Vehicle dynamics course
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This document provides an overview of a vehicle dynamics course. It discusses topics that will be covered such as vehicle dynamics fundamentals, load transfer, acceleration and braking performance, wheel alignment, handling, ride forces, suspension technologies, tires, and vehicle dynamic tests. The course will examine chapters on vehicle dynamics, longitudinal and lateral load transfer, tractive effort and forces, weight transfer, and the relationship between road loads and tractive resistance. It also provides examples of vehicle dynamic field tests. The goal is for students to gain an understanding of key vehicle dynamics concepts and metrics.
![Gradeability
91
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![Determination of Unknowns
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Vehicle dynamics course
- 1. 1 Vehicle Dynamics Course M.H. Monish Gowda Hima Kiran Vithal V. M. S. Ramaiah School of Advanced Studies Bangalore
- 2. 2 Vehicle Dynamics 1. Vehicle Dynamics and Fundamentals of Load Transfer 2. Acceleration and Braking Performance 3. Wheel Alignment, K & C and Steering Performance 4. Roll Centers, Roll Axis, Squat and Dive 5. Handling and Vehicle Dynamic Tests 6. Vehicle Roll Over and Fish Hook Test 7. Ride and Excitation Forces 8. Bounce and Pitch Centers 9. Suspension Technologies: Passive, Semi Active and Active Suspension 10. Tyres and Carpet Plots 11. Design & Development Process for Vehicle Dynamics 12. Vehicle Dynamic Examples 13. Vehicle Dynamic Field Tests
- 3. 3 Chapter-1 • Vehicle Dynamics and Fundamentals of Load Tranfer – Metrics – Road Loads- Tractive Resistances – Tractive Effort and Forces – Basics of Weight Transfer • Longitudinal Load Transfer • Lateral Load Transfer – Forces Between Road and Wheel
- 4. 4 Mobility Organisation for Economic Co-operation and Development (OECD)
- 5. 5 Automotive Mission Plan India • By 2016, India will emerge as the destination of choice in Asia for the design and manufacture of automobiles and automotive components. The output of the India’s automotive sector will be US$ 145 billion by 2016, contributing to 10% of India’s GDP and providing employment to 25 million persons additionally
- 6. 6
- 7. 7 Ground Vehicles Ground Vehicles Non Guided Ground Vehicles Guided Ground Vehicles Road Vehicles Off Road Vehicles
- 8. Passenger Car Square Back Fast Back Hatch Back Notch Back 8
- 9. Passenger Car-Anatomy and Packaging 9
- 10. Passenger Car Main Parts 10
- 13. 13 Automobile Drive Systems Rear Wheel Drive Four Wheel Drive Front Wheel Drive
- 15. 15 Centre of Gravity of the Vehicle X X Y Z Front Axle Rear Axle bc h L t GL Wrs WfsW
- 16. 16 Track width Wheel Base and Track Width of Cars
- 17. 17 Centre of Gravity -Positions L W W b rs
- 18. Height of CG Wf Wr W • Please see the Longitudinal Weight Transfer equation during grades • Wf= Wfs –W (h/L) (can be written as tan) • h= (L/W)[Wfs-Wf](1/tan] • L= Wheel Base Length • W= Total weight in N • Wfs= Load on front wheel on level ground= Wc/L in N • Wf= Load on front wheel when raised by angle in N
- 19. 19 Truck/Trailer dimensions and Terms
- 20. 20 Trucks
- 22. 22 Terminology • Sprung and Unsprung Mass Conventional passive suspension zs zu zr suspension spring suspension damper tyre stiffness Kt sprung mass (body) Ms unsprung mass (wheel, axle) Mu
- 23. 23 Terminology sonancewwif tSinZZ Input Hz m k T f srad m k n n n Re; : 2 11 2 / 0 Frequency of Vibration: Natural frequency and Resonance Force Transmitted- Damped Frequency: Isolated Mass Spring22 2 1 2 1 kZZm
- 24. 24 Jounce and Bounce Motion Jounce Stroke -Compression Bounce-Rebound V=Vehicle Velocity Period for one Cycle
- 25. 25 Wheel Excitations-Frequency and Vehicle Speed • Let us consider 15” dia rim, Tire aspect ratio= 70, tire width=235 mm • D= diameter of the wheel= 15”X25.4 +2x0.70X235= 710 mm • Distance travelled per revolution= D=2230.5=2.2305m • If the wheel makes one revolution per second, then the vehicle speed is • =2.2305*3600/1000= 8.029 km/h • In every second if the wheel experiences a jounce and bounce stroke, vehicle experiences 1 Hz excitation • If the vehicle speed increases, frequency of excitation also increases
- 27. 27 Damping
- 28. 28 Vibration Isolation and Vibration Damping • A good vibration damper takes mechanical energy out of the system. • Oil dampers (dashpots) have good damping capability but no isolation capability. • A good vibration isolator lowers the natural frequency of a system to below the excitation (or disturbing) frequency. Keeping these two frequencies "out of sync" greatly reduces the problems of vibration. • Properly designed metal springs and rubber mounts can be good isolators but have almost no damping capability. • Foam products can be good isolators but have limited life.
- 29. 29 Vibration Damping and Isolation If f>fn Isolation can be achieved Sprung mass natural frequency is 1Hz say, the excitation frequency is more than 1 Hz, then isolation happens, at 1 Hz, sprung mass resonates, however resonance amplitude is small because of damping. Human being is less tolerant to frequencies 2-8 Hz. Normally 1 Hz resonance is connected with low vehicle speed, the driver hardly experiences sprung mass resonance
- 31. 31 Automotive Challenges Current Challenges Lowest Possible Emissions Reduced Green House Gas Emissions Occupant Safety Stability and Comfort, Driving Experience Power Train Running System (Metrics)
- 32. 32 Actuators Throttle, Brake, Steering Plant Car Actual Performance Handling Ride Speed Direction Desired Performance Handling Ride Measure- Performance, Ride, Handling Disturbances Surface Irregularities Ground Condition Aerodynamics Visual, Aural and other inputs Driver Desired Speed and Direction Ground Vehicle- A Control System
- 33. 33 Metrics (Characteristics) of Ground Vehicle Driver Accelerator Brakes Steering System Surface irregularities Vehicle Performance Handling Ride Aerodynamic Inputs Ground Conditions Visual and Other Inputs
- 34. 34 Vehicle Performance • Performance refers to motor vehicle ability to • Accelerate A1 – Spinning SP (Acceleration 0.3g) • Decelerate, B1 – Skidding Sk (wheel lockups) • Develop Drawbar Pull D1= Tractive Effort-Rolling Resistance • Overcome Obstacles • Wheel slipping (insufficient friction) • Climbing hills (very high gradients)
- 35. 35 Acceleration and Deceleration Limits xx xx dga mamgWF g g gax gdx
- 36. 36 Acceleration Performance The time car takes to accelerate from 0 to 60 mph (0 to 97 km/h or 0 to 27 m/s) in the US and the UK, 0 to 100 km/h in rest of the world Suzuki Grand Vitara 0 to 60 mph in 7.2 secs 5.73 m/s2 Honda CR-V 0 to 60 mph in 8.6 secs 3.13 m/s2 Family Car 0 to 60 mph in 10.5 secs 2.55 m/s2 Tata Nano 0 to 60 km/h in 8 seconds 2.08 m/s2 Motor Bike (Honda Unicorn) 0 to 60 km/h in 5 secs 3.324 m/s2
- 37. 37 Performance of Cars 0-60mph 1 sec= 26.869, 2 sec= 13.43 3sec = 8.95, 2.63 sec= 10.21 m/s2
- 38. 38 Road mu • The coefficient of friction depends on the materials used; • for example, ice on steel has a low coefficient of friction, while rubber on pavement has a high coefficient of friction. • Coefficients of friction range from near zero to greater than one – under good conditions, a tire on concrete may have a coefficient of friction of 1.7 • Most dry materials in combination have friction coefficient values between 0.3 and 0.6. • Values outside this range are rarer, but teflon, for example, can have a coefficient as low as 0.04. • A value of zero would mean no friction at all, an elusive property – even magnetic levitation vehicles have drag. • Rubber in contact with other surfaces can yield friction coefficients from 1 to 2. Occasionally it is maintained that µ is always < 1, but this is not true. • While in most relevant applications µ < 1, a value above 1 merely implies that the force required to slide an object along the surface is greater than the normal force of the surface on the object. For example, silicone rubber or acrylic rubber-coated surfaces have a coefficient of friction that can be substantially larger than 1.
- 39. Road 39 F W F=W is a dimensionless scalar value which describes the ratio of the force of friction between two bodies and the force pressing them together.
- 41. 41 • Bugatti Veyron16.4 is a mid-engine sports car produced by Volkswagen AG introduced in 2005. • It is the quickest accelerating and decelerating road-legal production car in the world • The Bugatti Veyron 0-60 mph in 2.46 seconds • Powered by a 1,001 PS (987 hp/736 kW) W16 engine. • It is able to achieve an average top speed of 408.47 km/h (253.81 mph). • It is named after French racing driver Pierre Veyron, who won the 24 hours of Le Mans in 1939 while racing for the original Bugatti • Euro 1.4 million
- 42. 42 SSC Ultimate Aero TT • SSC Ultimate Aero Twin Turbo, 'World's Fastest Production Car' with an average top speed of 255.83 mph. • 1183 hp
- 43. 43 World’s Fastest Car Bugatti Veyron 16.4 (2011) 269.81 MPH(434.211km/h)
- 44. 44 Volkswagen Touareg SUV, 3.0 L, TDI, 239PS, 45 degree hill climbing, 500 mm water wading, 35 degree tilt driving, AWD
- 45. 45 Handling • Handling is concerned with the response of the vehicle to drivers' command and its ability to stabilize its motion against external disturbances-ease of maneuvering and stability – Understeering U1 – Oversteering O1 • Sliding may happen during maneuvers – Sliding SL
- 46. 46 Lateral Acceleration CF= m V2/R =m ay ay = V2/R R g R V a ly 2 Lane Change Maneuver
- 49. 49 Ride • Ride is related to the vibration of the vehicle excited by the surface irregularities and its effects on passengers comfort
- 50. 50 z zu z suspension spring suspension tyre stiffness Kt sprung mass (body) Ms unsprung mass (wheel, axle) Mu • Ride Comfort is a frequency weighted measure of vertical acceleration together with subjective assessments of harshness over various external road surface induced excitations. • Ride is determined by spring stiffness, damper and bushing characteristics, component weights and natural frequencies Ride
- 51. 51 Road Holding
- 52. 52 What do we perceive? • A Vibration under 20Hz can be felt by human beings
- 53. 53 What do we feel and hear? • We can feel frequencies between 20Hz and 200 Hz.
- 54. 54 What do we hear? • We can hear frequencies between 200Hz and 20kHz
- 55. 55 Channel 1: 1695 – Rear left axle position
- 56. 56 Channel 3: 1697 – Rear left chassis position
- 57. 57 Channel 4: 1698 – Rear left seat position
- 58. 58 Channel 1: 1695 (Rear Left Axle Position) Acceleration(m/s2) vs Time(s)
- 59. 59 Channel 1: 1695 (Rear Left Axle Position) Acceleration(m/s2) vs Frequency(Hz)
- 60. 60 Channel 3: 1697 (Rear Left Chassis Position) Acceleration(m/s2) vs Time(s)
- 61. 61Acceleration(m/s2) vs Frequency(Hz) Channel 3: 1697 (Rear Left Chassis Position)
- 62. 62 Channel 4: 1698 (Rear Left Seat Position) Acceleration(m/s2) vs Time(s)
- 63. 63Acceleration(m/s2) vs Frequency(Hz) Channel 4: 1698 (Rear Left Seat Position)
- 65. 65 Rolling Resistance (fr) • It is due to hysteresis in tire material due to deflection of the carcass while rolling – Primary factor: • Hysteresis – Secondary factors: • Friction between the tire and the road caused by sliding • Air Circulation inside the tire • Fan effect of the rotating tire on the surroundings Rolling Resistance WfF rR fr is the dimensionless rolling resistance coefficient or coefficient of rolling friction W is the load on the wheel
- 66. 66 Rolling Resistance Rolling resistance comprises the resisting forces acting on the rolling wheel. It is made up of rolling resistance, road surface resistance and slip resistance. Note: Use appropriate Symbols
- 68. 68 Factors Affecting Rolling Resistance (fr)
- 69. 69 Rolling Resistance Coefficients (fr) w h D W C W R f tx r Where: Rx = Rolling resistance force W = Weight on the wheel C = Constant reflecting loss and elastic characteristic of the tire material D = Outside diameter ht = Tire section height w = Tire section width
- 70. 70 Rolling Resistance Coefficients (fr) • Sidewall deflection is not a direct measurement of rolling friction. • In tires, tread thickness has much to do with rolling resistance. The thicker the tread, the higher the rolling resistance. Thus, the "fastest" bicycle tires have very little tread and heavy duty trucks get the best fuel economy as the tire tread wears out. • Smaller wheels, all else being equal, have higher rolling resistance than larger wheels. In some laboratory tests, smaller wheels appeared to have similar or lower losses than large wheels, but these tests were done rolling the wheels against a small-diameter drum, which would theoretically remove the advantage of large-diameter wheels, thus making the tests irrelevant for resolving this issue. Virtually all world speed records have been set on relatively narrow wheels, probably because of their aerodynamic advantage at high speed, which is much less important at normal speeds.
- 71. 71 Rolling Resistance • Material - different fillers and polymers in tire composition can improve traction while reducing hysteresis. The replacement of some carbon black with higher-priced silica–silane is one common way of reducing rolling resistance • Dimensions - rolling resistance in tires is related to the flex of sidewalls and the contact area of the tire. For example, at the same pressure, wider bicycle tires flex less in sidewalls as they roll and thus have lower rolling resistance • Extent of inflation - Lower pressure in tires results in more flexing of sidewalls and higher rolling resistance. This energy conversion in the sidewalls increases resistance and can also lead to overheating and may have played a part in the infamous Ford Explorer rollover accidents. • Over inflating tires (such a bicycle tires) may not lower the overall rolling resistance as the tire may skip and hop over the road surface. Traction is sacrificed, and overall rolling friction may not be reduced as the wheel rotational speed changes and slippage increases
- 72. 72 Rolling Resistance Coefficients (fr)
- 73. 73 Standing Waves When the tyre rotates at its critical speed, standing wave occurs In such conditions rolling resistance increases, and energy gets dissipated into heat A tyre is being run on a rolling drum Sharp Rolling Resistance is due to standing waves A standing wave, also known as a stationary wave, is a wave that remains in a constant position. This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite directions.
- 75. 75 Coast Down Test 1. dx= deceleration = (final velocity-initial Velocity)/time 2. dx = Fx/M 3. Fx= dx.M…..Total Tractive Resistance 4. Draw a graph of Total Tractive resistance V/S Speed 5. Draw a graph of Aerodynamic resistance V/S Speed 6. Subtract one graph from the other and get rolling Curve
- 76. 76 Pressure Distribution On a Vehicle Aerodynamic Loads
- 77. 77 Aerodynamic Forces and Moments Drag Force Lift Force Side Force ACVD DA 2 2/1 Where: CD = Aerodynamic drag coefficient A = Frontal area of the vehicle = Air density ACVL LA 2 2/1 Where: LA = Lift force CL = Lift Coefficient A = Frontal area ACVS SA 2 2/1 Where: SA = Side force V = Total wind velocity CS = Side force coefficient (function of the relative wind angle) A = Frontal area
- 78. 78 Aerodynamic Lift and Drag with Different Vehicle Styles
- 79. 79 Pitching Moment Yawing Moment Rolling Moment ALCVPM PM 2 2/1 Where: PM = Pitching moment CPM = Pitching moment coefficient A = Frontal area L = Wheelbase ALCVYM YM 2 2/1 Where: YM = Yawing moment CYM = Yawing moment coefficient A = Frontal area L = Wheelbase ALCVRM RM 2 2/1 Where: RM = Rolling moment CRM = Rolling moment coefficient A = Frontal area L = Wheelbase
- 80. 80 Moments Due to Aerodynamic Forces Rolling Pitching Yawing Side Coefficients
- 81. 81 Gradient Resistance RRG GVWr RT 10200 • Gradeability • It is the rise over run Where: 10200 = Factor T = Motor torque in newton metres R = Overall gear reduction including both axle and transmission r = Rolling radius of loaded driving type in millimetres GVW = Gross vehicle weight in kilograms RR = Rolling resistance expressed in percentage grade. • The "slope hill" to test the gradeability of military vehicles. There are several slopes, beginning with around 10% grade ("1 : 10" or 5.7 degrees), the steepest slope is around 70% ("1 : 1,66" or 35 degrees) "Heeresversuchsgelände Kummersdorf", south of Berlin
- 82. 82 Tractive Effort Tr =Tnfe TE = (Tnfe)/ rand fn N ratioreductionoverall rev/minengine Nroadwheelstheofrev/min r r
- 83. 83 Tractive Force Vs Tractive Resistance Vehicle Speed kmph TractiveForce(N) TractiveResistance(N) Tractive Effort to overcome Tractive resistance Tractive force at the Wheels for acceleration Max. speed Force Available for acceleration Effort : The force applied to an object or machine to cause motion
- 84. 84 Forces Acting on a Vehicle W: weight of the vehicle acting at its CG W/gax : Inertial force,if the vehicle is accelerating Wf, Wr: :Dynamic weights carried on the front and rear wheels. Fxf, Fxr : Tractive forces Rxf ,Rxr : Rolling resistance at the tyre contact patch DA: Aerodynamic force acting on the body of the vehicle Rhz , Rhx : Vertical and longitudinal forces acting at the hitch point when the vehicle is towing a trailer L: Wheel base length h: Height of the Centre of Gravity from the ground b: Distance of the Centre of gravity aft of the front axle c: Distance of the Centre of Gravity fore of rear axle Wr Grade:
- 85. 85 Newton’s 2nd Law • Translational Sytems FX = M.aX where: FX = Forces in the X-direction M = Mass of the body aX = Acceleration in the X-direction • Rotational System TX = IXX . X where: TX = Torques about the X-axis IXX = Moment of inertia about the X-axis X = Acceleration about the X-axis
- 86. 86 Loads on Axles Dynamic Axle Loads: • Wf = (W c cos - Rhx hh - Rhz dh - (W/g) ax h - DA ha - W h sin)/L • Wr = (W b cos +Rhx hh + Rhz (dh + L) + (W/g) ax h + DA ha + W h sin)/L Static Loads on Level Ground: • Wfs = W.(c/L) • Wrs = W.(b/L) The sine is zero and the cosine is one, and the variables Rhz, Rhx, ax and DA are zero. In Vehicles usually load on the front axle is greater than the rear axle
- 87. 87 Loads on Axles Load on the Axles during Low Speed Acceleration When the vehicle is accelerating on level ground at a low speed, DA is zero and assuming no trailer hitch forces) When the vehicle accelerates, load transfer takes place from the front axle to the rear axle Load on the Axles due to Grades Positive grade causes load to be transferred from the front to the rear axle The common grades on highways are limited to 4 percent (2.3deg) On primary and secondary roads they occasionally reach 10 to 12 percent (6.8 deg). L h g a WW L h g a L b WW L h g a WW L h g a L c WW x rs x r x fs x f )( )( L h WW L h L b WW L h WW L h L c WW rsr fsf )( )(
- 88. 88 B = 1233C = 1327 L = 2560
- 89. 89 Front Rear Longitudinal Load Transfer Due To Acceleration Direction of Travel Hard/Quick Acceleration Force or Weight Movement
- 90. 90 Longitudinal Load Transfer Due to Deceleration Front Axle Rear Axle Direction of Travel Hard/Quick Braking Force or Weight Movement Vehicle Movements
- 91. Gradeability 91 fWSinW W Sin = Wf = (W c cos - (W/g) ax h - DA ha - W h sin)/L Neglecting drag forces on a car, the grade can be calculated using the following equation for front wheel drive vehicle hL hgac x ])/([ For a rear wheel drive hL hgac x ])/([
- 92. 92 Lateral Acceleration and Lateral Load Transfer CF= m V2/R =m ay ay = V2/R g R V a ly 2 Outer side R Inner side
- 93. 93 Lateral Weight Transfer • Weight Transfer is directly a function of – Lateral Acceleration, ay/g – Weight, W – Height of the Center of Gravity, h – Wheel Track width, t Track Width t CG h F= W/g ay W Wl Wr
- 94. 94 • On a flat roadway the lateral weight transfer (Wl) is equal to t h g a W=W y lateral t h g a W t l WW t h g a W t l W=W yR l yL R • The weight on the right side (WR) in the turn is comprised of a static component and a component due to the lateral acceleration ay/g. Lateral Weight Transfer lL=Lateral dist from CG to left tire Track Width t CG h F= W/g ay W Wl Wr lLlR
- 95. 95 Lateral Load Transfer-Roll Over Potential Track Width t CG h F= W/g ay W Wl Wr hRA y tWhFy t W=M lr 0) 2 (
- 96. 96 • Rollover potential If the roll angle of the sprung mass is included in the analysis of a vehicle with a 50/50 L to R weight distribution. Lateral Weight Transfer t h g a W=Sinhh t W y RA 2 SinhhyhFy t W=MthenWif RArl )(0) 2 (0
- 97. 97 The weight on the inside wheels is defined as Dividing through by W Lateral Weight Transfer t h g a W= t Sinhh W yRA 2 1 t h g a = t Sinhh - yRA 2 1 With further transposing h h Sin h t g a RAy 1 2 Roll Over potential (8)
- 98. 98 • Potential rollover is possible when Wl=0 Lateral Weight Transfer 1 2 h h Sin h t g a RAy • It should be noted that roll angle of the sprung mass has limited effect on the steady-state rollover potential. • Static Stability Factor: SSF : ay/g = t/2h (8)
- 100. 100
- 101. Lateral Load Transfer 1. Load Transfer due to Centrifugal Force –Non Rolling 2. Load Transfer due to change of gravity position-Rolling Load Transfer 3. Load Transfer due to un-sprung weight 101
- 102. 102 Non Rolling Load Transfer Sprung Mass Roll Centre Centrifugal Force CG Fc= W/g ay
- 103. Rolling Load Transfer 103 W=1250 kg T=1600 mm, h=500 mm, =10 deg d= 500 sin 10= 86.8 mm Wo = W .li/t =1250 * (800+86.8)/1600 =693 kg Wi =557 kg
- 104. 104 Load Transfer due to Unsprung Weight Due to Unsprung Mass Vehicle taking a left turn Wus/g* h/t *ay
- 105. 105 Lateral Load Transfer W+W+WW+W+W=WW TTTTTTTT RusRnrRsFusFnrFsRF Mechanism of Dynamic Weight Transfer Sprung Mass Unsprung Mass Suspension CG RC t Rolling Load Transfer Rolling Load Transfer through Suspension Non rolling Load Transfer through Roll Centre (Centrifugal force) Unsprung Mass Transfer Lateral Load Transfer= Sprung Mass Rolling Mass Transfer+ Sprung Mass Non Rolling Load Transfer+ Unsprung Mass Load Transfer t h g a W=WWWW y latTLAT T RTOTAL F Road Surface
- 106. 106 Lateral Load Transfer Simulations
- 107. 107 Fish Hook Maneuver Fish Hook –Maneuver-side
- 108. 108 Variation of Load on Wheels-Simulations FL RL FR RR N o r m al W ei g ht
- 109. 109
- 110. 110 Forces between Road and Wheel • Forces-F – Horizontal forward forces at the contact of the tires with the road -Traction Forces – Vertical forces at the contact of the tires with the road - Reactions – Side forces at the tire contact with the road – While taking a turn • Study of response of vehicle to the forces that act at the four palm sized patches (at the tire and road contact)
- 111. 111 Forces between Road and Wheel Lateral and Vertical Forces
- 112. Exercise 112 Following data are given Wheel base length =2500 mm Wheel Track width = 1450 mm Vehicle Weight = 1250 kg Load on front axle= 825 kg Front wheel drive front Engine vehicle R= wheel Radius = 300 mm Maximum gradient for equilibrium = 32 deg Rolling resistance coefficient =0.015 Coefficient of Drag =0.28 Frontal Area of Vehicle= 2.25 sq.m Maximum Vehicle Speed = 150 kmph Road mu =0.7 Calculate: Real axle load Position of CG Height of CG considering equilibrium gradient as 32 deg
- 113. Exercise 113 Max Tractive Resistance Max Tractive Power assuming a maximum vehicle speed of 150 kmph Longitudinal load transfer at linear acceleration of 0.4g Lateral load transfer at lateral acceleration of 0.4g What is the body roll angle assuming the roll centre is 20 cm above the ground Load on each of the wheel when linear acceleration is 0.2g and lateral acceleration is 0.2g Maximum acceleration/deceleration possible Maximum cornering velocity possible Under what situation the Car Rolls Over Assume road is flat for all the calculations unless mentioned What should be the stiffness of each suspension spring assuming the stiffness ratio of tyre and suspension spring is 10
- 114. Forces on a Car with a Trailer 114 Car Trailer Hitch
- 115. Force Analysis on Trailer to Find Hitch Forces 115 h3 f h2 Taking moment about the point where the tire contacts the ground-counterclockwise moment is considered positive Ty =0 Forces along longitudinal axis Fx=0
- 116. Force Analysis on Car 116 h1
- 117. Determination of Unknowns 117 Unknowns are : Wf, Wr, Fxb, Fzb cb hFdcbFWbSinWh W cb hFdFSinWhCosW W fe SinhSinhfW F WF xbzb r xbzbc f b zb bxb 21 21 32 )(cos ]cos[ sin If there are drag forces and inertia forces they need to be considered while determining these forces
- 119. Gradeability 119
- 121. Truck Trailer System 121 LEFT- Trailer "Dive" during heavy braking increases the effect of tongue weight. RIGHT- Weight distributing hitch transfers loads to frame and to both axles of tow vehicle for safer stops and smoother ride.
- 122. 122 • Along X-axis- Longitudinal • Acceleration of the Vehicle • Braking Performance • About X-axis • Rolling caused by side forces • Along Z-Axis- Vertical • Bouncing (Ride) • About Z-Axis • Yaw caused by side forces • Along Y-Axis • Side force due to Cornering • Side force responsible for Roll • About Y Axis • Pitching Caused by Diving (braking) and Squatting (Acceleration) • Handling Vehicle Movements of Interest
- 123. 123
- 124. 124
- 125. 125