NBSIR 76-1175

The Static Force Calibration

of a Skid Resistance Measuring

System

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 1976

Final

Prepared for Federal Highway Administration

Office of Development

Washington, D. C. 20590

NBSIR 76-1175

THE STATIC FORCE CALIBRATION

OF A SKID RESISTANCE MEASURING

SYSTEM

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 1976

Final

Prepared for Federal Highway Administration

Office of Development

Washington, D. C. 20590

U S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary

Edward O. Vetter, Under Secretary

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

NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Acting Director
V
Federal Highway Administration Policy Statement

The opinions, findings, and conclusions expressed in this

publication are those of the authors and not necessarily those

the Federal Highway Administration.
*
Foreword

This report was drafted in May, 1973 to describe calibration

tests conducted by the authors on the skid resistance measuring system

designated by the FHWA as the Interim Reference System. Since that

time, the skid trailer has undergone several modifications, therefore

the data reported here may not represent the IRS as it exists today.

The equations and techniques, however, still apply to the IRS and

similar skid measuring systems, and may be useful to anyone involved

in skid resistance measurement programs.

The text has been revised from the 1973 draft.

i
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 in 2 = 6.4516* x 10 4 meter2

Force 1 lbf = 4.448 newton

*Exact values

ii
CONTENTS

Page

Foreword

1. INTRODUCTION 2

2. CHARACTERISTIC MOTIONS OF THE SYSTEM 4 2.1. Equations of Static Equilibrium 4

2.2. Traction Induced Motions 11

2.3. Discussion 28

3. THE WHEEL TRANSDUCER AS A DETECTOR OF SKID RESISTANCE 37

3.1. The Effect of System Variables on Skid Number 38

3.1.1. Hitch Height Variation 38

3.1.2. Hitch-to-Axle Length Variation 39

4. STATIC CALIBRATION OF THE WHEEL TRANSDUCER INSTRUMENTATION

USING A FORCE PLATE 40

4.1. The Importance of Procedure in Calibration of

the Force Plate 40

4.1.1. Positioning the Load on the Force Plate 46

4.1.2. The Combined Load Problem 46

4.1.3. Vertical Load Reduction 50

4.1.4. Lateral Force 50

4.1.5. Force Plate Displacement 53

4.1.6. A Combined Load Fixture for Calibration

of the Force Plate 53

4.1.7. Force Plate Reference Resistors 58

4.2. The Importance of Procedure in Calibration of

the Wheel Transducer Instrumentation 58

4.2.1. Tow Vehicle Characteristics 58

4.2.2. Trailer Characteristics 60

4.2.3. Transducer Orientation 60

4.2.4. Force Plate Operation 60

4.2.5. Free Wheel Support 61

5. MEASURED EFFECTS OF THE SYSTEM VARIABLES ON THE

CALIBRATION RESULTS 61

5.1. Hitch Height Variation 61

5.2. Trailer Weight Variation 64

5.3. Lateral Force Variation 64

5.4. Test Tire Center of Support Variation 69

5.5. Test Tire Inflation Variation 69

5.6. Test Wheel Temperature Variation 69

6. SUMMARY AND CONCLUSIONS 75

7. REFERENCES 77

iii
ILLUSTRATIONS

Page

1 . The FHWA interim reference skid measuring system ....... 3 2. Free body diagram of skid trailer with traction

applied 5 3. Suspension details 12

4. Shearing of the free tire (front view) 13

5. Trailer displacement measurement locations 14

6. Lateral displacement of the axle 13

7. Displacement of the trailer body at location 8 15

8. Shearing of the free tire and decrease in radius 16

9. Lateral displacement of the hitch. 17

10. Lateral displacement of the tow vehicle axle 17

11. Increase in test wheel radius 19

12. Forward displacement of the free wheel hub 20

13. Rearward displacement of the test wheel hub 20

14. Displacements associated with roll and pitch 21

15. Displacement of location 2 with change in traction

force 22

16. Displacement of the hitch 23

17. Displacement of the tow vehicle rear axle 24

18. Rotation of the left parallelogram suspension 25

19. Rotation of the right parallelogram suspension 25

20. Displacement of the force plate with respect to the

axle 26

21. Vertical force sustained by the test wheel 27

22. Lateral force test setup 29

23. Lateral force measurements 30

24. Vertical force sustained by the free wheel 31

25. Suspension forces given by computer program 33

26a. Trailer body yaw displacement vectors 35

26b. Effect of tow vehicle and tires on yaw instant centers .... 36

27. Use of the force plate 41

28. IRS wheel transducer calibrated with modified state

force plate 43

29. IRS wheel transducer calibrated with movement eliminated

in the mechanism of the modified state force plate 44

30. IRS wheel transducer calibrated with modified state

force plate with normal movement of the force plate

mechanism, after correction of a machining error 45

31. Locations of vertical test loads applied to the IRS

force plate 47

32. Modified state force plate. The platform has been

removed to show the roller bearing and screw mechanism .... 49

33. IRS force plate vertical load calibration 51

34. IRS force plate traction calibration 52

35. Displacement of the IRS force plate with respect to

the ground 54

iv
Page

36. Displacement of the IRS force plate with respect to

the axle for a warm tire and a cold tire 55

37. Change in test tire radius due to traction for a warm

tire and a cold tire 56

38. Calibration fixture for air-bearing force plate 57

39. Change in IRS hitch height with removal of water load 59

40. Change in wheel transducer traction output with hitch

height 62

41. Change in wheel transducer vertical output with hitch

height 63

42. Increased trailer body weight test 65

43. Change in wheel transducer traction output with change

in trailer body weight 66

44. Change in wheel transducer traction output with change

in shock absorber inflation pressure 67

45. Change in wheel transducer traction output with lateral

force applied at the tire-pavement interface 68

46. Change in wheel transducer traction output with lateral

force applied at the test wheel hub 70

47. Lateral displacement of the effective center of support

of the test tire 71

48. Change in wheel transducer traction output with lateral

displacement of the center of support of the test tire .... 72

49. Change in wheel transducer traction output with test

tire inflation pressure 73

50. Change in wheel transducer traction output with test

tire temperature 74

v
TABLES

1. Summary of static equilibrium forces

(with fwr

= 0) - X

2. Variation of IRS force plate vertical output due to

position of vertical test load.

3. Effects of system operating variables on the IRS wheel

transducer traction calibration.

Page

10

48

76

vi
THE STATIC FORCE CALIBRATION

OF A

SKID RESISTANCE MEASURING SYSTEM

R. W. Kearns and J. F. Ward

ABSTRACT

A variety of skid resistance measuring

systems have been designed to meet the requirements of ASTM Method E 274. When these systems

are compared on the same pavement, the measurements often vary widely. This report describes

procedures for the calibration and control of one such measuring system, the FHWA Interim

Reference System. This system employs a tow

vehicle and two-wheeled skid trailer. The procedures are chosen to minimize errors, leading

to an increased confidence in the measurement

results.

Equations of static equilibrium for the

skid trailer are derived and experimentally

verified. The motions of the system in re- sponse to static force are measured and

shown to depend on tow vehicle as well as trailer characteristics. Variables affecting

the force calibration are identified. These

include hitch height, trailer weight, lateral

force on the test tire, center of support of

the test tire, temperature of the test tire

and force transducer, and inflation pressure.

The use of a force plate as a calibrator

is described. It is shown that the calibrator

must itself have been calibrated under con- ditions covering its use with the trailer.

Calibration of the force plate under combined

vertical and traction force is described.

The procedures are adaptable to other

similar skid resistance measuring systems.

Key Words: Accident reduction, skidding;

highway safety; measurement, skid resistance;

pavement skid resistance; skid resistance

measurement; tire-pavement interface forces;

wet pavement skid resistance.
1. INTRODUCTION

The improvement of the skid resistance at the tire wet-pavement

interface is one of the important means of reducing automotive traffic

accidents. Slippery pavements must be identified before the condition

can be corrected. One means of identifying slippery pavements is to

measure the skid resistance using ASTM Method E 274-70. There are a variety of skid resistance measuring systems whose design is reported to

meet the requirements of the method. Unfortunately, the measurements

made with these systems lack precision and measurements made by these

systems on the same pavement vary widely. The trailer and tow vehicle

of the FHWA interim reference system (IRS) are shown in figure 1. The

method utilizes a measurement of the horizontal traction force on a locked standard test tire (ASTM E 249-66) as it is dragged over a wetted

pavement surface under constant load and at a constant speed while its

major plane is parallel to the direction of motion and perpendicular to

the pavement. In the system shown, the test tire is mounted on a towed

two-wheel trailer. The wetting of the pavement is controlled in amount

and distribution with the assistance of a flow channel located ahead of

the test tire. The horizontal traction force and the vertical wheel

load force are detected by a transducer associated with the test wheel.

The wheel transducer signals are conditioned and recorded within the tow

vehicle. The tow vehicle contains a supply of water. The system also

includes a speed detector and associated calibration equipment.

This report is directed toward one phase of the measurement process — the static calibration of the wheel transducer when it is mounted on the trailer and a traction force is applied at the tire-pavement interface. The traction force is applied by means of a force plate which

establishes a reference plane for the traction force. The traction

force is not the only force acting at the tire-pavement interface. The

vertical wheel load acts at the tire-pavement interface and an axial

force may or may not act there also. While the traction force applied

by the force plate is the input to the skid resistance measuring system

and the signal from the traction channel of the wheel transducer is the

desired output from the system, the design of the trailer and its method

of use affect the transfer from input to output.

The three dimensional force acting at the tire force-plate interface varies with the magnitude of the input force, the system design

characteristics, and the characteristics of the force plate. The characteristics of the force plate may alter the output signal from the

wheel transducer, since the force plate may not accurately simulate the

tire-pavement interface forces occurring in highway use. The effect of

the input traction force on the displacement of the system is discussed

in section 2. The forces and moments applied to the wheel transducer

are discussed in section 3. The calibration equipment and the calibration procedures for the force plate itself are discussed in section

4. Errors in the measurement process can occur, but their effect can be

minimized as discussed in section 4. The calibration procedures can

2
Pn

3

'igure

1.

The

FHWA

interim

reference

skid

measuring

system.
affect the results of calibrating the wheel transducer which is discussed in section 4. The calibration is conducted under static

conditions, however, the conditions change during operation. The

effect of certain changes can be estimated from the discussion in

section 5. These changes can be related to changes in skid number

which is discussed in section 3.

While the numerical values apply to the FWHA interim reference

system (IRS) as of this date, the process and techniques can be repeated

on any system to verify the skid measuring system design and analysis

with tests and observations. The correlation between theory and measurement will lead to an increased level of confidence in the measurement

results and may identify other parameters which should be controlled

during calibration and use of the system.

2. CHARACTERISTIC MOTIONS OF THE SYSTEM

The trailer and tow vehicle system can be described by a set of

mathematical equations relating the input to the output of the system.

A block diagram is a simplified device for the same purpose. The

physical elements appearing in block diagrams are described by a term

called the "transfer function." An input traction force at the tirepavement interface is modified by the transfer function of the trailer

and tow vehicle to an output from the wheel transducer. From a knowledge of the output from the wheel transducer alone, it is impossible to

distinguish between a change in the tire-pavement traction force and a change in the transfer function of the trailer and tow vehicle. The

transfer function of the IRS is such that during the static force

calibration, the application of the horizontal traction force changes

the equilibrium forces of the skid measurement system resulting in

translation and rotation of the trailer body, trailer axle, and tow

vehicle. A detailed knowledge of these changes is helpful in the design

of calibration equipments and test procedures. Application of this

knowledge can minimize measurement errors by controlling additional

variables of the measurement process and guiding system design improvements. In this section, the applicable force equations and the translations and rotations of the IRS trailer are given. Also, the correlation

between theory and measurements is experimentally verified.

2.1. Equations of Static Equilibrium

A free body diagram of the skid trailer is shown in figure 2. The

diagram is more general than that required by the ASTM method in that

there is provision for a horizontal traction force at both wheels. In

the following paragraphs, we develop equations for each of the external

forces acting on the trailer as a function of the horizontal traction

force, which is the input to the system. In the equations,

x = the horizontal longitudinal axis

y = the vertical axis

4
X

X X

_i oc £ £

0H

i—

I

ft

ft

03C

O

5

Figure

2.

Free

body

diagram

of

skid

trailer

with

tracti
z = the horizontal (lateral) axis

F

WL

x the traction force on the left wheel

the traction force on the right wheel

the total vertical force on the left wheel acting at the

tire-pavement interface

F

WR

= t *ie vert i- ca l force on the right wheel acting at the

y tire-pavement interface

AX = the effective longitudinal position of F^ with respect to the

wheel vertical center line x

r = the distance between the tire-pavement interface and the wheel

horizontal center line when FTTT = 0

WL

x Ar = the change in r

F _ = the lateral force on the right wheel

WR

z Fitt = the lateral force on the left wheel

WL

z L = the length from the center line of the trailer wheel to the hitch

AL = the change in L

F = the longitudinal force on the hitch

Hx

F = the vertical force on -the hitch

ri y

F = the lateral force on the hitch

H

z H = the height from a level pavement to the hitch

AH = the change in H

W = the total trailer weight

T = trailer wheel track width, center-to-center

H = the location of the center-of-gravity along the longitudinal

center line with respect to the trailer axle.

When a traction test is performed on the left wheel,

F > F

WL WR

x x

6
and since an air-bearing force plate is used

F

WL

°*

z Referring to the trailer top view and summing moments about the hitch.

WL

x \2 )

F

WR

x \

2 J

F

WR

z L ,

or ? - F \ — = F

WL WR 2L WR

X X / z

( 1 )

Refering to the trailer end view and summing moments about the hitch again.

fwr

h + fwl [2) fwr

z y

' / y

or fwr T + f

wl fwr

z y y

( 2 )

Referring to the trailer side view and summing moments about the hitch.

wa-O - <F

to + ) L + <F + F ) H. (3)

y y X X

Substituting equation 2 into equation 3, we obtain

W (L-£) = 2 fwr T + f

wl

z y

L + (fwr + f

wl > H • (4) x x

Substituting equation 1 into equation 4, we obtain

T

W (L-£) = 2 (FWL

F

WR ^ 2L T + F xx WL

y

2 (fwl

h + fwl L) - X y

L + (fwr + f

wl > H

X X

(5)

When Fwl = 0, . x y yo

arranging we obtain

Substituting this into equation 5, and re-

, , w .Jicil

WL 2L

y°

or i = L 1-2

WL

2 w

_^o ( 6 )

7
Substituting equation 6 into equation 5, we obtain

F. WL ~ W

WL

L (1 - 2 w

“ 2(fwl h + f

wl l) - X V

or

*WL

FWL

F

WL

y yo x

( 7 )

Equation 7 indicates that the vertical force on the test wheel decreases

as the horizontal traction force on the test wheel increases. This

result is used later in developing the force plate calibration procedures.

The skid resistance of the paved surface is reported as skid number,

SN, which is defined under the conditions of E 274 by the equation

SN =

fwl (100)

X

F

WL

f

wl (100>

X

f

wl

f

wl

yo x m

( 8 )

in which

F^ = the force required to slide the locked test tire at a stated

x speed while encountering a controlled water layer, and

FI7T = the effective wheel load.

WL

y

The reduction of vertical load on the free wheel is obtained by

substituting equation 1 into equation 2, giving

(FV - F )—(— )+ F = F

WL WR ' 2L V T / WL WR (9)

Substituting equation 7 into equation 9, we obtain

(F — F

^~ + F — F

WLxxWR ' L WL WL

yo 2

or WL

- F.WR

yo x But for a symmetrical weight distribution

— j = F

L WR

t- = F.WR

F = F WL WR

yo yo

8
therefore,

F

WR

= r WR

" FWR

y yo x

or the vertical force on the free wheel behaves as the vertical force on the test wheel. However, as the free wheel has no traction force occurring, the vertical force on the free wheel does not change from the "at

rest" value.

To obtain the variation of the load on the hitch as a function of

traction we refer to the trailer side view again and use the sum of the

forces in the vertical direction to get

( 10 )

F + F + F = W

H WL WR

y y y

or F = W - F - F

H WL WR

y y y

Substituting equations 10 and 7 into equation 11, we obtain

(ID

But,

Therefore,

+ F.WL

H

L

fwr + fwr

yo y

H

L

WR + (F

yo

WL + F.WR

H

L

W -

+ 2 (FWL + F.WR

H

L

( 12 )

Equation 12 indicates that the hitch force increases by the amount the

vertical forces on the wheels decrease. When there is no traction on the free wheel, the hitch force increases by the amount the vertical

force on the test wheel decreases.

An expression for the lateral force on the test wheel is not developed here. During a wheel load transducer calibration using an airbearing force plate, the lateral force on the test wheel is zero. Should the force plate resist a lateral force developed at the test

wheel the total lateral force as given by equation 1 is shared between

both trailer wheels.

A summary of the static equilibrium force equations of the skid

trailer is given in table 1. 9
Table 1. Summary of static equilibrium forces

(with fwe

= 0) x

Force Equation

Lateral force on the

free tire

TT = "F WE WL

z x

(1)

Vertical force on the

test tire

ip — L ' xp WL WL ” WL

y yox ( 7 )

Skid number

Vertical force on the

free tire

Vertical force on the

hitch

+ ( 13 )

Lateral force on the

hitch

Longitudinal force on the

hitch

10
2.2. Traction Induced Motions

The changes in the equilibrium forces with the application of the

horizontal traction force, as previously described, result in translations and rotations of the trailer and tow vehicle. Since the wheel

transducer is mounted on the axle, which in turn is coupled to the

trailer body through the suspension system, the movement of the trailer

changes the output from the wheel transducer. In this section, the

translations and rotations accompanying the application of a static

horizontal traction force will be identified and quantified. It will

also be shown that a given skid trailer will have a different static

(and hence dynamic) behavior when the tow vehicle and/or the tires of

either vehicle are changed since the tow vehicle characteristics and the

tire characteristics of both the tow vehicle and trailer influence the

translations and rotations of the trailer body.

From equation 1 it can be seen that as the force plate traction is

increased, lateral force is generated at the free-wheel tire-pavement

interface. For equilibrium, an opposing lateral force is developed at

the hitch point. The lateral force at the hitch acts through the

trailer body which transfers the force to the trailer axle through the

suspension system springs and the sway bar. (The suspension system

details for the trailer are shown in figure 3.) Thus there is a displacement of the trailer body with respect to the axle. The hitch force

appears at the axle and places the free tire in shear with the lateral

force at the tire-pavement interface. The shearing of the tire results

in a vertical displacement of the axle with respect to the pavement as can be seen from figure 4. Displacements are measured at the points

numbered in figure 5.

The lateral displacement of the axle with respect to the pavement

due to changes in horizontal traction force are given in figure 6. The

displacement of the trailer body with respect to the pavement due to

changes in traction force is given in figure 7. At 800 pounds of traction force the axle moves laterally, in the opposite direction to the

lateral tire-interface force, 0.37 inches, and the body moves 0.57

inches

The shearing of the free tire is accompanied by a decrease in the

free wheel radius as shown in figure 8. At 800 pounds of traction, the

axle moves downward 0.05 inches. The tire on the free wheel of the FHWA

interim reference system was an ASTM E 249-66 standard test tire.

The horizontal • force developed at the hitch is resisted by the tow

vehicle. In a similar manner to that already described, the tow vehicle

suspension and tow vehicle tires are subjected to the same shear force.

The variation in displacement of the hitch and axle of the tow vehicle

with variation in traction force are given in figures 9 and 10 respectively. The hitch is displaced 0.25 inches and the axle displaced 0.12

inches toward the test side when the traction force is 800 pounds.

11
Figure 3. Suspension details.
Figure 4. Shearing of the free tire (front view).

13
Figure 5. Trailer displacement measurement locations.
Figure 6. Lateral displacement of the axle.

Figure 7. Displacement of the trailer body at location 8.

15
Figure 8. Shearing of the free tire and decrease in radius.

16
Figure 9- Lateral displacement of the hitch.

Figure 10. Lateral displacement of the tow vehicle axle.

17
The test wheel radius changes too, but it increases since the

vertical load on the test tire decreases as traction increases. (See

eq. 7.) The increase in test tire radius with increase in traction is

shown in figure 11. At 800 pounds of traction force, the test wheel

radius increases 0.05 inches.

During a force plate test the hub of the free wheel moves forward

very slightly as the traction force is increased. At 800 pounds of

traction force the free wheel hub moves forward 0.020 inches. This

displacement is given in figure 12. However, during a force place test

the test wheel hub moves rearward 0.70 inches when the traction force is

800 pounds. The rearward displacement of the test wheel hub is given in

figure 13.

During a force plate test, the trailer body rotates in roll, pitch,

and yaw. The displacement measurements associated with roll and pitch

are made at locations 3, 4, 5, and 6 and are shown in figure 14. Location

6 is lower than location 5 and location 3 is lower than location 4 by

approximately 1.1 inches when the traction force is 800 pounds. This

1.1 inch displacement is in roll attitude. Location 3 is lower than

location 6 and location 4 is lower than location 5 by 0.15 inches when

the traction force is 800 pounds. This 0.15 inch displacement is in

pitch attitude. Yaw attitude changes are related to rotation about an instant center and will be discussed later. A displacement of location

2 is related to yaw and is given versus traction force in figure 15.

The complete displacement of the hitch is given in figure 16 while

the complete displacement of the tow vehicle rear axle is given in

figure 17.

The rotation of the left parallelogram suspension arms is given in

figure 18 while the rotation of the right is given in figure 19. The

rotation is plotted as a deviation from the orientation with F = 0.

WL

X

The rearward displacement of the force plate with respect to the

axle is given in figure 20 while the vertical force sustained by the

test wheel is given in figure 21. No slipping of the force plate with

respect to the tire or of the brakes was observed.

Experiments were conducted and measurements made to confirm the

changes in force stated by the equations. Also, the variation in

internal forces was calculated to confirm the observed change in length

of the suspension springs. The correlation of theory and measurement

enhances the degree of confidence one can place in the output measurements. After the system is modified and ready for use, additional

detailed work will be appropriate in this section.*

*Since this material was written, the suspension has been modified such

that the parallelogram trailing arms are horizontal when the trailer is

at rest. With this arrangement, arm rotation and trailer body roll due

to traction have been substantially eliminated.

18
INCREASE,

(in)

Figure 11. Increase in test wheel radius.

TRACTION

19
0.6

0

(D SPLACEMEIV T 1)

^

200 40 0 "—600 80c

TRACTION (|bf)

Figure 12. Forward displacement of the free wheel hub.

Figure 13. Rearward displacement of the test wheel hub.

20
DROP

(in.)

R'SE

(in.)

, TRACTION (Ibf)

TRACTION (Ibf)

0 200 400 600 800

mm i <o ISPLACEIV ENT 5

//

//

0 200 400 600 800

TRACTION (Ibf)

TRACTION (Ibf)

Figure l4. Displacements associated -with roll and pitch.

21
RIGHT

/ (in

)

TRACTION,(lbf)

Figure 15- Displacement of location 2 with change in traction force.

22
2 3

Figure

l6.

Displacement

of

the

hitch.
( u

!) 24 d n !VDIld3A

Figure

17.

Displacement

of

the

tow

vehicle

rear

axle.
LEFT

SUSPENSION

4

RIGHT

SUSPENSION

25

Figure

18.

Rotation

of

the

left

parallelogram

Figure

19

.

Rotation

of

the

right

parallelogram

suspension.

suspension.
0.6 r

(DISPLACEMENT 14)

200 400 600 800

TRACTION, Ibf

Figure 20. Displacement of the force plate with respect to the axle

26
WHEEL

LOAD

TRANSDUCER

VERTICAL

.LOAD

Figure 21. Vertical force sustained by the test wheel.

27
To experimentally confirm equation 1, both trailer wheels were supported on an air bearing and lateral force, F , was measured with

1 z a load cell. The experimental setup is shown in figure 22 and the test

results are given in figure 23. There was no traction force applied at

the free wheel. The lateral force increased proportionately with an increase in horizontal traction force. Rewriting equation 1 and using T

= 64 inches and L = 120 inches,

= 64= 1_

2L 2(120) 3.75

At 800 pounds traction the axial force was measured to be 210 pounds.

These values are equivalent to a ratio of 1/3.81. The theory and experimental verification agree within 1.6 percent.

Equation 7 indicates that the vertical force on the left wheel

decreases as the horizontal traction force increases. To verify this

result, the vertical load on the force plate was recorded while the

horizontal traction force was increased. The experimental results are given in figure 21. The initial load was 1092.5 pounds. (Additional

fixtures and dial gages weighing 7.5 pounds affected that force plate at

this time.) As the traction force was increased to 800 pounds, the

vertical load declined to 980 pounds. For H = 14.7 inches and L = 120

inches, the theoretical change in vertical load is 98 pounds, while the

measured value was 112.5 pounds. The theory and experiment agree within

15 percent.

Equation 10 indicates that the vertical force on the free tire

remains constant as the traction force is increased. To verify this

result the vertical load on the free tire was measured by means of an air-bearing force plate while the traction force was applied to the test

tire by means of another air-bearing force plate. Lateral force was restrained at the trailer axle. The experimental results are given in

figure 24. The vertical force remained constant within 5 pounds for a change in traction force of 800 pounds. The theory and experiment agree

within 0.6 percent. To evaluate the change caused by floating both

wheels instead of allowing the free wheel to shear under lateral force,

the air supply to the force plate under the free wheel was interrupted.

The test was repeated, hence, the second trace, with the result that the

vertical load remained constant but shifted by two pounds as shown in

figure 24.

2. 3. Discussion

It has been shown that the traction force generates a lateral force

which displaces the axle in the direction of the free tire and places

the free tire in shear (fig. 8). With no traction force present on the

free tire, the axle displaces outward (fig. 6) shearing the tire and

shortening the wheel radius (fig. 8). At a point on the hub, outward

28
29
250 (*qi) ' 3Daod lvadivi

z

o

»—M

<

Q£

<

o.

UJU

Q£

oLL.

30

Figure

23.

Lateral

force

measurements.
FORCE

PLATE

VERTICAL

OUTPUT

(Ibf)

v

f

200 400 600 800

wheel load transducer traction ( ibf

Figure 2h

Vertical force sustained by the free wheel.

31
of the free wheel, the axle moves slightly forward (fig. 12). Simultaneously, the test wheel is moving rearward (fig. 13) and due to the

reduction in vertical load, the test wheel radius increases (fig. 11).

The motion of the skid trailer axle consists of a lateral displacement toward the free wheel, a rolling of the axle due to the additive

effects of the changes in both wheel radii, and a yawing of the axle.

The axle yaw angle constitutes a steering angle and tends to steer the

skid trailer out of the tow vehicle trajectory.

While the equations given apply to the external forces acting on

the skid trailer, a computer program is being developed to study the internal forces acting on the skid trailer components. It is interesting

to note that the trailer rolls downward at the test wheel, while the

vertical load on the test wheel is being reduced, implying that the sus- pension spring is required to support more vertical force when the

traction is applied than when it is not. A portion of the numerical

results from the program are given in figure 25. All the forces acting

on the component of the suspension system of figure 3 are not given. As

shown, the force sustained by the spring on the test wheel side increases while the force sustained by the spring on the free rolling

wheel decreases. The nominal spring rate of the suspension springs was measured as 460 pounds/inch. By reviewing figure 16 for a traction

force of 400 pounds and using the trailer dimensions, the roll of the

trailer nominally agrees with the computer program solution. This

result is also in agreement with the measured rotations of the parallelogram linkages (figs. 18 and 19). The pitching of the trailer is

nominal compared with the rolling of the trailer.

The horizontal force developed at the hitch is resisted by the tow

vehicle. In a similar manner to that described for the skid trailer,

the tow vehicle suspension and the tow vehicle tire are subjected to a shear force. The hitch is displaced laterally 0.25 inches toward the

test wheel side (fig. 16) while the axle also moves laterally 0.12

inches in the same direction (fig. 17) when the traction force is 800

pounds. This would indicate that the horizontal spring rate of the tow

vehicle suspension system and the shear spring rate of the tow vehicle

tire are about equal since the deflections are equal under the same force. These results apply to the case of no water load. The vertical

spring rate of the tow vehicle suspension is non-linear with load (fig.

39). The horizontal spring rate may also depend on the water load.

While the magnitudes of the hitch forces depend on the trailer dimensions, notice that the magnitudes of the yaw displacements depend on the

spring rate of the tow vehicle, the spring rate of the tow vehicle

tires, and the spring rate of the trailer free tire (fig. 26).

The horizontal traction force develops a longitudinal force at the

hitch which is resisted by the tow vehicle. It is shown in figures 16

and 17 that this force resulted in the same displacement of the rear

axle as occurs at the hitch. Consequently, the longitudinal spring rate

32
1247

33

400

Ibf

TRACTION

APPLIED
of the tow vehicle suspension is quite high with respect to the longitudinal spring rate of the tow vehicle tires. Thus, the properties of

the tow vehicle tires determine, to a great degree, the longitudinal

displacement of the hitch.

The instant center of axle yaw rotation is about the laterally displaced footprint of the free tire. The trailer body yaw displacements

are shown in figure 26a as displacement vectors in the horizontal plane.

Each vector is identified by the system component which influences the

displacement the most. It is interesting to note how much the yaw

rotation of a given trailer depends on the tow vehicle and free tire

characteristics. Figure 26b indicates the changes in the instant center

location which correspond to changes in tow vehicle and tire characteristics. As the spring rate of the tow vehicle suspension and the tow

vehicle tires are made stiffer, the instant center of yaw rotation moves

further from the trailer so the trailer body rotates through a smaller

angle for the same hitch forces.

The trailer suspension design does determine the axle angular rotation which accompanies the trailer body rotation. The FHWA IRS trailer

axle rotation is nominally 2.5 times the body rotation. We do not want

the trailer to steer out of the tow vehicle trajectory, so we would not

want the axle to yaw. However, provision must be made for some axle

yawing so the trailer can make turns without scuffing the tires. The

trailer axle yaw should not be a large multiple of the trailer body yaw.

This ratio may be considered a f igure-of-merit for the trailer suspension system design. If the trailer is required to negotiate turns

without scuffing the trailer tires, the ratio must be greater than one.

It is interesting to note that if the trailer axle was rigidly mounted

in the trailer body, the axle would still rotate due to the characteristics of the tow vehicle and the tires of both vehicles. The asso- ciated scuffing might cloud the skid resistance measurement.

The trailer body pitches downward at the hitch due to the transfer

of vertical force from the test wheel to the hitch.

The foregoing paragraphs describe the motions of the trailer and

tow vehicle which occur under increasing and decreasing traction force.

These movements are related to the changes in the external forces acting

on the trailer and tow vehicle system which accompany the application of

a traction force at the tire-pavement interface. A set of mathematical

equations relating the system motions to the traction force would

constitute a "transfer function." Knowledge of the transfer function is

required to understand the relation of the wheel transducer output to

the traction force.

It is suggested that similar displacement measurements be made on other skid measuring systems and that the motions also be correlated with

the change in external forces which accompany the application of lateral

force to better understand the measuring systems. In the following

sections it will be shown that the application of this knowledge to the

calibration process can control and reduce measurement differences.

34
Figure 26a. Trailer body yaw displacement vectors.

35
TOW VEHICLE TIRE

TRAILER TIRE

TOW VEHICLE HORIZ.

SUSPENSION

TOW VEHICLE

T I RE

Displacements ——

Instant Condition Tow vehicle Trailer

center

Tire

Horizontal

suspension Tire Suspension

percent percent percent percent

1 Normal 100 100 100 100

2 Stronger tow

vehicle suspension

100 0 100 100

3 Stronger tow

vehicle tire

0 100 100 100

4 2 and 3 combined 0 0 100 100

5 Stronger trailer

tire

100 100 0 100

6 Stronger trailer

suspension

100 100 100 0

Figure 26b. Effect of tow vehicle and tires on yaw instant centers.

36
3. THE WHEEL TRANSDUCER AS A DETECTOR OF SKID RESISTANCE

The skid resistance to be measured occurs at the tire-pavement

interface. For practical reasons, the wheel load transducer is located

on the axle away from the point of application of the force. While a simple traction force is applied to the system by means of a force plate

(sec. 4) the force at the tire-pavement interface also includes vertical

and lateral components. The distributed forces at the tire-pavement

interface may be viewed as a general force of three rectangular com- ponents acting at an effective footprint. The effective footprint moves

with changes in the tire characteristics [1]*.

When a force is translated to a parallel position in space, while

maintaning rigid-body equivalence, a couple-moment is simultaneously

generated. Since the transducer is located on the axle, remote from the

force, the transducer is subjected to both generalized force and a generated moment. The moment can also be resolved into rectangular com- ponents so that the load on the transducer consists of three force

components and three moment components. The weight of the wheel and

components located between the footprint and the transducer are additional forces applied to the transducer during a static calibration.

Dynamic and inertial forces also act on the transducer during use.

The characteristics of the tow vehicle and trailer influence the

vertical component and the lateral component of the generalized force

acting in the tire-pavement interface. Also these characteristics influence the movement of the transducer with respect to the effective

footprint. By calibrating the transducer while it is installed in the

trailer and while the trailer is attached to the tow vehicle some of

these variables are taken into account. However, the calibration equipment to be described is subjected to the varying external forces

accompanying the application of the input traction force. The calibration equipment too, has a transfer function which depends on the characteristics of the system with which it is used. From a knowledge of

the output from the calibration equipment alone, it is impossible to

distinguish between a change in the traction force and a change in the

transfer function of the calibration equipment occuring under different

load conditions. The wheel load transducer is calibrated under varying

force conditions which depend on the method of using the trailer. There

is a need to calibrate the calibration equipment under the same varying

force conditions, as will be discussed in succeeding sections.

*Numerals in brackets denote the literature references cited at the end

of this report.

37
3.1. The Effect of System Variables on Skid Number

The skid resistance of paved surfaces measured in accordance with

the ASTM method E 274-70 is given in terms of skid numbers (SN) where

f

wl

SN = -—- x 100

f

wl

y

For trailers where F is not measured directly, wheel load reduction

y

is taken into account by means of equation 7, and equation 8 is used to

calculate the skid number:

SN 100 ( 8 )

Paragraph 1.2 of the ASTM method states:

"The method utilizes a measurement representing the

steady state friction force on a locked test wheel as it

is dragged over a wetted pavement surface under constant

load and at a constant speed while its major plane is

parallel to its direction of motion and perpendicular

to the pavement."

The yaw angle of the axle tends to steer the trailer on a trajectory such that the test tire's major plane is not necessarily

parallel to its direction of motion.

3.1.1. Hitch Height Variation

Many of the variables are related to a change in hitch height,

leading to rotation of the wheel transducer. In some cases the effects

are additive. The change in skid number for a change in hitch height

with the other values remaining constant is

8 (SN)

3H

x

L (100)

f

wl

f

wl

yo x

therefore.

3 (SN) =

(SN)

2 9H

100L

38
For a skid trailer with an L dimension of 120 inches, and measuring

a skid number of 50, for a -one inch change in hitch height, the change

in SN is

asN

(50)

2

( 120 )

( 1 )

( 100 ) 0.2

3SN

=

CL_2

SN 50

0.4%

The change in hitch height also results in a change of vertical

wheel load. Using equation 7,

WL

Z

3H

When Fttt = 800 pounds, the vertical load is further reduced 6-2/3

WL

x pounds for a one inch change in hitch height. Since the vertical load

is nominally 1000 pounds the additional change with a one inch change in

hitch height is 2/3 percent.

3.1.2. Hitch-to-Axle Length Variation

The footnrint displacement consists of the movement of the force

plate with respect to the axle plus the backward motion of the axle

which is approximately one inch at 800 pounds traction. (SN=80) Taking

the partial derivative of equation 8 again,

3 (SN)

3L

and ~

3 (SN) _ -(SN) _J_

3L 100 l

2

For a trailer with L and H dimensions of 120 and 12.9 inches re- spectively, measuring a SN of 80 the change in SN is

39
3SN

- (80)

2 (12 . 9)

(100) (120)

2 -0.057

SN

3SN -0.057

80

-0.07%

This same change in vertical load occurs at the hitch but in the

opposite direction.

4. STATIC CALIBRATION OF THE WHEEL TRANSDUCER INSTRUMENTATION

USING A FORCE PLATE

An air-bearing force plate is used to apply a traction force to the

trailer at the tire-pavement interface, during a static calibration of

the wheel transducer. In this section, the force plate and the fixture

for calibrating the force plate are described.

The force plate has two outputs, vertical load and horizontal

traction. Strain gages are mounted on internal beams such that the

beams bend in a vertical plane when a vertical load is present on the

plate and the beams bend in a horizontal plane when a horizontal traction force is applied to the plate. The force plate in use with a skid

trailer is shown in figure 27. The force plate is placed underneath the

test tire on the air-bearing platform. Adjustable flow valves are utilized to level the unit by distributing the incoming air to the air

bearings. The traction force is applied through the chain.

4.1. The Importance of Procedure in Calibration of the Force Plate

In this section, the force plate variables are identified. Their

relative importance in a specific application depends on the method of

using the force plate and the principles of design employed in the force

plate. These variables affect the results and should be considered when

developing the calibration procedures. Two force plates were studied; a commercial air-bearing force plate used with the FHWA IRS and a modified

commercial unit of another type, used by a state highway department. It

will be shown that a "small" shop error made during the modification of

the state unit resulted in erratic operation. The occurrence of the error may be considered fortunate since it led to examples for discussion which detail the merits of calibrating the force plate under

conditions of combined loading and force plate mechanism movement which

occur in use.

It is important to identify the crosstalk differences, nonlinearities, and hysteresis loops present in the force plate output.

Otherwise, when the force plate is used to calibrate a wheel transducer,

in an accounting of the errors, differences applicable to the force

plate will be charged to the wheel transducer.

40
4 L

igure

27.

Use

of

the

force

plate.
While using the modified state force plate to calibrate the interim

reference skid trailer an example of this occurred. The procedure rec- ommended for calibration of the force plate utilized an external load

cell. When the screw mechanism was turned, force was applied to the

internal and external load cells but without significant movements of

the force plate mechanism. The force plate calibration curve was quite

linear. When the force plate was then used to calibrate the wheel

transducer the results were as shown in figure 28. The calibration

curve indicates a 70 pound hysteresis loop width at a traction force of

350 pounds. That something was wrong became evident when a review of

the results showed that the wheel transducer output corresponded to more

force than was indicated as being applied by the force plate.

In attempting to identify the discrepancy the modified state force

plate was mounted above the IRS force plate, which in turn was mounted

on its air-bearing platform. The test was conducted without movement of

the state force plate mechanism with the result shown in figure 29. The

output was more linear with only a small hysteresis loop evident. This

result led to an inspection of the mechanism which revealed a machining

error in the modification. The error was corrected and a calibration

test conducted again with the result shown in figure 30.

The manufacturer of the state force plate recommends that a vibration be applied to the force plate by hitting the tire with a heavy

rubber mallet at each static loading before a record of the readings is

made. These results were obtained without the vibration since further

testing indicated the vibration increased the scatter of the data be- cause the direction of the Coulomb friction force was random.

The test results of the wheel load transducer output versus state

force plate traction output are given in figure 28 when rotation of the

screw mechamism of the state force plate occurred and in figure 29 when

rotation of the screw mechanism did not occur. The differences are due

to the mechanism movement which was made abnormal by the modification

error in machining. What is important here is that the procedure used

to calibrate the state force plate did not require movement of the

mechanism through the 1.1 inch displacement occurring during an IRS

transducer traction calibration test. Consequently, the modification

error was not identified during the state force plate calibration. Poor

results later would normally be charged to the wheel transducer rather

than the force plate.

It is clear that the force plate should be calibrated under the

conditions of use. Specifically,

a) The movement of the internal mechanism must be equal to or greater than that which occurs during use.

42
900

800

700

600

500

400

300

200

100

0

IRS WHEEL TRANSDUCER, (Ibf)

?ure 28 . IRS wheel transducer calibrated with modified state force plate.

4 3
MODIFIED

STATE

FORCE

PLATE.

(Ibf)

Figure 29. IRS wheel transducer calibrated with movement eliminated

in the mechanism of the modified state force plate.

44
MODIFIED

STATE

FORCE

PLATE

(Ibf)

0 1 00 200 300 400 500 600 700 800 900

IRS WHEEL TRANSDUCER, (Ibf)

Figure 30. IRS wheel transducer calibrated with modified state force

plate with normal movement of the force plate mechanism,

after correction of a machining error.

45
b) The force plate must be subjected simultaneously to the

external forces which are applied during use. If these

external forces vary, they should vary during calibration

or at least fixed forces which bound the variation in force

should be used.

The output of the force plate is influenced by the location of the

vertical load on the plate. The IRS force plate was mounted in a deadweight machine and subjected to different vertical loads at the seven locations shown in figure 31. Digital printed outputs from the vertical

load channel were obtained by means of automatic signal conditioning

equipment and are given in table 2. This is the variation due to a uniaxial load. Under a combined load the presence of the traction force

would increase the variation (see sec. 4.1.3). The scale factor of the

output readings shown is arbitrary.

The modified state force plate is shown in figure 32. The moving

platform is supported by six roller bearings and moved by means of an Acme screw. The force plate contains a load cell between the platform

and its drive. The drive speed is made continuous and variable by means

of an electric motor and its control.

The manufacturer recommends that the platform be positioned over only four bearings during a test. Since the bearings are stationary the

vertical load changes in location with respect to the bearings as a test

progresses. If the load is initially placed at the center of the platform, the support can change from one set of four bearings to another

set of four bearings, changing the loading conditions, consequently, the

manufacturer's directions lead to an off-center location for the vertical load.

During the force plate calibration of a wheel transducer, the

forces change in accordance with the equations developed in section 2.

The vertical force at the test wheel is reduced in accordance with

equation 7.

The total lateral force shared by the two trailer wheels is given

in equation 1:

4.1.1. Positioning the Load on the Force Plate

4.1.2. The Combined Load Problem

F, (F^ - F ) — WL WR ' 2L

T

WR,Z x x

46
(

ir

CN LaiJ

V

1 T

1. A/ r

--i

,2

1 1 J o C

K

2

£ V;/ l . IT

a ^V

V

DIMENSIONS IN INCHES

Figure 31. Locations of vertical test loads applied to

the IRS force plate.

47
Table 2. Variation of IRS force plate vertical output due

to position of vertical test load

Vertical

load 1 2

Position

3 1+ 5 6 7

lbf

a Reading Deviation from position 1 reading

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

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

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

600 U68 0 +1 +1 +2 0 +3

300 23I+ -1 +1 +1 +1 0 +2

0 0 0 0 0 0 0 0

a Arbitrary units.
Figure 32. Modified state force plate. The platform has been

removed to show the roller bearing and screw mechanism.

49
The lateral force acting at the test wheel should be applied to the

wheel transducer during a wheel transducer calibration. If the force

plate applies this lateral force during the wheel transucer calibration,

the force plate should be calibrated with the lateral force applied to

the plate.

4.1.3. Vertical Load Reduction

When calibrating the wheel transducer of the IRS, the reduction in

vertical load is 112 pounds when the horizontal traction force is 800

pounds. There is a difference between the traction output under a varying vertical load and the traction output under a constant vertical

load. Since the IRS force plate is used to calibrate wheel transducers

of trailers with a variety of geometries, the plate is calibrated for a variety of H/L ratios and FITT values. Values of FtTT from 885 to WL WL

yo yo

1085 lbf are allowable within ASTM method E 274-70. A partial survey of

trailer geometries revealed variations in H/L from 0.093 (Stevens

Institute of Technology) to 0.147 (State of Delaware).

The force plate vertical load channel is calibrated without any

horizontal traction force applied. The vertical load channel is balanced with only the weight of the plate itself acting. The calibration

curve for the force plate vertical load channel, under these conditions,

is shown in figure 33. The output values are in arbitrary units.

If the traction channel is balanced under no vertical load, the

addition of 1085 lbf of vertical load introduces an output of nominally

11 pounds into the traction channel output. To minimize this difference

the horizontal traction channel is balanced with 1085 lbf of vertical

load applied. The calibration curve for H/L ratios from 0.09 to 0.15 at

F of 1085 lbf is given in figure 34.

WL

yo

4.1.4. Lateral Force

The IRS force plate was calibrated without lateral force being

applied to the plate since use of the air-bearing platform eliminates

this force component. When calibrating the wheel transducer the lateral

force acting on the test wheel may be applied experimentally (see sec. 5.3).

To estimate the lateral force that would be present without an air bearing, a static trailer test was conducted where the lateral force

under the free tire was measured while the state force plate which has

no air bearing, was used to apply a traction force to the test tire.

When the traction force was 800 lbf, the lateral force at the free wheel

was 146 lbf. Since the total lateral force was 213 lbf (see sec. 2.2)

the lateral force applied to the state force plate during the application of the traction force was 67 lbf. Thus the design of this force

plate dictates that it be calibrated with three orthogonal components of

force comprising the combined load. Consequently, a calibration fixture

for this force plate must apply three forces simultaneously.

50
FORCE

PLATE

VERTICAL

OUTPUT

(Ibf

)

CALIBRATION BOX OUTPUT VALUES

396 590 786 983 1,181

REFERENCE LOAD CELL OUTPUT, (Ibf)

Figure 33. IRS force plate vertical load calibration.

51
FORCE

PLATE

TRACTION

OUTPUT

(Ibf)

CALIBRATION BOX OUTPUT VALUES

0 200 400 600 800 1,000

REFERENCE LOAD CELL OUTPUT, (Ibf)

Figure lU

IRS force plate traction calibration.

52
Notice from equation 1 that if traction forces of equal magnitude

were applied to both of the tires during use, the total lateral force

generated would be zero and there would be no need to calibrate the

force plate in the presence of a lateral force.

4.1.5. Force Plate Displacement

During a traction test the force plate moves if it is not restrained.

It is important in the force plate calibration procedure to take the

motions into consideration as well as the combined forces occuring

during use (see sec. 4.2). These motions have been identified for the

IRS. The rearward motion of the axle was shown in section 2.2. Note

the large displacement of the force plate with respect to the ground

shown in figure 35. There is also a displacement of the force plate

with respect to the axle. This displacement with changes in traction

force was shown in section 2.2. When the traction force is 800 lbf, the

displacement is 0.3 inches. This displacement is also a function of

tire temperature. The test was repeated after the tire was subjected to

a five mile warm-up run. During the repeat test the tire cooled from

108 °F to 90 °F, although the test duration was only a few minutes. The

displacement of the force plate with traction for the cold tire and the

warmed-up tire is shown in figure 36. For consistent results the warmedup tire temperature should be maintained during the test duration. The

change in test tire radius for the two tests is given in figure 37 (also see sec . 5.6).

4.1.6. A Combined Load Fixture for

Calibration of the Force Plate

The calibration of the force plate requires that a combined load be

generated and measured. Since the air-bearing platform eliminates the

lateral force acting on the force plate, the combined load reduces to

simultaneous vertical load and horizontal traction forces. A calibration fixture for that purpose is shown, with its associated instrumentation, in figure 38. The forces are generated by means of hydraulic

jacks and measured with load cells and universal digital indicators.

The force plate output signals are conditioned and converted to a digital printout by means of the automatic bridge balance unit shown.

Dial gages are used to maintain the attitude of the force plate surface

within 0.01 inches over the length of the plate.

To obtain a datum point the universal digital indicators are preset to the desired force value by the use of the load cell calibration

data. The hydraulic jacks are operated such that the desired combined

forces are applied simultaneously. When this condition occurs the

operator energizes the print-out command. An advantage of the fixture

is that the load cells can be removed and calibrated independently.

53
FORCE

PLATE

DISPLACEMENT,

in

FORCE PLATE TRACTION (ibf)

Figure 35. Displacement of the IRS force plate with respect to the ground.

54
0.5

Figure 36. Displacement of the IRS force plate with respect to the

axle for a warm tire and a cold tire.

55
TEST

TIRE

RADIUS

CHANGE,

(in)

FORCE PLATE TRACTION , ( I b

f)

Figure 37. Change in test tire radius due to traction for a -warm tire and a cold tire.

56
57

Figure

30.

Calibration

fixture

for

air-bearing

force

plate
The vertical load force is applied through a tire similator which

has a rubber area corresponding to that of a standard test tire sustaining a load of 1085 lbf. The horizontal traction force is applied through

a spring which has nominally the same spring rate as a test tire. The

rubber creeps under the combined loads and the spring allows the displacement to occur without unloading the force generated by the hydraulic

jack. The force plate is calibrated while floating on the air-bearing

platform.

4.1.7. Force Plate Reference Resistors

After the IRS force plate was calibrated, five shunt calibration

resistors were precisely adjusted to convenient values for each channel.

The purpose of each resistor is to shunt one leg of the Wheatstone

bridge such that the no-load output signal with the shunt resistor

connected is equivalent to the output signal obtained with a given force

applied. Five resistors are used so that any nonlinearities in the

instrumentation will become evident. The five points also allow the

recorder instrumentation scale to be expanded and still retain three

points to identify nonlinearities. The traction channel resistor values

were trimmed while the force plate was subjected to a vertical load of

1085 lbf.

Resistors constructed of materials with low temperature coefficients are used so changes in the calibration values with changes in

ambient temperature are reduced.

4.2. The Importance of Procedure in Calibration

of the Wheel Transducer Instrumentation

4.2.1. Tow Vehicle Characteristics

The wheel transducer calibration should occur with the skid trailer

mounted on the tow vehicle. It has been shown in section 2.2 that the

characteristics of the tow vehicle influence the motion of the trailer

during use and during a calibration test. Since the tow vehicle characteristics influence the results, the tow vehicle should be in its

normal operating condition.

Tests were conducted on the IRS tow vehicle to determine the change

in hitch height with changes in water load and fuel consumption. The

water load results are shown in figure 39. In order to minimize the

change in hitch height with water load consumption the system can be

operated with the tank always nearly full. Otherwise, a linear cor- rection for change in hitch height due to consumption of water can be

made. When the water tank is full, the change in fuel has a small

effect on hitch height. The effect may be larger in another system.

Deadweights were placed in the cab during the tests to simulate the

weight of the occupants.

58
>

o

0

<

9

ocLU1

Figure

39-

Change

in

IRS

hitch

height

with

removal

of

water

load.
It is interesting to note that when these procedures were followed

in calibrating another skid resistance measuring system, the occupant

weight had a greater effect on hitch height than did the entire water

load. A small truck was used as a tow vehicle, and the rear springs had

been reinforced to accommodate the water load, but the front springs were not altered. Consequently, the occupant weight compressed the

front springs thereby pivoting the truck and changing the hitch height.

This incident supports the importance of restricting transport of cargo

in the tow vehicle to further control hitch height.

4.2.2. Trailer Characteristics

The mathematical analysis of the trailer and the calibration of the

force plate assumed that the at-rest forces are at their nominal values.

It has been shown previously that the magnitude of crosstalk differences

depends on the nominal load values. Accordingly, before the wheel

transducer is calibrated, the center of gravity and weight of the trailer

are trimmed so the trailer wheel load forces are both 1085 lbf and the

vertical force at the hitch is within 100 to 200 lbf when the trailer is

properly oriented.

This operation is best conducted with an air-bearing force plate

under each trailer wheel. A stationary hitch ball mounted on a load

cell completes the set-up for simultaneous measurement at the three

points of support. The results are quite sensitive to the orientation

of the trailer.

4.2.3. Transducer Orientation

The transducer must be properly oriented on the trailer, establishing the traction axis parallel to the pavement. To accomplish this,

the transducer may be rotated with respect to the axle, or, the rotation

may be made by a change of hitch height. In either case, the trailer is

alternately lifted and lowered while the transducer is rotated until the

change in output of the transducer traction channel caused by the vertical load is minimized. The adjusted transducer and trailer orientation

must be maintained since, when the transducer is misalined, application

of force will give rise to false outputs.

4.2.4.

Force Plate Operation

Tests were conducted to compare the technique of re-orientating the

air-bearing force plate before taking each datum point to the technique

of a continuous recording without re-orienting. It was found that, if

the force plate was always supported on a film of air, no difference in

the output of the wheel transducer was evident. However, during a test,

it is still necessary to maintain the force plate orientation within

bounds consistent with the desired force plate accuracy.

60
4.2.5. Free Wheel Support

Tests were conducted to' investigate if the method of support of the

free wheel influenced the results. In one test, the free wheel was also

supported on an air bearing with the lateral force being applied through

a point on a load cell at the tire-pavement interface (sec. 2.2). In a second test, the air bearing was deactivated while the restraining point was retained. In a third test, the air bearing was deactivated and the

restraining point was removed. No difference in the results of the

three tests was evident.

5. MEASURED EFFECTS OF THE SYSTEM

VARIABLES ON THE CALIBRATION RESULTS

The wheel transducer has been calibrated on the trailer in a static

condition under rather idealized conditions. To identify the sources

and the magnitude of output variations which accompany variations in

system operation, a series of tests were conducted which will be described in this section.

5.1. Hitch Height Variation

It has been shown that changes in water load, fuel load, occupant

load and hitch load change the hitch height with respect to the pavement. To identify the magnitude of the changes in transducer output due

to changes in hitch height, the height was changed and the transducer

outputs recorded and presented as in figures 40 and 41. A one-inch

change in hitch height shifts the horizontal traction channel output by

8.3 lbf (fig. 40). This is due to the rotation of the transducer which

accompanies the change in hitch height. The parallelogram linkages keep

the transducer level with axle motion only if the trailer body remains

level. Since there is 1085 lbf vertical load present, and the tangent

of the pitch angle is 1/120, the change in horizontal traction output

due to the component of vertical load is

9 lbf.

The vertical load does decrease according to equation 7 with an increase

in traction so the offset is slightly smaller at the higher traction

forces. When the change in hitch height is upward, the component of the

vertical load subtracts from the traction measurement. When the change

in hitch height is downward, the component of the vertical load adds to

the traction measurement.

61
IRS

WHEEL

TRANSDUCER

TRACTION,

Ibf

800

600

400

200

200 400 600 800

IRS FORCE PLATE TRACTION^Ibf

Figure Lo. Change in wheel transducer traction output with hitch height.

62
IRS

WHEEL

TRANSDUCER

VERTICAL

OUTPUT

IRS FORCE PLATE TRACT ION, (ibf)

Figure U 1 . Change in wheel transducer vertical output with hitch height.

63
The change in hitch height also affects the vertical load output of

the wheel transducer as shown in figure 41. At zero traction the vertical output is slightly reduced since only a component of the weight

is being measured. When the change in hitch height is downward, a component of the increasing traction force further reduces the vertical

output. When the change in hitch height is upward, a component of the

increasing traction force increases the vertical output. As the traction

increases to 800 lbf, the contribution is

Changes in the vertical load on the trailer body change the pitch

angle of the trailer which rotates the transducer in a manner analogous

to a change in hitch height. A test to measure this effect is shown in

figure 42 with the results given in figure 43.

There is also a rotation and resultant change in the wheel transducer output for a change in the shock absorber inflation pressure if

the trailer is not re-oriented. As shown in figure 44, when the shock

absorber air spring inflation pressure is reduced from 70 psi to 20 psi,

the output of the transducer shifts 6 lbf. However, if the trailer is

re-oriented at 20 psi inflation pressure, the transducer output returns

to its normal characteristic. Additional test results show that the

offset is proportional to the change in shock absorber inflation pressure .

As mentioned in section 5.1, when a 600 pound additional load was

located on the trailer body symmetrically over the axle, the traction

output changed. However, when the trailer tongue was re-oriented, the

transducer output returned to its normal characteristic. The effective

change in hitch height was 1-5/8 inches. Since the change in transducer

output with change in hitch height is nominally 8 lbf /inch, the expected

change was 13 lbf. The measured change was 13 to 15 lbf.

Recall that the wheel transducer was calibrated in the absence of

lateral force acting at the test tire-pavement interface due to the use

of the air-bearing platform. This also simplified the calibration of

the force plate. However, during skids, the test tire is acted upon by

a portion of the lateral force generated in accordance with equation 1.

To estimate the effect of the lateral force, the test shown in figure 45 was conducted with the results shown in the accompanying graph. The 200

lbf acting at the tire-pavement interface is equivalent to a tension

force and a moment applied at the wheel axle. The presence of the

lateral force lowered the traction output by 14.4 lbf when the traction

800

5.2. Trailer Weight Variation

5.3. Lateral Force Variation

64
Figure b2. Increased trailer body weight test.

65
800

66

FORCE

PLATE

TRACTION,
67

FORCE

PLATE

TRACTION
800

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force was 800 lbf (however, the displacement of the axle caused a com- ponent of the 200 lbf tension force in the cable to act in the traction

direction. This component amounts to 13.5 lbf). To isolate the effect

of the moment from the tension force at the axle, the tension test of

figure 46 was conducted with the results shown in the accompanying

graph. For a 200 lbf tension load, the change in output is one lbf when

the traction is 800 lbf. Again, the difference between the 7 lbf change

shown in figure 46 and the one lbf result is attributed to the rotation

of the cable due to the displacement of the wheel. Proportional results were obtained when 100 lbf and 50 lbf were used for the tension force.

Accordingly, the greater part of the change in the wheel transducer

output which occurs when lateral force acts at the test tire-pavement

interface is due to the tendency of that force to bend the transducer.

5.4.

Test Tire Center of Support Variation

Displacement of the effective center of support in the lateral direction within the tire-pavement interface changes the output from the

wheel transducer. This lateral displacement would accompany a roll

motion of the trailer. To measure this effect the test tire was supported on a narrow block which was located on the force plate. Tests were conducted with the block located outboard, inboard and centrally

with respect to the tire center line. The force plate was displaced

laterally with the block so the force plate remained centrally loaded.

The test set-up is shown in figure 47 with the results shown in figure

48. The change is greater as the moment arm about the transducer is

increased tending to bend the transducer more. The lateral displacement

introduced an offset and a change in slope in the traction output test

results. The change between run 1 and run 2 is nominally small. The runs should not be compared by using only the change in slope values.

The result of both offset and slope must be compared.

5.5.

Test Tire Inflation Variation

The wheel transducer output changes with changes in test tire inflation pressure. The test wheel radius also changes with inflation

pressure. The test results are shown in figure 49. The coefficient of

change is nominally 1/5 lbf/psi change in inflation pressure. Since a change in wheel radius tilts the trailer, a re-orientation of the

trailer may eliminate the effect.

5.6.

Test Wheel Temperature Variation

Two series of tests were conducted to investigate the effect of

test wheel temperature on the wheel transducer calibration. The first

concerned the change in radius between a warm and cold test tire and the

change in the force plate displacement when the test tire was warm and

when it was cold (sec. 4.1.5). In the second series the test wheel was enclosed and the temperature within the enclosure was raised. The en- closure was free to move with the force plate as shown in figure 50.

69
IRS

WHEEL

TRANSDUCER

TRACTION,!

IRS FORCE PLATE TRACTION ,( Ibf

)

Figure b6. Change in wheel transducer traction output with lateral

force applied at the test wheel hub.

70
Figure h'J

Lateral displacement of the effective center

of support of the test tire.

71
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72
IRS

WHEEL

TRANSDUCER

TRACTION

Figure L9. Change in wheel transducer traction output with test tire inflation

\

73
800

FORCE

PLATE

TRACTION, (I

bf)
As the temperature increased to approximately 230 °F, the traction

channel output shifted 12 lbf, also shown in figure 50. A thermometer

touching the wheel transducer surface indicated 104 °F. Since the

transducer was located outside the enclosure, heat from the test wheel

was transferred to the transducer establishing a temperature gradient across the transducer. Subsequent temperature tests of the wheel

transducer alone, in an oven of uniform ambient temperature, indicated a temperature coefficient of 0.14 lbf offset per °F in the traction

channel and 3 lbf offset per °F in the vertical load channel.

6. SUMMARY AND CONCLUSIONS

This report has described the static calibration of one skid re- sistance measuring system (the IRS) designed to meet the requirements of

ASTM method E 274-70. The response of this system to static traction

force has been quantified. Operating variables have been identified

which should be controlled during calibration and use of the system.

The effect of the variables on the response has been quantified. Calibration and control procedures which minimize errors and lead to increased confidence in the results have been described. The procedures

can be adapted for use with any similar skid resistance measuring system.

Equations of static equilibrium for the skid trailer have been

derived and experimentally verified. The motions of the trailer under

static loading have been quantified. The results of the measurements

may be the basis for design modifications for improved performance. The

motions have been shown to be influenced by deflection of the tow vehicle

in response to forces at the hitch and by deflection of the free trailer

tire. To include these effects, skid trailer calibration should be

conducted with the trailer hitched to the tow vehicle and the tow vehicle

should be in its normal operating configuration. The characteristics of

the tow vehicle tires and of the free trailer tire should be controlled

in addition to the test tire characteristics.

It has been shown that a force plate used as a calibrator must

itself have been calibrated under conditions covering its use with the

trailer. A method for calibrating the IRS force plate has been described.

The effects of system operating variables on the IRS wheel transducer traction calibration are summarized in table 3.

75
Table 3. Effects of system operating variables on the IRS wheel

transducer traction calibration

Operating variable Effect on traction output

Change in hitch height

Upward

Downward

-8.3 lbf / in

+8.3 lbf / in

Change in vertical load

on trailer body

-Ih lbf

600 lbf vertical

Presence of lateral force at

test tire-pavement interface

-lh.h lbf @800 lbf

200 lbf lateral

Lateral displacement of the center

of support of the test tire

-6 lbf @800 lbf

1.5 in

Change in air shock absorber -6 lbf

inflation pressure -50 psi

Change in test tire 1 lbf

inflation pressure 5 psi

Change in test tire and

transducer temperature

15 lbf

135 0 F

76
7. REFERENCES

[1] Goodenow, Kolhoff, and Smithson, Tire-road friction measuring

system — a second generation, SAE paper 680137.

77
NBS-1 14A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBSIR 76-1175

2. Gov’t Accession

No.

3. Recipient’s Accession No.

4. TITLE AND SUBTITLE

The Static Force Calibration of a Skid Resistance

Measuring System

5. Publication Date December 1976

6 . Performing Organization Code

7. AUTHOR(S)

Robert W. Kearns and 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.

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

Federal Highway Administration

Department of Transportation

Washington, D. C. 20590

13. Type of Report & Period

Covered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

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

bibliography or literature survey, mention it here.)

A variety of skid resistance measuring systems have been designed to meet the

requirements of ASTM Method E 274. When these systems are compared on the same pavement, the measurements often vary widely. This report describes procedures for the

calibration and control of one such measuring system, the FHWA Interim Reference

System. This system employs a tow vehicle and two-wheeled skid trailer. The procedures are chosen to minimize errors, leading to an increased confidence in the

measurement results.

Equations of static equilibrium for the skid trailer are derived and experimentally verified. The motions of the system in response to static force are measured

and shown to depend on tow vehicle as well as trailer characteristics. Variables

affecting the force calibration are identified. These include hitch height, trailer

weight, lateral force on the test tire, center of support of the test tire, temperature

of the test tire and force transducer, and inflation pressure.

The use of a force plate as a calibrator is described. It is shown that the

calibrator must itself have been calibrated under conditions covering its use with

the trailer. Calibration of the force plate under combined vertical and traction

force is described.

The procedures are adaptable to other similar skid resistance measuring systems.

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

)

Accident reduction, skidding; highway safety; measurement, skid resistance;

pavement skid resistance; skid resistance measurement; tire-pavement interface

forces; wet pavement skid resistance.

18. AVAILABILITY [~X] Unlimited

For Official Distribution. Do Not Release to NTIS

[X] Order From Sup. of Doc., U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No. Cl

3

I ! Order I rom National Technical Information Service (NTIS)

Springfield, Virginia 22151

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(THIS REPORT)

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20. SECURITY CLASS

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22. Price

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