VEHICLE HANDLING BASICS

Transcription

1 RACE ENGINEERING ACADEMY VEHICLE HANDLING BASICS INTRODUCTION BY Dejan Ninic BE (Mech) PhD ENVIRAGE

2 VEHICLE HANDLING DEFINITIONS STABILITY BALANCE VEHICLE DYNAMICS RESPONSE GRIP

3 VEHICLE HANDLING DEFINITIONS STABILITY - the ability of the car to return to the intended direction after a disturbance BALANCE Neutral, Understeer, Oversteer RESPONSE The time delay after a disturbance (also position, speed, acceleration) GRIP Thrust capacity at the tyres. Maximum acceleration achievable (whether braking, accelerating or cornerning)

4 VEHICLE HANDLING DEFINITIONS INERTIA The force behind all dynamic analysis A body s resistance to acceleration resistance to deceleration resistance to cornering Inertia = Mass x Acceleration Thrust = Inertia Thrust = Mass x Acceleration Acceleration = Thrust / Mass

5 VEHICLE HANDLING OBJECTIVES Need to produce combined thrust

6 TYRE FORCES Contact patch forces

7 TYRE GRIP Factors influencing tyre grip include: Tyre pressure (contact patch area) Tyre inclination angle Tyre temperature Tyre spin (slip ratio) Tyre steered angle (slip angle) Tyre wear Tyre contact patch vertical load Static load (mass) Dynamic load (load transfer) Bumps Aerodynamic loads

8 TYRE PRESSURE

9 TYRE PRESSURE INCREASING CONTACT PATCH AREA INCREASING AVAILABLE GRIP

10 TYRE INCLINATION 0 degrees -3 degrees -5 degrees

11 TYRE TEMPERATURE

12 SLIP RATIO Slip ratio Measure of wheel spin (or wheel locking) SLIP RATIO = Vs/Vf - 1 = = 0% - 25% SLIP (typical) Vf Vs

13 SLIP RATIO Slip ratio Measure of wheel spin (or wheel locking) THRUST Peak Thrust SR 8% SLIP (typical) SLIP RATIO = Vs/Vf - 1 Vf Vs SLIP RATIO

14 SLIP RATIO

15 SLIP ANGLE α Vf Vl SLIP ANGLE = Vl/Vf = (typical) = 0 14 degrees

16 SLIP ANGLE Vf LATERAL FORCE Peak Thrust SA 6 degrees (typical) Vl SLIP ANGLE = Vl/Vf = (typical) = 0 14 degrees SLIP ANGLE

17 TYRE GRIP UNDER FORCE THE RUBBER DEFORMS INTO THE ROAD ASPERITIES PROVIDING A KEY ACTION VEHICLE MASS VERTICAL RESISTANCE

18 TYRE GRIP VERTICAL FORCE TRACTIVE FORCE CAPACITY VERTICAL RESISTANCE

19 TYRE GRIP TRACTIVE FORCE VERTICAL FORCE

20 RIGID CAR Overall Objective: Allow wheel to follow the contour of the road, WITH MINIMAL VARIATION OF THE CONTACT PATCH LOAD

21 COMPLIANCE Introduce controlled vertical wheel travel Allow for wheel motion over bumps and dips with minimal variation of the contact patch load Amount of wheel travel depends on the type of car and the road condition

22 WHEEL TRAVEL TYPEOF CAR CIRCUIT RACING ROAD CAR SAFARI OFF ROAD CAR TYPICAL REQUIRED WHEEL TRAVEL 60mm 200mm 400mm

23 NEED SUSPENSIONTO HAVE WHEEL TRAVEL

24 SPRING Support the mass of the car Stiffer = more RESPONSE, less body movement Softer = more GRIP, more body movement Body movement = Pitch, Roll and Heave Elastic member that stores and releases strain (deformation) energy

25 SPRING STIFFNESS Linear spring rate SPRING FORCE N, lb, kg SPRING DEFORMATION mm, in, m

26 TYPICAL SPRING Type of Car RATES Metric N/mm Imperial lb/in Family sedan Gravel rally Tarmac rally Circuit racing Formula Multiply Stiffness in lb/in by to get N/mm

27 CHOOSING SPRINGS Vehicle Mass (heavier car needs stiffer springs) Type of road surface (rough road needs soft springs) Type of tyre (level of grip) (more grip, gives more chassis movement, need stiffer springs)

28 CHOOSING SPRINGS Stiffer = Faster RESPONSE (less body roll) Stiffer may = More GRIP (stabilising the vertical load variation) Stiffer may = Less GRIP (car skips on the road surface) Stiffer may = Less GRIP (increases load transfer along the axle)

29 SPRUNG MOTION The system natural frequency can be calculated using the formula M K x Giving a frequency value in Hertz

30 SPRUNG MOTION Porsche Carrera 2.7L Front left sprung mass = 200kg Front left effective spring rate = 30 kn/m, K M x 1.95

31 SPRUNG MOTION Porsche Carrera 2.7L Rear left sprung mass = 320kg Rear left effective spring rate = 50 kn/m K M x, 1.99

32 SPRUNG MOTION Front Left Rear Left Sprung Mass 200 kg 320 kg Effective Spring Rate Natural Frequency 30 kn/m 50 kn/m 1.95 Hz 1.99 Hz FRONT AND REAR SPRING RATES ARE DIFFERENT BUT THE FREQUENCIES ARE VERY SIMILAR THE CAR IS BALANCED FROM A SPRING POINT OF VIEW

33 SPRUNG MOTION Type of Car Effective Stiffness N/mm Natural Frequency Hz Family sedan Gravel rally Tarmac rally Circuit racing Formula A CARS STIFFNESS IS BETTER CATEGORISED BY ITS NATURAL FREQUENCY THAN ITS SPRING STIFFNESS

34 SPRING STIFFNESS Progressive spring rate SPRING FORCE N, lb, kg SPRING DEFORMATION mm, in, m

35 ANTI-ROLL BAR

36 ANTI-ROLL BAR Stiffer = Faster RESPONSE (less body roll) Stiffer may = More GRIP (avoiding camber loss in roll) Stiffer may = Less GRIP (reduces articulation on bumpy roads) Stiffer may = Less GRIP (increases load transfer along the axle)

37 CHOOSING ANTI- ROLL BARS Corner Weights Spring Stiffness Estimate desired roll angle, or Estimate % resistance in roll performed in the ARB Can make a car handle perfectly without an ARB But it s convenient for tuning

38 DAMPER The damper is an absorber A spring, conversely, will return the energy used to deform it When a damper is compressed it resists the motion, but does not return it A damper converts the energy to heat and dissipates that heat to its surroundings

39 DAMPER Whilst driving over a bump, the wheel is forced up into the chassis

40 DAMPER A further proportion of the force is taken in the damper On the way up And on the way down The energy is released into the air stream

41 DAMPER The spring and damper work together to proportion the relative amount of work each does during the stroke

42 DAMPER A soft damper takes a lesser proportion of the force away from the spring This speeds the motion up and also increases its magnitude (by increasing the springs displacement) A stiff damper takes a greater proportion of the force away from the spring This slows the motion down and also reduces its magnitude (by reducing the springs displacement)

43 DAMPER The proportion of spring force to damper force that is necessary can be calculated using basic vibration theory

44 DAMPER A damper builder/designer must know your spring rate (and vehicle mass) to correctly rate your damper

45 DAMPER A damper builder/designer must know your spring rate (and vehicle mass) to correctly rate your damper If you don t know these, you need to measure them!

46 DAMPED SPRUNG MOTION The system s critical damping rate can be calculated using the following formula: M 2 K C x This give a damping rate in Ns/m

47 DAMPER CURVES Dampers are hydraulic Their resistance depends on the speed of the oil, not the quantity of oil, or the position of the shaft COMPRESSION EXTENSION

48 DAMPER CURVES DAMPER RATE SLOPE OF THE CURVE FOR A PARTICULAR SPEED EXPRESSED IN Ns/m

49 DAMPER Damper Construction Literally HUNDREDS of different damper constructions and differing damper functions Look at the generic construction and typical operation

50 DAMPER Damper Function SHAFT ENTERS BODY OIL FLOWS THROUGH THE PISTON AND THROUGH THE FOOT VALVE THE RESISTANCE IS A FUNCTION OF THE SIZE OF THE HOLES IN THE PISTON, AND THE SIZE OF THE HOLE IN THE FOOT VALVE

51 DAMPER Damper Function SHAFT ENTERS BODY OIL FLOWS THROUGH THE PISTON AND THROUGH THE FOOT VALVE AT LOW SPEED, MOST OF THE OIL PASSES THROUGH THE HOLE IN THE FOOT VALVE THE RESISTANCE CAN BE CONTROLLED BY THE FOOT VALVE

52 DAMPER CURVES ENVIRAGE

53 DAMPER Damper Function SHAFT ENTERS BODY OIL FLOWS THROUGH THE PISTON AND THROUGH THE FOOT VALVE AT A HIGHER SPEED, THE FOOT VALVE IS HEAVILY RESTRICTED, AND THE RESISTANCE INCREASES SUBSTANTIALLY

54 DAMPER CURVES ENVIRAGE

55 DAMPER Damper Function SHAFT ENTERS BODY OIL FLOWS THROUGH THE PISTON AND THROUGH THE FOOT VALVE AT A VERY HIGH SPEED, THE PRESSURE IS SO HIGH THAT THE SHIMS ARE FORCED TO FLEX, OPENING ADDITIONAL HOLES AND REDUCING THE RESISTANCE

56 DAMPER CURVES

57 DAMPER Damper Function SHAFT EXITS BODY OIL FLOWS THROUGH THE SHAFT AND OUT OF A SMALL PORT THE RESISTANCE IN EXTENSION IS CONTROLLED BY A VALVE IN THE SHAFT THAT METERS THE FLOW THROUGH THE SMALL PORT

58 DAMPER CURVES

59 DAMPER EFFECTS Starting with significantly less than Critical Damping More = more STABILITY (body control) More = more GRIP (optimised vertical contact patch load) More = more RESPONSE (reduces body movement)

60 DAMPER EFFECTS Starting with significantly MORE than Critical Damping More = less GRIP (damper will slow the motion of the wheel back to the ground reducing vertical contact patch load)

61 CHOOSING A DAMPER Corner Weights Spring rates Road surface type Tyre type Car configuration Mechanical grip vs. Aero grip

62 DAMPED SPRUNG MOTION The system s critical damping rate can be calculated using the following formula: M 2 K C x This give a damping rate in Ns/m

63 RECOMMENDED DAMPER CURVES

64 FURTHER CALCULATIONS Roll stiffness = combined stiffness of springs and dampers in roll Roll frequency Pitch stiffness= combined stiffness of springs and dampers in pitch and squat Pitch frequency Roll stiffness distribution Load transfer Load transfer distribution

65 RACE ENGINEERING ACADEMY VEHICLE HANDLING BASICS PART 2: HANDLING GUIDE BY Dejan Ninic BE (Mech) PhD ENVIRAGE

66 VEHICLE CHARACTERISTICS Mass and Mass distribution Centre of gravity height Wheel alignment Track width and wheel base Tyre information Spring rates Damper rates Suspension geometry

67 MASS DISTRIBUTION Centre of Gravity Height Track Width

68 WHEEL ALIGNMENT Wheelbase Length Wheelbase

69 WHEEL ALIGNMENT Ride Height Ride Height Measured to Sills

70 WHEEL ALIGNMENT Ride Height Ride Height Measured to Other Points on Vehicle

71 WHEEL ALIGNMENT Rake Angle Rake Angle

72 WHEEL ALIGNMENT Corner Weights

73 WHEEL ALIGNMENT Toe Direction of Travel Longitudinal Axis Toe Angle Toe Angle Longitudinal Axis Top View of Tyres

74 WHEEL ALIGNMENT Camber Up Camber Angle Camber Angle Vertical Axis Vertical Axis Front View of Tyres

75 WHEEL ALIGNMENT Caster Caster Angle Upper ball joint Vertical Axis Steering Axis Towards Front of Vehicle Lower ball joint

76 ALIGNMENT TOOLS Flat & level area to work on May need a set of wheel stands Camber gauge Pressure gauge String line Posts to form a fence around the car, or Alignment bars temporarily attached to the car Rulers and tape measures Scales to measure corner weights Notebook to track changes and comments

77 SUSPENSION KINEMATICS Types of suspension systems Double wishbone Source: Jazar, R.N. 2008, Vehicle Dynamics Theory and Application, Springer, New York, pg. 467

78 - McPherson Strut SUSPENSION KINEMATICS Source: Jazar, R.N. 2008, Vehicle Dynamics Theory and Application, Springer, New York, pg. 467

79 - Semi Trailing Arm SUSPENSION KINEMATICS Source: Jazar, R.N. 2008, Vehicle Dynamics Theory and Application, Springer, New York, pg. 469

80 - Live Axle - Panhard Rod SUSPENSION KINEMATICS Source: Jazar, R.N. 2008, Vehicle Dynamics Theory and Application, Springer, New York, pg. 460

81 - Live Axle - Watts Link SUSPENSION KINEMATICS Source: Jazar, R.N. 2008, Vehicle Dynamics Theory and Application, Springer, New York, pg. 462

82 SUSPENSION KINEMATICS - Multi-Link Source: Jazar, R.N. 2008, Vehicle Dynamics Theory and Application, Springer, New York, pg. 468

83 SUSPENSION MEASUREMENTS Wheel offset Wheel Offset (Positive Offset) Wheel Centreline Towards Car Centreline Source: sssection.gif

84 Scrub Radius SUSPENSION MEASUREMENTS Wheel Centreline Away From Car Centreline King Pin Inclination (KPI) Scrub Radius

85 ROLL-CENTRE % Anti-roll Roll Moment Arm Sprung Mass CG Roll Centre

86 SUSPENSION MEASUREMENTS Bump steer Motion ratio Camber gain 3D suspension pick-up measurement Roll-centre position Roll-centre migration Vertical Lateral

87 TYRE INFORMATION Ask your tyre supplier Optimum tyre pressure window Optimum tyre temperature window Optimum static and dynamic camber Maximum wear depth of the tyre Otherwise, you will need to test, measure and assess what your tyres need (using g-forces, tyre temperature distribution and driver feedback, etc.)

88 TOOLS FOR ASSESSING PERFORMANCE Tyre pressure gauge Tyre pyrometer (or infra red imaging camera) Stopwatch Data logger (Video Vbox Lite) Sensible and consistent driver with excellent feedback Video camera

89 TUNING FOR HANDLING Reminder of the VEHICLE DYNAMICS MODEL STABILITY BALANCE VEHICLE DYNAMICS RESPONSE GRIP

90 TYRE CHARACTERISTICS Pressure (typically between 25psi 34psi hot) Around 60% of a tyres stiffness is due to the pressure Less = more GRIP, but less RESPONSE More = inverse of above Insufficient = damage to tyre side wall, risk of pulling tyre off the rim Excessive = tyre slides easily Use tyre temperature profile to determine: Edges high temperature = low pressure Centre high temperature = high pressure

91 TYRE TEMPERATURE

92 TYRE CHARACTERISTICS Camber (typically between -1.5 and -5.0 static) More = more lateral RESPONSE, more lateral GRIP Less = better straight line GRIP Insufficient = tyre wears outside edge Excessive = tyre slides easily, tyre wears inside edge Use tyre temperature profile to determine: Outer edges high temperature = low camber Inner edges high temperature = high camber Should accept inside edge to run approximately 15 hotter than outside edge

93 TYRE TEMPERATURE

94 TYRE CHARACTERISTICS Vertical load Tyre is sensitive to vertical load More load gives more tractive capacity The returns are diminishing A pair of tyres working in unison achieve their best grip when their load is equally distributed The softer end of a car transfers less load and has a more equal load distribution On the same given tyre, a lighter car will have better performance so long as optimum temperature is achieved (consider racing categories that use performance ballast)

95 TRACTIVE CAPACITY 300kg 250kg 300kg 250kg L=R= 250kg TOTAL GRIP = L + R = = 500kg L=R= 300kg VERTICAL FORCE

96 TRACTIVE CAPACITY 50kg transferred 250kg 210kg 350kg 280kg R= 280kg 250kg L= 210kg TOTAL GRIP = L + R = = 490kg LESS THAN 500kg! 250kg 300kg 350kg VERTICAL FORCE

97 WHEEL ALIGNMENT Load Transfer is related to h/t Centre of Gravity Height h Track Width t

98 TYRE CHARACTERISTICS Vertical load Feel of the car: BALANCE Understeer/Oversteer Use tyre temperatures to determine: Front tyres are hotter than rears = more front mass stiffer front springs, dampers or ARBs higher roll-centre more front brake bias FWD Rear tyres are hotter = inverse of above

99 TYRE TEMPERATURE AVERAGE = 74.7⁰C AVERAGE = 79.5⁰C AVERAGE = 75.5⁰C AVERAGE = 81.2⁰C

100

101 TYRE CHARACTERISTICS Temperature typically 85 to 120 C in the pit lane depending on compound Low temperature = less GRIP, poor tyre wear More temperature = more GRIP, better tyre wear, but faster Insufficient = cold graining (irreversible bad wear) Excessive = Excessive wear A cold tyre will feel skatey and inconsistent in grip A hot tyre will feel mushy and tired Use wear pattern and tyre temps to determine

102 TUNING FOR HANDLING Determine what you can change on your car: Toe Camber Ride heights (including rake) Corner weights ARB settings Damper settings What else Learn how to do these before you head to the track to not lose time

103 TUNING FOR HANDLING Next: How much time do you have?! 10 minutes? 2 hours? 1 day? 2 weeks?

104 TUNING FOR HANDLING Then ask: BALANCE STABILITY VEHICLE DYNAMICS GRIP RESPONSE Braking STABILITY? Mid-corner STABILITY? High-speed STABILITY? To improve STABILITY: - Increase rear TOE-IN - (BALANCE Understeer) - Stiffen DAMPERS - (RESPONSE Faster) - (GRIP will change) - Reduce CAMBER - (BALANCE, RESPONSE, GRIP)

105 TUNING FOR HANDLING Then ask: BALANCE STABILITY VEHICLE DYNAMICS GRIP RESPONSE Turn-in RESPONSE? Change of direction? Throttle-lift RESPONSE? To improve RESPONSE: - Increase front TOE-OUT - (BALANCE Oversteer) - Stiffen DAMPERS - (RESPONSE Faster) - (GRIP will change) - Increase CAMBER - (BALANCE, RESPONSE, GRIP)

106 TUNING FOR HANDLING Then ask: BALANCE STABILITY VEHICLE DYNAMICS GRIP RESPONSE Corner Entry BALANCE? Mid-corner BALANCE? Corner Exit BALANCE? To shift BALANCE forward: - Increase front TOE-OUT - (RESPONSE Faster) - Increase front CAMBER - (RESPONSE Faster) - (GRIP will change) - Soften front ARB - (RESPONSE Slower)

107 TUNING FOR HANDLING Then ask: BALANCE STABILITY VEHICLE DYNAMICS GRIP RESPONSE Braking GRIP? Mid-corner GRIP? Traction on corner exit? To increase GRIP: - Determine optimum tyre PRESSURE - Calculate optimum SPRING RATE - Calculate optimum DAMPER RATE - Test for optimum CAMBER

108 SETUP CHANGE DIFFICULTY SENSITIVITY RATIO Tyre Pressure Damper Click ARB Setting Damper Change Spring Change Ride height/rake Static Toe Static Camber Corner Weights Caster Bump-steer Camber Gain Roll Centre Height Anti-dive/ Anti-squat

109 Toe Front: TUNING FOR HANDLING More toe-out can balance front camber setting (more toeout for more camber) More toe out gives better turn-in Rear: More toe-in gives better stability (understeer) Less toe-in can reduce understeer Too much toe can cause excessive tyre edge wear and excessive tyre edge temperature

110 TUNING FOR HANDLING Static Camber Keep trying for more until: Tyre inner edge is too hot (more than 20 hotter than outer) Tyre inner edge wear is significant Remember to reduce tyre hot pressure to suit: try 1psi (hot)/degree of camber Front: More camber gives better turn-in, better RESPONSE More camber gives better GRIP Rear: Match with front camber (typically keep rear static camber around 0.5 less than front) Too much camber can cause excessive tyre edge wear and excessive tyre edge temperature

111 TUNING FOR HANDLING Damper Settings Overall Rebound only Bump only Low Speed High Speed Gas Pressure

112 TUNING FOR HANDLING Damper Settings OVERALL damping means adjusting bump and rebound together (your dampers may only have one adjuster, so check with the dyno graphs or damper builder which characteristic the adjuster varies) Need to have the OVERALL damping correct for the spring and mass combination If a car heaves, rolls and pitches, feeling almost like a boat, you can increase OVERALL damping to make the car more responsive and better held If a car feels firm and feels like it is skating on the surface, reduce the OVERALL damping

113 TUNING FOR HANDLING Damper Settings Once you find a good overall setting, you can adjust BUMP and REBOUND separately. CAUTION, if you, say, increase BUMP stiffness, you should reduce REBOUND stiffness, otherwise the car will become overdamped You would then misinterpret an OVERALL damping change for a BUMP change Ideally, look at your damper curves and determine how much one-click does in BUMP and REBOUND Otherwise, start with one-click BUMP for one-click REBOUND

114 TUNING FOR HANDLING Damper Settings Increasing REBOUND (and reducing BUMP to match overall) Better chassis control (STABILITY) Better feel (STABILITY, RESPONSE, BALANCE) Reduced mechanical (tyre) GRIP Increase aero GRIP (better control of the under floor orientation relative to the ground)

115 TUNING FOR HANDLING Damper Settings Increasing BUMP (and reducing REBOUND to match overall) Increases tyre temperature (maybe more GRIP) Increased mechanical (tyre) GRIP (better unsprung wheel control) Better wheel control over curbs and bumps (up to a limit, after that the ride can become too harsh)

116 TUNING FOR HANDLING Damper Settings Low Speed BUMP (LSB) is for unsprung wheel control on normal road surfaces and for body control More LSB gives more control Excessive LSB gives harsh ride High Speed BUMP (HSB) is for unsprung wheel control on curbs, bumps and dips Excessive HSB causes bump loads to be transmitted to the chassis (harsh) Insufficient HSB causes damper to compress too far hitting the bump stops or chassis touching the ground

117 TUNING FOR HANDLING Damper Settings Gas pressure is used to give the damper increased force range (by mitigating cavitation through the piston) Gas pressure can be used for tuning More gas pressure takes less load from spring causing: Increased ride height (may need to adjust) Reduce spring compression (less stored energy in the spring good thing) Excessive pressure = a harsh ride (need to reduce some OVERALL damping or reduce spring rate) Insufficient pressure = hitting bump stops, chassis motion uncontrolled

118 RACE ENGINEERING ACADEMY VEHICLE HANDLING BASICS PART 3: DIFFERENTIALS BY Dejan Ninic BE (Mech) PhD ENVIRAGE

119 DISTANCE TRAVELLED BY OUTER REAR WHEEL DISTANCE TRAVELLED BY INNER REAR WHEEL Distance travelled by outer wheel is GREATER than distance travelled by inner wheel Outer drive shaft must complete MORE revolutions than inner drive shaft to negotiate the turn

120 WITHOUT A DIFFERENTIAL To negotiate a left-hand turn, without a differential, the right-hand wheel forces the lefthand wheel to slip. This will force the car to drive straight, rather than steer (understeer).

121 WITH A DIFFERENTIAL With a differential, the right-hand wheel and the left-hand wheel can turn independently during a turn. This will allow the car to turn, but may also cause it to turn excessively (oversteer). AIM 1: Transmit engine torque to the driven wheels. AIM 2: Allow independent rotation of the driven wheels during turning.

122 OPEN DIFFERENTIAL

123 OPEN DIFFERENTIAL SIDE GEARS TURNED BY PINIONS TOP VIEW SIDE VIEW

124 TORQUE DISTRIBUTION INPUT TORQUE = T LEFT SIDE OUTPUT TORQUE = L RIGHT SIDE OUTPUT TORQUE = R L = R = ½ T (EQUAL TORQUE DISTRIBUTION)

125 TYRES HAVE EQUAL GRIP T L R L = R = ½ T (EQUAL TORQUE DISTRIBUTION)

126 LEFT TYRE HAS LITTLE GRIP LEFT WHEEL SPINS AND CAR STANDS STILL 0 = 0 = 0 (NO TORQUE DISTRIBUTION)

127 SPEED OF ROTATION INPUT SPEED = NI LEFT SIDE OUTPUT SPEED = NL RIGHT SIDE OUTPUT SPEED = NR NI = ½ (NL + NR) NL = 2 NI - NR

128 SPEED OF ROTATION INPUT SPEED = NI LEFT SIDE OUTPUT SPEED = NL RIGHT SIDE OUTPUT SPEED = NR IF NR = 0? NL = 2 NI LEFT OUTPUT ROTATES TWICE AS FAST AS INPUT SPEED

129 SPEED OF ROTATION INPUT SPEED = NI LEFT SIDE OUTPUT SPEED = NL RIGHT SIDE OUTPUT SPEED = NR IF NI = 0? NL = - NR LEFT SIDE OUTPUT ROTATES OPPOSITE TO RIGHT SIDE

130 LEFT RIGHT TORQUE BALANCE T TORQUE BIAS = 1.0 L R L = R = ½ T (EQUAL TORQUE DISTRIBUTION)

131 SLIPPERY SITUATION ZERO THRUST TO MAKE CAR GO? ADD FRICTION! ZERO FRICTION ZERO TORQUE RESISTANCE ZERO TORQUE BALANCE

132 SLIPPERY SITUATION ENGINE CAN SUPPLY 200 UNITS OF TORQUE UNITS OF RESISTANCE = 100 UNITS TORQUE BALANCE

133 SLIPPERY SITUATION CAR MOVES FORWARD BUT, ALSO TURNS TO THE LEFT, EVEN IF THE STEERING IS HELD STRAIGHT! ENGINE REVS STILL RISE AS LEFT WHEEL IS SPINNING, BUT TORQUE CAN BE DELIVERED TO THE DIFFERENTIAL 100 UNITS OF RESISTANCE WILL REDUCE WHEEL SPIN BUT DO NOT PRODUCE FORWARD THRUST AS WHEEL IS SPINNING 100 UNITS OF TORQUE TRANSFERED PRODUCE FORWARD THRUST

134 SLIPPERY SITUATION THE MORE THE CAR MOVES FORWARD THE MORE THE CAR TURNS TO THE LEFT THE MORE TORQUE THE ENGINE CAN DELIVER THE MORE RESISTANCE WE ADD THE MORE TORQUE THAT IS TRANSFERED

135 LIMITED SLIP DIFFERENTIAL Almost all Limited Slip Differentials apply friction to eliminate excessive wheel spin Friction can be Constant (clutch pack, or cone) Linear (ramps and clutch pack : Hewland, ZF) Linear (geared: TorSen, hypoid) Progressive (viscous) Active (hydraulic piston and clutch pack, solenoid and clutch pack) Magnetic/Electric

136 LIMITED SLIP DIFFERENTIAL Some Limited Slip Differentials can lock completely Locking differentials include: Detroit Locker Cam and Pawl

137 LIMITED SLIP DIFFERENTIAL

138 OPEN DIFFERENTIAL TOP VIEW SIDE VIEW

139 CLUTCH PACK LSD TO ADD MORE PRELOAD WE CAN: STIFFEN THE SPRINGS, OR ADD MORE PLATES

140 CLUTCH PACK LSD ADDING MORE PRELOAD PRODUCES: MORE RESISTANCE MORE TORQUE TRANSFER MORE THRUST BUT ALSO MORE TENDENCY FOR THE CAR TO TURN

141 RAMP AND CLUTCH PACK LSD INPUT TORQUE FORCES RAMPS APART MORE FRICTION IS GENERATED TOP VIEW SIDE VIEW

142 RAMP AND CLUTCH PACK LSD THE GREATER THE TORQUE INPUT THE GREATER THE RAMP SEPARATION THE GREATER THE FRICTION THE GREATER THE THRUST BUT ALSO, THE GREATER THE TENDENCY TO TURN

143 RAMP AND CLUTCH PACK LSD RAMPS ARE TYPICALLY TAPERED BETWEEN 25 AND 90 A 25 RAMP PRODUCES MORE FRICTION THAN A 80 RAMP FOR THE SAME INPUT TORQUE A 90 RAMP WILL NOT CAUSE THE RAMPS TO SEPARATE

144 RAMP AND CLUTCH PACK LSD UNDER BRAKING THE OVER- RUN SIDE OF THE RAMPS OPERATE THE INPUT TORQUE IS NOTA FUNCTION OF HOW HARD THE BRAKES ARE APPLIED THE INPUT TORQUE IS A FUNCTION OF HOW MUCH ENGINE BRAKING IS USED

145 RAMP AND CLUTCH PACK LSD ACCELERATION RAMPS ARE TYPICALLY BETWEEN 25 AND 60 OVER-RUN RAMPS ARE TYPICALLY BETWEEN 60 AND 90

146 RAMP AND CLUTCH PACK LSD THIS DIFFERENTIAL CAN BECOME COMPLETELY LOCKED IF: RAMP ANGLES ARE TOO SHALLOW TOO MANY PLATES ARE USED TOO MUCH PRELOAD, OR ANY COMBINATION OF THE THREE

147 RAMP AND CLUTCH Can tune the amount of resistance to give Better traction Better corner-exit turning Greater braking stability Greater mid-corner, dropped throttle, stability Can tune using ADVANTAGES Preload Ramp Angles Number of Plates, and Type of Oil

148 RAMP AND CLUTCH DISADVANTAGES Internal friction Generates heat (and may need cooling) Increases fuel and tyre consumption Varies with temperature Requires regular servicing if used for racing Neglecting to service results in Increased wear Inconsistent behaviour Permanent damage to ramps and plates Complete rupture

149 Internal gearing Allows wheels to turn at independent speeds while still delivering equivalent torque Resists inside wheel from spinning when the resistance reduces to zero Multiplies the torque available on the inside wheel to the outside wheel (torque biasing) Torque Biasing Is typically in the order of 1.5 up to 4 times Depends on gearing Is not easily tuned TORSEN DIFFERENTIAL

150 TORSEN DIFFERENTIAL ENGINE CAN DELIVER TORQUE TO THRUST CAR ASSUME A TORQUE BIAS OF 3:1 ALMOST ZERO WHEEL SPIN! ASSUME ONLY 10 UNITS OF FRICTION AVAILABLE 30 UNITS OF FRICTION TRANSFERRED TO RIGHT SIDE

151 TORSEN DIFFERENTIAL ENGINE CAN NOT DELIVER TORQUE TO THRUST CAR ASSUME A TORQUE BIAS OF 3:1 ZERO UNITS OF FRICTION AVAILABLE 0 UNITS OF FRICTION TRANSFERRED TO RIGHT SIDE CAR STANDS STILL!

152 TORSEN ADVANTAGES Improved traction in slippery conditions compared to open differential Smooth biasing of torque Internal friction occurs only when gears are biasing torque so does not consume fuel during normal driving Excellent operation in very low grip situations (ice) as biasing is not excessive

153 TORSEN DISADVANTAGES Heavy Torque bias reduces as gears start to wear Need to change all of the gears to change the torque bias Expensive (although equivalent copies are becoming cheaper by the day)

154 LOCKED DIFFERENTIAL Typically called a spool differential Solid link between driven wheels Wheels are forced to move at the same speed Can be useful for applications in racing cars with high power Has been used successfully in racing (gokarts, Porsche , ) Most ramp and clutch differentials become fully locked under partial or full throttle applications

155 LOCKED ADVANTAGES Cheap Easy Consistent behaviour Reliable Excellent traction on corner exit

156 LOCKED DISADVANTAGES Difficult to manoeuvre car at slow speed Difficult to turn car into a corner Can bind up and release causing car to spin off the road Increases tyre wear as inside wheel is caused to slip

157 INFLUENCE ON HANDLING INPUT TORQUE LOW TORQUE HIGH TORQUE DIFF. FUNCTION LIMITING SLIP TORQUE MULTIPLYING LOCKED TRACTIVE CAPACITY HIGH GRIP NO WHEELSPIN MEDIUM GRIP INSIDE WHEEL SPIN LOW GRIP BOTH SPIN VEHICLE DYNAMICS DRIVE TRACTION UNDERSTEER OVERSTEER

158 WHICH IS BEST? Low power road car Medium power road car High power road car Open or TorSen TorSen or Clutch pack TorSen or Ramp and clutch pack Medium power circuit racing car Ramp and clutch pack High power circuit racing car Ramp and clutch pack, Locked High power circuit car with wings Locked Medium power gravel rally car High power gravel rally car TorSen or Ramp and clutch pack Ramp and clutch pack