Thurs fur the Degree of 5.4. 5
NICHJCAN STATE COLLEGE

Litiidfd C) , SC-llil'fi'idi‘l’
9 ‘

 

H
S
E
H
T

 

 

 

 

A STUDY OF AUTOMOBILE RIDING QUALITY

THESIS
Submitted as Part of the Requirements for the Master of Science

Degree.

by
Leonard Gustav §g§nggder

1958

TH ENG

 

Acknowledgment
I desire to acknowledge the interest and aid of Professor G. W.

Hobbs in the work herein outlined.

11“?“7SM-

l.
2.
5.
4.
5.
6.

7.

TABLE OF CONTENTS

Object

Introduction

Apparatus and Procedure
Discussion

Conclusions

Appendices l, 2, 5, 4, and 5

Bibliography

-1-

OBJECT
The object of this paper is the formulation of certain conclu-
sions, the application of which will result in improved car riding
quality.
Theory underlying the problem of ride will be investigated, and
a verification of theoretical conclusions by means of experimentation

on a model will be attempted.

INTRODUCTION

In the early days of motoring, those fortunate enough to travel
by automobile were concerned with certainty of arrival at a destina-
tion rather than with certainty of comfort in transit; it is, there-
fore, not unusual that efforts by manufacturers were directed along
the line of improving reliability of the motor car. In our day one
takes the reliability of a car as a foregone conclusion, and so it
is not surprising that the popular thought has been directed to the
next most desired quality of a car, namely, good riding quality.

For years no appreciable advance along this line was attempted
on a sure foundation; it is true that some manufacturers tried lar-
ger springs with some improvement in ride, however, the prevailing
Opinion was "call in the tire and shock absorber men and let them
work out our problem.” As a result of this, cut and try methods
were largely resorted to. The "absorber“ men reasoned that the
body should be more firmly fixed to the axle, and that high inter-

nal friction or so called "self damping“ springs should be used to

avoid body gallop. This resulted in not only a still more uncomfort-
able ride, but also a relatively unsafe one. The tire men, reasoning
correctly, developed softer or "balloon" tires, finally some even
proposing “donut" tires to get a maximum cushioning deepite the in-
herent steering and wheeling difficulties imposed by the latter.
However, it was soon evident that something deeper was at fault and
thus experimental investigations were started.

Various organizations collected voluminous data by experiment,
and from it modified the design of succeeding models; the basis for
Judgment, however, was the opinion of test drivers on the "feel" of
the ride. For the purpose of argument, it will be granted that one
is after a ride pleasant to the occupants; however, it is a well
known fact that Opinion varies greatly, and so it seemed that some
scientific method of ride evaluation should be determined. At pre—
sent the S.A.E. has a committee which is endeavoring to design in~
struments and set up procedures for testing; also some manufacturers
during the past few years have set up certain standards as necessary
to good riding quality by use of apparatus of their own devising.

The results obtained thus are valuable, but are, of course, empiri-
cal to a great degree, and it would be interesting to know what
actually are the underlying principles involved.

A few men have approached the problem theoretically; among these
is Timoshenko, who is noted for his work in vibration. He gives a
short but complete consideration to the problem in "Vibration Problems
in Engineering", and it is hoped to use this as the basis in investi-

gating the agreement of theory and practice.

-5-

PROCEDURE

To check the correctness of facts gained from examination of
theoretical material, it is necessary to run a test program on either
an actual car or a model. The idea of working with a test model is
fundamentally sound, especially in the case where an investigator's
facilities or funds are limited. In view of the above, a test model
was decided upon for the gathering of the experimental portion of the
experiment.

The apparatus designed by the writer and described herein is not
the first of its kind; the Chrysler Research Lab built the first in
1954; however, the two machines are of unsimilar construction, and
the information obtained therefrom is used differently. The Chrysler
machine was used only to get a practical weight distribution to give
the least spring reaction, this information then being used to locate
the engine in the Airflow models of 1954.

-The apparatus used in this test consists of a driving motor and
reduction gear box, model apparatus, and tape driving device (see
Figs. 1, 2, and 5). The model consists of two parts or "towers", both
similar in construction, and each supporting one end of the "body bar.”
The tower is the supporting system for a 6" diam. plywood wheel driven
from the gear box by V belt, and so constructed that wedges can be
fastened to its periphery; this is equivalent to the road. Resting
on the "road wheel" is a 2" diam. plywood wheel having a yoke on its
axle, and guided by slots in the tower frame. On the bottom of the
yoke is a spring of desired tension, and it is fastened to one end of

thebodybar.

.4-

Fig. l — Model Apparatus

Car Model Wheel

Road Wheel

Yoke

Spring

Body Bar

Guide Drum

Backing Plate and Tape Guide
Body Bar Guide

Tower Frame

Pen

Weights

-5-

 

 

Fig. 2 - Tape Driving Device

Driving Motor (Const. Speed DC)
Switch

Tape Guide

Driving Drum

Worm and Pinion Drive

Pinion and Gear Drive

Tape Takeoff Guide

Model Apparatus

 

 

-7-

 

 

 

Fig. 5 - Driving Mechanism

A - A C Motor
B - Gear Box

C - Model Apparatus

-9-

 

 

 

 

 

 

 

 

-10-

The body bar is loaded with weights of one-half pound, one pound,
and two pounds in such a way that any weight combination and distri-
bution may be obtained. At the point of attachment of the springs,
the body bar carries recording pens, one to record front body movement
in red ink, the other to record rear body movement in green ink on the
moving paper tape.

The tape driving device was the source of considerable difficulty
which necessitated considerable rebuilding before satisfactory Opera-
tion was assured. The device used at first comprised a paper tape
pulled against a backing plate through suitable guides and wound on a
drum driven by a small constant speed motor with worm reduction gear—
ing. With this model, results were obtained which would have been
sufficiently accurate for a cursory examination. However, due to
the fact that the radius of the paper drum was constantly changing
(paper being wound around the drum), and the motor was apt to slow
down very slightly if the tape had a tendency to stick, the abscissae
scale of the tape was ever changing slightly and therefore the driv—
ing unit was redesigned and rebuilt.

The present unit as shown in the figure is made up of a larger
constant speed motor, a worm reduction system, and a constant dis-
placement type of driving drum.

In this manner difficulties are overcome, since first, the driv-
ing motor has sufficient power to always run at constant speed; sec-
ond, by not rolling the tape or the drum, but using pins in the peri-

phery of the drum to give a positive diaplacement, a constant abscis-

-11-

see scale is available as is verified by measurement.

V The operation of the apparatus is as follows: wedges in any
desired combination are placed on the road wheels, and the desired
springs and weights placed on the body bar. The tape driving mech-
anism is started and the position of the tape adjusted so the body
bar pens trace a clear line on the tape without friction. The main
motor is started and revolves the road wheels, and as a result also
the car wheels, since they roll on the road wheels. As a wedge
strikes a car wheel, the wheel and all its complementary mechanism
(yoke, spring, and end of body bar) are diaplaced, and as the wheel
again runs on the road wheel, the spring and body bar continue to
oscillate; the whole sequence of events being recorded on the tape.
Ride analysis is made on the basis of tapes.

As will be brought out in the discussion, the problem of ride
brings out a pecularity that the car body oscillates about two cen-
ters; these centers shift with a change in springing, and an attempt
was made to investigate this also by use of the apparatus. A special
body bar with stylus working on sensitized paper was made, but after
numerous trials with graphical computations, it was found that no
check could be obtained with the present set up. This phase of ride
is therefore discussed only in theory.

Unsprung weight has some effect on riding quality, but due to a
lack of time and the fact that this is a study in itself, only the
factors of springs and weight distribution are considered. It would
seem that weight distribution could be investigated by use of the

same or similar apparatus.

-12-

DISCUSSION

The problem of good riding quality in an automobile is one in
vibration prevention. Any structure has a certain frequency of vi-
bration to which it will respond; such frequency is called its nat-
ural frequency Of vibration. It is possible to give a momentary
impulse to the system which will cause the structure to oscillate in
its given period, the oscillations gradually damping out. Now, the
disturbing force may be of such nature that it gives impulses in step
with the natural frequency. This is troublesome since the amplitude
of vibration of the structure may become so great as to cause fail-
ure; also if one has a body vibrating at some frequency, it is possi—
ble to have a disturbing force acting just Opposite to the vibration
and thus damp it out, or if the period of the second disturbing force
is different from the body oscillation period, alternate reinforce-
ment.and damping of oscillations may take place.

By an analysis of the situation, it becomes evident that in an
automobile the latter case is generally the rule. Before vibration
theory was fully understood, it was thought that a certain system of
suspension could be deveIOped which would be self damping, i.e. the
vibration caused by spring action in passing over bumps from front to
-rear would be damped out due to action of one spring on another. That.
this is possible of accomplishment for a given Speed no one will deny,
and in the older cars where thirty-five M.P.H. was driving speed, such
a design was perhaps advantageous in obtaining a better ride at this

speed. Today, however, our cars are driven at road speeds of forty-

-15-

five to eighty which complicates the matter beyond solution by this
means, for the time ensuing between a reaction on a front spring due
to a bump and a reaction on a rear spring due to the same bump is very
evidently determined by the speed of the car, while the rate of vibra-
tion of the car springs is fixed. Because of this complexity in the
problem of ride quality, more fundamental ways of bettering riding
quality must be resorted to.

In the trend of modern thought, the problem of ride must be
analyzed from the viewpoint of vibration theory. Research by General
Motors shows the following vibrations as affecting the problem:

First, main body vibration (60-150 cycles/min. for different
cars.)

Second, tire vibration (250-550), in which car oscillates
on tires only.

Third, vibration of unsprung masses (400-600), in which
tires with accompanying unsprung mass leave ground and then
bounce as a rubber ball.

The first factor only will be considered in this paper, the others
each being problems in themselves. Elements affecting this factor are
springs, weight distribution, and shock absorbers; the latter affecting
the problem mechanically only.

From Newton's second law F = Ma the underlying principles of rid-
ing comfort and the accompanying principle of safety are drawn. The
force deiivered to a vehicle striking an obstruction depends on the

acceleration given the vehicle, determined by the Speed with which it

{‘4'

I ‘T“\‘

owe, ”W V‘

r F 6 090"“
P
a (000- «

. -l4-

     

 

it
3

 

; Ame/emit}: fine?" .5.

I
I
i
$

1

 

 

1 AM a. :
Jabs/(ea j onc/ 76+ce
We»: ”44/ plff'oc/e 76V

2;;

 

60

-15-

travels on impact. In a vehicle having no springs, this force is enor-
nous (see Fig. 4); in fact equaling the average (5400#) car weight at
twenty-eight M.P.H., so that at speeds greater than this the car leaves
the road resulting in a dangerous ride due to lack of control. Also

a car subjected to large impact forces from the road will naturally
have its life shortened due to damaged parts, and again we have sac-
rificed safety.

In a car with hard ride characteristics one, however, is not only
sacrificing safety, but also comfort. Everyone has experienced the
uncomfortable sensation induced by great acceleration or deceleration
of a vehicle in motion; the picture in the vertical or "ride" plane
is similar. The greater the acceleration in a vertical direction,
the greater the discomfort of the passengers.

Consider a system composed of a weight suspended by a spring.
Under the action of the weight W the spring is stretched a certain
amount 6 and the system is in equilibrium since 6 K = W where K is
the Bpring constant . If now the weight is displaced downward, the
spring force is increased in prOportion to the elongation of the

spring ; write the general equation

F = W + Kx
where
F = total spring force
x = displacement from center

If now the force displacing the spring downward is removed, vi-

brations will result because of spring force, and a problem in dyna-

-15-

mice is set up. However, by applying D'Alemberts(l) principle, a pro-
blem in dynamics can be reduced to one in statics, therefore proceed
as follows: in motion, forces acting on the body are (l) gravity W,

downward +, (2) spring force W + Kx, upward -. Therefore,

i913; =W- (W+Kx)
g dt 2

or ‘fl'dzx = - Kx
gdt2

Simplify by dividing through by E_ and let §g_ = m2
g W

then d2x+m2x‘FO

3??

This is the equation of motion, and is a differential equation of the
second order, the general solution being

x = Cl sin mt + Cg cos mt
Determine the constants by the boundary condition;

when x = x0 V =.Q£.= 0 (at instant of release t = 0)
dt

substituting

H
O

02 = xo since Cos mtJt = o = 1 Sin mtJt = 0
Now differentiate the general solution with respect to t

glm-mcl cos mt 4- mo sin mt
dt '

substituting in boundary conditions
Cl = 0
Solution then becomes
1 = x0 cos mt which is the equation of simple harmon-

ic motion. In order for the motion to complete one complete cycle

 

(1) See Kimball, or better Timoshenko - Engineering Mechanics - Dynamics.

-17-

t must equal 2 77
m

or T = 2 77
m

 

where T is period

butf=_l_._
T

where f - frequency cycles/sec.

 

 

f = m
2 7T
2 -
Since m - §g_
w
f = l 1/ §g_
2‘fi' w
but 6:31
K

 

.', f = l or f = 5.15 43 = const = 586 in./sec.
2” is v?

or the frequency varies inversely as the square root of the deflection
and depends only on it.

The acceleration in SHM is given by

a = 47:2 x Let 411?- = a const.fl
T2
,2 a =/?x f2

or the acceleration varies directly as the frequency squared.

A basis is now available~for setting down the fundamental prin-
ciples of springing.

To obtain a low acceleration, the static deflection under load
(and only the deflection) must be made large.

To do this it is necessary to either use softer springs or in-

-18..

crease the load each carries, however, the first is to be preferred
as will be shown now. Discomfort in ride due to a road obstruction
may be divided into two parts, direct (that from body rise)’and po—
tential (that resulting from free oscillation of springs). It is
evident that when a car passes over a bump the height of bump equals
the spring deflection plus the body rise. If it were possible to
keep the body rise at zero, no acceleration in a vertical direction
would ensue, and therefore a ride of maximum comfort would result.
Since this is impossible, it is necessary to use a spring of maximum
deflection to keep body rise at a minimum, i.e. minimum direct effect.
However, a spring having a large deflection will return to zero, then
oscillate Just as far in an Opposite direction, drawing the body with
it, therefore, the softer Spring brings up the disadvantage Of a
greater potential effect. The obvious solution, of course, is the
employment of a suitable damper or absorber to damp the free oscilla-
tion. The question now naturally arises;

What frequency is most suitable for comfort, and what deflec-
tion must therefore be used? .

Experiment on human subjects alone can answer the question.
General Motors engineers by use of the bouncing table set the table
at 80 cycles/min.(2), and Chrysler engineers at 70 to 100. On the
basis of previous theory, a frequency - deflection curve for springs
might be constructed (see Fig. 5) to determine the required frequency,
but the result would be slightly in error due to the fact that the

system is supported by two Springs rather than one. When this is

(2) See S.A.E. Journal, Vol. 2—0 P. 7.7

 

 

 

' 2"

§

K
~-__ee4h6%_—meaaa.

 

-19-

panes-.5 - A

a;

_. - Ala-i- __ f ._ _ .m- _._ _

@uoac/ ’ a/[ec £10” (rye

7%. 1/ m, ”12/,”
$24.”. !

 

.3

U , wig-M-
bl—

-20-

true, the theory for simple suSpension is not exactly fitting, although
it will give approximate results. For this reason it is necessary to
consider the problem according to Timoshenko's methods.

For the theoretical consideration of the problem of vibrations of
vehicles, reference is made to Timoshenko's "Vibration Problems in
Engineering"(5). Although study has enabled the writer to follow the
reasoning behind most of Timoshenko's discussion, several of his steps
in the solution are too widely separated, and due to inability to find
suitable references, it was necessary to assume the author's correct-
ness of solution on these points. The time and Space necessary for a
complete step by step presentation of the theoretical aspects are not
justified in a work of this nature, therefore a brief sketch with re-
sults is given here.

Timoshenko considers the vehicle as having only a motion in one
plane (as apparatus), therefore the problem involves two degrees of
freedom, an up and down freedom of motion, and a rotative freedom of
motion. By dealing with increase and decrease in energy, substitut-
ing in.LaGrange's equations, the equations for free vibrations of the
vehicle are obtained, and these are solved giving finally a frequency
equation which has two roots as the solution.

(5) To those interested in reviewing the complete presentation,

see ”Vibration Problems in Engineering" - Timoshenko - P. 128. Also
the following, which should be read as an introduction to the above.

“Vibration Prevention in Engineering" — Kimball.
"Engineering Mechanics - Dynamics“ - Timoshenko (Chapters on
Motion). .
In "Vibration Problems in Engineering"
Articles 24, 25,'26, and briefly 28 and 29.

-21-

In the theory the coordinates are designated
Z = vertical diaplacement of CG of body
6 t angle of rotation of body about CG

The equations of free vibration are

i'z‘: - mz - 11 e) - K2(z + 12 e)
3 (1)
g-iz'é = 11 K1(Z - 11 e) - 12 K2(Z + 12 e)
(i designating the second derivative of Z)
The frequency equation is
(a-p2)<.e--p2>-1_>£=o (2)

i2 12

whose roots are (above considered as equation in pa)

 

 

p2=l (2-+a):v.l_(9-+a)2-ae+193 (5)
2 12 4 12 12 12
=.1.(c +6):V.1_(£_-a)2+?23 <4)
2 ';§ 4 12 12

very evidently then there are two frequencies of vibration (therefore
two modes), one of higher frequendy on using the + sign in (4), and
one of lower frequency on using the - sign.

Using equation 4, Timoshenko assumes the following data and solves
for frequency;

= spring weight = 966#

12 = rad. of gy. = 15 rt.3

11 = distance front spring to CG = 4' Then

12 = distance rear spring to co = 5' 81 = 4"
K1 = front spring const. = lOOO#/ft. 62 = 2.15"

rear Spring const. = 2400#/ft.

{N
M
II

the results are

2
p1 = 109 p2 = 244
or pl = 10.5 rad./sec. p2 = 15.6 rad./sec.
then fl = 10.5 x 60 = 100 oscill./min.
2
f2 = 15.6 x 60 = 149 oscill./min.
2

Assume for the moment that the above Springs are simply loaded, then
‘ by a previously proved equation

f = 5.1-

U!

3:

f1 = 3.13 = 1.56 oscill./sec. or 94 oscill./min.
2

f2 = 5.13 = 2.14 oscill./sec. or 128 oscill./min.
1.466

By comparison with the above, it is seen that for conventional spring-
ing the higher frequency is about twelve per cent more than for the
simple case and the lower about ten per cent more.(4)

Having considered the matter of theoretical frequency, it is now
necessary to briefly consider the theory of the modes of vibration.(5)
Timoshenko by mathematical manipulation (here is included much mater-
ial that cannot be followed without a knowledge of higher mathematics)
in one step arrives at an expression for locating two points about

which the vehicle oscillates (two modes of vibration). One point or

center is within the wheel base, the other outside; the two conditions

(4) G M by experiment (no data available) uses 15 and 10.

(5) See appendix 5.

-24-

are shown in Fig. 6. When motion is about the center within the wheel
base, the car can be said to be pitching, and the oscillation is of
the higher frequency; about the center without the wheel base, the car
is bouncing, and oscillation is of lower frequency.

Upon inspection it is noted that with Timoshenko's assumptions
(one Spring stiffer than the other and weight distributed so K1 11(K2 12)
the center of bounce falls outside the end of the vehicle carrying the
stiffer spring, and the center of pitch is between the CG and spring
toward the end carrying the weaker spring.

Very evidently the location of the pivot points are dependent
not on the spring deflections, but on the relative deflection thereof;
the centers shifting with a charge in relative Springing.

At this point it is well for the purpose of clearness to leave
the author's discussion and refer briefly to a fact from mechanics.
If the vehicle bOdy be considered as a compound pendulum, the springs
merely acting to support the body against the force of gravity, the
idea of center of percussion may be applied.(6) This means that a
body may be struck at a certain point such that the impact will pro-
duce only rotation about another point; the point Of impact is the
center of percussion, and the center of percussion and pivot center
are interchangeable. If a and b denote the distances from CG to the.
two points, it can be proved that

. 12 = a b.

Returning now to the discussion, it is seen that the material

(6) See any text on Engineering Mechanics.

- —25-

 

 

 

 

 

 

 

 

 

 

-25-

above agrees exactly with the theory on centers of oscillation, and
the conclusion may be drawn that if an impact is given to the pitch
center, bounce will take_place (i.e. rotation about bounce center) and
vice versa.

Formerly it was standard practice to use stiffer front Springs
than rears due to steering difficulties necessitating small movement
of the front axle. This resulted in the bounce center to the front
Of the car, and due to relation between relative spring deflections,
the common location of this center was about at the front bumper; the
pitch or rear center was slightly in front of rear axle. As already
stated, to produce a pure motion of either type, the Opposite center
must be struck. If another point is struck, a combination motion is
produced, but as the point of impact approaches either center, the
motion becomes more and more nearly a motion characteristic of that
center. Thus in the earlier cars the front axle, being very near the
bounce center, on striking a bump gave mostly a pitching motion to
the car, and the rear mostly bounce. Thus, the higher frequency
pitching motion was the motion initially given and therefore predom—
inant until modified by the rear reaction. These conditions at times
gave rise to an annoying "neck snap" and thus two more theoretical
considerations must be considered.

The expression for the product of m & n (distances from CC to

pivot centers, see Fig. 6) is given as

 

 

b __ b
m: (ML-8) - .1-(£--a)2+b2) ( .1-(_°_-8)'+ .1..(_C_-'a +322) (5)
212 412 1“ 212 412 12

-27-

Referring to Equation 5. If h = 0 (than K1 11 = Kg 12 since b
in the discussion is a const. equal to (- K] 1] + K2 12)g)
W

n = O and m -> one (by applying L'HOSpitals rule) so that the
car's two centers have shifted so one is at CC, the other is at an in-
finite distance away. To fulfill this condition, the Springs must
have equal deflection.(7)

The motion of the car has now been modified so there is an up and
down movement to the road (formerly bounce) and a pitching about the CG;
thus with only one rotation center it is comparatively easy to provide
an absorber of soft action to gently damp the action, thus giving a
pleasant ride.

It should be noted that if the rear spring is softer than the
front (as formerly) the above pleasant ride condition may be attained
either by softening the front spring until K1 11 = Kg 12 or stiffening
the rear until the same condition is reached. The "type“ of ride will
be the same, but, as proved previously, the frequency of oscillation
will be greater with the stiffer springs.

Should, however, K1 11 = Kg 12 with the driver in the car, when
the rear Seat is loaded, the relation would no longer hold, since the
rear spring would take almost all the additional weight and the de;
sired ride would not be assured. It is, therefore, to be recommended
that the car be designed so that 2p 510(1 11 2 K2 12) under maximum
load, then very evidently when the rear seat is empty 5, > 8, ,
which is the same as saying that the center of bounce is not at an in-

finite distance from the auto, but at some point nearer so that now

(7). See Appendix 2.

-28...

the car will again rotate about this center as well as the center of
pitch. However, the bounce center is still sufficiently far from the
car so that the ride will be almost as pleasant as for the design con-
dition. This, therefore, seems to be the soundest plan of springing.

There remains now one more factor to consider, it is that of fly-
wheel effect and axle interaction effect. Both of these effects are
the result of change in radius of gyration, which relation is based
on the equations for a compound pendulum just previously given. For
this reason, this portion of the discussion is given here, although
flywheel effect affects angular acceleration.

As weight is moved from the CG outward, the radius of gyration
is increased, and the moment of inertia about the CC is increased,
but

M = ICX

M = moment

I = moment of inertia

0( = angular acceleration
So if I is increased, 0( must be decreased, thus less angular acceler-
ation will be imparted to the car and passengers. This explains the
practice of placing sand bags in the back of a coupe to increase rid~
ing comfort.

Axle reaction effect is based on the compound pendulum relation
as previously given

12 = a b

-29-

If it would be possible to have the two centers of vibration at the
axles, the axles (and Springs) would be independent, thus the action
of the front spring would produce only rotation about the rear, i.e.
no interaction, and vice versa. Obviously, this would simplify the
matter of ride regulation. This requires that

11 = a and 12 = b

or
12=eb=1112

The above condition is fulfilled when the sprung weight of the car is
split into two weights concentrated over the axles; for instance the
engine over the front, the body CG over the rear. Certainly the
ifront is capable of attainment, but the second would result in such
I a grotesque appearing car as to be practically impossible. Therefore,
it can be said that axle interaction can be theoretically prevented
but due to present design cannot be actually achieved, although a
very close approach can be made to it. Without a doubt it will be
achieved in time.

The theoretical discussion is now complete and it would perhaps
be desirable to summarize the conclusions arrived at.

1. Good ride requires low accelerations, and more Spec-
ifically low angular acceleration to eliminate "neck
snap.”

2. Spring frequency depends on static deflection only,
and: soft Springs must be used

5. Acceleration depends on Spring frequency, which in
turn is dependent on static deflection, therefore,

soft Springs should be used.

4.

5.

6.

7.

-50-

Required spring deflections may be taken from a
frequency—deflection curve if allowance is made

for the 10% greater frequency in the lower fre-
quency Of vibration and 12% greater in the higher.
The modes of vibration are pitch and bounce. The
center about which the body bounces is outside the
wheel base at the end of car carrying the stiffer
Spring and the center of pitch (higher frequency
vibration) is within the wheel base between cc and
end carrying softer spring. As the deflections are
made more nearly equal, the pitch center approaches
CG and bounce center moves away from car, until when
deflections are equal, pitch center is at CC, and
bounce center is aticxa. This results in best ride
as far as type of ride is concerned.

If the radius of gyration squared equals the prod.
of the distances from CG to axles (or springs), the
action of one spring will not induce vibration in
the other. This requires a concentration of weight
over the axles.

Moving weight from the CG outward improves ride since
it decreases angular acceleration, however, it should
only be done until

i2 = 11 12 (condition 6 above).

Z- 7 “gum/a front 0'14
6 ‘//= 5:0»; fionzfifi reef

7/yjoe .40ng

D

22

d
0
l

14
T

 

 

I3

 

i
I

W...

 

41

all

 

 

 

 

7| il
a I l
2 0 III a lulu-r
I ’ l
l 2 ,l
# s
A [III / 0 III: l
t
/ filll [I
7 6

 

oJl

 

l
.L

l l

 

 

-52-

 

412 # 7/.

 

 

 

 

 

 

 

 

 

 

 

 

 

--- .- 21, \e
v V /
fi-‘AZ’I—lfl ‘
1 a... Z
(a. 5
km fl;
‘5
. A ‘ w M
-_ -_ -__, -V-\ AV V A x/\ it 1"\ 1 \ / Z _ _--..-.
a“ - . r -_ . v , ’ a ... - "W’M’I—W‘yf .
nS——~&t“~——a-

 

 

 

 

 

 

 

-55-

a... 2 m.)

 

f" or
..,, __ V. _. .1 - gaff-w ---____-_----__..-----._----.-,.----- _. -

Cvie 3 (Off)
Jo}. 3

C... 4

 

 

 

 

 

 

 

 

 

-54-

CM 6

 

M6

. ”i

‘_ {I If
“x F K6
\
O A. - 7 ' 7 K ~ ~ "9" w *#\~sfi‘w2_“~..-- ' 7 ”\JMWJI— L /
. M""” ’ " ‘ ' ~ 'mn—I‘. -$m-~_vaA__w.A.-w‘u '_" .WK...

 

 

C... 7

6.... c3

 

 

 

 

 

   

‘/\ Pa fl ‘4, - ’ ‘
I a. v ' I ’ - . - ' l ‘. I 1
‘. ‘ » f; ; . ' ' ‘

 

 

. “A...
M /0 { A4,: “’2'
v? .
Mg" K“!
,/‘--~«-""'“* -J v v”, \J \/ V ~65 \./\/\/\ V_\u/v\\
_/ .x -/ / / , J J x/ 'w-x- -/- V'i/ \/’

 

 

 

 

 

 

 

[056 /0
‘4’.” .
/K As:

b6...-
My

 

C... //

 

 

 

—56—

A brief consideration will now be given the results obtained by
experiment in order to attempt a check in the above conclusions based
on theory.

1. The values for frequency correction Should be checked.
To check anyone frequency experimentally, the Speed of the moving tape
must be known; since the original plan of the paper did not include
this phase, this data is lacking and therefore in checking, the ratio
between frequencies for two springs for any assumed time: A t is taken
to the ratio of the true computed frequency of the same Springs. This,
although slightly more work, gives just as accurate a check as by tape
Speed computations.

Case 9

 

D
‘4EFF— 13' -??£;
V} T Spring D = 2#/in.
/‘ .2“
{MB=-15rA+15+2=o
FA == _1_5_ then FB = _2_¢_1_
15 15
5A = _:_L_5_ = .577 and 6 B = .924
_1_§
2
Q = 5.15 = 5.15 = 4.15 ‘37see. or 248 ‘i/min.
(1.577 '753
Case 11
Same loading - Spring A in front Spring A = l#/in.

FA 8: FB 3 same

8,=1_5_=1.15 63=gg=1.a4
15 15

fA = 5.15 = 2.95 cy./ or 176 ‘f/nin.
1.07 sec.-

-57-

Front Springs have least deflection bounce center to front and fre-

)
quency must be corrected by value for pitch = 12%.
Correcting
Q = 278
rA = 197

Ratio q = 278 = 1.4

fA 197

From curves for a time 43 t, which is any convenient distance

Case 9 f 2.75 cycles for A t

r=2 .. nAt

11
Ratio .11 = 2.25 = 1.58
r 2

which agrees very closely (error 1.4%) with the 1.4 obtained by com-
putation.
Therefore, frequency correction values as determined by theory
are checked.
2. Acceleration varies directly with frequency. This is
proved by use Of tapes for Case 2 and 5.

First, by laying off a time interval 4 t, it is seen
that for the same time interval A t, Curve 2 has three cycles, while
Curve 3 has approximately two and three-quarter cycles, therefore,
very evidently Curve 2 has greater frequency. Now, by laying off tan-
gents to the curve, the velocity can be obtained since the curve is a
displacement-time curve, so if the tangent be layed off for a given
interval, the change in 810pe per unit of time will be the accelera-

tion. This is done, the change in slape being oC , and it is seen by

-58-

superimposing 2 on 5 that Cx'z is greater for the same time interval,
therefore, Case 2 (higher frequency) has the greater acceleration.(8)

5. Frequency varies inversely with static spring deflection.
This is most strikingly shown by a comparison of Cases 4 and 7. Here
the only difference is in the softer springing used on the front in 7.
The gently undulating curve in 7 contrasts sharply with the almost
total lack of spring action in 4. Very evidently one cycle in 7, by
inspection, takes much more space, i.e. time)than one in 4, therefore,
the frequency of 7 is much lower. The effect of loading on the same
spring can be seen from a number of curves, say 8 a 9. Here, using
the rear curve for the direct spring action, it is seen that 8 has a
lower frequency than 9; that this should be so is evident from the
loading, since in Case 9 a portion of the 2# weight is carried by
the front spring, which is not the case in 8. Also by a check of the
red curves of 6 and 8, it is seen that 6 has a lower frequency than
8, as might be deduced from the fact that the forward weight in 6 has
been moved out, increasing the deflection and therefore lowering the
frequency.

4. Increase in radius of gyration improves riding quality,
the maximum improvement being attained when 12 = ab = 11 12 (weight
concentrated over axles.) This fact is very nicely brought out by a
number of comparisons. In cases 2, 5, and 4, the loading was changed
(8). To verify results, two tapes of 2 and 5 were made at different

speeds; the graphical constructions resulted in the same con-
clusions as given above.

0

-59-

slightly to give a change in i.(9) This is the case as shown in 2
(original). As the rear weight is moved inward, i.e. 12.<_ab Case 5
(original) and 4, the induced reaction of the rear is shown by the
green curve in which the waves become more pronounced indicating poor
riding quality. A comparison of both 2 and 5 (new) leads to the same
conclusion. It may be noticed that the new Case 2 tape shows a slight
rear reaction. This is probably due to the fact that the weight hook
directly below the spring on the apparatus was broken during the run-
ning of the two new tapes, and in order to conserve time the weight
was hooked to the body bar as close to the spring as possible (approx.
1/8") instead of being directly below the spring as in 2 original.

In a like manner if the front weight be moved, the rear being
over the axle, a reaction is again impressed on the rear as shown by
Case 6; the curve here is very similar to 5 (original).

"Flywheel effect” may be shown by the following comparisons.
Case 6 has the front shifted outward, increasing inertia and also
static deflection, now by comparison with the red (front) curve of 8,
the frequency is seen to be lowered. In case 8 and 9 (rear curves)

the inertia and deflections are also increased, but the inertia is not

(9) A word of explanation should be inserted here in regard to load-
ings 2 and 5. The original set of tapes (all made under same speed
conditions) included the small strips marked 2 and 5 preceded by the
word original. The tapes were badly blotted when inking in the graph-
ical computations and therefore it was necessary to discard all but
the portion included (sufficient for purpose used). These tapes were
rerun but at a different speed and therefore cannot be compared in
scale with the remaining tapes. For comparison with the remaining
tapes, the original 2 and 5 are used, the newer tapes being used for
a comparison between themselyes.

-40-

as great as in Case 6 since the weights in 6 are more removed from
the CG than in 8. The change in deflection is the same in all cases
as the weights are moved,(lo) however, the change in frequency be-
tween 6 and 8 (front) is greater than between 8 and 9 (rear), there-
fore, since the additional decrease in frequency could not have been
caused by deflection (since it would affect both comparisons equally
if deflection changes are equal), it must be concluded that the in-
crease in inertia (”flywheel effect") must have caused the additional
change.

With the data at hand, very good and bad pictures of axle inter-
action are available. Cases 9 and 10 are types of undesirable ride,
one being almost the Opposite of the other. Case 11 shows a very de-
sirable type of ride making use of a flexible front spring and a
weight distribution designed to give about as near above axle con-
centrations as practically possible. In Case 9 a bad resonance con—
dition is illustrated. Here the reaction of the front is in step
with the oscillations produced by the rear bump, with the result that
the rear oscillations are reinforced to such an extent that they do
not die out until the rear system is again disturbed. Obviously this
would be uncomfortable. Case 10 shows a case of the worst ride re-
cord obtained. Interaction here is very bad due to the rear weight
being moved in so far; the constantly varying and irregular shape of
the curves throughout their length testify of a ride that is constant-

ly choppy and ever changing in characteristic. This in a car would

(10) See appendix 5 for proof.

 

-42-

added to obtain frequency in pitch.

7. Assuming a frequency value of 80 cycles/min. as a min—
imum for comfort, by use of the frequency—deflection curve and cor-
rection factors, it may be said that a car Spring must have a minimum
static deflection of 6 inches.

8. Weight should be concentrated over or as near over the
Springs (axles) as possible in order to eliminate axle interaction.
An arrangement whereby the engine is over the front axle of the car
and the cc of body is 1/10 of wheel base before rear axle will give
a ride almost as fine as if the CG was over the axle. A distance of
1/4 to 1/5 of wheel base will give a fair ride.

Verified by theory but not experiment (appendix 4).

l. The centers of oscillation are similar to centers
of percussion in action and vary with relative springing. The bounce
center is outside the wheel base to end of stiff spring, and pitch
center is within wheel base and toward end of soft spring.

2. For a most satisfactory ride, the static deflec-
tions of springs should be the same when the car is fully loaded,
since then the car will have angular movement (pitch) about one cen-

ter (CG) and move up and down in translation parallel to the road.

~45—

APPENDIX 1
Computations for force - MPH curve.
Curb weight = 5400# 20 MPH
Rise 1" in 2' travel

9.3”
§Q=_ M

 

 

O
88 x
x = 29.5'/sec. Vx = 29.25
Time for 2' = .0684 sec. Vy = 1.22
By impulse and momentum:—
Impulse = Change in momentum
Tangent e = .0417 e = 2°26'
.0684 Fx = 5400 (29.5 - 29.25)
52.2
Fx = 77.2#
.0684 E? = 5400 (1.22)
52.2
Ey = 1885#
‘ -———2 ——2
‘4; F: 1885 +77
2'
= 1888#
721‘
APPENDIX 2
F. V 5
iii ‘Q _JL~ "‘ T
- W11 + (11 + 12) F2 3 O
2 11 + I2
F1=W(12 ). K2 5.=F2

-44-

Assume 51 —- 82
K1 = F1
K2 F2 2‘32
1 Kl= 2
f (_.__.2_._)
El.= 1 + 1
K2 f ( I1 3
11 + 12
fl=lz or K111=K212
K2 11

Thus, to obtain this result, equal deflections must be assumed.

.APPENDIX 5

Specifications for Thesis Model

Desoto
Engine and Transmission 757#
Steering Gear 28
Radiator 46
Bumpers . (32 apiece) 64
Battery 54
Frame and Body 1802
Gas Tank and Gas 124
Spare Tire 29

2904#
On model

Engine weight to include from above

Engine and Transmission 757#
Radiator 46
Battery 54

 

Total engine 857#

-<—-~ 1.

-45-

Body total 2904#
Use front weight 1#
857
Rear weight 2# (2000#)
2047# ' ’ .
APPENDIX 4

An idea for possible checking of the centers of oscillation oc-
curred to the writer too late for experimentation. The plan is as
follows, and possibly is a method of proving the one theoretical
point not checked by experiment.

Curves are taken as previously, except that in this case the two
are made on the same zero diaplacement axis instead of having separate
axes. A straight line is ruled on a piece of tracing paper, and thru
the curves (along zero axis). A straight edge with stylus or point
at each end is constructed so that the distance between styluses and
pen points on model body bar are equal. Now by moving the tracing
paper horizontally, the straight edge resting on it, at all times
keeping the axis of paper and original axis coincident and placing
the bar so one and traces along the front and the other along the
rear curve, a series of lines may be laid off along the straight
edge. The point of convergence of these lines should give the center
of oscillations of the bar. The method obviously may require some

revision or refinement on trial.
APPENDIX 5

A a
’3 -.z§ I:

.17

I

-45-

 

 

£MB=15Fa=15=0 (Mgzlsrazlszo
Fa=l Fa=;_L_§—l.15
13
1.15 — 1.00 = .15 Difference
.4 4B ‘4 47
f '3 I 3 v i
W Jr Jr W
’ 2- t 1
£MA=15FB-26=0 (MAzlsFB-m
FB=2# FB=_2__4_=1.85
13

2.00 - 1.85 = .15 Difference
All Springs are 11),,
Scale = 2#/in.
To change F8 and Pb to deflection, divide by 2, but this is di-
viding by a constant and will not affect the relative results as far
as the two subtractions are concerned, therefore, assume scale = l

to simplify computation.

1.
2.

5.

5.

-47-

BIBLIOGRAPHY

”Vibration Problems in Engineering" - Timoshenko.
"Vibration Prevention in Engineering" - Kimball.
"Engineering Mechanics - Dynamics" - Timoshenko.
"Analytical Mechanics for Engineers" - Seeley and Ensign.\
"S.A.E. Transactions" - Vol. 20 - Part 2.

" 21 - Part 2.

" 27

" 29

" 51

 

“"325“; Sheet NO- ...................................
MECHANICAL ENGINEERING LABORATORY
MICHIGAN STATE COLLEGE
. A I
/ . //9 i’" /_—-/ fi_
Running L08 0‘ ......... _ w/ic/‘xli"’)-.fol.. ..... ” ........................................................................ ,
// ............................................................................................................................................................
......... /H"’-~/
Observers{ {
________________________________________________________________________________________________________________________ Datenww,‘_._.,_____,,._.., 193.......
R
\_ ‘ Q
E" if \‘
\ "1:; Q

/ _- f/ " x
l , I f .,/ ./' r’. “d 4.
jiffy”; xfléa/Afl //*"” “a ’ f
I/ ’5
K)?” V ' .r‘ 4 L 14/ ’

 

 

 

com-acem-a-wNHNO-

Form 257-0

..........................................

Sheet No. ...................................

MECHANICAL ENGINEERING LABORATORY
MICHIGAN STATE COLLEGE

................................................................................................................................................................

 

 

1 ,. {L
L I {/3
L I‘
(I? I / (0
__. .2 2:5 27- 7. I I 3 1
I ____r__--._. _ -’.-_ _I-_____,._ l __ I -

 

 

 

(

i—tt—iHi—d
ODNHO

H
nub
"f gmmwmfi‘QM/N

$5
2.,
{fi‘\“ViY\-\V
{h

8 {'5 56 33
\ h‘ \_ -.
t )

M
N b N

N

(x N
w
_;k

€4.31

~X 2’.” "r -‘3
1 ‘ -

.7 ‘;. A
J 'A (’5 Q (a

I} '3

 

 

w" J
C

..‘
fl”
a ‘-. ' ’

 

.i“
as

l

. ‘
9
->

 

N

‘

v, "’

 

llHlllLlLIL!LILIIHLILllLll|||||IllllllliLLllLllll

169 503