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CHAPTER 25

VIBRATION TESTING

MACHINES

David O. Smallwood

INTRODUCTION

This chapter describes some of the more common types of vibration testing

machines which are used for developmental, simulation, production, or exploratory

vibration tests for the purpose of studying the effects of vibration or of evaluating

physical properties of materials or structures. A summary of the prominent features

of each machine is given. These features should be kept in mind when selecting a

vibration testing machine for a specific application. Digital control systems for

vibration testing are described in Chap. 27. Applications of vibration testing

machines are described in other chapters.

A vibration testing machine (sometimes called a shake table or shaker and

referred to here as a vibration machine ) is distinguished from a vibration exciter in

that it is complete with a mounting table which includes provisions for bolting the

test article directly to it. A vibration exciter, also called a vibration generator, may be

part of a vibration machine or it may be a device suitable for transmitting a vibratory

force to a structure. A constant-displacement vibration machine attempts to maintain

constant-displacement amplitude while the frequency is varied. Similarly, a constant-

acceleration vibration machine attempts to maintain a constant-acceleration ampli-

tude as the frequency is changed.

The load of a vibration machine includes the item under test and the supporting

structures that are not normally a part of the vibration machine. In the case of equip-

ment mounted on a vibration table, the load is the material supported by the table.

In the case of objects separately supported, the load includes the test item and all fix-

tures partaking of the vibration. The load is frequently expressed as the weight of the

material. The test load refers specifically to the item under test exclusive of support-

ing fixtures. A dead-weight load is a rigid load with rigid attachments. For nonrigid

loads the reaction of the load on the vibration machine is a function of frequency.

The vector force exerted by the load, per unit of acceleration amplitude expressed in

units of gravity of the driven point at any given frequency, is the effective load for

that frequency. The term load capacity, which is descriptive of the performance of

reaction and direct-drive types of mechanical vibration machines, is the maximum

25.1

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CHAPTER TWENTY-FIVE

dead-weight load that can be vibrated at the maximum acceleration rating of the

vibration machine. The load couple for a dead-weight load is equal to the product of

the force exerted on the load and the distance of the center-of-mass from the line-of-

action of the force or from some arbitrarily selected location (such as a table sur-

face). The static and dynamic load couples are generally different for nonrigid loads.

The term force capacity, which is descriptive of the performance of electrody-

namic shakers, is defined as the maximum rated force generated by the machine.

This force is usually specified, for continuous rating, as the maximum vector ampli-

tude of a sinusoid that can be generated throughout a usable frequency range. A cor-

responding maximum rated acceleration, in units of gravity, can be calculated as the

quotient of the force capacity divided by the total weight of the coil table assembly

and the attached dead-weight loads. The effective force exerted by the load is equal

to the effective load multiplied by the (dimensionless) ratio g , which represents the

number of units of gravity acceleration of the driven point [see Eq. (25.1)].

DIRECT-DRIVE MECHANICAL VIBRATION

MACHINES

The direct-drive vibration machine consists of a rotating eccentric or cam driving a

positive linkage connection which forces a displacement between the base and table

of the machine. Except for the bearing clearances and strain in the load-carrying

members, the machine tends to develop a displacement between the base and the

table which is independent of the forces exerted by the load against the table. If the

base is held in a fixed position, the table tends to generate a vibratory displacement

of constant amplitude, independent of the operating rpm. Figure 25.1 shows the

direct-drive mechanical machine in its simplest forms. This type of machine is some-

times referred to as a brute force machine since it will develop any force necessary to

produce the table motion corresponding to the crank or cam offset, short of break-

ing the load-carrying members or stalling the driving shaft.

The simplest direct-drive mechanical vibration machine is driven by a constant-

speed motor in conjunction with a belt-driven speed changer and a frequency-

indicating tachometer. Table displacement is set during shutoff and is assumed to

hold during operation. An auxiliary motor driving a cam may be included to pro-

vide frequency cycling between adjustable limits. More elaborate systems employ

FIGURE 25.1 Elementary direct-drive mechanical vibration machines:

( A ) Eccentric and connecting link. ( B ) Scotch yoke. ( C ) Cam and follower.

25.3

VIBRATION TESTING MACHINES

a direct-coupled variable-speed motor with electronic speed control, as well as

amplitude adjustment from a control station. Machines have been developed

which provide rectilinear, circular, and three-dimensional table movements—the

latter giving complete, independent adjustment of magnitude and phase in the

three directions.

Many types of mechanisms are used to adjust the displacement amplitude and

frequency of the mounting table. For example, the displacement amplitude can be

adjusted by means of eccentric cams and cylinders.

PROMINENT FEATURES

Low operating frequencies and large displacements can be provided conveniently.

Theoretically, the machine maintains constant displacement regardless of the

mechanical impedance of the table-mounted test item within force and frequency

limits of the machine. However, in practice, the departure from this theoretical

ideal is considerable, due to the elastic deformation of the load-carrying members

with change in output force. The output force changes in proportion to the square

of the operating frequency and in proportion to the increased displacement

resulting therefrom. Because the load-carrying members cannot be made infi-

nitely stiff, the machines do not hold constant displacement with increasing fre-

quency with a bare table. This characteristic is further emphasized with heavy

table mass loads. Accordingly, some of the larger-capacity machines which operate

up to 60 Hz include automatic adjustment of the crank offset as a function of oper-

ating frequency in order to hold displacement more nearly constant throughout

the full operating range of frequency.

The machine must be designed to provide a stiff connection between the ground

or floor support and the table. If accelerations greater than 1 g are contemplated,

the vibratory forces generated between the table and ground will be greater than

the weight of the test item. Hence, all mass loads within the rating of the machine

can be directly attached to the table without recourse to external supports.

The allowable range of operating frequencies is small in order to remain within

bearing load ratings. Therefore, the direct-drive mechanical vibration machine can

be designed to have all mechanical resonances removed from the operating fre-

quency range. In addition, relatively heavy tables can be used in comparison to the

weight of the test item. Consequently, misplacing the center-of-gravity of the test

item relative to the table center for vibration normal to the table surface and the

generation of moments by the test item (due to internal resonances) usually have

less influence on the table motions for this type of machine than would other

types which are designed for wide operational frequency bands.

Simultaneous rectilinear motion normal to the table surface and parallel to the

table surface in two principal directions is practical to achieve. It may be obtained

with complete independent control of magnitude and phase in each of the three

directions.

Displacement of the table is generated directly by a positive drive rather than by

a generated force acting on the mechanical impedance of the table and load. Con-

sequently, impact loads in the bearings, due to the necessary presence of some

bearing clearance, result in the generation of relatively high impact forces which

are rich in harmonics. Accordingly, although the waveform of displacement might

be tolerated as such, the waveform of acceleration is normally sufficiently dis-

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CHAPTER TWENTY-FIVE

torted to preclude recognition of the fundamental driven frequency, when dis-

played on a time base.

REACTION-TYPE MECHANICAL VIBRATION

MACHINE

A vibration machine using a rotating shaft carrying a mass whose center-of-mass is

displaced from the center-of-rotation of the shaft for the generation of vibration, is

called a reaction-type vibration machine. The product of the mass and the distance of

its center from the axis of rotation is referred to as the mass unbalance, the rotating

unbalance, or simply the unbalance. The force resulting from the rotation of this

unbalance is referred to as the unbalance force.

The reaction-type vibration machine consists of at least one rotating-mass unbal-

ance directly attached to the vibrating table. The table and rotating unbalance are

suspended from a base or frame by soft springs which isolate most of the vibration

forces from the supporting base and floor. The rotating unbalance generates an

oscillating force which drives the table. The unbalance consists of a weight on an arm

which is relatively long by comparison to the desired table displacement. The unbal-

ance force is transmitted through bearings directly to the table mass, causing a vibra-

tory motion without reaction of the force against the base. A vibration machine

employing this principle is referred to as a reaction machine since the reaction to the

unbalance force is supplied by the table itself rather than through a connection to

the floor or ground.

CIRCULAR-MOTION MACHINE

The reaction-type machine, in its simplest form, uses a single rotating-mass un-

balance which produces a force directed along the line connecting the center-of-

rotation and the center-of-mass of the displaced mass. Referred to stationary

coordinates, this force appears normal to the axis of rotation of the driven shaft,

rotating about this axis at the rotational speed of the shaft. The transmission of this

force to the vibration-machine table causes the table to execute a circular motion in

a plane normal to the axis of the rotating shaft.

Figure 25.2 shows, schematically, a machine employing a single unbalance pro-

ducing circular motion in the plane of the vibration-table surface. The unbalance is

driven at various rotational speeds, causing the table and test item to execute circu-

lar motion at various frequencies. The counterbalance weight is adjusted to equal

the test item mass moment calculated from d, the plane of the unbalance force,

thereby keeping the combined center-of-gravity coincident with the generated

force. Keeping the generated force acting through the combined center-of-gravity of

the spring-mounted assembly eliminates vibratory moments which, in turn, would

generate unwanted rotary motions in addition to the motion parallel to the test

mounting surface. The vibration isolator supports the vibrating parts with minimum

transmission of the vibration to the supporting floor.

For a fixed amount of unbalance and for the case of the table and test item acting

as a rigid mass, the displacement of motion tends to remain constant if there are no

resonances in or near the operating frequency range. If balance force must remain

constant, requiring the amount of unbalance to change with shaft speed.

25.5

VIBRATION TESTING MACHINES

FIGURE 25.2

Circular-motion reaction-type mechanical vibration

machine.

RECTILINEAR-MOTION MACHINE

Rectilinear motion rather than circular motion can be generated by means of a

reciprocating mass. Rectilinear motions can be produced with a single rotating

unbalance by constraining the table to move in one direction.

Two Rotating Unbalances. The most common rectilinear reaction-type vibra-

tion machine consists of two rotating unbalances, turning in opposite directions

and phased so that the unbalance forces add in the desired direction and cancel in

other directions. Figure 25.3 shows schematically how rectilinear motion perpen-

dicular and parallel to the vibration table is generated. The effective generated

force from the two rotating unbalances is midway between the two axes of rota-

tion and is normal to a line connecting the two. In the case of motion perpendicu-

lar to the surface of the table, simply locating the center-of-gravity of the test item

over the center of the table gives a proper load orientation. Tables are designed so

that the resultant force always passes through this point. This results in collinear-

FIGURE 25.3 Rectilinear-motion reaction-type mechanical

vibration machine using two rotating unbalances: ( A ) Vibra-

tion perpendicular to table surface. ( B ) Vibration parallel to

table surface.

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