Road vehicles — Heavy commercial vehicles and buses – Mass moment of inertia measurement

This document provides standard methods for determining a vehicle’s roll, pitch, and yaw mass moments of inertia (MOI) and roll-yaw product of inertia (POI). It applies to heavy vehicles, that is commercial vehicles and buses as defined in ISO 3833 (trucks and trailers with maximum weight above 3,5 tons and buses and articulated buses with maximum weight above 5 tons, according to ECE and EC vehicle classification, categories M3, N2, N3, O3 and O4). Mass moment of inertia measurements are performed separately for each single unit.

Véhicules routiers — Véhicules utilitaires lourds et autobus — Mesure du moment d'inertie de masse

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Published
Publication Date
15-May-2022
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4060 - Close of voting
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24-Jul-2021
Completion Date
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INTERNATIONAL ISO
STANDARD 21234
First edition
2022-05
Road vehicles — Heavy commercial
vehicles and buses – Mass moment of
inertia measurement
Véhicules routiers — Véhicules utilitaires lourds et autobus — Mesure
du moment d'inertie de masse
Reference number
ISO 21234:2022(E)
© ISO 2022
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ISO 21234:2022(E)
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© ISO 2022

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© ISO 2022 – All rights reserved
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ISO 21234:2022(E)
Contents Page

Foreword ..........................................................................................................................................................................................................................................v

Introduction .............................................................................................................................................................................................................................. vi

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ..................................................................................................................................................................................... 1

3 Terms and definitions .................................................................................................................................................................................... 1

4 Principles ..................................................................................................................................................................................................................... 2

5 Variables ....................................................................................................................................................................................................................... 3

5.1 Reference system ................................................................................................................................................................................. 3

5.2 Variables to be measured .............................................................................................................................................................. 3

6 Measuring equipment .................................................................................................................................................................................... 4

7 Test conditions .......................................................................................................................................................................................................4

7.1 General ........................................................................................................................................................................................................... 4

7.2 Ambient conditions............................................................................................................................................................................. 4

7.3 Test surface ................................................................................................................................................................................................ 4

7.4 Test vehicle ................................................................................................................................................................................................. 4

7.5 Operating and other liquids ........................................................................................................................................................ 5

7.6 Loading conditions, suspension and mechanical parts ..................................................................................... 5

8 Determination of the I , I , I , and I mass moments of inertia ...................................................................5

xx yy zz xz

8.1 General ........................................................................................................................................................................................................... 5

8.1.1 Platform levelness ............................................................................................................................................................. 5

8.1.2 Platform weight and stiffness ................................................................................................................................. 5

8.1.3 Pivot location ......................................................................................................................................................................... 6

8.1.4 Vehicle weight ....................................................................................................................................................................... 6

8.1.5 Vehicle/platform MOI comparison ..................................................................................................................... 6

8.1.6 Vehicle location on the platform ........................................................................................................................... 6

8.1.7 Vehicle restraints ............................................................................................................................................................... 6

8.1.8 Platform oscillation amplitude .............................................................................................................................. 6

8.1.9 Pivot bearing damping .................................................................................................................................................. 7

8.1.10 Oscillation period measurement .......................................................................................................................... 7

8.2 Determination of I and I using a stable pendulum ........................................................................................ 8

xx yy

8.2.1 General guidance ................................................................................................................................................................ 8

8.2.2 Procedure ................................................................................................................................................................................. 9

8.2.3 Determination of I and I ...................................................................................................................................... 9

xx yy

8.2.4 Data presentation ........................................................................................................................................................... 10

8.3 Determination of I and I using an unstable pendulum ........................................................................... 10

xx yy

8.3.1 General guidance ............................................................................................................................................................. 10

8.3.2 Procedure .............................................................................................................................................................................. 10

8.3.3 Calculation of I and I ........................................................................................................................................... 11

xx yy

8.3.4 Data presentation ...........................................................................................................................................................12

8.4 Determination of I using a torsional pendulum .................................................................................................12

8.4.1 General guidance .............................................................................................................................................................12

8.4.2 Procedure .............................................................................................................................................................................. 12

8.4.3 Calculation of I ...............................................................................................................................................................12

8.4.4 Data presentation ........................................................................................................................................................... 13

8.5 Determination of I using a torsional pendulum ................................................................................................. 13

8.5.1 General guidance ........................................................................................................................................... ..................13

8.5.2 Procedure .............................................................................................................................................................................. 13

8.5.3 Calculation of I .............................................................................................................................................................. 13

8.5.4 Data presentation ........................................................................................................................................................... 14

8.6 Determination of I using a multi-filar torsional pendulum ..................................................................... 14

8.6.1 General guidance ........................................................................................................................................... .................. 14

iii
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ISO 21234:2022(E)

8.6.2 Procedure .............................................................................................................................................................................. 15

8.6.3 Calculation of I ............................................................................................................................................................... 16

8.6.4 Data presentation ........................................................................................................................................................... 16

8.7 I , I , I , and I results checks .......................................................................................................................................... 16

xx yy zz xz

8.8 Parallel Axis Theorem................................................................................................................................................................... 16

Bibliography .............................................................................................................................................................................................................................17

© ISO 2022 – All rights reserved
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ISO 21234:2022(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are

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

editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www.iso.org/patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to

the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see

www.iso.org/iso/foreword.html.

This document was prepared by Technical Committee ISO/TC 22, Road vehicles, Subcommittee SC 33,

Vehicle dynamics and chassis components.

Any feedback or questions on this document should be directed to the user’s national standards body. A

complete listing of these bodies can be found at www.iso.org/members.html.
© ISO 2022 – All rights reserved
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ISO 21234:2022(E)
Introduction

Methods are presented for determining the roll (I ), pitch (I ), and yaw (I ) mass moments of inertia

xx yy zz

(MOI) and roll-yaw (I ) product of inertia (POI) of an individual vehicle unit about the vehicle unit axis

system and centre of gravity reference point. I , I , I , and I are fundamental mass properties that

xx yy zz xz

provide information on a vehicle’s mass distribution and rotational acceleration responses to applied

forces. The I and I components of the inertia tensor are less significant to vehicle dynamics and are

xy yz

not addressed in this document. The MOIs are determined using a pendulum device with measurements

of oscillation period and reaction forces. The location of the vehicle unit’s centre of gravity (CG)

reference point is required beforehand. Knowledge of a vehicle unit’s mass moments of inertia supports

vehicle modelling work, design validation, and planning for other dynamic tests yet to be performed.

Performing measurements for MOI determination of heavy commercial vehicles and buses may be

challenging in practice due to the wide variety of vehicles that vary significantly in terms of weight,

size, and number of axles. Adaptability of a heavy vehicle MOI facility’s layout is an important attribute.

© ISO 2022 – All rights reserved
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INTERNATIONAL STANDARD ISO 21234:2022(E)
Road vehicles — Heavy commercial vehicles and buses –
Mass moment of inertia measurement
1 Scope

This document provides standard methods for determining a vehicle’s roll, pitch, and yaw mass

moments of inertia (MOI) and roll-yaw product of inertia (POI). It applies to heavy vehicles, that is

commercial vehicles and buses as defined in ISO 3833 (trucks and trailers with maximum weight above

3,5 tons and buses and articulated buses with maximum weight above 5 tons, according to ECE and EC

vehicle classification, categories M3, N2, N3, O3 and O4). Mass moment of inertia measurements are

performed separately for each single unit.
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 612, Road vehicles — Dimensions of motor vehicles and towed vehicles — Terms and definitions

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
stable pendulum

pendulum apparatus for supporting a vehicle on a nominally planar surface where the combined vehicle

and pendulum CG height is below the pivot point
3.2
unstable pendulum

pendulum apparatus for supporting a vehicle on a nominally planar surface where the combined vehicle

and pendulum CG height is above the pivot point
3.3
torsional pendulum
pendulum apparatus where the restoring force is torsion
3.4
multi-filar torsional pendulum

torsional pendulum (3.3) with multiple vertical wires, cables or chains supporting the vehicle and test

platform (3.5) where the torsional restoring force is due to gravity and spring force in twisting cables

© ISO 2022 – All rights reserved
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ISO 21234:2022(E)
3.5
platform

nominally planar surface of the pendulum on which the vehicle unit or trailer is parked

3.6
vehicle restraint
device used to restrain vehicle motion on the test platform (3.5)
3.7
tare MOI
MOI determined for the test fixture only, with no test vehicle
3.8
vehicle MOI
MOI determined for the vehicle only
3.9
platform MOI
MOI determined for the platform (3.5) only
3.10
roll MOI
mass MOI about the vehicle X axis
3.11
pitch MOI
mass MOI about the vehicle Y axis
3.12
yaw MOI
mass MOI about the vehicle Z axis
3.13
roll-yaw POI
mass product of inertia coupling between the X and Z axes
V V
3.14
radius of gyration

distance from the axis of rotation to a point where the total mass of the body may be concentrated, so

that the MOI about the axis remains the same
4 Principles

This document specifies methods to determine the vehicle’s roll, pitch, and yaw MOIs and roll-yaw POI

about the vehicle axis system originating from the vehicle CG reference point. Based on the vehicle axis

system defined in ISO 8855, the MOI determinations described in this document include I , I , I , and

xx yy zz
I .

The I and I MOIs are determined using a stable or unstable pendulum fixture, where the period of

xx yy

oscillation of the fixture and fixture with the vehicle are measured to calculate the MOIs. The I MOI is

determined using a torsional or multi-filar torsional pendulum, where again the period of oscillation is

measured. The I POI is determined using a torsional pendulum with an integrated roll axis, where the

roll axis is constrained and the roll reaction moment is measured.
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ISO 21234:2022(E)

The accuracy of MOI measurements is dependent on vehicle condition during measurement,

measurement equipment accuracy, potential movement of heavy sprung or unsprung masses within

the vehicle, such as engine and transmission assemblies and suspensions, and movement of the vehicle

on the platform during the measurement process. Potential movement of fuel, coolants, and oils will

also affect measurement accuracy.
5 Variables
5.1 Reference system
The reference system specified in ISO 15037-2 shall apply.
5.2 Variables to be measured

With the vehicle at the load condition specified for the test, measure and record the following in

accordance with the dimensions given in ISO 612 and ISO 8855:
— W total vehicle load (or weight);
— W load of the platform including the restraint components;
— h pivot height from the platform surface;

— h platform plus restraints vertical CG distance below (or above) the pivot axis, including the roll

pivot axis for I measurement;

— h vehicle vertical CG distance below (or above) the pivot axis, including the roll pivot axis for I

v xz
measurement;

— h system (platform, restraints, and vehicle) vertical CG distance below (or above) the pivot axis;

— θ pitch angle of the platform relative to the gravity vector (positive for the front of the vehicle

pitched down);

— θ static pitch angle of the platform relative to the gravity vector (positive for the front of the

p, static
platform pitched down);

— φ static roll angle of the platform relative to the gravity vector (positive for the platform

p, static
rolled to the left);
— T platform (plus restraints) undamped period of oscillation;

— T total system (platform, restraints and vehicle) undamped period of oscillation;

— X longitudinal offset displacement of the vehicle CG relative to the platform centreline (positive for

forward vehicle displacement);

— Y lateral offset displacement of the vehicle CG relative to the platform centreline;

— n number of oscillations of the platform;

— R radial distance on a multi-filar pendulum from the yaw axis centroid to the vertical support cables;

— L length of the multi-filar pendulum vertical support cables;
— ѱ platform yaw angle amplitude;
— ѱ vehicle yaw angle amplitude;
— L unstable pendulum moment arm length from reaction spring to pivot;
— K unstable pendulum reaction spring stiffness (force/displacement);
© ISO 2022 – All rights reserved
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ISO 21234:2022(E)
— K torsional pendulum reaction spring stiffness (moment/angle);
— M roll reaction moment for the torsional pendulum used for I determination;
x xz

— M measured roll reaction moment for the torsional pendulum used for I determination.

meas xz
6 Measuring equipment

The measuring equipment, transducer installation, data processing, and typical operating ranges shall

be in accordance with ISO 15037-2.

Table 1 — Variables, typical operating ranges and recommended maximum errors of variables

not listed in ISO 15037-2 for MOI measurement
Variable Typical operating range Recommended maximum errors
of the combined transducer and
recorder system
Suspension air-spring inflation pressure (500–1 000) kPa 15 kPa
Vehicle, axle or track load Up to 40 000 kg (392 400 N) 0,2 %
Distance ≤2 000 mm ±2 mm
>2 000 mm ±0,05 %
Angles ±5° ±0,05°
Static distance X, Y ±20 mm ±3,0 mm
Dynamic Distance X(t), Y(t) ±10 mm ±0,5 mm
Time period 2 min ±1,0 ms
Roll moment (0–1 500) N-m 0,5 %
7 Test conditions
7.1 General

The limits and specifications indicated below shall be maintained during the test. Any deviations shall

be identified in the test report.
7.2 Ambient conditions

The surface shall be clean and dry. If the test is conducted outdoors, the ambient wind speed is

recommended to be less than 1 m/s. Ambient temperature shall be recorded if the test is conducted

outdoors.
7.3 Test surface

The test surface, when applicable, should be in accordance with ISO 15037-2 and the surface should be

stiff enough to avoid surface deformation when measuring the vehicle.
7.4 Test vehicle

The load condition shall be reported as described in ISO 15037-2. Tyre pressures, suspension setting (if

applicable) and load condition shall be recorded.

On vehicles with multiple adjustable seats or other devices such as beds, adjust the items to a mid-

travel position (longitudinal and vertical) and adjust the seat back torso angle to the manufacturers

designated specification or as close as possible to 15°. The positions shall be reported.

On vehicles with steering wheel reach and rake, the position shall be reported.
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ISO 21234:2022(E)
7.5 Operating and other liquids

The fuel tanks shall be completely full or empty, including the urea tanks. Fuel motion within an unfilled

fuel tank can have an adverse effect on the results. If the displacement of other liquids carried on the

vehicle (operating and otherwise), such as engine oil, is expected to influence the results, precautions

should be taken to fill the fluid tanks, drain the fluids, or note the potential issue. Tank conditions

(empty or full) and locations shall be reported.
Note any leaking fluids during vehicle inclination.
7.6 Loading conditions, suspension and mechanical parts

Vehicle payload shall be held in place to avoid displacement due to inclination or yawing of the vehicle.

If the vehicle has a suspended cab or semi-suspended cab, the cab shall be locked at its standard height

when the vehicle is in a horizontal plane with no driver in the cab. Other components with flexible

mounting may need to be constrained as well, if deflection will adversely influence the results.

Immediately prior to each test event, all self-regulating suspensions shall be adjusted such that they are

at the proper ride height or, in the case of the suspensions for certain auxiliary axles, at the prescribed

inflation pressure. Initial ride height of each suspension shall be reported.

Tyre condition and pressure shall be in accordance with vehicle manufacturer recommendations and

ISO 15037-2. In case a range is specified for tyre pressure, the highest-pressure value should be selected

to minimize tyre deflection.

Suspended components such as the engine, gearbox, and axles may move laterally and /or longitudinally

when tilting or yawing the vehicle. Such displacements may influence measurement accuracy and

should be noted accordingly.
8 Determination of the I , I , I , and I mass moments of inertia
xx yy zz xz
8.1 General

Two methods are presented for measuring the parameters needed to calculate each of the I , I , and

xx yy

I MOIs. The methods vary by the type of pendulum device used. A single method is presented for

determining the I POI. In general, the pendulum fixtures are mechanically re-configurable to enable

measurement of various MOIs. Reconfiguration might include simply repositioning the vehicle on the

platform to align the vehicle longitudinal or lateral axis with the pendulum rotational axis and adjusting

pivot and spring hardware to facilitate different MOI and POI measurements.
8.1.1 Platform levelness

The platform’s empty, static equilibrium position, θ and φ , should be checked via

p, static p, static

inclinometers to verify its levelness. It is recommended that the empty platform is level within 0,1° for

best results and no more than 0,5°.
8.1.2 Platform weight and stiffness

It is recommended that the platform be as light as possible compared to the weight of the vehicle under

test, while providing sufficient stiffness to avoid measurement errors due to deflection. When loaded

with the test vehicle, it is recommended that the platform deflection is less than 2,5 mm at the vehicle’s

CG (as measured from the pivot when compared to the unloaded platform). Significant measurement

errors are introduced when the deflection is greater than this, although corrections for deflection can

be made. In general, a stiff platform is more important than a light platform.
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ISO 21234:2022(E)
8.1.3 Pivot location

The MOI platform’s pivot height whether for a stable or unstable (inverted) compound pendulum is

very important for measurement accuracy. For any given vehicle, an optimal pivot height exists that

minimizes the MOI measurement error. Except for yaw pivots, the pivot height should be adjusted so

that it is located at a height between the test vehicle’s CG height and the vehicle’s radius of gyration, k ,

[2], [3]

about the axis in question (approximately half the wheelbase for typical trucks) . Measurement

error is reduced by increasing the amplitude of the platform pitch angle (remaining less than 5°) while

[2]

simultaneously reducing the period . Trade-offs between pitch angle and period are achieved by

adjusting the pivot height, and experimentation will likely be required to produce the desired results.

For test fixtures intended to measure a wide range of vehicle sizes and weights, the pivot height should

be adjustable.

For stable pendulum measurements, experience has indicated satisfactory pivot heights, h , for trucks

[2]

on the order of 635 mm . It is recommended that h is not smaller than 20 % of the h . If the pivot

v p

height is too small, period measurement error and vehicle acceleration motion relative to the platform

are increased.
8.1.4 Vehicle weight

In practice, it is recommended that the test vehicle weighs at least 50 % of the carrier platform’s weight.

This limitation is due to the influence of the platform’s weight on overall measurement error.

8.1.5 Vehicle/platform MOI comparison

The vehicle’s anticipated moment of inertia values shall be within the capabilities of the facility. MOI

accuracy is reduced when the vehicle’s MOI is less than that of the pl
...

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