car Velocity as a Function of TimeTable 6.1: Clutch Sequence Car VelocityModeInitial VelocityFinal VelocityMotor-Only0 mph4.38 mphPower 14.38 mph35.13 mphPower 335.13 mph60.02 mph7 Conclusions & RecommendationsOur result of an 8.18 second 0 to 60 mph is an improvement from the current transmission model used in the Toyota Prius. There are a few reasons that our time differs from the current model. Our estimate for the rolling resistance was lenient and assumed the car rolled without slip. In actuality, there would be some slip causing a different approximation for the rolling resistance. Another reason our value differs is that we treated the shift time as instantaneous. To get a better model of the actual car, we should have added the times to shift between clutch configurations. We also assumed the car could be treated as a point mass. The model could be improved by redoing the conservation of linear momentum calculations for a rear wheel drive car. The model could also be improved by incorporating conservation of angular momentum. Despite all of these apparent shortcomings, we believe this transmission design is a reliable and worthwhile representation of the actual hybrid transmission.8 ReferencesTsai, Lung-Wen.; Schultz, Gregory A., Motor Integrated Parallel Hybrid Transmission. US 6,837,816. (4 January 2005).Tsai, L., Schultz, G. and Higuchi, N., “A Novel Parallel Hybrid Transmission,” Proceedings of ASME Design Engineering Technical Conferences, 2000.Appendix A: Planetary Gear AnalysisMode No. 1: Motor OnlySunPlanetRingRatio: , where and Mode No. 2: Power 1SunPlanetRingRatio: , where Mode No. 3: Power 2SunPlanetRingRatio: SunPlanet Ring Ratio: Mode No. 4: Power 3SunPlanet Ring Ratio: , where Appendix B: Simulink Models Motor Only ModePower 1 ModePower 2 ModePower 3 ModeAppendix C: Matlab Code%*%Program Description:%The following program calculates the time it takes for a car to accelerate%from 0 to 60 MPH. The program also outputs the initial and final%velocities during each operational mode for the transmission. %Input: N_101 - number of teeth on sun gear 101% N_102 - number of teeth on ring gear 102% N_103 - number of teeth on planet gear 103% N_201 - number of teeth on sun gear 201% N_202 - number of teeth on ring gear 202% N_203 - number of teeth on planet gear 203% t_final_mo - length of time spent in motor-only mode s% t_final_p1 - length of time spent in power 1 mode s% t_final_p2 - length of time spent in power 2 mode s% t_final_p3 - length of time spent in power 3 mode s%Output: zeroSixtyTime - time for car to accelerate from 0 to 60 mph s% velocity_final_mo - velocity at end of motor only interval mph% velocity_final_p1 - velocity at end of power 1 interval mph% velocity_final_p2 - velocity at end of power 2 interval mph% velocity_final_p3 - velocity at end of power 3 interval mph %* %number of teeth on each gear in the transmission (varied inputs) N_101=65;N_102=125;N_103=(N_102-N_101)/2;N_201=122;N_202=150;N_203=(N_202-N_201)/2; %*%MOTOR ONLY MODE t_initial_mo=0;t_final_mo=0.3; %length of time in motor-only mode (varied input)v_0_mo=0; %velocity at start of motor only mode mph %runs Simulink model for motor only modesim(motor_only,t_initial_mo,t_final_mo)t_mo=time;velocity_mo=velocity_out; %plots the motor only mode over prescribed length of time%figure(1)%plot(t_mo,velocity_mo)%grid%xlabel(Time s)%ylabel(Car velocity in MPH)%title(Motor Only Mode) %velocity at beginning of interval mphvelocity_initial_mo=velocity_mo(1)%velocity at end of interval mphvelocity_final_mo=velocity_mo(t_final_mo-t_initial_mo)*100+1)%* %*%POWER ONE MODE t_initial_p1=0;t_final_p1=2.72; %length of time in power 1 mode (varied input)v_0_p1=velocity_final_mo*5280/3600; %velocity at start of power 1 mode mph %runs Simulink model for power 1 mode sim(power_one,t_initial_p1,t_final_p1)t_p1=time;velocity_p1=velocity_out; %plots the power 1 mode over prescribed length of time%figure(2)%plot(t_p1,velocity_p1)%grid%xlabel(Time s)%ylabel(Car velocity in MPH)%title(Power One Mode) %velocity at beginning of interval mphvelocity_initial_p1=velocity_p1(1) %velocity at end of interval mphvelocity_final_p1=velocity_p1(t_final_p1-t_initial_p1)*100+1)%* %*%POWER TWO MODE t_initial_p2=0;t_final_p2=0; %length of time in power 2 mode (varied input)v_0_p2=velocity_final_p1*5280/3600; %velocity at start of power 2 mode mph %runs Simulink model for power 2 mode sim(power_two,t_initial_p2,t_final_p2)t_p2=time;velocity_p2=velocity_out; %plots the power 2 mode over prescribed length of time%figure(3)%plot(t_p2,velocity_p2)%grid%xlabel(Time s)%ylabel(Car velocity in MPH)%title(Power Two Mode) %velocity at beginning of interval mphvelocity_initial_p2=velocity_p2(1)%velocity at end of interval mphvelocity_final_p2=velocity_p2(t_final_p2-t_initial_p2)*100+1)%* %*%POWER THREE MODE t_initial_p3=0;t_final_p3=6; %length of time in power 3 mode (varied input)v_0_p3=velocity_final_p2*5280/3600; %velocity at start of power 3 mode mph %runs Simulink model for power 3 mode sim(power_three,t_initial_p3,t_final_p3)t_p3=time;velocity_p3=velocity_out; %plots the power 3 mode over prescribed length of time%figure(4)%plot(t_p3,velocity_p3)%grid%xlabel(Tim