lesson 7- excitations-bearings.pdf

7/25/2019 Lesson 7- Excitations-Bearings.pdf

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6 SOURCES OF VIBRATIONS IN ROLLING BEARINGS

6.1. BEARING CHARACTERISTIC FREQUENCIES

6.1.1 Kinematics of rolling bearings for low speed applications

In a first evaluation, in a rolling bearing, mounted on a rotating shaft and a

rotating housing, exist:

- the inner ring rotation at angular speed of the shaft, ;-

the outer ring rotation at angular speed of the housing, ;-

the rolling elements orbital movement around the bearing axis, at the cage

angular speed, ;-

the rolling elements rotation around their own axes with a particular

angular speed, .

Fig.6.1 Basic angular speeds in a rolling bearing

When a load occurs between a rolling element and raceway, a contact surfaceis formed. When the rolling element rotates relative to the deformed surface, the

simple rolling motion does not occur; rather, a combination o rolling and sliding

motions occur. Hence, a system of complex equations needs to be developed to

calculate the rolling element speeds. Also, for angular-contact bearings, if the

rolling motion does not occur on a line exactly parallel to the raceway, a parasitic

motion called spinning occurs. Such a motion is pure sliding contributing


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significantly to bearing friction power loss.Finally, motions between roller ends and

ring flanges in roller bearings are also pure sliding and can result in substantial

power loss. In most applications, particularly those operating at relatively slow

shaft or outer-ring speeds, these internal speeds can be calculated with sufficient

accuracy using simple kinematical relationships; that is, the balls or rollers areassumed to roll on the raceways without sliding.

In the case of slow-speed rotation or an applied load of large magnitude, rolling

bearings can be analyzed while neglecting dynamic effects. As a general case,

it will be assumed that both inner and outer rings rotate with non-zero angular

speeds: eor the outer ring, and ifor the inner ring. It will be further assumed

that a common contact angle exists on both raceways.

Conditions of pure rolling motions of the ball on both outer raceway, (point E),

and inner raceway, (point I), provide the equations to obtain the angular speeds:

the angular speeds of the cage, the angular speed of the ball.

Fig. 6.2 Low speed kinematics of an angular contact ball bearing


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= cos ,

= (1 + ), = (1 )[Point ] ( ) 2 (1 + ) =

2

[Point ] ( )

2(1 ) =

2

= (1 + ) + (1 )2

= 2 ( )(1 )If only inner ring rotates:

= 2 (1 )

= 2 (1 )

6.1.2 Bearing characteristic frequencies

We consider the following notations:

= inner ring rotational frequency; = outer ring rotational frequency, ( = 0)


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= rolling element spin frequency= fundamental train (cage) frequency relative to outer ring

= fundamental train (cage) frequency relative to inner ring

=rolling element pass frequency of outer ring =rolling element pass frequency of inner ringFor stationary outer ring and rotating inner ring, the fundamental frequencies are

derived from the bearing geometry and kinematics.

=

21

cos

=2 1 + cos

= =

w = 2 [1

]

A single defect on a ball or roller would contact both raceways in one ball or roller

revolution so that the defect frequency is 2w. In addition, the defect couldcontact one or both sides of the cage pocket, but this will have little influence on

vibration measured external to the bearing.

The presented equations assume the rolling elements roll over the raceways

surfaces and no sliding is present. However in practice this is rarely the case and

due to a number of factors the rolling elements undergo a combination of rolling

and sliding. As a consequence, the actual characteristic defect frequency may

differ slightly from those predicted, but this is very dependent on the type of

bearing, operating conditions and running internal clearance. This sliding can be


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taken into account by multiplying the theoretical frequencies with a sliding factor

ethat usually takes value between 0.9 and 1.0.

Generally the bearing characteristic frequencies will not be integer multiples of

the inner ring rotational frequency.That notice helps to distinguish the bearing

characteristic frequencies from other sources of vibration.

Since most vibration frequencies are proportional to speed it is important when

comparing vibration signatures that data are obtained at identical speeds.

Speed changes will cause shifts in the frequency spectrum causing inaccuracies

in both the amplitude and frequency measurement.

The rolling element pass frequency divided by the shaft rotational frequency is

called the bearing speed ratio. The actual value of the bearing speed ratio is a

function of the bearing loads, internal clearance, condition of lubrication.

If the bearing speed ratio is below predicted values it may indicate insufficient

loading, excessive lubrication or insufficient radial internal clearance, which

could result in increased friction generating higher operating temperature and

premature failure.

A higher than predicted bearing speed ratio may indicate excessive loading,

excessive internal clearance or insufficient lubrication.

Rolling bearings are a mechanical system whose parts rolling elements, inner andouter rings, and cage interact to generate complex vibration signatures. Like any

other manufactured part rolling bearings have degrees of imperfections and

generate vibration as the surfaces interact during the rolling motion. Nowadays,

also the amplitudes of the surface imperfections are in the order of nanometers,

significant vibrations can still be produced in the entire audible frequency range

( 20 Hz20 kHz). If a defect was present on the active raceways a more or less

significant change in the vibration pattern of the particular bearing is detected.

A number of harmonics and sum and difference frequencies are also evident in

the spectrum.

In the following the main sources of rolling bearing vibration are discussed with a

special attention on vibration induced by bearing failures.


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6.2 STRUCTURAL ELEMENTS AND VARIABLE COMPLIANCE

Under the applied load the concentrated contacts implied in a rolling bearing

manifest local deflection, and consequently the rolling bearing manifests like a

non-linear spring. Figure 6.3. However for each particular operating conditions a

bearing spring constant may be determined by taking the slope of the force-

deflection curve.

Fig. 6.3 The load-deflection relationship in a radial rolling bearing

Rolling bearing present a hardening non-linear characteristic that means the

stiffness increases with increasing load or built-in preload, and consequently

increased bearing stiffness raises the value of resonant frequency associated with

this spring. The radial stiffness decreases with increasing contact angle, whereas

the axial stiffness decreases.

Variable compliance

Rolling bearings carry loads with a finite number of rolling elements whose angular

positions, with respect to the line of action of the load, continually changes in

time, Figure 6.4. This mere change of position causes the inner and outer raceways

to undergo periodic relative motion..

Fig. 6.4 Bearing model for variable compliance


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The greater the number of loaded elements less the movement. For radially

loaded or misaligned bearings running clearance determines the extent of the

loaded zone, and hence variable compliance increases with clearance

The movement is periodic with base frequency equal to the rate at which the

rolling elements pass through the load zone. The non-linear character of the

deflection-load relationship determines a non-sinusoidal character of vibrations

derived from variable compliance so that the frequency analysis of the

movement yields the base frequency and a series of harmonics. These kind of

vibrations are an inherent feature of rolling bearings, even the bearing is

geometrically perfect, but do not indicate a poor quality, and explain why

bearing failure detection is best performed by monitoring frequencies other than

the fundamental bearing frequencies.

Variable compliance levels can be higher than those produce by roughness andwaviness of the rolling surfaces. It can be reduced to a negligible level by using

rolling bearings with a sufficiently high axial pre-load.

6.3 GEOMETRIC IMPERFECTIONS AS SOURCE OF VIBRATION

It is convenient to consider geometrical imperfections in terms of wavelength

compared to the width of the contact area achieved between the most loaded

rolling element and raceway:

- surface features of wavelength of the order of the contact width or less

are termed roughness,

- surface features of wavelength longer than the contact width are termed

waviness, (Figure 6.5).


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Fig. 6.5Waviness and roughness of rolling surfaces versus width of the contact

area and thickness of lubricating film.

6.3.1 Surface roughness as source of vibration.

When the roughness heights are high comparing with the thickness of the

lubricating film, Figure 6.5, the asperities of contacting surfaces interact randomly

resulting a random sequence of small impulses which excite all the natural modes

of bearing and supporting structures.

Surface roughness induces vibration predominantly at frequency above sixty

timesthe rotation frequency of the bearing, that means that the high frequency

part of the frequency spectrum represent a series of resonances.

Local film variation as a function of local surface roughness is usuallycharacterized by so called lambda parameterand defined as the ratio of the

minimum film thickness h0 to the composite roughness of two surfaces in contact:

= +


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where , are RMS surface roughness of the raceway and rolling element,respectively.

To evaluate the effect of ratio on film thickness and lubrication quality ofcommon rolling bearings, the diagram presented in Figure 6.6 is largely used.

Fig. 6.6Percent film versus lubrication parameterer ratio

Evaluation of the roughness values for a particular EHD lubrication regime

The simulation has been performed in the following general conditions:

- an EHD regime with the minimum film thickness:

=0.3 ;- the roughness of the rolling element has been considered to be finer than

that of the contacting raceway:

=

The lambda ratio becomes:

= + =1.29 , =0.23

1


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Further, admitting that =1.25, results: =.

Minimum

EHD Film

Thickness

Lubrication parameter

1 2 3 4

. 0.2 0.1 0.06 0.04

6.3.2 Waviness as source of vibration.

Waviness can occur in the machining process. A ring type element is compressesat the points of contact in the chuck , three jaw or five jaw, causing stresses in the

ring. The ring is turned or ground perfectly circular; however when it is discharged

from the chuck, the stresses are released and the ring becomes lobed. The

number of lobes per circumference is called waviness. Careful attention is

required to the form and precision of all associated bearing components.Any

geometric errors on the outside diameter of the shaft or bore of the housing can

be reflected on the bearing raceways leading to the increase in vibration level.

Waviness produces vibration that are usually predominant at frequencies below

sixty times rotational frequency, but can induce vibration at frequencies up to

three hundred times the rotational frequency.


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6.4 DISCRETE DEFECTS AS SOURCE OF VIBRATION.

Discrete defects can take a variety of forms: identations, scratches along and

across the roling surfaces, pits, debris and particle in the lubricant.

Bearing manufacturers have adopted simple vibration measurements on thefinished product to detect such defects. However this type of measurement

provides vibration data which are valid for that type and size of bearing.

A number of harmonics and sum and difference frequencies are also evident in

the spectrum.

Rolling element pass frequency can be generated as:

a result of elastic proprieties of the raceway material due to variable

compliance , or as

the rolling element pass over a defect on the raceway.

The frequency generated at the inner and outer ring raceway can be estimated

roughly as:

=0.6and =0.4, respectively.Imperfections on the surface of raceways and rolling elements, as a result of the

manufacturing elements, interact to induce other discrete frequencies and

sidebands, Table 1.

Table 1. Frequencies related to surface imperfections

Surface defect

FrequencyComponent Imperfection

Inner raceway Excentricity

Waviness


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Discrete defect

Outer raceway Waviness

Discrete defect

Rolling element Diameter variation

Waviness 2

Discrete defect 2

Bearing vibration signal is usually complex and the frequencies generated will

add and subtract and are present in bearing vibratrion spectra. Over the years a

number of diagnostic algorithms have been developed to detect bearings faults

by measuring the vibration signatures on the bearing housing. These methods

take advantage of both the characteristics frequencies and the natural

frequencies of the bearing.

6.4.1Discrete fault on outer raceway

A discrete fault on outer raceway will generate a series of high pulses at a rate

equal to the ball pass frequency relative to the outer ring. Usually the outer ring is

stationary and the amplitude of the pulse will remain theoretically the same and

will appear as a single discrete peak within the frequency domain-

6.4.2 Discrete defect on the inner raceway

A discrete defect on the inner raceway will generate a series of high pulses at a

rate equal to the ball frequency relativ to the inner raceway. Because the inner

ring is rotating, the defect will enter and leave the load zone causing a variation


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in the roling element-raceway contact force, hence deflections. While in the load

zone the amplitudes of the pulses will be highest but then reduce as the defect

leaves the zone, resulting in a signal which is amplitude modulated. In the

frequency domain this not only gives rise to a discrete peak at the carrier

frequency (ball pass frequency) but also creates a pair of sidebands spacedeither side of the carrier frequency by an amount equal to the modulating

frequency (inner ring rotational frequency), Figure 6.7 and Figure 6.8.

Fig. 6.7Amplitude modulation

Notes about the side bands evolution:

I.

as the level of the amplitude modulation increases so will the sidebands;

II.

as the defect increases in size more sidebands are generated and at some

point the ball pass frequency may no longer be generated, but instead a

series of peaks will be generated spread at the inner ring rotational

frequency.

Although defects on the inner and outer raceways tend to behave in a similar

manner, for the same size defect the amplitude of the spectrum of an inner

raceway defect is much less. This is because a defect on the inner raceway

comes into the loaded zone once per revolution and the generated signal has

to travel through more structural interfaces before reaching the transducer


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location. Consequently a foult on the outer raceway tends to be easier to

detect.

Likewise the rolling element pass frequency can also be modulated at the

fundamental train frequency. If a rolling element has a defect it will enter and

leave the load zone at the fundamental train frequency causing amplitude

modulation and result in sidebands around the ball pass frequency.

Amplitude modulation at the fundamental train frequency can also occur if

the cage is located radially on the inner or outer ring.

6.4.3 Rolling element defect as source of vibration

Defects on the rolling elements can generate: a frequency twice ball spin

frequency (when the defect strikes both raceways), harmonics and the

fundamental train frequency.

Sometimes the generated frequency may not be so high because the rolling

element is not always in the loaded zone when the defect strikes. Also, when

a defect on ball is orientated in the axial direction it not always contact the

inner and outer raceway. When more rolling elements are defective, sum of

the ball spin frequency can be generated and if these defects are severe then

vibration at the fundamental train frequency can be generated.

6.4.4 Cage defect as source of vibration

The cage tends to rotate at 0.4 times inner ring speed and has a low mass.

Unlike the raceway defects, cage failures do not usually excite specific natural

frequencies. In the case of cage failures the signature is likely to have a

random bursts of vibration as the rolling elements slide and the cage starts to

wear or deform and a wide band of frequencies is likely to occur.

As a cage starts to deteriorate wear can start to occur on the sliding surfaces( in the cage pocket, or on the cage guiding surfaces in the case of ring

guided cage). This kind of cage wear leads to a less stable rotation of the cage

or a greater excursion of the rolling elements, resulting an increased sideband

presence around the other bearing fundamental frequencies, like the ball spin

frequency.


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Excessive clearance can cause vibration at the fundamental train frequency

as the rolling elements accelerate and deccelerate through the loaded zone.

Consequently large impact forces result between the roling elements and the

cage pockets, Figure 6.8. Also, outer raceway defects and roller defects can

be modulated with the same fundamental train frequency (FTF).

Fig. 6.8- Impact forces between the rolling elements and cage pockets

6.4.5 Cotamination as source of vibration

Contaminants can cause wear and damage to the rolling contact

surfacesand generate vibration across a broad frequency range. In the early

stages the crest factor of the time signal increases, but it is unlikely that this will

be detected in the presence of other sources of vibration.

J.S. Laccey

An Overviw of Bearing Vibration Analysis

Maintenance & asset management, vol.23, no.6, nov/dec 2008, pp.32-42


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lesson 7- excitations-bearings.pdf

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