Mechanical Engineering ME 481 Vehicle Design Fall 2000 Lecture Notes By Richard B. Hathaway, Ph.D., PE Professor Mechanical and Aeronautical Engineering Section 1 Energy Consumption and Power Requirements in Design 2 Aerodynamics and Rolling Resistance GENERAL FORMULAS - AERODYNAMIC Dynamic Pressure: 2 2 1 vP d  Drag Force: )( 2 1 2 REfAvF d  ACvF dd 2 2 1  2 0 )()2.1( 2 1 vvACF dd  Aero Power f(RE) A V (2) = P 3  C d = coefficient of drag  = air density  1.2 kg/m 3 A = projected frontal area (m 2 ) f(RE) = Reynolds number v = vehicle velocity (m/sec) V 0 = headwind velocity ENGLISH UNITS V A C ) 10 X (6.93 = HP 3 d -6 aero where: A = area (ft 2 ) V = velocity (MPH) C d = drag coefficient 3 SI UNITS                           W kW AC V (2) = P d 3 KW 1000 1 1000 3600 2.1 3 )( 862 0 2 VV V A C x ) 10 x .(1 = P d -6 aero  P = power (kw) A = area (m 2 ) V = velocity (KpH) V 0 = headwind velocity C d = drag coefficient  = 1.2 kg/m 3 GENERAL FORMULAS – ROLLING RESISTANCE ENGLISH UNITS 375 V x W C = HP rrrr where: C rr = coefficient of rolling resistance W = weight (lbs) V = velocity (MPH) SI UNITS V x M x C x ) 10 x (2.72 = P V x M x C x 3600 9.81 = P rr 3- rr rrrr       where: P = power (kw) C rr = coefficient of rolling resistance M = mass (kg) V = velocity (KpH) 4 TRACTIVE FORCE REQUIREMENTS. Vehicles require thrust forces, generated at the tires, to initiate and maintain motion. These forces are usually referred to as tractive forces or the tractive force requirement. If the required tractive force (F) is broken into components the major components of the resisting forces to motion are comprised of acceleration forces (F accel = ma & I forces), Gradeability requirements (F grade ), Aerodynamic loads (F aero ) and chassis losses (F roll resist ). F = F aero + F roll resist + F grade + F accel = (/2) C d A v 2 + C rr m g + %slope m*g + m a = (/2) C d A v 2 + m g{C rr + % slope + a/g} in SI units: A = frontal area (m 2 ) v = velocity (m/s) m = mass (kg) C rr = coefficient of roll resistance (N/N) usually approx .015 C d = coefficient of aero drag for most cars .3 - .6 % slope = Rise/Run = Tan of the roadway inclination angle Steady state force are equal to the summation of F aero + F roll resist + F grade Fgrade resist Froll Faero  ss F Transient forces are primarily comprised of acceleration related forces where a change in velocity is required. These include the rotational inertia requirements (F I  ) and the translational mass (F ma ) requirements, including steady state acceleration. VEHICLE ENERGY REQUIREMENTS. The energy consumption of a vehicle is based on the tractive forces required, the mechanical efficiency of the drive train system, the efficiency of the energy conversion device and the efficiency of the storage system. Examples of the above might best be demonstrated with the following. Storage efficiency: A flywheel used for energy storage will eventually lose its total energy stored due to bearing and aerodynamic losses. A storage battery may eventually discharge due to intrinsic losses in the storage device. These losses can be a function of the % of the total system capacity at which the system is currently operating. A liquid fuel usually has extremely high storage efficiency while a flywheel may have considerably les storage efficiency. Both however have the storage efficiency a function of time. 5 100x E EE EfficiencyStorge initial fianlinitial store            Conversion efficiency: An internal combustion engine changes chemical energy to mechanical energy. The system also produces unwanted heat and due to moving parts has internal friction which further reduces the system efficiency. A storage battery has an efficiency loss during the discharge cycle and an efficiency loss during the charge cycle. These efficiencies may be a function of the rate at which the power is extracted. 100x E PE EfficiencyConversion fuel deliveredfuel conv   mechanicalthermalconv x  Drive system Efficiency: Conversion of chemical or electrical to mechanical energy does not complete the power flow to the wheels. Drive train inefficiencies further reduce the power available to produce the tractive forces. These losses are typically a function of the system design and the torque being delivered through the system. 100x P PP EfficiencyMechanical sourcepower tractivesourcepower drivemech    n redredreddrivemech xx  21  6 Reasonable Efficiencies to use for cycle comparisons (Efficiencies shown are only approximations)  Electric Motor (Peak)  = 95%  Electric Motor Efficiency (Avg if 1 spd Trans)  = 75%  Electric Motor Efficiency (Avg if CVT)  = 95%  Transmission Efficiency (0.95) = 1)-(R   Battery Efficiency (Regen)  = 75-85%  Battery & Generator Efficiency (Regen)  = 50-55%  Battery & Motor Efficiency (Accel)  = 80%  Solar Cell Efficiency  = 15%  IC Engine (Peak Efficiency)  = 30%  Flywheel Efficiency (Storage and Conversion Average)  = 70% 7 Experimental Coast Down Testing 1) Perform a high speed and a low speed test with an incremental ( 5km/hr) velocity change at each velocity. 2)High Speed Low Speed V a1 = 60 km/h V a2 = 20 km/h V b1 = 55 km/h V b2 = 15 km/h 3) Record the times over which the velocity increments occur. T h = 4 sec T l = 6 sec 4) Determine the mean speed at each velocity. 5) Determine the mean deceleration at each velocity. 6) Determine the drag coefficient 7) Determine the coefficient of rolling resistance. 8 h kmvv v ba    2 11 1 h kmvv v ba    2 22 2 s hkm t vv a ba / 1 11 1    s hkm t vv a ba / 2 22 2    )( )(6 2 2 2 1 21 vv aa A m c d    )( )( 10 2.28 2 2 2 1 2 21 2 12 3 vv vava c rr    Section 2 Weight and Weight Factors in Design 9 WEIGHT and ROTATIONAL INERITA EFFECTS: Thrust force (F), at the tire footprint, required for vehicle motion: F = F aero + F roll resist + F grade + F accel = (/2) C d A v 2 + C rr m g + %slope m*g + m a F = (/2) C d A v 2 + m g{C rr + % slope + a/g} in SI units: A = frontal area (m 2 ) v = velocity (m/s) m = mass (kg) C rr = coefficient of roll resistance (N/N) usually approx .015 C d = coefficient of aero drag for most cars .3 - .6 % slope = Rise/Run = Tan of the roadway inclination angle If rotational mass is added it adds not only rotational inertia but also translational inertia. r a = k m = I = dt d I = T tire vehicle wheelcomp 2 compi   a r k m = r a k m = r T = F 2 tire 22 2 2 tire 2 tire wheel i                 1  = angular acceleration k = radius of gyration t = time T = Torque m = mass  = ratio between rotating component and the tire Therefore if the mass rotates on a vehicle which has translation, a * m 1 + r k = F R 2 tire 22 i t&r           2 F = F aero + F roll resist + F grade + F accel = (/2) C d A v 2 + C rr W t + %slope W t + W t a/g                   m + r k m a + Slope% + C g m + V A C = F t 2 tire 22 rrrt 2 d tire   2 3  = angular velocity of the component T i = applied torque to overcome inertia I = mass moment of inertia  wheel = angular acceleration of the wheel a = translational acceleration of the vehicle r tire = rolling radius of the tire (meters) T wheel = applied torque at the wheel F i = tractive force at the tire footprint to overcome inertia F i(r&t) = tractive force at the tire footprint required for losses and translational and rotational inertia 10 [...]... by the vehicle stiffness  Vehicles typically are called upon to meet deflection criteria in design a) meeting deflection criteria will establish designs that inherently meet stress related criteria b) Chassis design will require the engineer assure that key deflection limits are imposed for critical locations on the chassis, frame and body c) Vehicles modeled to meet crash standards may also meet deflection... Synchromesh which provides a quicker and more responsive gear change and a closer feel for engine performance Design consideration for gears:  Engine speed vs Vehicle speed graph is plotted for determining the gear ratios  Various important gear design parameters are calculated as follows:  Normal tooth thickness  Tooth thickness (at tip)  Profile overlap  Measurement over balls  Span measurement... define bending due to the frame “kick-ups” that are present in rear wheel drive and dependent rear suspension vehicles 1 This is measured with the frame supported and weight added to the rear extremities of the vehicle at or near the rear bumper location 2 The measure was to assure adequate stiffness as the frame was shaped to allow clearance for rear axle movement  A parameter that is commonly used... of manual transmission are:  Sliding mesh type  Constant mesh type  Synchromesh gear box The various components of a manual gearbox and their respective design considerations are listed: Design considerations for shaft: There are 3 shafts in the gearbox, namely: Input or clutch shaft, Intermediate or lay shaft and Output or main shaft  Input or clutch shaft: Design consideration: Shear and torsional... standards in the design process d) All measures; deflection, stress and yield, and impact must be verified in the design process STIFFNESS IS MEASURED IN A NUMBER OF MODES a) Torsional ridgidity is commonly used as measure of the overall stiffness quality 1 Fundamentally this is a measure of the deflection that occurs if all the load were place on diagonally opposite tires of the vehicle As deflection... -r 27 Section 4 Suspension Design Considerations 28 EXPERIMENTAL DETERMINATION OF THE STRUCTURAL INTEGRITY OF VEHICLES  Vehicle stiffness is an important parameter which influences ride quality, handling properties, and vehicle aesthetics  Vehicle stiffness determines the quality of fit of many external panels and the interaction of the surface panels as uniform and asymmetric loads are applied ... circle diameter in millimeters It is denoted by pd Mathematically, Diametrical pitch, pd  T   D pc where, T = Number of teeth 21 D = Pitch circle diameter 12 Module: It is ratio of pitch circle diameter in millimeters to the number of teeth It is usually denoted by m Mathematically, Module, m = D / T 13 Clearance: The radial distance from the top of the tooth to the bottom of the tooth, in a meshing... lower to permit reducing the hump on the floor Terms used in gear design: 1 Pitch circle: An imaginary circle, which by pure rolling action would give the same motion as the actual gear 2 Pitch circle diameter: The diameter of the pitch circle The size of the gear is usually specified by the pitch circle diameter It is also called as pitch diameter 3 Pitch point: The common point of contact between two... FLYWHEELS  Mechanical (Kinetic Energy) 1 I 2 2 KINETIC ENERGY POWER = time KE = 6 IV HYDRAULIC  Accumulator (Pressure, Volume) (Potential Energy) POWER = Q x P V BATTERY  Generator recharging  Solar Recharging (Electrical Energy) 14 ENERGY CONVERSION I INTERNAL COMBUSTION ENGINES:  Otto cycle  Diesel cycle  Brayton cycle II EXTERNAL COMBUSTION ENGINES:  Stirling cycle  Rankine cycle III MECHANICAL: ... to a hydraulic wheel cylinder which utilizes the hydraulic pressure to create a mechanical apply force WHEEL CYLINDER APPLY FORCE Fwc  Pmc x Awc  Pmc x  Awc   2 d wc = Fmc x   A  = ( F pedal x M.A pedal ) + F booster x  4  mc   d 2 wc   2     d mc  The wheel cylinder mechanical force is applied to the metal backing of the friction material The friction material, upon apply, is forced . Mechanical Engineering ME 481 Vehicle Design Fall 2000 Lecture Notes By Richard B. Hathaway, Ph.D., PE Professor Mechanical and Aeronautical Engineering. thickness (at tip)  Profile overlap  Measurement over balls  Span measurement over teeth etc., With the input parameters being  Number of teeth  Module