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).
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. 1-1951, 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 Z24.1-1951, 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. 1-1951, 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 Z24.1-1951, item 2.1 05.)
1.4 Self-Excited Vibration : Vibrations are termed self-excited 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 Steady-State Vibration : Steady-state 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.
2.1 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 PEAK-TO-PEAK AMPLITUDE (DOUBLE AMPLITUDE) : Peak-to-Peak 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. 1-1951, 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. 1-1951, 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 Z24.1-1951, 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 z-axis. (See Fig. 2.)
5.1.1.2 Pitch : The angular component of ride vibrations of the sprung mass
about the vehicle y-axis.
5.1.1.3 Roll : The angular component of ride vibrations of the sprung mass
about the vehicle x-axis.
5.1.2 SHAKE : The intermediate frequency (5-25 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 x-axis.
5.1.2.2 Beaming : A mode of vibration involving predominantly bending
deformations of the sprung mass about the vehicle y-axis.
5.1.3 HARSHNESS : The high frequency (25-100 Hz) vibrations of the structure
and/or components that are perceived tactually and/or audibly.
5.1.4 BOOM : A high intensity vibration (25-100 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 Fore-and-Aft 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 self-excited oscillation of steerable wheels about
their steering axes, occurring without appreciable tramp.
5.2.3.3 Shimmy : A self-excited 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. Swing-Arm 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 "toed-in" if the forward portion of the wheel is turned toward a
central longitudinal axis of the vehicle, and "toed-out" if turned away.
6.4.2 STATIC TOE (IN [MM]) : Static toe-in or toe-out 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
"toed-in" by this amount; and where smaller, the wheels are "toed-out." (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 METAL-TO-METAL 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 METAL-TO-METAL 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 TORQUE-ARM 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 TORQUE-ARM 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 TORQUE-ARM 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 cross-sectional 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 FREE-ROLLING TIRE : A loaded rolling tire operated without application
of driving or braking torque.
7.2.6 STRAIGHT FREE-ROLLING TIRE : A free-rolling 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 free-rolling 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 right-hand.
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 free-rolling 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 free-rolling tire to the vertical load.
7.5.3 BRAKING (DRIVING) STIFFNESS COEFFICIENT : The ratio of braking
(driving) stiffness of a straight free-rolling tire to the vertical load.
7.5.4 ALIGNING STIFFNESS COEFFICIENT (ALIGNING TORQUE COEFFICIENT) : The
ratio of aligning stiffness of a straight free-rolling 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 free-rolling 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 ( 150-800 Hz) resulting from
either longitudinal slip or slip angle or both.
7.7.2.1 Cornering Squeal : The squeal produced by a free-rolling 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 (15-100 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 (15-100 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 Non-Uniformity Characteristics :
7.8.1 RADIAL RUN-OUT :
7.8.1.1 Peak-to-Peak Radial Wheel Run-Out : 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 Peak-to-Peak Unloaded Radial Tire Run-Out : 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 Peak-to-Peak Loaded Radial Tire Run-Out : The difference between
maximum and minimum values of the loaded radius on a true running wheel.
7.8.2 LATERAL RUN-OUT :
7.8.2.1 Peak-to-Peak Lateral Wheel Run-Out : The difference between maxi-mum
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 Peak-to-Peak Lateral Tire Run-Out : 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 free-rolling 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 Peak-to-Peak (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 peak-to-peak 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 free-rolling 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 Peak-to-Peak (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 peak-to-peak 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
free-rolling 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 Earth-Fixed Axis System (X,Y,Z) : This system is a right-hand orthogonal
axis system fixed on the earth. The trajectory of the vehicle is described
with respect to this earth-fixed axis system. The X- and Y-axis are in a
horizontal plane and the Z-axis is directed downward.
8.2 Vehicle Axis System (x,y,z) : This system is a right-hand orthogonal
axis system fixed in a vehicle such that with the vehicle moving steadily in
a straight line on a level road, the x-axis is substantially horizontal,
points forward, and is in the longitudinal plane of symmetry. The y-axis
points to driver' s right and the z-axis points downward. (See Fig. 2.)
8.3 Angular Orientation : The orientation of the vehicle axis system (x,y,z)
with respect to the earth-f 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 Z-axis. (2) A pitch
rotation, O, about the vehicle y-axis. (3) A roll rotation, 0, about the
vehicle x-axis.
8.4 Motion Variables :
8.4.1 VEHICLE VELOCITY : The vector quantity expressing velocity of a point
in the vehicle relative to the earth-fxed 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 x-direction.
8.4.1.2 Side Velocity (v) : of a point in the vehicle is the component of
the vector velocity in the y-direction.
8.4.l.3 Normal Velocity (w) : of a point in the vehicle is the component of
the vector velocity in the z-direction.
8.4.1.4 Forward Velocity : of a point in the vehicle is the component of the
vector velocity perpendicular to the y-axis 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 x-axis 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 x-axis.
8.4.1.7 Pitch Velocity (q) : The angular velocity about the y-axis.
8.4.1.8 Yaw Velocity (r) : The angular velocity about the z-axis.
8.4.2 VEHICLE ACCELERATION : The vector quantity expressing the acceleration
of a point in the vehicle relative to the earth-fxed 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 x-direction.
8.4.2.2 Side Acceleration : The component of the vector acceleration of a
point in the vehicle in the y-direction.
8.4.2.3 Normal Acceleration : The component of the vector acceleration of a
point in the vehicle in the z-direction.
8.4.2.4 Lateral Acceleration : The component of the vector acceleration of a
point in the vehicle perpendicular to the vehicle x-axis 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 X-Y plane of
the vehicle x-axis and the X-axis of the earth-fixed axis system. (See Fig.
3.)
8.4.4 SIDESLIP ANGLE (ATTITUDE ANGLE) (B) : The angle between the traces on
the X-Y plane of the vehicle x-axis 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 steady-state 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 X-Y plane and X-axis of the earth-f 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 y-axis and the
ground plane.
8.4.8 VEHICLE ROLL GRADIENT : The rate of change in vehicle roll angle with
respect to change in steady-state lateral acceleration on a level road at a
given trim and test conditions.
8.4.9 VEHICLE PITCH ANGLE : The angle between the vehicle x-axis 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
x-direction.
8.5.2 SIDE FORCE (Fy) : The component of the force vector in the
y-direction.
8.5.3 NORMAL FORCE (Fz) : The component of the force vector in the
z-direction.
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 x-axis, positive clockwise when looking in the
positive direction of the x-axis.
8.6.2 PITCHING MOMENT (My) : The component of the moment vector tending to
rotate the vehicle about the y-axis, positive clockwise when looking in the
positive direction of the y-axis.
8.6.3 YAWING MOMENT (Mz) : The component of the moment vector tending to
rotate the vehicle about the z-axis, positive clockwise when looking in the
positive direction of the z-axis.
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 STEADY-STATE : Steady-state 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 steady-state
are referred to as steady-state 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 steady-state (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 STEADY-STATE RESPONSE GAIN : The ratio of change in the steady-state
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 ever-increasing 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 steady-state 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 straight-ahead 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 steady-state 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 steady-state 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 x-z plane at which
external lateral forces applied to the sprung mass produce no steady-state
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
x-axis 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 steady-state 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 tire-road 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 tire-road
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 tire-road 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
tire-road 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 tir
