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Correlation between Belt Natural Frequencies and

Vibration Spectra

This tech-note is a continuation of the previous study. In the last tech-note, we reported

the results of V-belt natural frequencies under different tensions and examined whetherthey follow string theory or beam theory. We learned that:1. natural frequencies are function tension,2. natural frequencies follow string theory in the sense that the higher modes are

integral multiples of the fundamental, and

3. string theory overestimates the natural frequencies measured using a hammer testunder medium to high tension; for low tension, it underestimates it.

In this tech-note, we present the results of:1. how the natural frequencies get excited for belts in differing lengths,2. correlation between machine operating speed and natural frequency excitement,

3. whether natural frequencies show up in the vibration spectra,4. belt dynamic stiffness versus static stiffness, and5. belt length effect on excitation and RPM.

Test Setup

All tests were done on SpectraQuests Machinery Fault Simulator (MFS) using two A30

(30 inches long) and two A42 (42 inches long) belts. Data was acquired using

SpectraQuests SpectraPadportable data acquisition system, and analysis was performedwith VibraQuest software. Two single axis accelerometers and one tri-axial

accelerometer made by IMI, and one Monarch strobe light were also used during the test.In order to eliminate effects of gearing mechanism, the belts were mounted directly on a

block which was mounted on a sliding platform. The platform could be easily moved to

adjust the belt tension.

Test Setup MFS with A42 Belt Mounted

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To excite resonances in the belts, we tried to put tape on the upper sheave, and a metal

ball was taped to each belt. But it did not excite the belt resonance frequency up to 5000

RPM. In the end, we had to tape two metal balls on the belts to excite the resonancewithin the speed range of operation.

Wrapped tape on the belt

Test Procedure

1. Install the 30-inch belts on to the machine.2. Turn the screw to adjust the tension.3. Do a running up test first by slowly increasing the motor speed, and try to locate

the drive frequency at which the belts will enter resonance (vibration level is

much higher).

Observe the transverse vibration level

4. Run the machine at the frequency we get from last step.5. Collect steady state data, and use the strobe light to get the transverse vibration

frequency, which is the natural frequency of the belt.

6. Repeat the above steps for other tensions.7. Repeat the above steps for 42-inch belt.

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Test Data and Analysis

To detect the resonance frequency, startup and coast down data were collected, and

strobe light was used to detect the resonance. Once the resonance frequency was

determined, the MFS was operated under steady state conditions at those speeds.

The following two tables provide summary of results. Each table contains data for MFSspeed, belt speed (or Belt Pass Frequency), and strobe measured resonance frequencies.Table 1 illustrates 30-inch belt data, and Table 2 is for 42-inch belt data.

Table 1 30-inch beltTension MFS Speed (Hz) Belt Speed, BPF (Hz) Resonance Frequency (Hz)

Inner Belt Outer Belt Inner Belt Outer Belt Inner Belt Outer Belt

Low 46.2 42.8 22.3 20.7 37.48 31.49

Medium 46.9 41.9 22.7 20.3 51.68 46.38

High 65.3 65.3 31.6 35.6 72.14 67.13

Graphs 1 and 2 illustrate MFS speed, belt speed, and resonance frequency for inner and

outer belts at three different tensions respectively.

Comparison of MFS Speed, Belt Speed and Resonance Frequency, 30

inch Inner Belt

10

20

30

40

50

60

70

80

Low Medium High

Tension

Frequency(

Hz)

MFS Speed (Hz)

Belt Speed, BPS (Hz)

Resonance Frequency (Hz)

Graph 1

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Comparison of MFS Speed, Belt Speed and Resonance Frequency, 30

inch Outer Belt

10

20

30

40

50

60

70

Low Medium High

Tension

Frequency

(Hz)

MFS Speed (Hz)

Belt Speed, BPS (Hz)

Resonance Frequency (Hz)

Graph 2

42-inch beltTension Drive Frequency (Hz) Belt Passing Frequency (Hz) Resonance Frequency (Hz)

Inner Belt Outer Belt Inner Belt Outer Belt Inner Belt Outer Belt

Low 51.7 44.5 17.9 15.4 20.5 18

Medium 63 53 21.8 18.3 26 22Medium-High 60 53.6 20.7 18.5 30.5 28.5

Graphs 3 and 4 illustrate MFS speed, belt speed, and resonance frequency for inner and

outer belts at three different tensions respectively.

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Comparison for MFS Speed, Belt Speed and Resonance Frequency,

42-inch Inner Belt

10

20

30

40

50

60

70

Low Medium Medium-High

Tension

Frequency

(Hz)

MFS Speed (Hz)

Belt Speed, BPS (Hz)

Resonance Frequency (Hz)

Graph 3

Comparison of MFS Speed, Belt Speed and Resonance Frequency, 42-

inch Outer Belt

10

15

20

25

30

35

40

45

50

55

60

Low Medium Medium-High

Tension

Frequency

(Hz)

MFS Speed (Hz)

Belt Speed, BPS (Hz)

Resonance Frequency (Hz)

Graph 4

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It can be seen from the data that the belt resonance frequencies increase with tension.Higher speeds are required to excite the resonance at higher tensions. The ratio of

resonance frequency and belt speed is not constant (varies from 1 to 2.5). The inner belt

seems to have higher resonance frequencies indicating higher dynamic stiffness. And theexcitation of resonance seems to be complicated.

The following plot illustrates vibration spectra for 42 inch belt operating at steady statespeed of 2532 RPM.

The belt vibration frequency is shown in spectrum

42-inch belt, low tension

We can see the peaks at resonance frequency and the running speed. The data wascollected on the bearing house in the vertical direction.

Conclusion

Natural frequency excitation

It was not possible to excite the belt natural frequency with one defected spot. Toexcite the belt natural frequency, the defects have to be introduced to two

locations on the belt. This indicates that the belt resonances are not easy to excite

under normal low speed operation.

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Detection of belt natural frequency from spectrum

The relationship between belt natural frequency and machine speed is not very

clear. If the belt frequency is excited, it can be detected from spectrum. But

exceptions are also noted.

Relation between natural frequency excitation and tension

The higher RPM was required to excite the belt natural frequency under higher

tension.

Difference of the belt properties

Hammer test indicated small differences (about 5-10%), but the differences of

natural frequencies under running condition were higher (about 10%-20%). This

indicates that the dynamic stiffness changes with speed.

The belt length effect

Since the short belt has higher BPF, the natural frequency was excited at lowermachine speed.

The results of these studies are interesting, based as they are on experimental data

obtained from using SpectraQuests Machinery Fault Simulator and data acquisition andanalysis software. The study is not conclusive enough to make predictive models from

the data. Further work will be performed to draw some solid conclusions.