RACE ENGINEERING ACADEMY VEHICLE HANDLING BASICS INTRODUCTION BY Dejan Ninic BE (Mech) PhD ENVIRAGE
VEHICLE HANDLING DEFINITIONS STABILITY BALANCE VEHICLE DYNAMICS RESPONSE GRIP
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)
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
VEHICLE HANDLING OBJECTIVES Need to produce combined thrust
TYRE FORCES Contact patch forces
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
TYRE PRESSURE
TYRE PRESSURE INCREASING CONTACT PATCH AREA INCREASING AVAILABLE GRIP
TYRE INCLINATION 0 degrees -3 degrees -5 degrees
TYRE TEMPERATURE
SLIP RATIO Slip ratio Measure of wheel spin (or wheel locking) SLIP RATIO = Vs/Vf - 1 = 0.0 0.25 = 0% - 25% SLIP (typical) Vf Vs
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
SLIP RATIO
SLIP ANGLE α Vf Vl SLIP ANGLE = Vl/Vf = 0.0-0.25 (typical) = 0 14 degrees
SLIP ANGLE Vf LATERAL FORCE Peak Thrust SA 6 degrees (typical) Vl SLIP ANGLE = Vl/Vf = 0.0-0.25 (typical) = 0 14 degrees SLIP ANGLE
TYRE GRIP UNDER FORCE THE RUBBER DEFORMS INTO THE ROAD ASPERITIES PROVIDING A KEY ACTION VEHICLE MASS VERTICAL RESISTANCE
TYRE GRIP VERTICAL FORCE TRACTIVE FORCE CAPACITY VERTICAL RESISTANCE
TYRE GRIP TRACTIVE FORCE VERTICAL FORCE
RIGID CAR Overall Objective: Allow wheel to follow the contour of the road, WITH MINIMAL VARIATION OF THE CONTACT PATCH LOAD
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
WHEEL TRAVEL TYPEOF CAR CIRCUIT RACING ROAD CAR SAFARI OFF ROAD CAR TYPICAL REQUIRED WHEEL TRAVEL 60mm 200mm 400mm
NEED SUSPENSIONTO HAVE WHEEL TRAVEL
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
SPRING STIFFNESS Linear spring rate SPRING FORCE N, lb, kg SPRING DEFORMATION mm, in, m
TYPICAL SPRING Type of Car RATES Metric N/mm Imperial lb/in Family sedan 20 115 Gravel rally 30 170 Tarmac rally 55 315 Circuit racing 200 1140 Formula 1 250 1430 Multiply Stiffness in lb/in by 0.175 to get N/mm
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)
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)
SPRUNG MOTION The system natural frequency can be calculated using the formula M K x Giving a frequency value in Hertz
SPRUNG MOTION Porsche Carrera 2.7L Front left sprung mass = 200kg Front left effective spring rate = 30 kn/m, K M x 1.95
SPRUNG MOTION Porsche Carrera 2.7L Rear left sprung mass = 320kg Rear left effective spring rate = 50 kn/m K M x, 1.99
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
SPRUNG MOTION Type of Car Effective Stiffness N/mm Natural Frequency Hz Family sedan 20 1.2 Gravel rally 30 1.6 Tarmac rally 55 2.2 Circuit racing 200 3.8 Formula 1 250 6.0 A CARS STIFFNESS IS BETTER CATEGORISED BY ITS NATURAL FREQUENCY THAN ITS SPRING STIFFNESS
SPRING STIFFNESS Progressive spring rate SPRING FORCE N, lb, kg SPRING DEFORMATION mm, in, m
ANTI-ROLL BAR
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)
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
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
DAMPER Whilst driving over a bump, the wheel is forced up into the chassis
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
DAMPER The spring and damper work together to proportion the relative amount of work each does during the stroke
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)
DAMPER The proportion of spring force to damper force that is necessary can be calculated using basic vibration theory
DAMPER A damper builder/designer must know your spring rate (and vehicle mass) to correctly rate your damper
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!
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
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
DAMPER CURVES DAMPER RATE SLOPE OF THE CURVE FOR A PARTICULAR SPEED EXPRESSED IN Ns/m
DAMPER Damper Construction Literally HUNDREDS of different damper constructions and differing damper functions Look at the generic construction and typical operation
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
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
DAMPER CURVES ENVIRAGE
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
DAMPER CURVES ENVIRAGE
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
DAMPER CURVES
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
DAMPER CURVES
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)
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)
CHOOSING A DAMPER Corner Weights Spring rates Road surface type Tyre type Car configuration Mechanical grip vs. Aero grip
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
RECOMMENDED DAMPER CURVES
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
RACE ENGINEERING ACADEMY VEHICLE HANDLING BASICS PART 2: HANDLING GUIDE BY Dejan Ninic BE (Mech) PhD ENVIRAGE
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
MASS DISTRIBUTION Centre of Gravity Height Track Width
WHEEL ALIGNMENT Wheelbase Length Wheelbase
WHEEL ALIGNMENT Ride Height Ride Height Measured to Sills
WHEEL ALIGNMENT Ride Height Ride Height Measured to Other Points on Vehicle
WHEEL ALIGNMENT Rake Angle Rake Angle
WHEEL ALIGNMENT Corner Weights
WHEEL ALIGNMENT Toe Direction of Travel Longitudinal Axis Toe Angle Toe Angle Longitudinal Axis Top View of Tyres
WHEEL ALIGNMENT Camber Up Camber Angle Camber Angle Vertical Axis Vertical Axis Front View of Tyres
WHEEL ALIGNMENT Caster Caster Angle Upper ball joint Vertical Axis Steering Axis Towards Front of Vehicle Lower ball joint
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
SUSPENSION KINEMATICS Types of suspension systems Double wishbone Source: Jazar, R.N. 2008, Vehicle Dynamics Theory and Application, Springer, New York, pg. 467
- McPherson Strut SUSPENSION KINEMATICS Source: Jazar, R.N. 2008, Vehicle Dynamics Theory and Application, Springer, New York, pg. 467
- Semi Trailing Arm SUSPENSION KINEMATICS Source: Jazar, R.N. 2008, Vehicle Dynamics Theory and Application, Springer, New York, pg. 469
- Live Axle - Panhard Rod SUSPENSION KINEMATICS Source: Jazar, R.N. 2008, Vehicle Dynamics Theory and Application, Springer, New York, pg. 460
- Live Axle - Watts Link SUSPENSION KINEMATICS Source: Jazar, R.N. 2008, Vehicle Dynamics Theory and Application, Springer, New York, pg. 462
SUSPENSION KINEMATICS - Multi-Link Source: Jazar, R.N. 2008, Vehicle Dynamics Theory and Application, Springer, New York, pg. 468
SUSPENSION MEASUREMENTS Wheel offset Wheel Offset (Positive Offset) Wheel Centreline Towards Car Centreline Source: http://www.dfisica.ubi.pt/~hgil/utils/pneus/info/cro sssection.gif
Scrub Radius SUSPENSION MEASUREMENTS Wheel Centreline Away From Car Centreline King Pin Inclination (KPI) Scrub Radius
ROLL-CENTRE % Anti-roll Roll Moment Arm Sprung Mass CG Roll Centre
SUSPENSION MEASUREMENTS Bump steer Motion ratio Camber gain 3D suspension pick-up measurement Roll-centre position Roll-centre migration Vertical Lateral
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.)
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
TUNING FOR HANDLING Reminder of the VEHICLE DYNAMICS MODEL STABILITY BALANCE VEHICLE DYNAMICS RESPONSE GRIP
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
TYRE TEMPERATURE
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
TYRE TEMPERATURE
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)
TRACTIVE CAPACITY 300kg 250kg 300kg 250kg L=R= 250kg TOTAL GRIP = L + R = 250 + 250 = 500kg L=R= 300kg VERTICAL FORCE
TRACTIVE CAPACITY 50kg transferred 250kg 210kg 350kg 280kg R= 280kg 250kg L= 210kg TOTAL GRIP = L + R = 280 + 210 = 490kg LESS THAN 500kg! 250kg 300kg 350kg VERTICAL FORCE
WHEEL ALIGNMENT Load Transfer is related to h/t Centre of Gravity Height h Track Width t
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
TYRE TEMPERATURE AVERAGE = 74.7⁰C AVERAGE = 79.5⁰C AVERAGE = 75.5⁰C AVERAGE = 81.2⁰C
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
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
TUNING FOR HANDLING Next: How much time do you have?! 10 minutes? 2 hours? 1 day? 2 weeks?
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)
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)
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)
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
SETUP CHANGE DIFFICULTY SENSITIVITY RATIO Tyre Pressure 1 7 7.0 Damper Click 2 7 3.5 ARB Setting 3 8 2.7 Damper Change 6 9 1.5 Spring Change 6 9 1.5 Ride height/rake 4 8 2.0 Static Toe 4 5 1.3 Static Camber 5 8 1.6 Corner Weights 5 6 1.2 Caster 5 7 1.4 Bump-steer 7 9 3.0 Camber Gain 7 7 1.0 Roll Centre Height 8 6 0.8 Anti-dive/ Anti-squat 8 5 0.6
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
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
TUNING FOR HANDLING Damper Settings Overall Rebound only Bump only Low Speed High Speed Gas Pressure
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
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
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)
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)
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
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
RACE ENGINEERING ACADEMY VEHICLE HANDLING BASICS PART 3: DIFFERENTIALS BY Dejan Ninic BE (Mech) PhD ENVIRAGE
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
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).
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.
OPEN DIFFERENTIAL
OPEN DIFFERENTIAL SIDE GEARS TURNED BY PINIONS TOP VIEW SIDE VIEW
TORQUE DISTRIBUTION INPUT TORQUE = T LEFT SIDE OUTPUT TORQUE = L RIGHT SIDE OUTPUT TORQUE = R L = R = ½ T (EQUAL TORQUE DISTRIBUTION)
TYRES HAVE EQUAL GRIP T L R L = R = ½ T (EQUAL TORQUE DISTRIBUTION)
LEFT TYRE HAS LITTLE GRIP LEFT WHEEL SPINS AND CAR STANDS STILL 0 = 0 = 0 (NO TORQUE DISTRIBUTION)
SPEED OF ROTATION INPUT SPEED = NI LEFT SIDE OUTPUT SPEED = NL RIGHT SIDE OUTPUT SPEED = NR NI = ½ (NL + NR) NL = 2 NI - NR
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
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
LEFT RIGHT TORQUE BALANCE T TORQUE BIAS = 1.0 L R L = R = ½ T (EQUAL TORQUE DISTRIBUTION)
SLIPPERY SITUATION ZERO THRUST TO MAKE CAR GO? ADD FRICTION! ZERO FRICTION ZERO TORQUE RESISTANCE ZERO TORQUE BALANCE
SLIPPERY SITUATION ENGINE CAN SUPPLY 200 UNITS OF TORQUE + 100 UNITS OF RESISTANCE = 100 UNITS TORQUE BALANCE
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
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
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
LIMITED SLIP DIFFERENTIAL Some Limited Slip Differentials can lock completely Locking differentials include: Detroit Locker Cam and Pawl
LIMITED SLIP DIFFERENTIAL
OPEN DIFFERENTIAL TOP VIEW SIDE VIEW
CLUTCH PACK LSD TO ADD MORE PRELOAD WE CAN: STIFFEN THE SPRINGS, OR ADD MORE PLATES
CLUTCH PACK LSD ADDING MORE PRELOAD PRODUCES: MORE RESISTANCE MORE TORQUE TRANSFER MORE THRUST BUT ALSO MORE TENDENCY FOR THE CAR TO TURN
RAMP AND CLUTCH PACK LSD INPUT TORQUE FORCES RAMPS APART MORE FRICTION IS GENERATED TOP VIEW SIDE VIEW
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
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
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
RAMP AND CLUTCH PACK LSD ACCELERATION RAMPS ARE TYPICALLY BETWEEN 25 AND 60 OVER-RUN RAMPS ARE TYPICALLY BETWEEN 60 AND 90
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
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
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
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
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
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!
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
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)
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 917-10, 917-30) Most ramp and clutch differentials become fully locked under partial or full throttle applications
LOCKED ADVANTAGES Cheap Easy Consistent behaviour Reliable Excellent traction on corner exit
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
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
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