NBSIR 75-738

A Method and Means of Calibration an

Air-Bearing Force Plate for Use With a

Towed Pavement Friction Test Trailer

Robert W. Kearns and John F. Ward

Engineering Mechanics Section

Mechanics Division

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

December 1974

Final

Prepared for Federal Highway Administration

Washington, D. C. 20234

NBSIR 75-738

A METHOD AND MEANS OF CALIBRATING AN

AIR-BEARING FORCE PLATE FOR USE WITH A

TOWED PAVEMENT FRICTION TEST TRAILER

Robert W. Kearns and John F. Ward

Engineering Mechanics Section

Mechanics Division

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

December 1974

Final

Prepared for Federal Highway Administration

Washington, D. C. 20234

U.S. DEPARTMENT OF COMMERCE, Rogers C.B. Morton, Secretary

James A. Baker, III, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Acting Director

The opinions, findings, and conclusions expressed in this publication are those of the authors and not necessarily those of the Federal Highway

Administration.

CONTENTS

Page

1. INTRODUCTION 1 1.1 Background 2 1.2 Other Preliminary Investigations 3 1.3 Variations in Traction Induced Forces and

Displacements 3

2. CALIBRATION APPARATUS 5 3. CALIBRATION 7

4. REPORT 9

5. USE OF THE FORCE PLATE 9

6. DISCUSSION AND CONCLUSIONS 11

7. RECOMMENDATIONS FOR FUTURE WORK 11

8. REFERENCES 12

Appendix A. The Calibration Fixture 26

Appendix B. Load Cell Calibration Reports 31

Appendix C. The Calibration Box 34

ILLUSTRATIONS

1 IRS Force Plate Mounted on Air-Bearing Platform 13

2 Initial Results of . Cal ibrating the IRS Wheel Transducer

with a Modified Commercial Force Plate ..... 14

3 Initial Results of Calibrating the IRS Wheel Transducer

with a Modified Commercial Force Plate Supported on an Air-Bearing Platform 15

4 Eccentric Load Positions 16

5 Tire-Surface Interface Area Versus Load for

ASTM E 249 Test Tire 17

6 Tire-Surface Interface Area Versus Load for

ASTM E 501 Test Tire 18

7 Longitudinal Displacement of the Force Plate during the

Calibration of the IRS Wheel Load Transducer 19

8 Lateral Displacement of the Force Plate during the

Calibration of the IRS Wheel Load Transducer 20

9 Rotation of Coordinate Axes Accompanying Pitching of

the Force Plate from Level 21

10 Nomenclature of the Loading Fixture 22

11 Dial Gage Locations 23

12 Force Plate Calibration Block Diagram 24

13 Summary Report Sheet 25

A-l Force Plate Calibration Fixture Assembly 27

A-2 Footprint Platen 28

A-3 Air-Bearing Support Surface 29

A-4 Jack Beam 30

B<-1 Horizontal Load Cell Calibration Data 32

B-2 Vertical Load Cell Calibration Data 33

C-l Schematic of One Channel of the Calibration Box 35
In view of present accepted practice in this technological area, U. S. customary units of measurement have

been used throughout this paper. It should be noted that

the U. S. A. is a signatory to the General Conference

on Weights and Measures which gave official status to

the metric SI system of units in 1960. Readers interested

in making use of the coherent system of SI units will

find conversion factors in ASTM Standard Metric Practice

Guide, ASTM Designation E 380-70 (available from American

Society for Testing and Materials, 1916 Race Street, Philadelphia, Pennsylvania 19103).

Length 1 in = 0.0254 meter

Area 1 in2 — 6.4516 x 10 meter2

Force 1 lbf = 4.448 newton

Exact value
A METHOD AND MEANS OF CALIBRATING AN AIR-BEARING FORCE PLATE

FOR USE WITH A TOWED PAVEMENT-FRICTION-TEST TRAILER

Robert W. Kearns

John F. Ward

The equations for the variation of the

external forces acting at the tire-pavement

interface of a symmetrical two-wheeled towed

trailer are given. Estimates, derived from

experimental results, have been made for the

displacement of the tire-plate interface with

respect to the ground of an unrestrained locked

test tire on the trailer. A description of

the force plate calibration test frame, instrumentation and test method is given. The means of applying simultaneous vertical (normal)

and horizontal (longitudinal) forces at the

contact surface of the air-bearing plate in

accordance with the equations are discussed.

The change in force plate output with changes

in the dimensions of the trailer calibrated

in-turn with the force plate are given. A method of locating the coordinate axes of the

internal force sensors with respect to level

is given. Consistent application of these methods to both the force plate and trailer tranducer calibrations results in reduced verticalto-horizontal cross-axis differences.

Key Words: Calibration procedures; force plate;

pavement skid resistance; skid accident re- duction; tire-pavement interface forces.

L. INTRODUCTION

The measurement of the skid resistance of highways under wet

weather conditions is part of the Federal Highway Administration's

(FHWA) skid accident reduction program. Such measurements are bein

made by highway departments^ of the various states in accordance

with ASTM Method E-274 [lj. The methods and means to systematicall

relate the skid resistance quantities to the National Measurement

System are being developed at the National Bureau of Standards

(NBS). NBS maintains and operates for FHWA an Interim Reference

System (IRS) which is used for evaluating and calibrating other

skid-resistance-measuring systems maintained by FHWA to which the

state systems relate [2j.

^Figures in brackets indicate the literature references at the end

of this report.

1
The ASTM E 274 method of skid-resistance testing utilizes

the measurement of the frictional force occurring at the tire-pavement

interface on a locked test wheel as it is dragged over a wetted

pavement at a constant speed.

Wheel transducers are usually instrumented to measure force

at the tire-pavement interface or torque about the wheel axle.

Because of the effects of the flexible suspension system and tires

on the trailer making the measurement, there is a need to calibrate

the whe'el transducer in situ. A force plate is a loading platform

on which a locked test wheel of the trailer is placed during the

calibration of the trailer instrumentation. Transducers associated

with the force plate act in series with the force components occurring at the tire-pavement interface. During wheel transducer calibration, signals from the plate transducers are compared with signals

from the wheel transducers for a variety of longitudinal forces

applied to the tire through the plate.

The force plate used with the IRS is shown in Figure 1. Since

the plate is mounted on an air-bearing platform a lateral force

is not developed in the plate during use. Any lateral force re- quired for equilibrium of the trailer occurs at the other trailer

tire. This report discusses the development of the equipment and

method used to calibrate the force plate for the in situ calibration of the IRS force type wheel transducer.

1.1 Background

During preliminary investigations with force plates a Stevens

Institute of Technology force plate, which had been modified by

personnel of the Maryland State Highway Administration, was calibrated in accordance with a proposed method of calibration being

considered by an ASTM committee. The force standard was an external

load cell. In a calibration test frame a screw mechanism was turned

to vary the magnitude of the force applied to the force plate and

standard in series. The result of the calibration was quite linear.

The force plate was then used to calibrate the IRS wheel transducer.

Figure 2 illustrates the unacceptable result of the test. In the

investigation of possible causes for the nonl inearity , the force

plate was temporarily placed on an air-bearing platform and the

test was repeated with the result shown in Figure 3. In the latter

test the force plate mechanism remained stationary with respect

to the loading point, as it was during calibration, while in the

initial transducer test the mechanism of the force plate was moved

through nominally one inch of displacement.

Inspection of the mechanism revealed that a machining error occurred during the modification of the force plate. The error was corrected and the calibration results returned to their normal

values. The procedure by which this plate had been calibrated had

failed to reveal the problem because the procedure did' not require

2
movement of the force plate mechanism commensurate with that occurring during use.

1.2 Other Preliminary Investigations

An experiment was conducted to quantify the effect of application of the normal force eccentric to the friction surface of

the plate. The force plate was mounted in a deadweight calibration machine with vertical force being applied at the locations

shown in Figure 4. Using the reading at the center of the plate

(position 1 ) as a reference, the deviation in reading for loads

applied at the other positions is shown in Table 1. The forces

were applied through a ball and distributed on the plate through

a rubber footprint corresponding to the tire-pavement area of an ASTM E 249 tire loaded with 1085 Ibf. With the center of the footprint located within two inches of the center of the force plate

the variation is less than one-half percent of applied load.

The area of the tire^-pavement interface varies with load.

For measurement, a tire was placed in a testing machine. The tread was covered with ink. Paper was then placed between the tire tread

and a flat surface. The load was increased to a desired value and

then reduced to zero leaving an imprint of the tire-surface area

on the paper. A series of such impressions were made to develop

the variation in area with load. The impressions obtained with

the ASTM E 249 tire are summarized in Figure 5. The impressions

obtained with the ASTM E 501 tire are summarized in Figure 6.

1.3 Variations in Traction Induced Forces and Displacements

When a traction force is applied at the tire-pavement interface of the locked test wheel of a symmetrical two-wheeled trailer,

the normal and the lateral forces change in accordance with the

following equations:

F

WL

z

= -

,

F

WL

y

+ F

WR

y

" [-^-) "WL.. (2)

where x = the longitudinal axis, positive direction rearward

y = the lateral axis, positive direction to the left

when viewed in the positive direction of the x axis

z = the normal axis, positive direction downward

Firr = the longitudinal traction force on the left wheel

WL

x

FrTT = the total normal force on the left wheel acting at

WL

z the tire-pavement interface.

F^ = tne normal force on the left wheel acting at the

z tire-pavement interface when the applied traction

is zero.

3
the Lateral force on the right wheel

the lateral force on the left wheel

the effective normal force unloading constant where

H is the hitch height and L is the length from the

center line of the trailer wheel to the hitch

the effective lateral force constant where T is

the track width or distance between the centerlines

of the two trailer tires and L is the length from

the center line of the trailer wheel to the hitch

Equation (1) shows that the normal load on the test wheel

decreases as the traction force increases where the amount of re- duction is a function of the dimensions of the trailer. Equation

(2) shows that the lateral force increases with an increase in

traction where, again, the amount depends upon the dimensions of

the trailer. In highway use Equation (2) indicates that the lateral

force is shared by both wheels.

The force plate supplied with the IRS is instrumented to measure the longitudinal and vertical components of an applied force,

but not the lateral component. This is consistent with the use

of an air-bearing force plate. It should be pointed out that use

of the force plate without applying the share of the lateral force - acting at the test wheel tire-pavement interface fails to apply

the effects of this force component to the transducer during its

cal ibration.

Because the trailer suspension system and tires are flexible

the tire-pavement interface shifts as the friction force increases

and decreases. The measured displacement of the tire-pavement

interface of the IRS, while supported on an air-bearing platform,

along the longitudinal axis is given in Figure 7 and along the

lateral axis in Figure 8, as a function of applied friction force.

These figures indicate a movement of approximately up to 1.1 inches

in the longitudinal direction and up to approximately 0.4 inches

in the lateral direction with a traction force applied of 800 poundsforce .

The force plate outputs are also sensitive to variations in

the friction surface orientation with respect to level. Freedom

of movement about level is introduced by the air-bearing platform.

Variations in plate pitch angle orientation, or rotation about

the lateral axis, result in a transformation of coordinates as shown in Figure 9.

The variations in output of the sensitive axes as a function

of pitch angle 8 are:

WR

y

H =

L

_T =

2L

4
E

T

= S^WL Sin 9 + F

WL

C ° S 6) C3)

z x

E = K (F F sin 0) L L WL cos 6 - WL

z X

where Ep = traction output signal (4)

E = normal load signal

E^ = traction constant

load constant

The variations in plate roll angle orientation or rotation

about the longitudinal axis have only a second order effect on the plate traction axis.

2. CALIBRATION APPARATUS

The two-axis loading fixture (Figure 10) provides the means

of applying known forces simultaneously to the two sensitive axes

of the force plate. The fixture utilizes the air-bearing platform

used with the plate during trailer wheel transducer calibration.

The traction force is generated by the horizontal hydraulic jack

(detail 11) and measured by the horizontal load cell (detail 2).

A change in vertical force is generated by the vertical hydraulic

jack (detail 19) and measured by the vertical load cell (detail

18). Friction between the force plate and the support surface (detail

9) is negligible due to the air-bearing. Forces are transmitted

through ball joints for freedom of alinement. The fixture contains

adjustable members to allow calibration in a controlled orientation.

The vertical force is applied to the surface of the force

plate through a rubber footprint simulating the footprint of an ASTM test -tire at a normal load of 1085 lbf (Figure 5 or Figure 6).

In calibration, the horizontal force is applied to the surface

of the force plate by means of friction through the footprint,

up to the point of slippage. In order to provide a calibration

range which exceeds the horizontal force which results in slippage,

the excess horizontal force is applied to the plate through a lip

(Figure 10, detail 5). The horizontal force is transmitted through

a spring (detail 20) connecting the horizontal hydraulic jack (detail

11) to the jack beam (detail 12). This spring allows the footprint

to creep without changing the position of the hydraulic jack piston

and helps the force to remain constant under this condition.

The footprint is located in the center of the force plate

friction surface. The drawbar and force plate index marks are alined.

The height of the traction load cell anchor pin (detail 1 ) is adjusted so the load cell axis is level and alined with the drawbar

when the friction surface is maintained at a pitch angle. The vertical tie rods (detail 14) are maintained vertical. The vertical

load cell axis is parallel to the vertical tie rods.

5
When the footprint is centrally Located^ the force plate will

not yaw with changes in traction force.

Scale drawings of the fixture assembly and components are shown in Appendix A.

The applied loads are measured by load cells and readout indicators. These instruments were calibrated by the calibration

service of the National Bureau of Standards using deadweights which

have been systematically related to the National Measurement System

[3], Typical load cell calibration results are given in Appendix B.

The level of the force plate can be adjusted by means of valves

in the lines supplying air to each of three air-bearings. The plate

orientation is measured with three dial gages and maintained in

a preferred position throughout the test by use of the air valves.

The dial gages are located as shown in Figure 11.

The instrumentation includes readout indicators for the horizontal and vertical load cells, signal conditioners for the force

plate, an analog-to-digital converter and a pointer. The desired

values of force are entered into the load cell indicators, which

display null indications when the loads are reached. The force

plate signals are conditioned, amplified, and converted to digital

values. The printer records the digitized force plate outputs automatically when a button is depressed. The force plate bridge excitation is supplied by the converter.

As discussed in the introduction, the loading fixture should

allow any force plate motions to occur during plate calibration

which occur during trailer wheel transducer calibration. In the case of a force plate supported by an air-bearing platform, the

force plate moves with the tire footprint during wheel transducer

calibration. No components of the force plate move with respect

to the footprint, except the slight deformation of the internal

strain gaged beams. During the calibration of the force plate in

this fixture, the slight deformation of the strain gaged beams

occurs, and no components move with respect to the footprint. An

external shift of about 0.3 inch of the normal force away from

the drawbar occurs due to the motion of the tire footprint with

respect to the wheel hub. The center of pressure moves less than

this amount. The test results of Table 1 indicate a movement of

this magnitude would introduce a difference of less than one-third

percent of force plate full scale output.

A calibration box is provided with each force plate so the

calibration results are independent of the analog-to-digital con- verter used during calibration. This also enables the force plate

to be used with a variety of readout displays.

When a force is applied to the force plate, an internal Wheatstone bridge strain gage circuit becomes unbalanced. With no force

6
I applied to the force plate, the bridge can be unbalanced with a resistor shunting one leg of the bridge. The resistors contained

in the calibration box are trimmed such that the bridge unbalance

that each produces is equivalent to the bridge unbalance which

would have occurred by the forces stated on the box and/or in the

calibration table results, in accordance with the calibration equation loading conditions. A schematic diagram of the calibration

box is given in Appendix C.

The calibration box is located in the cabling which connects

the force plate to the readout instrumentation. The strain gage

bridge is completed within the force plate. The cabling resistance

is in series with the readout instrumentation and the power supply

as shown in Figure C-l when the switch is in the N position. In

this case, the effect of the cable resistance is to change the

output impedance of the signal supplying the differential amplifier

and to decrease the current from the power supply. The effect is

to de-sensitize the bridge [4j. The force plate is calibrated using

the cabling assigned to the plate. With the use of a regulated

power supply and high input impedance amplifier the effect becomes

negligible even for moderate temperature changes.

When a calibration resistor is connected into the circuit,

the amount of bridge unbalance is affected by the value of the

resistance of cable 1. However, the calibration resistor is trimmed

with the cable connected to minimize this effect. When the unit

is used at a temperature other than that at which it was calibrated, the change in the cable resistance and calibration resistance

needs to be considered. The temperature coefficient of the fixed

resistors used in the IRS system is less than 5 ppm/°C. The temperature coefficient of the trim potentiometers is less than 25 ppm/°C.

The cable resistance has a temperature coefficient of 4,000 ppm/°C.

However, since the ratio of the cable resistance to the calibration

resistance is 1 to 50,000 and the trimpot value is small compared

to the calibration resistance value, the total variation is less

than a quarter pound-force within the temperature range from 10°C

to 40° C.

The vertical load channel resistors are trimmed to equivalent force values of 250, 500, 750, 1,000, 1,500 and 1,750 pounds.

The traction channel resistors are trimmed, in the presence of

the stated vertical load, to equivalent force values of 200, 300,

400, 500, 600, 700, 800, 900, 1,000 and 1,500 pounds.

A block diagram of the calibration system is shown in Figure

12.

3. CALIBRATION

The operator is provided with a complete step-by-step procedure. For the purpose of this report, the procedure will be briefly

summarized.

7
The force plate and air-bearing platform are inserted in the

loading fixture and with the air-bearing in operation all parts

are carefully aligned to ensure proper position. Electrical connections are made and electronic instrumentation warmed up. Ambienttemperature is monitored and recorded throughout the procedure.

To establish the force plate friction surface pitch angle

at which the coordinate axes of the internal force sensors corres- pond to the axes of the applied forces, the force plate traction

output is electronically adjusted to zero with no load applied

to the force plate. With no traction forces on the plate a vertical load is then applied to the center of the plate simulating

the static wheel load of a trailer. The air-bearing valves are adjusted such that the force plate is level in the lateral direction and pitched as necessary to return the traction output to zero. The pitch angle is measured using dial indicators referenced

to zero by a sensitive bubble level. This orientation is recorded

and maintained during the remainder of the test.

Calibration of the vertical load axis of the force plate is

done with the horizontal traction axis unloaded. Data is recorded

for both increasing and decreasing vertical loads.

Calibration of the traction axis is done with the vertical

load varied to simulate the unloading effect of the trailer as shown by Equation 1. The effective normal force unloading constant

of the trailer to be calibrated by the force plate is measured

and the trailer vertical load corresponding to the traction force

is computed. Traction data is recorded for both increasing and

decreasing traction loads. Sets of traction calibration data are recorded for different H/L ratios covering the range of geometries

of skid measurement trailers, and for a range of initial vertical

static loads.

Linear calibration curves are fitted to the data for the vertical and traction axis calibration by the method of least squares

with equal weighting. Hysteresis and linearity are expressed as percentages of full scale outputs. For each calibration where independent runs have been obtained, data is pooled and a linear

calibration equation is fitted to all points.

The reference resistors in the calibration box are trimmed

to match the calibration curves as calculated for one H/L value.

The vertical load channel resistors are trimmed with no external

loads applied to the force plate and the electronics set to zero. The traction channel resistors are trimmed with

1) the traction channel electronics set to zero when no external loads are applied

to the plate, and

8
2) the vertical static load applied to the

plate with the friction surface orientated at the previously determined pitch

angle and with no vertical load calibration resistors connected.

The least squares equation may indicate that a calibration

resistor should be trimmed for the no load case. Since extremely

large resistor values would then be required, perhaps as much as 300 megohms, the trimming of the output to zero is impractical.

Instead, the expected offset under no load conditions is calculated and recorded in the table of equivalent calibration forces.

A table of equivalent calibration forces is calculated for

each selectable resistor corresponding to all sets of traction

calibration data recorded using other H/L ratios.

4. REPORT

The following calibration test information is reported:

1) Date

2) Force plate identification

3) Calibration box identification

4) Traction force indicator and load cell identification

5) Vertical load indicator and load cell identification

6) Ambient temperature range during calibration

7) Friction surface pitch angle

8) Linearity and hysteresis expressed as a percent of

full scale. When the least squares linear fit is

based on pooled data, the average linearity and hysteresis are reported.

9) Equivalent calibration forces for each selectable

resistor corresponding to all sets of traction calibration data recorded using H/L ratios and/or static

vertical loads. The expected offset values under

no load conditions are included.

A summary report sheet is shown in Figure 13.

5. USE OF THE FORCE PLATE

When using the force plate to establish known forces at the

tire-pavement interface of a two-wheeled towed trailer:

9
5.1 Connect the force plate and calibration box to a suitable readout unit and source of strain gage

excitation. Place the force plate on a smooth level

floor.

5.2 Scale the normal load readout instrumentation:

a. With no external force applied, set the

gain and offset of the normal load readout

electronics. Use the values of any two normal

load reference points other than N as given

in the calibration summary (Figure 13) to

obtain readout in engineering units. If

the readout is linear, a linear force scale

will result.

b. Place the normal load reference resistor

switch in the N (no resistor) position for

force measurement.

c. Activate the air-bearing platform. Set the

friction surface roll angle to zero. Set

the friction surface pitch angle to the

value specified in the calibration summary

and maintain the angles during force measurement.

5.3 Scale the traction readout instrumentation:

a. Center the vertical load provided by the

test wheel of the trailer on the force plate.

Activate the air-bearing platform. Set the

friction surface roll angle to zero. Set

the surface pitch angle to the value specified

in the calibration summary.

b. From the summary, select the traction resistor equivalent force value column applicable

to the H/L ratio and static wheel load of

the trailer.

c. With no external traction force applied,

set the gain and offset of the traction force

readout electronics. Use the values of any

two of the traction reference points to obtain readout in engineering units. If the

readout system is linear, a linear force

scale will result.

d. Place the traction reference resistor switch

in the N position for force measurement.

Maintain the friction surface at the specified angles during force measurement.

10
5.4 Measure the force.

a. Apply the force through the force plate.

b. Re-adjust, as necessary, the friction surface

orientation to the specified angles.

c. When the readout instrumentation matches the

recorded value for a calibration resistance, ' the force has the value given in the report

of calibration.

6. DISCUSSION AND CONCLUSIONS

A calibration method and the apparatus needed to calibrate

a two-axis air bearing force plate have been developed. The fixture

developed can reproduce the loading conditions found during the

in situ calibration of the wheel force transducer of a symmetrical two-wheeled skid measurement trailer.

The apparatus can easily be duplicated by other laboratories.

Calibration service for load cells with their indicators is available from several sources, including the NBS. The simplicity of

the apparatus calls for more operator skill and time than would

be the case if the loads were developed by servomechanisms. The

operator must simultaneously null two force indicators by adjustments of two hydraulic jacks while maintaining the .force plate

in position with three air-bearing valves. The choice of the null

indicators for loading and a printing readout help make it possible

for the calibration to be performed by one man.

The fixture must be in good mechanical alinement to minimize

angular errors. Preliminary results with the equipment indicate

that the measurement errors do not exceed one percent of full scale.

7. RECOMMENDATIONS FOR FUTURE WORK

A method of calibrating the plate which is consistent with

the calibration of a torque-type transducer needs to be developed.

Beyond that, a method of calibrating a wheel transducer, in situ,

which includes the lateral force component acting at the tire-pavement interface is needed.

11
8. REFERENCES

1. "Standard Method of Test for Skid Resistance of Paved Surfaces

using a Full Scale Tire" Designation E274-70. Annual Book

of ASTM Standards, Part II. American Society for Testing and

Materials, Philadelphia, Pa. (1973).

2. Watson, John R. and Cook, Larry M., "A National Program to

Standardize Skid Resistance Measurements" Public Roads, A

Journal of Highway Research. Vol. 37 No. 3, pp 77-80 (December

1972).

3. Staff, Engineering Mechanics Section, Daniel J. Chwirut, Coordinator, "Research and Testing Facilities of the Engineering

Mechanics Section, National Bureau of Standards Special Publication 370 21 pages (January 1973).

4. Dove, R. C. and Adams, P. H., "Variable-Resistance Strain

Gages" Chapter 2, Experimental Stress Analysis and Measurement,

pp 99-119, Charles E. Merrill Books, Inc., Columbus, Ohio

(1964).

USCOMM-NBS-DC 12
FIGURE 1 INTERIM REFERENCE SYSTEM (IRS) FORCE PLATE

MOUNTED ON AIR-BEARING PLATFORM.

IRS WHEEL TRANDUCER OUTPUT, Ibf

FIGURE 3. INITIAL RESULTS OF CALIBRATING THE IRS WHEEL

TRANSDUCER WITH A MODIFIED COMMERCIAL

FORCE PLATE SUPPORTED ON AN AIR BEARING

PLATFORM.
CENTER LINE

— 2 in ["*- .

> | 4.5 in

J *

—

1

:

l. . —(

4

. 5 I s

8 z

.E ^

CN

t t

!

4.5 in

FIGURE 4. ECCENTRIC LOAD

CENTER LINE

TABLE 1. FORCE PLATE VERTICAL LOAD OUTPUT

VARIATION WITH LOCATION

Position

vertical

1 oad 1 2 1 3 1 4 1 5 1 6 1 7

Ibf

Readinq * Deviation From Position 1 Reading

1500 1173 -4 + 1 + 1 + 1 -1 +3

1200 939 -3 0 -1 + 1 -1 + 2

900 703 - 1 + 1 + 1 +2 0 + 3

600 468 0 + 1 + 1 +2 0 -f 3

300 234 - 1 + 1 +1 + 1 0 + 2

0 0 0 0 0 0 0 0

*Arbitrary scale
FIGURE 5. TIRE-SURFACE INTERFACE AREA VERSUS LOAD FOR

ASTM E249 TEST TIRE. EACH BACKGROUND SQUARE

IS ONE SQUARE INCH.
FIGURE 6. TIRE-SURFACE INTERFACE AREA VERSUS LOAD FOR ASTM E501

TEST TIRE. EACH BACKGROUND SQUARE IS ONE SQUARE INCH.
FIGURE 7. LONGITUDINAL DISPLACEMENT OF THE FORCE

PLATE DURING THE CALIBRATION OF THE IRS

WHEEL LOAD TRANSDUCER
FIGURE 8. LATERAL DISPLACEMENT OF THE FORCE PLATE DURING

CALIBRATION OF THE IRS WHEEL LOAD TRANSDUCER*
FIGURE 9. ROTATION OF COORDINATE AXES ACCOMPANYING PITCHING OF

THE FORCE PLATE FRICTION SURFACE FROM LEVEL.

21
2) ®Q (*)(*)

f 3®

FIGURE 10. NOMENCLATURE OF THE

1. HORIZONTAL LOAD CELL ANCHOR PIN

2. HORIZONTAL LOAD CELL

3. LINK

4. FORCE PLATE DRAWBAR

5. LIP

6. FORCE PLATE

7. FOOTPRINT

8. AIR-BEARING BASE

9. AIR-BEARING SUPPORT SURFACE

10. HORIZONTAL TIE RODS

LOADING FIXTURE.

11. HORIZONTAL JACK

12. HORIZONTAL JACK BEAM

13. H-BEAM FRAMEWORK

14. VERTICAL TIE RODS

15. TYPICAL BALL JOINT TIE ROD END

16. VERTICAL JACK BEAM

17. LOADING BALL

18. VERTICAL LOAD CELL

19. VERTICAL JACK

20. SPRING
FIGURE 11. DIAL GAGE LOCATIONS.
FORCE

INDICATOR

TRACTION

REFERENCE

CAL. RESISTORS

VERTICAL LOAD

REFERENCE

CAL. RESISTORS

VERTICAL

LOAD

CELL

FOOTPRINT

FORCE PLATE

AIR SPRING PLATFORM

EZZZZ3

TRACTION

READOUT

VERTICAL LOAD

READOUT

FORCE

INDICATOR

FIGURE 12. FORCE PLATE CALIBRATION BLOCK DIAGRAM
lO

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-4-

O /—i

C/J LO f—\ U ' lO rnP-1 CN! cO r-H

CN] r—1

r-H r—1

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Appendix A. The Calibration Fixture

Figure A-L Force Plate Calibration Fixture Assembly

Figure A-2 Footprint Platen

Figure A-3 Air-Bearing Support Surface

Figure A-4 Jack Beam

26


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Appendix B. Load Cell Calibration Reports

This appendix contains the calibration reports of the load

cells used with the fixture. The cell calibrated in tension is

used in the horizontal force channel. The cell calibrated in com- pression is used in the vertical force channel

.

31
CNI TAB - NATIONAL BUREAU OF STANDARDS LOAn CELL CALIBRATION

BLH LOAD CELL NO. 3542G-A» nLH INDICATOR MO,

CAPACITY 2»000 LBF COMPRESSION AND TENSION

2006 213. 04/10. 35. 3-A

JANUARY 7»1Q75

TENSION CALIBRATION DATA FO" 23 DEGREES C

DEFLECTIONS OBSERVED DEFLECTIONS

DURING CALIBRATION

APPLIED

DEVIATION FROM

CALIBRATION EQUATION ADJUSTED TO -------- CALIBRATION

CHANGE FRO^

PREVIOUS

CALIBRATION

HUN Dl HI 11 KUN C. Dl IM 1 RUM ? poi uttam

LBr 1 1XI T TC UNI T b

1 IM T TC UNJ, 1 bI IM T TC 1UNIM T

I TC1 b

1UNIM T TC 1 1 b1UNIM T1 TC1 7»

1 A A 100 . tDUH . ~ . 0 t . O dOU f . O A n 200 • DDI ' > n 1 ti t>U 1 4 . 1 . y 1*1 cnl C Cr»

.

"X A A Jul). (Odd . fOd 1* . — 1 • j

-» . f fOdj . cr> •

Ll a a 1 U U >j<1 .

1 no.

- lUUOOi *^ Q l.O 1 II U 3 X . c

c A A OU U « Icjj 1 1 . — l.O 1 A 1 » d

1 9C7Q ~ . 600. 15047. 15050. 1.0 4.0 15046. 5.

700. 17552. 17552, -.9 -.9 17553. 5.

800. 20058. 20060. -1.5 .5 20059. 5.

900. 22565. 22566. -.7 .3 22566. 5.

1000. 25072. 25075. .3 3.3 25072. 6.

1100. 27575. 27577. -2.2 -.2 27577. 6.

1200. 30085. 30083. 2.5 .5 30083. 6.

1300. 32586. 32584. -1.4 -3.4 32587. 7.

1400. 35092. 35090. -.0 -2.0 350^2. 8.

1 o u u . 375^5. 37596. X • J \J r J - 1 1 . 1600. 40104. 40102. 3.7 1.7 40100. °.

1 f O U • 42604. 42599. 1 . X — (I Q tto1 '*+ .

1 n

1 q o n loUU • 45110. 45108. d . O

tic; 1 f)~7 1 1 XI.

1900. 47607. 47609. -3.1 -1.1 47610. 12.

2000. 50116. 50113. 3.2 .2 50113. 13.

CALIBRATION READING 33195.00

0/1 RATIO SWITCH SET TO 3 MV/V

DEFLECTION = (A) + ( B ) (LOAD

)

+ (C) (LOAD SQUARED)

WHERE A = - 2.3151°6+00 UNITS

3 = 2.509041+01 UNTTS/LBF

C = - 1.643605-05 UNITS/(LBF SQUARED)

STANDARD DEVIATION r 2.065774+nO UNITS

UNCERTAINTY = .20 LRF

* * * * ***** ****** * * MINIMUM WORK IN 3 LOAD = 400.00 LPF AS .05 PERCENT REF. STD.

MINIMUM WORKING LOAD - oQ.OO LPP Fop ASTM METHOD E4.

B-l. HORIZONTAL LOAD CELL CALIBRATION DATA

32
O'.'fj T TAB - MATIONAI '- : ^T A NPARDS LOAn CFI L C

A LT np ATTor'

*LH LOAD CELL N iC . "<">231-A# ^LH I MP| TCAT0R M 0. 1^fiH Q 21 3.04/10. 36. 3-A

CAPACITY 2^00 L

P F COMPRESSION Arjn TENSION JANUARY 7»1 Q 7^

CO*iP!>FSSTON C\LI n &£TTON 9 A T A FO n 23 HFGRFE5 C PEFLECTIO' IS OBSERVED 9FVT*TIC M FROM OFFLECTIONS CHANGE "0'-'

DURING CALIBRATION CALIBRATION FQUATION AOJUSTFD jr- p^c-yronS

APPLIED -------- -------- CALIPRATIOM CALIBRATION

LOAH RUN 1 P'l'N 2

P "N 1 RUN 2 FOUA T T onj EQUATION

L-jF units UNITS LIMIT

1 o n • 29Q7

.

2998

.

2 . 2 20 ft 5Q90 . 6992 • - , g 3 0 c

.

8935

.

6986 • -? . 3 ^ V M •

i 1 anq 11 996

.

, q

bCO. 14°77. 1U979, -4.3

60')

.

1707p

.

17980. -.a

700. 20977. ^0979. . 1 600. 23H72. 23976. -3.3

90 0 . 2697?. 26976. -2.0

1000. 29958

.

?Q970. -5.?

110 0. 32972. 32976. -.7

120C . 55°73. 3^978. . 4 1300 . 33971. ^3976. -1 .8

14 0 0 . 41 Q75. 41980. 1 .5

1500 . 44Q68. 44972. -6.5

1 bOQ . 47976, 47980. . 0 17C0. 50976, 50981

.

-1 .8

1600. '53977. 53982

.

-3.0

1900 . 56964. 5698*. 1.5

2000. 699*2. 5<=982. -3.5

UNTTS L'\TTS UNITS

3. ? 2 QQ 5

.

-u

,

1 .

3

5991. _ c -1.3 8937.

,o 11934. -7.

-2.3 14931

.

- p . 1 .

1

17979. -9.

2.1 2P c>-7 7, -10.

.7 23 o7 5. -1 1 . 2.0 26°7 4. -12.

-3.2 29^73. -1^.

3.3 32977. -13.

5.

a

3^973. -I 7 . 3.? 333-7^

.

-1".

6. c 41974. -20.

-2.5 44975

.

-21

.

4.0 47976. -23.

3.2 50978

.

-24.

2.C 53930

.

-26.

3.5 56 QQ 3. -2 s5 . -3.5 5"985. -33.

CALIBRATION READING 5m 54.00

DtFLECTTON - (A) + (R) (LOAP) + fC) f LOAP 50UARED)

ft'HFPE A - -9.370117-01 UNTTS

R - 2.P95499+OI UMITS/LBF

C = 1.^11303-05 UNTTS/(LRF ^OMApr^)

STANDARD DEVIATION = 3.040775+00 UNITS

UNCERTAINTY - . ?4 L pt7

MINIMUM WORKING LOAD = 4*0. nr> L p F A3 .06 Pcrpr^ T PFF. S T ">. MINIMUM WORKIM3 LOAD = 05.no |_ p F F^n /VSTM MFTHOH FU.

NOTE: Use cable with 1500 ohm resistor permanently attached.

B-2. VERTICAL LOAD CELL CALIBRATION DATA

33
Appendix C. The Calibration Box

Figure C-L Schematic Diagram of One Force Channel of the

Calibration Box

34
CD
NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBSIft 75-738

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

A METHOD AND MEANS OF CALIBRATING AN AIR-BEARING FORCE PLATE

FOR USE WITH A TOWED PAVEMENT -FRICTION TEST TRAILER

5. Publication Date December 1974

6. Performing Organization Code

7. AUTHOR(S)

Robert W. Kearns, John F. Ward

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 2130440

11. Contract/Grant No. InterAgency Government Order

1-1-1261

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Federal Highway Administration

Washington, D. C. 20234

13. Type of Report & Period Covered

Final

14. oponsonng Agency Code

FHWA

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less (actual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

The equations for the variation of the external forces acting at the tirepavement interface of a symmetrical two-wheeled towed trailer are given. Estimates,

derived from experimental results, have been made for the displacement of the tireplate interface with respect to the ground of an unrestrained locked tejst tire on

the trailer. A description of the force plate calibration test frame, instrumentation

and test method is given. The means of applying simultaneous vertical (normal) and

horizontal (longitudinal) forces at the contact surface of the air-bearing plate in

accordance with the equations are discussed. The change in force plate output with

changes in the. dimensions of the trailer calibrated in-turn with the force plate are given. A method of locating the coordinate axes of the internal force sensors with

respect to level is given. Consistent application of these methods to both the

force plate and trailer transducer calibrations results in reduced vertical-tohorizontal cross-axis differences.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons

)

Calibration procedures; force plate; pavement skid resistance; skid accident

reduction; tire-pavement interface forces.

18. AVAILABILITY [x] Unlimited 19. SECURITY CLASS

(THIS REPORT)

21. NO. OF PAGES

| | For Official Distribution. Do Not Release to NTIS

UNCLASSIFIED 40

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Washington. D.C. 20402. SD Cat. No. C13

Office 20. SECURITY CLASS

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