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Automotive suspension engineering FAQ
SAE Dynamics Glossary
Definitions to Common Suspension Nomenclature by Joest
Posted: 23 Jan 03 (Edited 19 May 04)

Some terminology you may find in the professional world of suspension design. Try the following link for a nicely formatted HTML version. For those that do not use the link, credits go to SAE Vehicle Dynamics Glossary (SAE J670e).
Please send comment to: racecar543@yahoo.com
http://www.adams.com/product/product_line/ainsight/sae_vda.htm
Table of Contents 1. Mechanical VibrationQualalitative Terminology 1.1 Vibration (Oscillation), General 1.2 Free Vibration 1.3 Forced Vibration 1.3.1 RESONANCE 1.4 SelfExcited Vibration 1.5 Simple Harmonic Vibration 1.6 SteadyState Vibration 1.7 Periodic Vibration 1.8 Random Vibration 1.9 Transient Vibration 2. MECHANICAL VIBRATIONQUANTITATIVE TERMINOLOGY 2.1 PERIOD 2.2 CYCLE 2.3 FREQUENCY 2.3.1 NATURAL FREQUENCY 2.3.2 EXCITING FREQUENCY 2.3.3 FREQUENCY RATIO 2.3.4 RESONANT FREQUENCY 2.4 AMPLITUDE 2.4.1 PEAKTOPEAK AMPLITUDE (DOUBLE AMPLITUDE) 2.4.2 STATIC AMPLITUDE 2.4.3 AMPLITUDE RATIO(RELATIVE MAGNIFICATION FACTOR) 2.5 VELOCITY 2.6 Acceleration 2.7 Jerk 2.8 Transmissibility 3. Vibrating Systems 3.1 Degree of Freedom 3.2 Linear 3.3 Nonlinear 3.4 Undamped 3.5 Damped 3.5.1 VISCOUS DAMPING 3.5.2 CRITICAL DAMPING 3.5.3 DAMPING RATIO 3.5.4 COULOMB DAMPING 3.5.5 COMPLEX DAMPING 4. Components and Characteristics of Suspension Systems 4.1 Vibrating Mass and Weight 4.1.1 SPRUNG WEIGHT 4.1.2 SPRUNG MASS 4.1.3 DYNAMIC INDEX 4.1.4 UNSPRUNG WEIGHT 4.1.5 UNSPRUNG MASS 4.2 Spring Rate 4.2.1 STATIC RATE 4.2.2 DYNAMIC RATE 4.3 Resultant Spring Rate 4.3.1 SUSPENSION RATE (WHEEL RATE) 4.3.2 TIRE RATE (STATIC) 4.3.3 RIDE RATE 4.4 Static Deflection 4.4.1 TOTAL STATIC DEFLECTION 4.4.2 EFFECTIVE STATIC DEFLECTION 4.4.3 SPRING CENTER 4.4.3.1 Parallel Springing 4.5 Damping Devices 4.5.1 SHOCK ABSORBER 4.5.2 SNUBBER 5. Vibrations of Vehicle Suspension Systems 5.1 Sprung Mass Vibrations 5.1.1 RIDE 5.1.1.1 Vertical (Bounce) 5.1.1.2 Pitch 5.1.1.3 Roll 5.1.2 SHAKE 5.1.2.1 Torsional Shake 5.1.2.2 Beaming 5.1.3 HARSHNESS 5.1.4 BOOM 5.2 Unsprung Mass Vibrations 5.2.1 WHEEL VIBRATION MODES 5.2.1.1 Hop 5.2.1.1.1 Parallel hop 5.2.1.1.2 Tramp 5.2.1.2 Brake Hop 5.2.1.3 Power Hop 5.2.2 AXLE VIBRATION MODES 5.2.2.1 Axle Side Shake 5.2.2.2 Axle ForeandAft Shake 5.2.2.3 Axle Yaw 5.2.2.4 Axle Windup 5.2.3 STEERING SYSTEM VIBRATIONS 5.2.3.1 Wheel Flutter 5.2.3.2 Wheel Wobble 5.2.3.3 Shimmy 5.2.3.4 Wheelfight 6. Suspension Geometry 6.1 Kingpin Geometry 6.1.1 WHEEL PLANE 6.1.2 WHEEL CENTER 6.1.3 CENTER OF TIRE CONTACT 6.1.4 KINGPIN INCLINATION 6.1.5 KINGPIN OFFSET 6.2 Wheel Caster 6.2.1 CASTER ANGLE 6.2.2 RATE OF CASTER CHANGE 6.2.3 CASTER OFFSET 6.2.4 CENTRIFUGAL CASTER 6.3 Wheel Camber 6.3.1 CAMBER ANGLE 6.3.2 RATE OF CAMBER CHANGE 6.3.2.1 Swing Center 6.3.2.2. SwingArm Radius 6.3.,3 WHEEL TRACK (WHEEL TREAD) 6.3.4 TRACK CHANGE 6.3.5 RATE OF TRACK CHANGE 6.4 Wheel Toe 6.4.1 STATIC TOE ANGLE (DEG) 6.4.2 STATIC TOE (IN [MM]) 6.5 Compression 6.5.1 RIDE CLEARANCE 6.5.2 METALTOMETAL POSITION (COMPRESSION) 6.5.3 BUMP STOP 6.6 Rebound 6.6.1 REBOUND CLEARANCE 6.6.2 METALTOMETAL POSITION (REBOUND) 6.6.3 REBOUND STOP 6.7 Center of Parallel Wheel Motion 6.8 Torque Arm 6.8.1 TORQUEARM CENTER IN BRAKING 6.8.2 TORQUEARM CENTER IN DRIVE 6.8.3 TORQUEARM RADIUS 7. Tires and Wheels 7.1 General Nomenclature 7.1.1 STANDARD LOADS AND INFLATIONS 7.1.2 RIM DIAMETER 7.1.3 RIM WIDTH 7.1.4 TIRE SECTION WIDTH 7.1.5 TIRE OVERALL WIDTH 7.1.6 TIRE SECTION HEIGHT 7.1.7 OUTSIDE DIAMETER 7.1.8 FLAT TIRE RADIUS 7.1.9 DEFLECTION (STATIC) 7.1.9.1 Percent Deflection 7.1.10 TIRE RATE (STATIC) 7.1.11 SIDEWALL 7.1.11.1 Sidewall Rib 7.1.12 BEAD 7.1.12.1 Bead Base 7.1.12.2 Bead Toe 7.1.13 TREAD (TIRE) 7.1.13.1 Tread Contour 7.1.13.2 Tread Radius 7.1.13.3 Tread Arc Width 7.1.13.4 Tread Chord Width 7.1.13.5 Tread Contact Width 7.1.13.6 Tread Contact Length 7.1.13.7 Tread Depth 7.1.13.8 Gross Contact Area 7.1.13.9 Net Contact Area 7.1.13.10 Tread Pattern 7.2 Rolling Characteristics 7.2.1 LOADED RADIUS (Re) 7.2.2 STATIC LOADED RADIUS 7.2.3 SPIN AXIS 7.2.4 SPIN VELOCITY (Q) 7.2.5 FREEROLLING TIRE 7.2.6 STRAIGHT FREEROLLING TIRE 7.2.7 LONGITUDINAL SLIP VELOCITY 7.2.8 LONGITUDINAL SLIP (PERCENT SLIP) 7.2.9 EFFECTIVE ROLLING RADIUS (Re) 7.2.10 WHEEL SKID 7.3 Tire Forces and Moments 7.3.1 TIRE AXIS SYSTEM (FIG. I ) 7.3.2 TIRE ANGLES 7.3.2.1 Slip Angle (a) 7.3.2.2 Inclination Angle (Y) 7.3.3 TIRE FORCES 7.3.3.1 Longitudinal Force (Fx) 7.3.3.2 Driving Force 7.3.3.3 Driving Force Coefficient 7.3.3.4 Braking Force 7.3.3 .5 Braking Force Coefficient (Braking Coefficient) 7.3.3.6 Rolling Resistance Force 7.3.3.7 Rolling Resistance Force Coefficient 7.3.3.8 Lateral Force (Fy) 7.3.3.9 Lateral Force Coefficient 7.3.3.10 Slip Angle Force 7.3.3.11 Camber Force (Camber Thrust) 7.3.3.12 Normal Force (Fz) 7.3.3.13 Vertical Load 7.3.3.14 Central ForceThe component of the tire force vector in the 7.3.3.15 Tractive Force 7.3.3.16 Drag Force 7.3.4 TIRE MOMENTS 7.3.4.1 Overturning Moment (Mx) 7.3.4.2 Rolling Resistance Moment (My) 7.3.4.3 Aligning Torque (Aligning Moment) (Mz) 7.3.4.4 Wheel Torque (T) 7.3.4.5 Driving Torque 7.3.4.6 Braking Torque 7.4 Tire Force and Moment Stiffness 7.4.1 CORNERING STIFFNESS 7.4.2 CAMBER STIFFNESS 7.4.3 BRAKING (DRIVING) STIFFNESS 7.4.4 ALIGNING STIFFNESS (ALIGNING TORQUE STIFFNESS) 7.5 Normalized Tire Force and Moment Stiffnesses (Coefficients) 7.5.1 CORNERING STIFFNESS COEFFICIENT (CORNERING COEFFICIENT) 7.5.2 CAMBER STIFFNESS COEFFICIENT (CAMBER COEFFICIENT) 7.5.3 BRAKING (DRIVING) STIFFNESS COEFFICIENT 7.5.4 ALIGNING STIFFNESS COEFFICIENT (ALIGNING TORQUE COEFFICIENT) 7.6 Tire Traction Coefficients 7.6.1 LATERAL TRACTION COEFFICIENT 7.6.2 DRIVING TRACTION COEFFICIENT 7.6.3 BRAKING TRACTION COEFFICIENT 7.6.3.1 Sliding Braking Traction Coefficient 7.7 Tire Associated Noise and Vibrations 7.7.1 TREAD NOISE 7.7.1.1 Sizzle 7.7.2 SQUEAL 7.7.2.1 Cornering Squeal 7.7.2.2 Braking (Driving) Squeal 7.7.3 THUMP 7.7.4 ROUGHNESS 7.7.5 HARSHNESS 7.7.6 SLAP 7.8 Tire and Wheel NonUniformity Characteristics 7.8.1 RADIAL RUNOUT 7.8.1.1 PeaktoPeak Radial Wheel RunOut 7.8.1.2 PeaktoPeak Unloaded Radial Tire RunOut 7.8.1.3 PeaktoPeak Loaded Radial Tire RunOut 7.8.2 LATERAL RUNOUT 7.8.2.1 PeaktoPeak Lateral Wheel RunOut 7.8.2.2 PeaktoPeak Lateral Tire RunOut 7.8.3 RADIAL FORCE VARIATION 7.8.3.1 PeaktoPeak (Total) Radial Force Variation 7.8.3.2 First Order Radial Force Variation 7.8.4 LATERAL FORCE VARIATION 7.8.4.1 PeaktoPeak (Total) Lateral Force Variation 7.8.4.2 First Order Lateral Force Variation 7.8.5 LATERAL FORCE OFFSET 7.8.5.1 Ply Steer Force 7.8.5.2 Conicity Force 8. Kinematics 8.1 EarthFixed Axis System (X,Y,Z) 8.2 Vehicle Axis System (x,y,z) 8.3 Angular Orientation 8.4 Motion Variables 8.4.1 VEHICLE VELOCITY 8.4.1.1 Longitudinal Velocity (u) 8.4.1.2 Side Velocity (v) 8.4.l.3 Normal Velocity (w) 8.4.1.4 Forward Velocity 8.4.1.5 Lateral Velocity 8.4.1.6 Roll Velocity (p) 8.4.1.7 Pitch Velocity (q) 8.4.1.8 Yaw Velocity (r) 8.4.2 VEHICLE ACCELERATION 8.4.2.1 Longitudinal Acceleration 8.4.2.2 Side Acceleration 8.4.2.3 Normal Acceleration 8.4.2.4 Lateral Acceleration 8.4.2.5 Centripetal Acceleration 8.4.3 HEADING ANGLE (Y) 8.4.4 SIDESLIP ANGLE (ATTITUDE ANGLE) (B) 8.4.5 SIDESLIP ANGLE GRADIENT 8.4.6 COURSE ANGLE (t)) 8.4.7 VEHICLE ROLL ANGLE 8.4.8 VEHICLE ROLL GRADIENT 8.4.9 VEHICLE PITCH ANGLE 8.5 Forces 8.5.1 LONGITUDINAL FORCE (Fx) 8.5.2 SIDE FORCE (Fy) 8.5.3 NORMAL FORCE (Fz) 8.6 Moments 8.6.1 ROLLING MOMENT (Mx) 8.6.2 PITCHING MOMENT (My) 8.6.3 YAWING MOMENT (Mz) 9. Directional Dynamics 9.1 Control Modes 9.1.1 POSITION CONTROL 9.1.2 FIXED CONTROL 9.1.3 FORCE CONTROL 9.1.4 FREE CONTROL 9.2 Vehicle Response 9.2.1 STEERING RESPONSE 9.2.2 DISTURBANCE RESPONSE 9.2.3 STEADYSTATE 9.2.4 TRANSIENT STATE 9.2.5 TRIM 9.2.6 STEADYSTATE RESPONSE GAIN 9.2.7 STEERING SENSITIVITY (CONTROL GAIN) 9.3 Stability 9.3.1 ASYMPTOTIC STABILITY 9.3.2 NEUTRAL STABILITY 9.3.3 DIVERGENT INSTABILITY 9.3.4 OSCILLATORY INSTABILITY 9.4 Suspension Steer and Roll Properties 9.4.1 STEER ANGLE (S) 9.4.2 ACKERMAN STEER ANGLE (Sa) 9.4.3 ACKERMAN STEER ANGLE GRADIENT 9.4.4 STEERING WHEEL ANGLE 9.4.5 STEERING WHEEL ANGLE GRADIENT 9.4.6 OVERALL STEERING RATIO 9.4.7 UNDERSTEER/OVERSTEER GRADIENT 9.4.8 NEUTRAL STEER 9.4.9 UNDERSTEER 9.4.10 OVERSTEER 9.4.11 STEERING WHEEL TORQUE 9.4.12 STEERING WHEEL TORQUE GRADIENT 9.4.13 CHARACTERISTIC SPEED 9.4.14 CRITICAL SPEED 9.4.15 NEUTRAL STEER LINE 9.4.16 STATIC MARGIN 9.4.17 SUSPENSION ROLL 9.4.18 SUSPENSION ROLL ANGLE 9.4.19 SUSPENSION ROLL GRADIENT 9.4.20 ROLL STEER 9.4.20.1 Roll Understeer 9.4.20.2 Roll Oversteer 9.4.21 ROLL STEER COEFFICIENT 9.4.22 COMPLIANCE STEER 9.4.22.1 Compliance Understeer 9.4.22.2 Compliance Oversteer 9.4.23 COMPLIANCE STEER COEFFICIENT 9.4.24 ROLL CAMBER 9.4.25 ROLL CAMBER COEFFICIENT 9.4.26 COMPLIANCE CAMBER 9.4.27 COMPLIANCE CAMBER COEFFICIENT 9.4.28 ROLL CENTER 9.4.29 ROLL AXIS 9.4.30 SUSPENSION ROLL STIFFNESS 9.4.31 VEHICLE ROLL STIFFNESS 9.4.32 ROLL STIFFNESS DISTRIBUTION 9.5 Tire Load Transfer 9.5.1 TIRE LATERAL LOAD TRANSFER 9.5.2 TIRE LATERAL LOAD TRANSFER DISTRIBUTION 9.5.3 TIRE LONGITUDINAL LOAD TRANSFER 9.5.4 OVERTURNING COUPLE 9.5.5 OVERTURNING COUPLE DISTRIBUTION 10. Aerodynamic Nomenclature 10.1 Aerodynamic Motion Variables 10.1.1 AMBIENT WIND VELOCITY (Va) 10.1.2 AMBIENT WIND ANGLE (Va) 10.1.3 RESULTANT AIR VELOCITY VECTOR (Vr) 10.1.4 AERODYNAMIC SIDESLIP ANGLE (Ba) 10.1.5 AERODYNAMIC ANGLE OF ATTACK (aa) 10.2 Aerodynamic Force and Moment Coefficients 10.2.1 REFERENCE DIMENSIONS 10.2.1.1 Vehicle Area (A) 10.2.1.2 Vehicle Wheelbase (l) 10.2.2 STANDARD AIR PROPERTIES 10.2.2.1 The density of standard dry air shall be taken as 2378 x 106 10.2.2.2 The viscosity of standard dry air shall be taken as 373 x 109 10.2.3 FORCE COEFFICIENTS 10.2.3.1 The Longitudinal Force Coefficient (Cx) is based on the 10.2.3.2 Side Force Coefficient (Cy) is based on the aerodynamic force 10.2.3.3 The Normal Force Coefficient (Cz) is based on the aerodynamic 10.2.4 MOMENT COEFFICIENTS 10.2.4.1 The Rolling Moment Coefficient (CMx) is based on the rolling 10.2.4.2 The Pitching Moment Coefficient (CMy) is based on the pitching 10.2.4.3 The Yawing Moment Coefficient (CMz) is based on the yawing 11. NOTES
Appendix A SAE J670e Vehicle Dynamics Terminology
SAE Recommended Practice Issued by the Vehicle Dynamics Committee July 1952 Last revised July 1976
NOTE: Italicized words and phrases appearing in a definition are themselves defined elsewhere in this Terminology.
1. Mechanical VibrationQualalitative Terminology :
1.1 Vibration (Oscillation), General : Vibration is the variation with time of the displacement of a body with respect to a specified reference dimension when the displacement is alternately greater and smaller than the reference. (Adapted from ANS Z24. 11951, item 1.040.)
1.2 Free Vibration : Free vibration of a system is the vibration during which no variable force is externally applied to the system. (Adapted from ANS Z24.11951, item 2.135.)
1.3 Forced Vibration : Forced vibration of a system is vibration during which variable forces outside the system determine the period of the vibration. (Adapted from ANS Z24. 11951, item 2.130.)
1.3.1 RESONANCE : A forced vibration phenomenon which exists if any small change in frequency of the applied force causes a decrease in the amplitude of the vibrating system. (Adapted from ANS Z24.11951, item 2.1 05.)
1.4 SelfExcited Vibration : Vibrations are termed selfexcited if the vibratory motion produces cyclic forces which sustain the vibration)n.
1.5 Simple Harmonic Vibration : Vibration at a point in a system is simple harmonic when the displacement with respect to time is described by a simple sine function.
1.6 SteadyState Vibration : Steadystate vibration exists in a system if the displacement at each point recurs for equal increments of time. (Adapted from ANS Z24.1  1951, items 11.005 and I .045.)
1.7 Periodic Vibration : Periodic vibration exists in a system when recurring cycles take place in equal time intervals.
1.8 Random Vibration : Random vibration exists in a system when the oscillation is sustained but irregular both as to period and amplitude.
1.9 Transient Vibration : Transient vibration exists in a system when one or more component oscillations are discontinuous.
2. MECHANICAL VIBRATIONQUANTITATIVE TERMINOLOGY :
2.1 PERIOD : Period of an oscillation is the smallest increment of time in which one complete sequence of variation in displacement occurs. (Adapted from ANS Z24.1  1951, item 1.050.)
2.2 CYCLE : Cycle of oscillation is the complete sequence of variations in displacement which occur during a period. (Adapted from ANS Z24.1  1951, item 1.055.)
2.3 FREQUENCY : Frequency of vibration is the number of periods occurring in unit time. (Adapted from ANS Z24.1  1951, item 1.060.)
2.3.1 NATURAL FREQUENCY : Natural frequency of a body or system is a frequency of free vibration. (Same as ANS Z24.1  1951, item 2.140.)
2.3.2 EXCITING FREQUENCY : Exciting frequency is the frequency of variation of the exciting force.
2.3.3 FREQUENCY RATIO : The ratio of exciting frequency to the natural frequency.
2.3.4 RESONANT FREQUENCY : Frequency at which resonance exists (Same as ANS Z24.1  1951, item 2. ] 10.)
2.4 AMPLITUDE : Amplitude of displacement at a point in a vibrating System is the largest value of displacement that the point attains with reference to its equilibrium position. (Adapted from ANS Z24.1  ] 951, item 1.070.)
2.4.1 PEAKTOPEAK AMPLITUDE (DOUBLE AMPLITUDE) : PeaktoPeak amplitude of displacement at a point in a vibrating system is the sum of the extreme values of displacement in both directions from the equilibrium position. (Adapted from ANS Z24. 11951, item I .075.)
2.4.2 STATIC AMPLITUDE : Static amplitude in forced vibration at a point in a system is that displacement of the point from its specified equilibrium position which would be produced by a static force equal to the maximum value of exciting force.
2.4.3 AMPLITUDE RATIO(RELATIVE MAGNIFICATION FACTOR) : The ratio of a forced vibration amplitude to the static amplitude.
2.5 VELOCITY : Velocity of a point in a vibrating system is the time rate of change of its displacement. (Adapted from ANS Z24. 11951, item 1.345.)
In simple harmonic vibration, the maximum velocity,
Vm = Wx where: W= 2*pi*f f = frequency x = amplitude
2.6 Acceleration : Acceleration of a point is the time rate of change of the velocity of the point. (Same as ANS Z24.11951, item 1.355.)
In simple harmonic vibration, the maximum acceleration,
2.7 Jerk : "Jerk" is a concise term used to denote the time rate of change of acceleration of a point.
In simple harmonic motion, the maximum jerk,
2.8 Transmissibility : Transmissibility in forced vibration is the ratio of the transmitted force to the applied force.
3. Vibrating Systems :
3.1 Degree of Freedom : The number of degrees of freedom of a vibrating system is the sum total of all ways in which the masses of the system can be independently displaced from their respective equilibrium positions.
EXAMPLES: A single rigid body constrained to move only vertically on supporting springs is a system of one degree of freedom. If the same mass is also permitted angular displacement in one vertical plane, it has two degrees of freedom; one being vertical displacement of the center of gravity; the other, angular displacement about the center of gravity.
3.2 Linear : Linear vibrating systems are those in which all the variable forces are directly proportional to the displacement, or to the derivatives of the displacement, with respect to time.
3.3 Nonlinear : Nonlinear vibrating systems are those in which any of the variable forces are not directly proportional to the displacement, or to its derivatives, with respect to time.
EXAMPLE: A system having a variable spring rate.
3.4 Undamped : Undamped systems are those in which there are no forces opposing the vibratory motion to dissipate energy.
3.5 Damped : Damped systems are those in which energy is dissipated by forces opposing the vibratory motion.
Any means associated with a vibrating system to balance or modulate exciting forces will reduce the vibratory motion, but are not considered to be in the same category as damping. The latter term is applied to an inherent characteristic of the system without reference to the nature of the excitation.
3.5.1 VISCOUS DAMPING : Damping in which the force opposing the motion is proportional and opposite in direction to the velocity.
3.5.2 CRITICAL DAMPING : The minimum amount of viscous damping required in a linear system to prevent the displacement of the system from passing the equilibrium position upon returning from an initial displacement.
3.5.3 DAMPING RATIO : The ratio of the amount of viscous damping present in a system to that required for critical damping.
3.5.4 COULOMB DAMPING : Damping in which a constant force opposes the vibratory motion.
3.5.5 COMPLEX DAMPING : Damping in which the force opposing the vibratory motion is variable, but not proportional, to the velocity.
In the field of aircraft flutter and vibration, complex damping is also used to denote a specific type of damping in which the damping force is assumed to be harmonic and in phase with the velocity but to have an amplitude proportional to the amplitude of displacement.
4. Components and Characteristics of Suspension Systems :
4.1 Vibrating Mass and Weight :
4.1.1 SPRUNG WEIGHT : All weight which is supported by the suspension, including portions of the weight of the suspension members.
In the case of most vehicles, the sprung weight is commonly defined as the total weight less the weight of unsprung parts.
4.1.2 SPRUNG MASS : Considered to be a rigid body having equal mass, the same center of gravity, and the same moments of inertia about identical axes as the total sprung weight.
4.1.3 DYNAMIC INDEX : (k2/ab ratio) is the square of the radius of gyration (k) of the sprung mass about a transverse axis through the center of gravity, divided by the product of the two longitudinal distances (a and b) from the center of gravity to the front and rear wheel centers.
4.1.4 UNSPRUNG WEIGHT : All weight which is not carried by the suspension system, but is supported directly by the tire or wheel, and considered to move with it.
4.1.5 UNSPRUNG MASS : The unsprung masses are the equivalent masses which reproduce the inertia forces produced by the motions of the corresponding unsprung parts.
4.2 Spring Rate : The change of load of a spring per unit deflection, taken as a mean between loading and unloading at a specified load.
4.2.1 STATIC RATE : Static rate of an elastic member is the rate measured between successive stationary positions at which the member has settled to substantially equilibrium condition.
4.2.2 DYNAMIC RATE : Dynamic rate of an elastic member is the rate measured during rapid deflection where the member is not allowed to reach static equilibrium.
4.3 Resultant Spring Rate :
4.3.1 SUSPENSION RATE (WHEEL RATE) : The change of wheel load, at the center of tire contact, per unit vertical] displacement of the sprung mass relative to the wheel at a specified load.
If the wheel camber varies, the displacement should be measured relative to the lowest point on the rim centerline.
4.3.2 TIRE RATE (STATIC) : The static rate measured by the change of wheel load per unit vertical displacement of the wheel relative to the ground at a specified load and inflation pressure.
4.3.3 RIDE RATE : The change of wheel load, at the center of tire contact, per unit vertical displacement of the sprung mass relative to the ground at a specified load.
4.4 Static Deflection :
4.4.1 TOTAL STATIC DEFLECTION : Total static deflection of a loaded suspension system is the overall deflection under the static load from the position at which all elastic elements are free of load.
4.4.2 EFFECTIVE STATIC DEFLECTION : Effective static deflection of a loaded suspension system equals the static load divided by the spring rate of the system at that load.
Total static deflection and effective static deflection are equal when the spring rate is constant.
4.4.3 SPRING CENTER : The vertical line along which a vertical load applied to the sprung mass will produce only uniform vertical displacement.
4.4.3.1 Parallel Springing : Describes the suspension of a vehicle in which the effective static deflections of the two ends are equal; that is, the spring center passes through the center of gravity of the sprung mass.
4.5 Damping Devices : As distinct from specific types of damping, damping devices refer to the actual mechanisms used to obtain damping of suspension systems.
4.5.1 SHOCK ABSORBER : A generic term which is commonly applied to hydraulic mechanisms for producing damping of suspension systems.
4.5.2 SNUBBER : A generic term which is commonly applied to mechanisms which employ dry friction to produce damping of suspension systems.
5. Vibrations of Vehicle Suspension Systems :
5.1 Sprung Mass Vibrations : 5.1.1 RIDE : The low frequency (up to 5 Hz) vibrations of the sprung mass as a rigid body.
5.1.1.1 Vertical (Bounce) : The translational component of ride vibrations of the sprung mass in the direction of the vehicle zaxis. (See Fig. 2.)
5.1.1.2 Pitch : The angular component of ride vibrations of the sprung mass about the vehicle yaxis.
5.1.1.3 Roll : The angular component of ride vibrations of the sprung mass about the vehicle xaxis.
5.1.2 SHAKE : The intermediate frequency (525 Hz) vibrations of the sprung mass as a flexible body.
5.1.2.1 Torsional Shake : A mode of vibration involving twisting deformations of sprung mass about the vehicle xaxis.
5.1.2.2 Beaming : A mode of vibration involving predominantly bending deformations of the sprung mass about the vehicle yaxis.
5.1.3 HARSHNESS : The high frequency (25100 Hz) vibrations of the structure and/or components that are perceived tactually and/or audibly.
5.1.4 BOOM : A high intensity vibration (25100 Hz) perceived audibly and characterized as sensation of pressure by the ear.
5.2 Unsprung Mass Vibrations :
5.2.1 WHEEL VIBRATION MODES :
5.2.1.1 Hop : The vertical oscillatory motion of a wheel between the road surface and the sprung mass.
5.2.1.1.1 Parallel hop : is the form of wheel hop in which a pair of wheels hop in phase.
5.2.1.1.2 Tramp : is the form of wheel hop in which a pair of wheels hop in opposite phase.
5.2.1.2 Brake Hop : An oscillatory hopping motion of a single wheel or of a pair of wheels which occurs when brakes are applied in forward or reverse motion of the vehicle.
5.2.1.3 Power Hop : An oscillatory hopping motion of a single wheel or of a pair of wheels which occurs when tractive force is applied in forward or reverse motion of the vehicle.
5.2.2 AXLE VIBRATION MODES :
5.2.2.1 Axle Side Shake : Oscillatory motion of an axle which consists of transverse displacement.
5.2.2.2 Axle ForeandAft Shake : Oscillatory motion of an axle which consists purely of longitudinal displacement.
5.2.2.3 Axle Yaw : Oscillatory motion of an axle around the vertical axis through its center of gravity.
5.2.2.4 Axle Windup : Oscillatory motion of an axle about the horizontal transverse axis through its center of gravity.
5.2.3 STEERING SYSTEM VIBRATIONS :
5.2.3.1 Wheel Flutter : Forced oscillation of steerable wheels about their steering axes.
5.2.3.2 Wheel Wobble : A selfexcited oscillation of steerable wheels about their steering axes, occurring without appreciable tramp.
5.2.3.3 Shimmy : A selfexcited oscillation of a pair of steerable wheels about their steering axes, accompanied by appreciable tramp.
5.2.3.4 Wheelfight : A rotary disturbance of the steering wheel produced by forces acting on the steerable wheels.
6. Suspension Geometry :
6.1 Kingpin Geometry :
6.1.1 WHEEL PLANE : The central plane of the tire, normal to the spin axis.
6.1.2 WHEEL CENTER : The point at which the spin axis of the wheel intersects the wheel plane.
6.1.3 CENTER OF TIRE CONTACT : The intersection of the wheel plane and the vertical projection of the spin axis of the wheel onto the road plane. (See Note 1.)
6.1.4 KINGPIN INCLINATION : The angle in front elevation between the steering axis and the vertical.
6.1.5 KINGPIN OFFSET : Kingpin offset at the ground is the horizontal distance in front elevation between the point where the steering axis intersects the ground and the center of tire contact.
The kingpin offset at the wheel center is the horizontal distance in front elevation from the wheel center to the steering axis.
6.2 Wheel Caster :
6.2.1 CASTER ANGLE : The angle in side elevation between the steering axis and the vertical. It is considered positive when the steering axis is inclined rearward (in the upward direction) and negative when the steering axis is inclined forward.
6.2.2 RATE OF CASTER CHANGE : The change in caster angle per unit vertical displacement of the wheel center relative to the sprung mass.
6.2.3 CASTER OFFSET : The distance in side elevation between the point where the steering axis intersects the ground, and the center of tire contact. The offset is considered positive when the intersection point is forward of the tire contact center and negative when it is rearward.
6.2.4 CENTRIFUGAL CASTER : The unbalance moment about the steering axis produced by a lateral acceleration equal to gravity acting at the combined center of gravity of all the steerable parts. It is considered positive if the combined center of gravity is forward of the steering axis and negative if rearward of the steering axis.
6.3 Wheel Camber :
6.3.1 CAMBER ANGLE : The inclination of the wheel plane to the vertical. It is considered positive when the wheel leans outward at the top and negative when it leans inward.
6.3.2 RATE OF CAMBER CHANGE : The change of camber angle per unit vertical displacement of the wheel center relative to the sprung mass.
6.3.2.1 Swing Center : That instantaneous center in the transverse vertical plane through any pair of wheel centers about which the wheel moves relative to the sprung mass.
6.3.2.2. SwingArm Radius : The horizontal distance from the swing center to the center of tire contact.
6.3.,3 WHEEL TRACK (WHEEL TREAD) : The lateral distance between the center of tire contact of a pair of wheels. For vehicles with dual wheels, it is the distance between the points centrally located between the centers of tire contact of the inner and outer wheels. (See S A E J693.)
6.3.4 TRACK CHANGE : The change in wheel track resulting from vertical suspension displacements of both wheels in the same direction.
6.3.5 RATE OF TRACK CHANGE : The change in wheel track per unit vertical displacement of both wheel centers in the same direction relative to the sprung mass.
6.4 Wheel Toe :
6.4.1 STATIC TOE ANGLE (DEG) : The static toe angle of a wheel, at a specified wheel load or relative position of the wheel center with respect to the sprung mass, is the angle between a longitudinal axis of the vehicle and the line of intersection of the wheel plane and the road surface. The wheel is "toedin" if the forward portion of the wheel is turned toward a central longitudinal axis of the vehicle, and "toedout" if turned away.
6.4.2 STATIC TOE (IN [MM]) : Static toein or toeout of a pair of wheels, at a specified wheel load or relative position of the wheel center with respect to the sprung mass, is the difference in the transverse distances between the wheel planes, taken at the extreme rear and front points of the tire treads. When the distance at the rear is greater, the wheels are "toedin" by this amount; and where smaller, the wheels are "toedout." (See Note 2.)
6.5 Compression : The relative displacement of sprung and unsprung masses in the suspension system in which the distance between the masses decreases from that at static condition.
6.5.1 RIDE CLEARANCE : The maximum displacement in compression of the sprung mass relative to the wheel center permitted by the suspension system, from the normal load position.
6.5.2 METALTOMETAL POSITION (COMPRESSION) : The point of maxi mum compression travel limited by interference of substantially rigid members.
6.5.3 BUMP STOP : An elastic member which increases the wheel rate toward the end of the compression travel.
The bump stop may also act to limit the compression travel.
6.6 Rebound : The relative displacement of the sprung and unsprung masses in a suspension system in which the distance between the masses increases from that at static condition.
6.6.1 REBOUND CLEARANCE : The maximum displacement in rebound of the sprung mass relative to the wheel center permitted by the suspension system, from the normal load position.
6.6.2 METALTOMETAL POSITION (REBOUND) : The point of maxi mum rebound travel limited by interference of substantially rigid members.
6.6.3 REBOUND STOP : An elastic member which increases the wheel rate toward the end of the rebound travel.
The rebound stop may also act to limit the rebound travel.
6.7 Center of Parallel Wheel Motion : The center of curvature of the path along which each of a pair of wheel centers moves in a longitudinal vertical plane relative to the sprung mass when both wheels are equally displaced.
6.8 Torque Arm :
6.8.1 TORQUEARM CENTER IN BRAKING : The instantaneous center in a vertical longitudinal plane through the wheel center about which the wheel moves relative to the sprung mass when the brake is locked.
6.8.2 TORQUEARM CENTER IN DRIVE : The instantaneous center in a vertical longitudinal plane through the wheel center about which the wheel moves relative to the sprung mass when the drive mechanism is locked at the power source.
6.8.3 TORQUEARM RADIUS : The horizontal distance from the torque arm center to the wheel center.
7. Tires and Wheels :
7.1 General Nomenclature :
7.1.1 STANDARD LOADS AND INFLATIONS : Those combinations of loads and inflations up to the maximum load and inflation recommended by the Tire & Rim Association and published in the yearly editions of the Tire & Rim Association Yearbook.
7.1.2 RIM DIAMETER : The diameter at the intersection of the bead seat and the flange. (See Tire & Rim Association Yearbook.) Nominal rim diameter (i.e., ]4, 15, 16.5, etc.) is commonly used.
7.1.3 RIM WIDTH : The distance between the inside surfaces or the rim flanges. (See Tire & Rim Association Yearbook.)
7.1.4 TIRE SECTION WIDTH : The width of the unloaded new tire mounted on specified rim, inflated to the normal recommended pressure, including the normal sidewalls but not including protective rib, bars, and decorations. (See Tire & Rim Association Yearbook.)
7.1.5 TIRE OVERALL WIDTH : The width of the unloaded new tire, mounted on specified rim, inflated to the normal recommended pressure, including protective rib, bars, and decorations. (See Tire & Rim Association Yearbook.)
7.1.6 TIRE SECTION HEIGHT : Half the difference between the tire outside diameter and the nominal rim diameter.
7.1.7 OUTSIDE DIAMETER : The maximum diameter of the new unloaded tire inflated to the normal recommended pressure and mounted on a specified rim. (See Airplane Section, Tire & Rim Association Yearbook.)
7.1.8 FLAT TIRE RADIUS : The distance from the spin axis to the road surface of a loaded tire on a specified rim at zero inflation.
7.1.9 DEFLECTION (STATIC) : The radial difference between the undeflected tire radius and the static loaded radius, under specified loads and inflation.
7.1.9.1 Percent Deflection : The static deflection expressed as a percentage of the unloaded section height above the top of the rim flange.
7.1.10 TIRE RATE (STATIC) : See 4.3.2.
7.1.11 SIDEWALL : The portion of either side of the tire which connects the bead with the tread.
7.1.11.1 Sidewall Rib : A raised circumferential rib located on the sidewall.
7.1.12 BEAD : The portion of the tire which fits onto the rim of the wheel.
7.1.12.1 Bead Base : The approximately cylindrical portion of the bead that forms its inside diameter.
7.1.12.2 Bead Toe : That portion of the bead which joins the bead base and the inside surface of the tire.
7.1.13 TREAD (TIRE) : The peripheral portion of the tire, the exterior of which is designed to contact the road surface.
7.1.13.1 Tread Contour : The crosssectional shape of tread surface of an inflated unloaded tire neglecting the tread pattern depressions.
7.1.13.2 Tread Radius : The radius or combination of radii describing the tread contour.
7.1.13.3 Tread Arc Width : The distance measured along the tread contour of an unloaded tire between one edge of the tread and the other. For tires with rounded tread edges, the point of measurement is that point in space which is at the intersection of the tread radius extended until it meets the prolongation of the upper sidewall contour.
7.1.13.4 Tread Chord Width : The distance measured parallel to the spin axis of an unloaded tire between one edge of the tread and the other. For tires with rounded tread edges, the point of measurement is that point in space which is at the intersection of the tread radius extended until it meets the prolongation of the upper sidewall contour.
7.1.13.5 Tread Contact Width : The distance between the extreme edges of road contact at a specified load and pressure measured parallel to the Y' axis at zero slip angle and zero inclination angle.
7.1.13.6 Tread Contact Length : The perpendicular distance between the tangent to edges of the leading and following points of road contact and parallel to the wheel plane.
7.1.13.7 Tread Depth : The distance between the base of a tire tread groove and a line tangent to the surface of the two adjacent tread ribs or rows.
7.1.13.8 Gross Contact Area : The total area enclosing the pattern of the tire tread in contact with a flat surface, including the area of grooves or voids.
7.1.13.9 Net Contact Area : The area enclosing the pattern of the tire tread in contact with a flat surface, excluding the area of grooves or other depressions.
7.1.13.10 Tread Pattern : The molded configuration on the face of the tread. It is generally composed of ribs, rows, grooves, bars, lugs, and the like.
7.2 Rolling Characteristics :
7.2.1 LOADED RADIUS (Re) : The distance from the center of tire contact to the wheel center measured in the wheel plane.
7.2.2 STATIC LOADED RADIUS : The loaded radius of a stationary tire inflated to normal recommended pressure.
NOTE: In general, static loaded radius is different from the radius of slowly rolling tire. Static radius of a tire rolled into position may be different from that of the tire loaded without being rolled.
7.2.3 SPIN AXIS : The axis of rotation of the wheel. (See Fig. 1.)
FIG. 1: TIRE AXIS SYSTEM <<...OLE_Obj...>> 7.2.4 SPIN VELOCITY (Q) : The angular velocity of the wheel on which the tire is mounted, about its spin axis. Positive spin velocity is shown in Fig. 1.
7.2.5 FREEROLLING TIRE : A loaded rolling tire operated without application of driving or braking torque.
7.2.6 STRAIGHT FREEROLLING TIRE : A freerolling tire moving in a straight line at zero inclination angle and zero slip angle.
7.2.7 LONGITUDINAL SLIP VELOCITY : The difference between the spin velocity of the driven or braked tire and the spin velocity of the straight free rolling tire. Both spin velocities are measured at the same linear velocity at the wheel center in the X' direction. A positive value results from driving torque.
7.2.8 LONGITUDINAL SLIP (PERCENT SLIP) : The ratio of the longitudinal slip velocity to the spin velocity of the straight freerolling tire expressed as a percentage.
NOTE: This quantity should not be confused with the slip number that frequently appears in kinematic analysis of tires in which the spin velocity appears in the denominator.
7.2.9 EFFECTIVE ROLLING RADIUS (Re) : The ratio of the linear velocity of the wheel center in the X' direction to the spin velocity. (See 7.3.1.)
7.2.10 WHEEL SKID : The occurrence of sliding between the tire and road interface which takes place within the entire contact area. Skid can result from braking, driving and/or cornering.
7.3 Tire Forces and Moments :
7.3.1 TIRE AXIS SYSTEM (FIG. I ) : The origin of the tire axis system is the center of tire contact. The X' axis is the intersection of the wheel plane and the road plane with a positive direction forward. The Z' axis is perpendicular to the road plane with a positive direction downward. The Y' axis is in the road plane, its direction being chosen to make the axis system orthogonal and righthand.
7.3.2 TIRE ANGLES :
7.3.2.1 Slip Angle (a) : The angle between the X' axis and direction of travel of the center of tire contact.
7.3.2.2 Inclination Angle (Y) : The angle between the Z' axis and the wheel plane.
7.3.3 TIRE FORCES : The external force acting on the tire by the road having the following components:
7.3.3.1 Longitudinal Force (Fx) : The component of the tire force vector in the X' direction.
7.3.3.2 Driving Force : The longitudinalforce resulting from driving torque application.
7.3.3.3 Driving Force Coefficient : The ratio of the driving force to the vertical load.
7.3.3.4 Braking Force : The negative longitudinal force resulting from braking torque application.
7.3.3.5 Braking Force Coefficient (Braking Coefficient) : The ratio of the braking force to the vertical load.
7.3.3.6 Rolling Resistance Force : The negative longitudinal force resulting from energy losses due to deformations of a rolling tire.
NOTE: This force can be computed from the forces and moments acting on the tire by the road.
Fr = (MyCOSY + MzSINY)/Rl
7.3.3.7 Rolling Resistance Force Coefficient : (Coefficient of Rolling Resistance) The ratio of the rolling resistance to the vertical load.
7.3.3.8 Lateral Force (Fy) : The component of the tire force vector in the Y' direction.
7.3.3.9 Lateral Force Coefficient : The ratio of the lateral force to the vertical load.
7.3.3.10 Slip Angle Force : The lateral force when the inclination angle is zero and plysteer and conicity forces have been subtracted.
7.3.3.11 Camber Force (Camber Thrust) : The lateral force when the slip angle is zero and the plysteer and conicity forces have been subtracted.
7.3.3.12 Normal Force (Fz) : The component of the tire force vector in the Z' direction.
7.3.3.13 Vertical Load : The normal reaction of the tire on the road which is equal to the negative of the normal force.
7.3.3.14 Central Force : The component of the tire force vector in the : direction perpendicular to the direction of travel of the center of tire contact. Central force is equal to lateral force times cosine of slip angle minus longitudinal force times sine of slip angle.
7.3.3.15 Tractive Force : The component of the tire force vector in the direction of travel of the center of tire contact. Tractive force is equal to lateral force times sine of slip angle plus longitudinal force times cosine of slip angle.
7.3.3.16 Drag Force : The negative tractive force.
7.3.4 TIRE MOMENTS : The external moments acting on the tire by the road having the following components:
7.3.4.1 Overturning Moment (Mx) : The component of the tire moment vector tending to rotate the tire about the X' axis, positive clockwise when looking in the positive direction of the X' axis.
7.3.4.2 Rolling Resistance Moment (My) : The component of the tire moment vector tending to rotate the tire about the Y' axis, positive clockwise when looking in the positive direction of the Y' axis.
7.3.4.3 Aligning Torque (Aligning Moment) (Mz) : The component of the tire moment vector tending to rotate the tire about the Z' axis, positive clockwise when looking in the positive direction of the Z' axis.
7.3.4.4 Wheel Torque (T) : The external torque applied to the tire from the vehicle about the spin axis; positive wheel torque is shown in Fig. I.
7.3.4.5 Driving Torque : The positive wheel torque.
7.3.4.6 Braking Torque : The negative wheel torque.
7.4 Tire Force and Moment Stiffness : (may be evaluated at any set of operating conditions)
7.4.1 CORNERING STIFFNESS : The negative of the rate of change of lateral force with respect to change in slip angle, usually evaluated at zero slip angle.
7.4.2 CAMBER STIFFNESS : The rate of change of lateral force with respect to change in inclination angle, usually evaluated at zero inclination angle.
7.4.3 BRAKING (DRIVING) STIFFNESS : The rate of change of longitudinal force with respect to change in longitudinal slip, usually evaluated at zero longitudinal slip.
7.4.4 ALIGNING STIFFNESS (ALIGNING TORQUE STIFFNESS) : The rate of change of aligning torque with respect to change in slip angle, usually evaluated at zero slip angle.
7.5 Normalized Tire Force and Moment Stiffnesses (Coefficients) :
7.5.1 CORNERING STIFFNESS COEFFICIENT (CORNERING COEFFICIENT) : The ratio of cornering stiffness of a straight freerolling tire to the vertical load.
NOTE: Although the term cornering coefficient has been used in a number of technical papers,for consistency with definitions of other terms using the word coefficient, the term cornering stiffness coefficient is preferred.
7.5.2 CAMBER STIFFNESS COEFFICIENT (CAMBER COEFFICIENT) : The ratio of camber stiffness of a straight freerolling tire to the vertical load.
7.5.3 BRAKING (DRIVING) STIFFNESS COEFFICIENT : The ratio of braking (driving) stiffness of a straight freerolling tire to the vertical load.
7.5.4 ALIGNING STIFFNESS COEFFICIENT (ALIGNING TORQUE COEFFICIENT) : The ratio of aligning stiffness of a straight freerolling tire to the vertical load.
7.6 Tire Traction Coefficients :
7.6.1 LATERAL TRACTION COEFFICIENT : The maximum value of lateral force coefficient which can be reached on a freerolling tire for a given road surface, environment and operating condition.
7.6.2 DRIVING TRACTION COEFFICIENT : The maximum value of driving force coefficient which can be reached on a given tire and road surface for a given environment and operating condition.
7.6.3 BRAKING TRACTION COEFFICIENT : The maximum of the braking force coefficient which can be reached without locking a wheel on a given tire and road surface for a given environment and operating condition.
7.6.3.1 Sliding Braking Traction Coefficient : The value of the braking force coefficient of a tire obtained on a locked wheel on a given tire and road surface for a given environment and operating condition.
7.7 Tire Associated Noise and Vibrations :
7.7.1 TREAD NOISE : Airborne sound (up to 5000 Hz) except squeal and slap produced by the interaction between the tire and the road surface.
7.7.1.1 Sizzle : A tread noise (up to 4000 Hz) characterized by a soft frying sound, particularly noticeable on a very smooth road surface.
7.7.2 SQUEAL : Narrow band airborne tire noise ( 150800 Hz) resulting from either longitudinal slip or slip angle or both.
7.7.2.1 Cornering Squeal : The squeal produced by a freerolling tire resulting from slip angle.
7.7.2.2 Braking (Driving) Squeal : The squeal resulting from longitudinal slip.
7.7.3 THUMP : A periodic vibration and/or audible sound generated by the tire and producing a pounding sensation which is synchronous with wheel rotation.
7.7.4 ROUGHNESS : Vibration (15100 Hz) perceived tactually and/or audibly, generated by a rolling tire on a smooth road surface and producing the sensation of driving on a coarse or irregular surface.
7.7.5 HARSHNESS : Vibrations (15100 Hz) perceived tactually and/or audibly, produced by interaction of the tire with road irregularities.
7.7.6 SLAP : Airborne smacking noise produced by a tire traversing road seams such as tar strips and expansion joints.
7.8 Tire and Wheel NonUniformity Characteristics :
7.8.1 RADIAL RUNOUT :
7.8.1.1 PeaktoPeak Radial Wheel RunOut : The difference between the maximum and minimum values of the wheel bead seat radius, measured in a plane perpendicular to the spin axis (measured separately for each bead seat).
7.8.1.2 PeaktoPeak Unloaded Radial Tire RunOut : The difference between maximum and minimum undeflected values of the tire radius, measured in plane perpendicular to the spin axis on a true running wheel.
7.8.1.3 PeaktoPeak Loaded Radial Tire RunOut : The difference between maximum and minimum values of the loaded radius on a true running wheel.
7.8.2 LATERAL RUNOUT :
7.8.2.1 PeaktoPeak Lateral Wheel RunOut : The difference between maximum and minimum indicator readings, measured parallel to the spin axis on the inside vertical portion of a rim flange (measured separately for each flange).
7.8.2.2 PeaktoPeak Lateral Tire RunOut : The difference between maximum and minimum indicator readings, measured parallel to the spin axis at the point of maximum tire section, on a true running wheel (measured separately for each sidewall).
7.8.3 RADIAL FORCE VARIATION : The periodic variation of the normal force of a loaded straight freerolling tire which repeats each revolution at a fixed loaded radius, given mean normal force, constant speed, given inflation pressure and test surface curvature.
7.8.3.1 PeaktoPeak (Total) Radial Force Variation : The difference between maximum and minimum values of the normal force during one revolution of the tire.
7.8.3.2 First Order Radial Force Variation : The peaktopeak amplitude of the fundamental frequency component of the Fourier series representing radial force variation. Its frequency is equal to the rotational frequency of the tire.
7.8.4 LATERAL FORCE VARIATION : The periodic variation of lateral force of a straight freerolling tire which repeats each revolution, at a fixed loaded radius, given mean normal force, constant speed, given inflation pressure and test surface curvature.
7.8.4.1 PeaktoPeak (Total) Lateral Force Variation : The difference between the maximum and minimum values of the lateral force during one revolution of the tire.
7.8.4.2 First Order Lateral Force Variation : The peaktopeak amplitude of the fundamental frequency component of the Fourier series representing lateral force variation. Its frequency is equal to the rotational frequency of the tire.
7.8.5 LATERAL FORCE OFFSET : The average lateral force of a straight freerolling tire.
7.8.5.1 Ply Steer Force : The component of lateral force offset which does not change sign (with respect to the Tire Axis System) with a change in direction of rotation (positive along positive Y' axis). The force remains positive when it is directed away from the serial number on the right side tire and toward the serial number on the left side tire.
7.8.5.2 Conicity Force : The component of lateral force offset which changes sign (with respect to the Tire Axis System) with a change in direction of rotation (positive away from the serial number or toward the whitewall). The force is positive when it is directed away from the serial number on the right side tire and negative when it is directed toward the serial number on the left side tire.
8. Kinematics : Force and Moments Notation
8.1 EarthFixed Axis System (X,Y,Z) : This system is a righthand orthogonal axis system fixed on the earth. The trajectory of the vehicle is described with respect to this earthfixed axis system. The X and Yaxis are in a horizontal plane and the Zaxis is directed downward.
8.2 Vehicle Axis System (x,y,z) : This system is a righthand orthogonal axis system fixed in a vehicle such that with the vehicle moving steadily in a straight line on a level road, the xaxis is substantially horizontal, points forward, and is in the longitudinal plane of symmetry. The yaxis points to driver' s right and the zaxis points downward. (See Fig. 2.)
8.3 Angular Orientation : The orientation of the vehicle axis system (x,y,z) with respect to the earthf xed axis system (X,Y,Z) is given by a sequence of three angular rotations. The following sequence of rotations (see Note 6), starting from a condition in which the two sets of axes are initially aligned, is defined to be the standard:
(1) A yaw rotation, Y, about the aligned z and Zaxis. (2) A pitch rotation, O, about the vehicle yaxis. (3) A roll rotation, 0, about the vehicle xaxis.
8.4 Motion Variables :
8.4.1 VEHICLE VELOCITY : The vector quantity expressing velocity of a point in the vehicle relative to the earthfxed axis system (X,Y,Z). The following motion variables are components of this vector resolved with respect to the moving vehicle axis system (x,y,z).
8.4.1.1 Longitudinal Velocity (u) : of a point in the vehicle is the component of the vector velocity in the xdirection.
8.4.1.2 Side Velocity (v) : of a point in the vehicle is the component of the vector velocity in the ydirection.
8.4.l.3 Normal Velocity (w) : of a point in the vehicle is the component of the vector velocity in the zdirection.
8.4.1.4 Forward Velocity : of a point in the vehicle is the component of the vector velocity perpendicular to the yaxis and parallel to the road plane.
8.4.1.5 Lateral Velocity : of a point in the vehicle is the component of the vector velocity perpendicular to the xaxis and parallel to the road plane.
FIG. 2: DIRECTIONAL CONTROL AXIS SYSTEM <<...OLE_Obj...>> 8.4.1.6 Roll Velocity (p) : The angular velocity about the xaxis.
8.4.1.7 Pitch Velocity (q) : The angular velocity about the yaxis.
8.4.1.8 Yaw Velocity (r) : The angular velocity about the zaxis.
8.4.2 VEHICLE ACCELERATION : The vector quantity expressing the acceleration of a point in the vehicle relative to the earthfxed axis system (X,Y,Z). The following motion variables are components of this vector, resolved with respect to the moving vehicle axis system.
8.4.2.1 Longitudinal Acceleration : The component of the vector acceleration of a point in the vehicle in the xdirection.
8.4.2.2 Side Acceleration : The component of the vector acceleration of a point in the vehicle in the ydirection.
8.4.2.3 Normal Acceleration : The component of the vector acceleration of a point in the vehicle in the zdirection.
8.4.2.4 Lateral Acceleration : The component of the vector acceleration of a point in the vehicle perpendicular to the vehicle xaxis and parallel to the road plane. (See Note 7.)
8.4.2.5 Centripetal Acceleration : The component of the vector acceleration of a point in the vehicle perpendicular to the tangent to the path of that point and parallel to the road plane.
8.4.3 HEADING ANGLE (Y) : The angle between the trace on the XY plane of the vehicle xaxis and the Xaxis of the earthfixed axis system. (See Fig. 3.)
8.4.4 SIDESLIP ANGLE (ATTITUDE ANGLE) (B) : The angle between the traces on the XY plane of the vehicle xaxis and the vehicle velocity vector at some specified point in the vehicle. Sideslip angle is shown in Fig. 3 as a negative angle.
8.4.5 SIDESLIP ANGLE GRADIENT : The rate of change of sideslip angle with respect to change in steadystate lateral acceleration on a level road at a given trim and test conditions.
8.4.6 COURSE ANGLE (t)) : The angle between the trace of the vehicle velocity vector on the XY plane and Xaxis of the earthf xed axis system. A positive course angle is shown in Fig. 3. Course angle is the sum of heading angle and sideslip angle (v=y+B).
FIG. 3: HEADING, SIDESLIP, AND COURSE ANGLES <<...OLE_Obj...>> 8.4.7 VEHICLE ROLL ANGLE : The angle between the vehicle yaxis and the ground plane.
8.4.8 VEHICLE ROLL GRADIENT : The rate of change in vehicle roll angle with respect to change in steadystate lateral acceleration on a level road at a given trim and test conditions.
8.4.9 VEHICLE PITCH ANGLE : The angle between the vehicle xaxis and the ground plane.
8.5 Forces : The external forces acting on the vehicle can be summed into one force vector having the following components:
8.5.1 LONGITUDINAL FORCE (Fx) : The component of the force vector in the xdirection.
8.5.2 SIDE FORCE (Fy) : The component of the force vector in the ydirection.
8.5.3 NORMAL FORCE (Fz) : The component of the force vector in the zdirection.
8.6 Moments : The external moments acting on the vehicle can be summed into one moment vector having the following components:
8.6.1 ROLLING MOMENT (Mx) : The component of the moment vector tending to rotate the vehicle about the xaxis, positive clockwise when looking in the positive direction of the xaxis.
8.6.2 PITCHING MOMENT (My) : The component of the moment vector tending to rotate the vehicle about the yaxis, positive clockwise when looking in the positive direction of the yaxis.
8.6.3 YAWING MOMENT (Mz) : The component of the moment vector tending to rotate the vehicle about the zaxis, positive clockwise when looking in the positive direction of the zaxis.
9. Directional Dynamics :
9.1 Control Modes :
9.1.1 POSITION CONTROL : That mode of vehicle control wherein inputs or restraints are placed upon the steering system in the form of displacements at some control point in the steering system (front wheels, Pitman arm, steering wheel), independent of the force required.
9.1.2 FIXED CONTROL : That mode of vehicle control wherein the position of some point in the steering system (front wheels, Pitman arm, steering wheel) is held fixed. This is a special case of position control.
9.1.3 FORCE CONTROL : That mode of vehicle control wherein inputs or restraints are placed upon the steering system in the form of forces, independent of the displacement required.
9.1.4 FREE CONTROL : That mode of vehicle control wherein no restraints are placed upon the steering system. This is a special case of force control.
9.2 Vehicle Response : The vehicle motion resulting from some internal or external input to the vehicle. Response tests can be used to determine the stability and control characteristics of a vehicle.
9.2.1 STEERING RESPONSE : The vehicle motion resulting from an input to the steering (control) element. (See Note 8.)
9.2.2 DISTURBANCE RESPONSE : The vehicle motion resulting from unwanted force or displacement inputs applied to the vehicle. Examples of disturbances are wind forces or vertical road displacements.
9.2.3 STEADYSTATE : Steadystate exists when periodic (or constant) vehicle responses to periodic (or constant) control and/or disturbance inputs do not change over an arbitrarily long time. The motion responses in steadystate are referred to as steadystate responses. This definition does not require the vehicle to be operating in a straight line or on a level road surface. It can also be in a turn of constant radius or on a cambered road surface.
9.2.4 TRANSIENT STATE : Transient state exists when the motion responses, the external forces relative to the vehicle, or the control positions are changing with time. (See Note 9.)
9.2.5 TRIM : The steadystate (that is, equilibrium) condition of the vehicle with constant input which is used as the reference point for analysis of dynamic vehicle stability and control characteristics.
9.2.6 STEADYSTATE RESPONSE GAIN : The ratio of change in the steadystate response of any motion variable with respect to change in input at a given trim.
9.2.7 STEERING SENSITIVITY (CONTROL GAIN) : The change in steady state lateral acceleration on a level road with respect to change in steering wheel angle at a given trim and test conditions.
9.3 Stability : (See Note 10.)
9.3.1 ASYMPTOTIC STABILITY : Asymptotic stability exists at a pre scribed trim if, for any small temporary change in disturbance or control input, the vehicle will approach the motion defined by the trim.
9.3.2 NEUTRAL STABILITY : Neutral stability exists at a prescribed trim if, for any small temporary change in disturbance or control input, the resulting motion of the vehicle remains close to, but does not return to, the motion defined by the trim.
9.3.3 DIVERGENT INSTABILITY : Divergent instability exists at a pre scribed trim if any small temporary disturbance or control input causes an ever increasing vehicle response without oscillation. (See Note 11.)
9.3.4 OSCILLATORY INSTABILITY : Oscillatory instability exists if a small temporary disturbance or control input causes an oscillatory vehicle response of everincreasing amplitude about the initial trim. (See Note 12.)
9.4 Suspension Steer and Roll Properties : (Fig. 4) (See Note 13.)
FIG. 4: STEER PROPERTIES (SEE NOTE 17) <<...OLE_Obj...>> 9.4.1 STEER ANGLE (S) : The angle between the projection of a longitudinal axis of the vehicle and the line of intersection of the wheel plane and the road surface. Positive angle is shown in Fig. 3.
9.4.2 ACKERMAN STEER ANGLE (Sa) : The angle whose tangent is the wheelbase divided by the radius of turn.
9.4.3 ACKERMAN STEER ANGLE GRADIENT : The rate of change of Ackerman steer angle with respect to change in steadystate lateral acceleration on a level road at a given trim and test conditions. (See Note 14.)
9.4.4 STEERING WHEEL ANGLE : Angular displacement of the steering wheel measured from the straightahead position (position corresponding to zero average steer angle of a pair of steered wheels).
9.4.5 STEERING WHEEL ANGLE GRADIENT : The rate of change in the steering wheel angle with respect to change in steadystate lateral acceleration on a level road at a given trim and test conditions.
9.4.6 OVERALL STEERING RATIO : The rate of change of steering wheel angle at a given steering wheel trim position, with respect to change in average steer angle of a pair of steered wheels, assuming an infinitely stiff steering system with no roll of the vehicle (see Note 15).
9.4.7 UNDERSTEER/OVERSTEER GRADIENT : The quantity obtained by subtracting the Ackerman steer angle gradient from the ratio of the steering wheel angle gradient to the overall steering ratio.
9.4.8 NEUTRAL STEER : A vehicle is neutral steer at a given trim if the ratio of the steering wheel angle gradient to the overall steering ratio equals the Ackerman steer angle gradient.
9.4.9 UNDERSTEER : A vehicle is understeer at a given trim if the ratio of the steering wheel angle gradient to the overall steering ratio is greater than the Ackerman steer angle gradient.
9.4.10 OVERSTEER : A vehicle is oversteer at a given trim if the ratio of the steering wheel angle gradient to the overall steering ratio is less than the Ackerman steer angle gradient.
9.4.11 STEERING WHEEL TORQUE : The torque applied to the steering wheel about its axis of rotation.
9.4.12 STEERING WHEEL TORQUE GRADIENT : The rate of change in the steering wheel torque with respect to change in steadystate lateral acceleration on a level road at a given trim and test conditions.
9.4.13 CHARACTERISTIC SPEED : That forward speed for an understeer vehicle at which the steering sensitivity at zero lateral acceleration trim is one half the steering sensitivity of a neutral steer vehicle.
9.4.14 CRITICAL SPEED : That forward speed for an oversteer vehicle at which the steering sensitivity at zero lateral acceleration trim is infinite.
9.4.15 NEUTRAL STEER LINE : The set of points in the xz plane at which external lateral forces applied to the sprung mass produce no steadystate yaw velocity.
9.4.16 STATIC MARGIN : The horizontal distance from the center of gravity to the neutral steer line divided by the wheelbase. It is positive if the center of gravity is forward of the neutral steer line.
9.4.17 SUSPENSION ROLL : The rotation of the vehicle sprung mass about the xaxis with respect to a transverse axis joining a pair of wheel centers.
9.4.18 SUSPENSION ROLL ANGLE : The angular displacement produced by suspension roll.
9.4.19 SUSPENSION ROLL GRADIENT : The rate of change in the suspension roll angle with respect to change in steadystate lateral acceleration on a level road at a given trim and test conditions.
9.4.20 ROLL STEER : The change in steer angle of front or rear wheels due to suspension roll.
9.4.20.1 Roll Understeer : Roll steer which increases vehicle understeer or decreases vehicle oversteer.
9.4.20.2 Roll Oversteer : Roll steer which decreases vehicle understeer or increases vehicle oversteer.
9.4.21 ROLL STEER COEFFICIENT : The rate of change in roll steer with respect to change in suspension roll angle at a given trim.
9.4.22 COMPLIANCE STEER : The change in steer angle of front or rear wheels resulting from compliance in suspension and steering linkages and produced by forces and/or moments applied at the tireroad contact.
9.4.22.1 Compliance Understeer : Compliance steer which increases vehicle understeer or decreases vehicle oversteer.
9.4.22.2 Compliance Oversteer : Compliance steer which decreases vehicle understeer or increases vehicle oversteer.
9.4.23 COMPLIANCE STEER COEFFICIENT : The rate of change in compliance steer with respect to change in forces or moments applied at the tireroad contact.
9.4.24 ROLL CAMBER : The camber displacements of a wheel resulting from suspension roll.
9.4.25 ROLL CAMBER COEFFICIENT : The rate of change in wheel inclination angle with respect to change in suspension roll angle.
9.4.26 COMPLIANCE CAMBER : The camber motion of a wheel resulting from compliance in suspension linkages and produced by forces and/or moments applied at the tireroad contact.
9.4.27 COMPLIANCE CAMBER COEFFICIENT : The rate of change in wheel inclination angle with respect to change in forces or moments applied at the tireroad contact.
9.4.28 ROLL CENTER : The point in the transverse vertical plane through any pair of wheel centers at which lateral forces may be applied to the sprung mass without producing suspension roll. (See Note 16.)
9.4.29 ROLL AXIS : The line joining the front and rear roll centers.
9.4.30 SUSPENSION ROLL STIFFNESS : The rate of change in the restoring couple exerted by the suspension of a pair of wheels on the sprung mass of the vehicle with respect to change in suspension roll angle.
9.4.31 VEHICLE ROLL STIFFNESS : Sum of the separate suspension roll stiffnesses.
9.4.32 ROLL STIFFNESS DISTRIBUTION : The distribution of the vehicle roll stiffness between front and rear suspension expressed as percentage of the vehicle roll stiffness.
9.5 Tire Load Transfer :
9.5.1 TIRE LATERAL LOAD TRANSFER : The vertical load transfer from one of the front tires (or rear tires) to the other that is due to acceleration, rotational, or inertial effects in the lateral 
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