ISO 23365:2022

INTERNATIONAL ISO
STANDARD 23365
First edition
2022-07
Heavy commercial vehicles and
buses — Definitions of properties
for the determination of suspension
kinematic and compliance
characteristics
Véhicules utilitaires lourds et autobus — Définitions des propriétés
pour la détermination des caractéristiques cinématiques et de
conformité des suspensions
Reference number
© ISO 2022
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ii
Contents  Page
Foreword . vi
Introduction .vii
1  Scope . 1
2  Normative references . 1
3  Terms and definitions . 1
4  Principle . 4
5 Variables . 5
5.1 Reference system . 5
5.2 Variables to be determined . 5
5.2.1 Vehicle geometry . 5
5.2.2 Motion variables . 5
5.2.3 Forces and moments . 5
5.2.4 Steering geometry . 6
5.2.5 Kinematics . 6
5.2.6 Compliances . 7
5.2.7 Ride and roll stiffness . 7
5.2.8 Force reactions . . 8
6  Measuring equipment . 8
6.1 Measurement accuracy . 8
6.2 Derived variable accuracy . 9
7  Suspension parameter measurement guidance . 9
7.1 Steering geometry . 9
7.1.1 Steering ratio . 9
7.1.2 Overall steering ratio (i ) . 10
S
7.1.3 Ackermann error . . . 11
7.1.4 Inclination angle (ε ). 11
W
7.1.5 Camber angle (ε ) . 11
V
7.1.6 Castor angle (τ) . 11
7.1.7 Castor offset at ground (n ) . 11
k
7.1.8 Castor offset at wheel centre (n ) .12
τ
7.1.9 Steering-axis inclination angle (σ).12
7.1.10 Steering-axis offset at ground (r ) .12
k
7.1.11 Steering-axis offset at wheel centre (r ) .12
σ
7.1.12 Normal steering-axis offset at ground (q ) .13
T
7.1.13 Normal steering axis offset at wheel centre (q ) .13
W
7.1.14 Scrub radius (r) . 13
7.2 Kinematics . 14
7.2.1 General . 14
7.2.2 Ride track change (b ) .15
z
7.2.3 Ride track change gradient (b ’) . 15
z
7.2.4 Ride steer (δ ) . 16
z
7.2.5 Ride steer gradient (δ ’) . 16
z
7.2.6 Total ride toe (δ ) . 16
z(R-L)
7.2.7 Total ride toe gradient (δ ’) . 16
z(R-L)
7.2.8 Ride camber (ε ) . 16
Vz
7.2.9 Ride camber gradient (ε ’) . 16
Vz
7.2.10 Ride castor (τ ) . 17
z
7.2.11 Ride castor gradient (τ ’) . 17
z
7.2.12 Roll steer (δδ ) . 17
ϕϕ
V
iii
′′
7.2.13 Roll steer gradient (δδ ) . 17
ϕϕ
V
7.2.14 Roll camber (εε ) . 17
Vϕϕ
V
′
7.2.15 Roll camber gradient (εε ) . 17
Vϕϕ
V
7.3 Compliances . 18
7.3.1 General . 18

′
7.3.2 Longitudinal force compliance, with suspension torque (x ) . 18
F
X

′
7.3.3 Longitudinal force compliance, without suspension torque (x ) . 19
F
XW

′
7.3.4 Longitudinal force camber compliance, with suspension torque (εε ) . 19
VF
X

′
7.3.5 Longitudinal force camber compliance, without suspension torque (εε ) . 19
VF
XW

′
7.3.6 Longitudinal force steer compliance, with suspension torque (δδ ) .20
F
X

′
7.3.7 Longitudinal force steer compliance, without suspension torque (δδ ) .20
F
XW

′
7.3.8 Longitudinal force windup compliance, with suspension torque (ττ ) .20
F
X

′
7.3.9 Longitudinal force windup compliance, without suspension torque (ττ ) .20
F
XW

′
7.3.10 Lateral force compliance at the wheel centre ( y ) . 21
F
YW

′
7.3.11 Lateral force compliance at the contact centre ( y ) . 21
F
Y

′
7.3.12 Lateral force camber compliance (εε ) . 21
VF
Y

′
7.3.13 Lateral force steer compliance (δδ ) . 21
F
Y

′
7.3.14 Aligning moment camber compliance (εε ) .22
VM
Z

′
7.3.15 Aligning moment steer compliance (δδ ) .22
M
Z
7.4 Ride and roll stiffness .22
7.4.1 General .22
7.4.2 Ride rate (K ) . 22
Z
7.4.3 Suspension ride rate (K ) . 23
ZK
7.4.4 Roll stiffness (K ) .23
ϕϕ
V
7.4.5 Suspension roll stiffness (K ) . . 23
ϕϕ
K
7.4.6 Auxiliary roll stiffness (K ) . 24
ϕϕ ,aux
V
7.4.7 Auxiliary suspension roll stiffness (K ) . 24
ϕϕ ,aux
K
7.4.8 Vertical displacement tandem axle load redistribution stiffness (K ) . 24
tz
7.4.9 Vertical suspension displacement tandem axle load redistribution stiffness
(K ) . 25
tzK
7.4.10 Tandem axle twist stiffness (K ) . 25
φt
7.4.11 Tandem axle suspension twist stiffness (K ) . 25
φtK
7.4.12 Tyre normal stiffness (K ) . 25
ZT
7.5 Force reactions . 25


′
7.5.1 Anti-squat and anti-dive force gradient (F ) . 25
ZF
X
iv


′
7.5.2 Jacking force gradient (F ) . 26
ZF
Y

′
7.5.3 Longitudinal force tandem axle load redistribution gradient (W ) .26
DtF
XT
8  Data presentation .26
8.1 Steering ratio . 26
8.2 Kinematic properties .30
8.3 Compliance properties . 31
8.4 Ride and roll stiffness properties . 32
8.5 Force reaction properties . 32
Annex A (informative) Mathematic fit of steering ratio as a function of steering wheel angle .34
Bibliography .35
v
Foreword
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described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
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This document was prepared by Technical Committee ISO/TC 22, Road vehicles, Subcommittee SC 33,
Vehicle dynamics and chassis components.
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vi
Introduction
The dynamic behaviour of a road vehicle is a very important aspect of active vehicle safety. Any given
vehicle, together with its driver and the prevailing environment, constitutes a closed-loop system that
is unique. The task of evaluating the dynamic behaviour is therefore, very difficult since the significant
interaction of these driver-vehicle-environment elements are each complex in themselves. A complete
and accurate description of the behaviour of the road vehicle shall necessarily involve information
obtained from a number of different tests.
Static properties of the vehicle and its systems can have an important impact on the vehicle dynamic
behaviour and a driver’s or automation’s ability to generate the desired motion. Test conditions have a
strong influence on test results. Therefore, only vehicle dynamic and static properties obtained under
virtually identical test conditions are comparable to one another.
Since this test method quantifies only one small part of the complete vehicle handling characteristics,
the results of these tests can only be considered significant for a correspondingly small part of the
overall dynamic behaviour.
Moreover, insufficient knowledge is available concerning the relationship between overall vehicle
dynamic properties and accident avoidance. A substantial amount of work is necessary to acquire
sufficient and reliable data on the correlation between accident avoidance and vehicle dynamic
properties in general and the results of these tests in particular. Consequently, it is important for any
application of this test method for regulation purposes the proven correlation between test results and
accident statistics.
vii
INTERNATIONAL STANDARD ISO 23365:2022(E)
Heavy commercial vehicles and buses — Definitions of
properties for the determination of suspension kinematic
and compliance characteristics
1  Scope
This document applies to heavy vehicles—that is, to commercial vehicles and buses as defined in
ISO 3833—that are covered by the categories M3, N2, N3, O3, and O4 of ECE and EC vehicle regulations.
These categories pertain to trucks and trailers with maximum weights above 3,5 tonnes and to buses
with maximum weights above 5 tonnes.
Vehicle suspension kinematic and compliance (K&C) properties that impact vehicle stability and
dynamic behaviour are described in this document and common methods of measurement are outlined.
These methods are applicable to heavy vehicles. The measurements are performed on a single unit and
typically one or two axles at a time.
This document will define or reference the key suspension kinematic and compliance parameters
necessary for characterizing and simulating vehicle suspension performance. These parameters also
provide system-level descriptions of quasi-static behaviour that can be cascaded into subsystem and
component performance targets. The suspension variables required for determining suspension
characterization of one vehicle end, i.e. for a single axle or for multiple axles inter-related through
suspension configuration (for example, walking-beam), are provided. Metrics pertaining to the
chassis connection between the front and rear suspensions are not included. Some typical methods of
measurement will be discussed, however detail on how the measurements are executed is not within
the scope of this document.
2  Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 8855, Road vehicles — Vehicle dynamics and road-holding ability — Vocabulary
ISO 15037-2, Road vehicles — Vehicle dynamics test methods — Part 2: General conditions for heavy
vehicles and buses
3  Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 8855, ISO 15037-2 and the
following apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
side view swing centre
point in a plane parallel to the X -Z plane that intersects the wheel centre and locates the instantaneous
V V
centre of rotation of the wheel centre resulting from a displacement in the Z direction
V
3.2
side view swing arm angle
angle from a horizontal line parallel to the X -Z plane that intersects the side view swing centre (3.1)
V V
and the line that intersects the side view swing centre and wheel centre
3.3
longitudinal force compliance, with suspension torque

′
x
F
X
rate of change of the wheel centre displacement in the X direction with respect to a force exerted on
V
the geometric centre of the tyre contact patch in the X direction
V
3.4
longitudinal force compliance, without suspension torque

′
x
F
XW
rate of change of the wheel centre displacement in the X direction with respect to a force exerted on
V
the wheel centre in the X direction
V
3.5
longitudinal force camber compliance, with suspension torque

′
ε
VF
X
rate of change of camber angle with respect to a force exerted on the geometric centre of the tyre
contact patch in the X direction
V
3.6
longitudinal force camber compliance, without suspension torque

′
ε
VF
XW
rate of change of camber angle with respect to a force exerted on the wheel centre in the X direction
V
3.7
longitudinal force steer compliance, with suspension torque

′
δ
F
X
rate of change of steer angle with respect to a force exerted on the geometric centre of the tyre contact
patch in the X direction
V
3.8
longitudinal force steer compliance, without suspension torque

′
δ
F
XW
rate of change of steer angle with respect to a force exerted on the wheel centre in the X direction
V
3.9
longitudinal force windup compliance, with suspension torque

′
τ
F
X
rate of change of the axle or hub assembly angle about the Y axis with respect to a force exerted on the
V
geometric centre of the tyre contact patch in the X direction
V
3.10
longitudinal force windup compliance, without suspension torque

′
τ
F
XW
rate of change of the axle or hub assembly angle about the Y axis with respect to a force exerted on the
V
wheel centre in the X direction
V
3.11
lateral force compliance at the wheel centre

′
y
F
YW
rate of change of wheel centre displacement in the Y direction with respect to a force exerted on the
V
geometric centre of the tyre contact patch in the Y direction
V
3.12
lateral force compliance at the contact centre

′
y
F
Y
rate of change of geometric centre of the tyre contact patch displacement in the Y direction with
V
respect to a force exerted on the geometric centre of the tyre contact patch in the Y direction
V
3.13
lateral force camber compliance

′
ε
VF
Y
rate of change of camber angle with respect to a force exerted on the geometric centre of the tyre
contact patch in the Y direction
V
3.14
lateral force steer compliance

′
δ
F
Y
rate of change of steer angle with respect to a force exerted on the geometric centre of the tyre contact
patch in the Y direction
V
3.15
aligning moment camber compliance

′
ε
VM
Z
rate of change of camber angle with respect to a moment exerted on the tyre contact patch about the Z
V
axis
3.16
aligning moment steer compliance

′
δ
M
Z
rate of change of steer angle with respect to a moment exerted on the tyre contact patch about the Z
V
axis
3.17
auxiliary roll stiffness
K
ϕ ,aux
V
contribution to roll stiffness beyond that which results from ride rate and symmetric vertical tyre
contact patch-to-body displacement
3.18
auxiliary suspension roll stiffness
K
ϕ ,aux
K
contribution to suspension roll stiffness beyond that which results from suspension ride rate and
symmetric vertical wheel-to-body displacement
3.19
total ride toe
δ
z(R-L)
change in the difference of the left steer angle from the right steer angle observed in ride mode (3.22)
3.20
total ride toe gradient
δ ’
z(R-L)
differential of total ride toe (3.19) with suspension travel as observed in ride mode (3.22)
3.21
wheel pad
surface of the kinematic and compliance measurement facility that supports each tyre contact patch
and is typically capable of applying forces at the geometric centre of the tyre contact patch in the X and
Y directions, moments at the tyre contact patch about the Z axis, and optionally displacements in the
Z direction
Note 1 to entry: The wheel pads are assumed to represent the ground plane. If the vehicle sprung mass is not
rolled relative to the wheel pads, it can be assumed that the intermediate axis system and vehicle axis system
coincide.
3.22
ride mode
motion of vehicle suspension produced by near-equal Z displacements of the wheel centres on a single
T
axle relative to the vehicle body, with wheel pad (3.21) X and Y forces and Z moments controlled to as
T

near-zero as practicable, and preferably with the change in M held as near to zero as practicable
X
3.23
roll mode

motion of single axle produced by a pure roll moment, M , resulting from equal and opposite change in
X
the forces applied to the left and right tyre contact centres of each axle in the Z direction, with wheel
T
pad (3.21) X and Y forces and Z moments controlled to as near-zero as practicable
T
4  Principle
This document defines the common suspension kinematic and compliance (K&C) properties of
suspensions that relate to the change in orientation of the road wheel and tyre to the road surface as
a result of, and relative to, forces, moments and displacements input to the tyre contact patches. The
forces, moments and displacements are intended to reflect those encountered in real-world manoeuvres.
Characterization of these properties is essential to modelling the ride and handling behaviour of road
vehicles as the motion of the tyre contact patch relative to the sprung mass is determined by both the
sprung mass to tyre orientation and the tyre to road surface orientation.
The intent of K&C measurements is to isolate the change in ground and wheel planes to vehicle sprung
mass orientation that result from each of the relevant primary forces, moments and displacements.
For instance, lateral force steer compliance is measured by suppressing other inputs that steer angle
is sensitive to, such as change in longitudinal force or steer moment. The lateral force steer compliance
is isolated by controlling the wheel pad longitudinal force and steer moment to zero and constraining
the vertical position of the contact patch to avoid introducing kinematic effects resulting from trim
height change. Similarly, other measurements are made with constraints defined to isolate the change
resulting from particular forces, moments or displacements to facilitate the principle of superposition
when used in a vehicle simulation.
While it is essential to isolate the reactions to specific forces, moments or displacements, the inputs shall
be representative of naturally occurring inputs. For example, when measuring the roll characteristics
of a suspension, it is strongly preferred to simulate the sprung mass roll relative the ground plane. This
may be achieved using asymmetric vertical displacement of the wheel pads or by rolling the vehicle
body relative to the wheel pads. In either case, the sum of the normal forces exerted on the axle shall
remain constant. This is more representative of on-road behaviour than the input of equal and opposite
vertical displacements at the tyre contact patches.
5 Variables
5.1  Reference system
Variables used to characterize vehicle suspension K&C properties are typically determined in the
following manner:
— the change in wheel orientation as defined by the wheel axis system (X , Y , Z ) resulting from a
W W W
displacement, force, or moment aligned to the intermediate axis system (X, Y, Z) (see ISO 8855);
— the displacement of the wheel centre as defined by the intermediate coordinate system (x, y, z)
resulting from a force aligned to the intermediate axis system (X, Y, Z) (see ISO 8855);
— the change in vehicle sprung mass orientation as defined by the vehicle axis system (X , Y , Z )
V V V
resulting from a displacement, force, or moment aligned to the intermediate axis system (X, Y, Z)
(see ISO 8855).
NOTE Ideally the changes in wheel orientation due to tyre forces and moments would be determined relative
to the tyre forces and moments in the tyre axis system (X , Y , Z ), since this is the reference system in which tyre
T T T
force and moment properties are provided. However, it typically is not practical to maintain contact patch shear
force alignment with the tyre axis system in a K&C machine and so, the shear forces are normally aligned with
the intermediate axis system. For the small angles that normally result during compliance measurements, the
differences can be neglected.
5.2  Variables to be determined
Variable definitions not found in ISO 8855 can be found in Clause 3. To describe the relative suspension
motions resulting from external forces and moments, the principal relevant variables are the following:
5.2.1  Vehicle geometry
— wheel centre
— contact centre
— contact patch
— tandem axle spacing
— b, track
5.2.2  Motion variables
— φ , vehicle roll angle
V
— φ , suspension roll angle
K
— ride displacement
— bogie orientation variables (pitch, roll, twist)
5.2.3  Forces and moments

— F , longitudinal force
X

— F , lateral force
Y

— F , vertical force
Z

— M , roll moment
X

— M , steering-axis torque
S

— F , tyre longitudinal force at the contact centre
XT

— F , tyre lateral force at the contact centre
YT

— F , tyre vertical force at the contact centre
ZT

— F , longitudinal force at the wheel centre
XW
5.2.4  Steering geometry
— δ, steer angle
— δ , kinematic steer angle
kin
— δ , mean kinematic steer angle
m,kin
— δ , included kinematic steer angle
inc,kin
— static toe angle
— total static toe angle
— δ , steering wheel angle
H
— Ackermann error
— steering ratio
— i , overall steering ratio
S
— ε , inclination angle (actual measurement)
W
— ε , camber angle (calculated)
V
— τ, castor angle
— n , castor offset at ground
k
— n , castor offset at wheel centre
τ
— δ , mean steer angle
m
— σ, steering-axis inclination angle
— r , steering-axis offset at ground
K
— r , steering-axis offset at wheel centre
σ
— r, scrub radius
5.2.5  Kinematics
— b , ride track change
z
— b ’, ride track change gradient
z
— δ , ride steer
z
— δ ’, ride steer gradient
z
— ε , ride camber
Vz
— ε ’, ride camber gradient
Vz
— τ , ride castor
z
— τ ’, ride castor gradient
z
— δ , roll steer
ϕ
V
′
— δ , roll steer gradient
ϕ
V
— ε , roll camber
Vϕ
V
′
— ε , roll camber gradient
Vϕ
V
— τ , roll castor
φV
— τ ’, roll castor gradient
φV
— roll centre height
— side view swing arm angle
5.2.6  Compliances

′
— x , longitudinal force compliance, with suspension torque
F
X

′
— x , longitudinal force compliance, without suspension torque
F
XW

′
— ε , longitudinal force camber compliance, with suspension torque
VF
X

′
— ε , longitudinal force camber compliance, without suspension torque
VF
XW

′
— δ , longitudinal force steer compliance, with suspension torque
F
X

′
— δ , longitudinal force steer compliance, without suspension torque
F
XW

′
— τ , longitudinal force windup compliance, with suspension torque
F
X

′
— τ , longitudinal force windup compliance, without suspension torque
F
XW

′
— y , lateral force compliance at the contact centre
F
Y

′
— y , lateral force compliance at the wheel centre
F
YW

′
— ε , lateral force camber compliance
VF
Y

′
— δ , lateral force steer compliance
F
Y

′
— ε , aligning moment camber compliance
VM
Z

′
— δ , aligning moment steer compliance
M
Z
5.2.7  Ride and roll stiffness
— K , ride rate
Z
— K , suspension ride rate
ZK
— K , roll stiffness
ϕ
V
— K , suspension roll stiffness
ϕ
K
— K , auxiliary roll stiffness
ϕ ,aux
V
— K , auxiliary suspension roll stiffness
ϕ ,aux
K
— K , vertical displacement tandem axle load redistribution stiffness
tz
— K , vertical suspension displacement tandem axle load redistribution stiffness
tzK
— K , tandem axle twist stiffness
φt
— K , tandem axle suspension twist stiffness
φtK
— K , tyre normal stiffness
ZT
5.2.8  Force reactions


′
— F , anti-squat and anti-dive force gradient
ZF
X


′
— F , jacking force gradient
ZF
Y

′
— W , longitudinal force tandem axle dynamic load transfer
DtF
XT
6  Measuring equipment
6.1  Measurement accuracy
Variables measured to characterize vehicle suspension kinematic and compliance properties
are presented in Table 1. Typical operating ranges are presented, as well as minimum accuracy
recommendations. Either accuracy (percentage of full scale or absolute) may be used. Several references
are made throughout this document to holding forces or moments to “as near-zero as practicable”
to minimize their influence on a particular measurement. The values presented in the “near-zero
threshold” column represent the recommended maximum controlled and measured value for such
forces or moments.
Table 1 — Variables to be measured
Accuracy
Typical
Absolute  Near-zero
a
Variable operating
(% of full
accuracy threshold
range
scale)
ε , inclination angle ±10° ±1,0 0,1°
W
τ, castor angle ±10° ±1,0 0,1°
δ, steer angle (K&C test) ±5° ±2,0 0,1°
δ , kinematic steer angle (steering ratio test) ±45° ±0,2 0,1°
kin
δ , steering-wheel angle (steering ratio test) ±1 080° ±0,1 1,0°
H
suspension longitudinal displacement ±100 mm ±1,0 1,0 mm
suspension lateral displacement ±100 mm ±1,0 1,0 mm
suspension ride displacement ±150 mm ±0,7 1,0 mm
ride displacement ±200 mm ±0,25 0,4 mm
φ , suspension roll angle ±4° ±1,5 0,06°
K
φ , vehicle roll angle ±5° ±0,6 0,03°
V
Table 1 (continued)
Accuracy
Typical
Absolute  Near-zero
a
Variable operating
(% of full
accuracy threshold
range
scale)

±4 000 N·m ±0,25 10,0 N·m 20 N·m
M , tyre aligning moment
ZT

±30 000 N ±0,25 75 N 100 N
F , tyre longitudinal force at contact centre
XT

±30 000 N ±0,25 75 N 100 N
F , tyre lateral force at contact centre
YT

(60 000±60 000) N ±0,2 120 N 100 N
F , tyre normal force at contact centre
ZT

±30 000 N ±0,25 75 N 100 N
F , longitudinal force at wheel centre
XW
6.2 Derived variable accuracy
Variables calculated to characterize vehicle suspension kinematic and compliance properties are
presented in Table 2.
Table 2 — Derived variables
Accuracy
Typical operating  Absolute
a
Variable
range accuracy
(% of full scale)
i , overall steering ratio 15 to 30 ±1,5 0,5
S

′
ε , aligning moment camber compliance
(-1,5 to 2,5)°/kNm ±10,0 0,25°/kNm
VM
Z

′
δ , aligning moment steer compliance (0 to 0,5)°/kNm ±5,0 °/kNm
M
Z

′
ε , lateral force camber compliance
(-2,5 to 2,5)°/kN ±5,0 0,1°/kN
VF
Y

′
y , lateral force compliance at the contact
(0,005 to 10,0) mm/
F
Y ±5,0 mm/kN
kN
centre

′
δ , lateral force steer compliance (-0,05 to 2,0)°/kN ±5,0
F
Y
K suspension roll rate (500 to 40 000) Nm/° ±5,0
φK
K , suspension ride rate (11 to 2 400) N/mm ±5,0
ZK
ε ’, ride camber gradient (-0,1 to 0,1)°/mm ±2,0 ±0,02°/mm
Vz
τ ’, ride castor gradient (-0,05 to 0,05)°/mm ±10,0 ±0,02°/mm
Z
δ ’, ride steer gradient (-0,15 to 0,15)°/mm ±2,0 ±0,000 4°/mm
z
′
ε , roll camber gradient (0 to 1)°/° ±2,0 ±0,01°/°
Vϕ
V
τ ’, roll castor gradient (0 to 0,5)°/° ±10,0 ±1,0 %
φV
roll centre height (-100 to 1,000) mm ±2,5 ±2,5 mm
δ ’, roll steer gradient (-0,25 to 0,25)°/° ±2,0 ±0,25 %
φV
7  Suspension parameter measurement guidance
7.1  Steering geometry
7.1.1  Steering ratio
Steering ratio, defined in ISO 8855, is the rate of change of steering-wheel angle with respect to the
mean kinematic steer angle at a given steering-wheel angle. Testing is conducted by the simultaneous
measurement of steering-wheel angle and the left and right kinematic steer angles as the steering-wheel
is turned throughout its range of motion. Mean kinematic steer angle is determined by averaging the
coincident individual kinematic steer angles on the axle for calculation of the steering ratio. In practice,
the wheel pad vertical position is held fixed relative to the vehicle body as the steering-wheel is turned
at a slow smooth rate, on the order of one turn per minute with any available power assist activated.
Forces in the X-Y plane and moments about the Z axes are controlled to as near-zero as practicable.
T
It is recommended that a minimum of three continuous lock-to-lock steer cycles be completed for
analysis. The straight ahead steering-wheel angle position is best determined by driving the vehicle
straight ahead and noting the position of the steering-wheel prior to making K&C measurements. This
position should be defined as zero. Alternatively, if absolute steer angles are measured, zero steering-
wheel angle can be defined where the mean steer angle is zero. Although the steering ratio test can
commence from the straight-ahead steering-wheel position, smoothing and/or curve fitting of the data
may be performed better when the test commences from the steering-wheel angle turned full clockwise
or counter-clockwise to avoid the discontinuity in the data occurring near-zero steering-wheel angle.
One recommended method of characterizing steering ratio as a function of steering-wheel angle is to
fit a formula to the data. It is recommended that the steering-wheel angle and left and right steer angle
data be smoothed prior to calculating steering ratio. A moving mean filter works adequately as long as
there are sufficient data points beyond the range over which the ratio is to be calculated. A sample plot
of left and right steer angles versus steering-wheel angle is shown in Clause 8. A moving mean filter
will result in truncation of several initial and final data points in the time-history data traces. After
smoothing, point-to-point or other numerical differentials can be taken to calculate steering ratios for
the left, right, and mean steer angles. Curve fits can be applied to the cross plot of steering ratio for left,
right, and mean kinematic steer angle versus steering-wheel angle.
The steering gear, steering linkage geometry, and steering shaft joints contribute to nonlinearities
in the relationship between steering ratio and steering-wheel angle. Although it is possible to fit a
polynomial curve or Fourier series to this relationship, a more specialised fit should be considered. Basic
steering ratio may include first-order and second-order polynomial terms to represent asymmetry and
curvature. Typical steering shaft universal joint phasing anomalies may be represented by including
a scaled sinusoidal term having a period of two cycles per steering-wheel revolution. Minimizing the
squared difference between the ratio calculated from the raw data and the curve fit formula results
will provide the values for the coefficients. The term values determined from the curve fits can be used
to characterize the various steering ratio properties. If individual left and right steering ratio curve fits
are determined, they can be used to provide continuous smooth data for calculating properties such
as Ackermann error or turn diameter as a function of steering-wheel angle. An example cross plot of
steering-wheel angle and the left and right kinematic steer angles and curve fits for left wheel, right
wheel, and overall steering ratio versus steering-wheel angle are shown in Clause 8.
NOTE 1 A unique steerin
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