NISTIR 7183 

Vibration Signatures for Three Positive Displacement 

Compressors 

David A. Yashar 

W. Vance Payne 

U.S. DEPARTMENT OF COMMERCE 

National Institute of Standards and Technology 

Building Environment Division 

Building and Fire Research Laboratory 

Gaithersburg, Maryland 20899-8631 

National Institute of Standards and Technology 

Technology Administration 

United States Department of Commerce 
NISTIR 7183 

Vibration Signatures for Three Positive Displacement 

Compressors 

David A. Yashar 

W. Vance Payne 

U.S. DEPARTMENT OF COMMERCE 

National Institute of Standards and Technology 

Building Environment Division 

Building and Fire Research Laboratory 

Gaithersburg, Maryland 20899-8631 

December 2004 

U.S. Department of Commerce 

Donald L. Evans, Secretary 

National Institute of Standards and Technology 

Arden L. Bement, Jr., Director

ii
Vibration Signatures for Three Positive Displacement 

Compressors 

David A. Yashar and W. Vance Payne 

Abstract 

This report presents vibration data for three positive displacement compressors which will be 

used to evaluate Microelectromechanical Systems (MEMS) vibration sensors at a later time. The 

axial, radial and tangential vibration signatures of three compressors were measured under 

different operating conditions. An open-drive four cylinder compressor’s vibration signatures 

were measured at discharge pressures of 1724 kPa (250 psig) and 2413 kPa (350 psig), with 

three different drive frequencies. A hermetic scroll compressor’s vibration signatures were 

measured at three drive frequencies with a discharge pressure of 1724 kPa (250 psig), and at one 

drive frequency with a discharge pressure of 2241 kPa (325 psig). Finally a large, six-cylinder, 

chiller compressor’s vibration signatures were measured with two, four, and six of the cylinders 

engaged. 

Keywords: compressor vibration

i
TABLE OF CONTENTS 

Abstract.................................................................................................................ii 

List of Tables........................................................................................................iii 

List of Figures.......................................................................................................iv 

Nomenclature........................................................................................................vi 

Acknowledgment ..................................................................................................vii 

 1: Introduction............................................................................................ 1 

 2: Experimental Setup................................................................................ 2 

2.1: Data acquisition equipment and uncertainty...................2 

2.2: Four cylinder, reciprocating compressor........................ 3 

2.3: Hermetic, scroll compressor...........................................3 

2.4: Six cylinder, reciprocating compressor .......................... 4 

 3: Experimental Procedure.........................................................................5 

3.1: Four cylinder, reciprocating compressor test procedure 5

3.2: Hermetic, scroll compressor test procedure.................... 5 

3.3: Six cylinder, reciprocating compressor test procedure...6 

 4: Experimental Results.............................................................................7 

4.1: Four cylinder, reciprocating compressor vibration 

 signatures........................................................................ 7 

4.2: Hermetic, scroll compressor vibration signatures ..........10 

4.3: Six cylinder, reciprocating compressor vibration 

 signatures........................................................................ 14 

 5: Concluding Remarks.............................................................................. 18 

References............................................................................................................. 19 

Appendix A: Vibration Analysis Derivations......................................................20 

ii
List of Tables 

2.1.1: Data acquisition card and accelerometer specifications............................ 2 

3.1.1: Four cylinder, reciprocating compressor test conditions...........................5 

3.2.1: Hermetic, scroll compressor test conditions.............................................. 6 

3.3.1: Six cylinder, reciprocating compressor test conditions.............................6 

iii
List of Figures 

2.1.1: Triaxial accelerometer ................................................................................................3

2.2.1: Four cylinder, open-drive, reciprocating compressor.................................................3 

2.3.1: Hermetic, scroll compressor.......................................................................................4 

2.4.1: Six cylinder, reciprocating compressor ......................................................................4 

4.1.1: Axial acceleration for four-cylinder reciprocating compressor at three 

frequencies at the low discharge pressure..................................................................7 

4.1.2: Radial acceleration for four-cylinder reciprocating compressor at three 

frequencies at the low discharge pressure..................................................................7 

4.1.3: Tangential acceleration for four-cylinder reciprocating compressor at 

three frequencies at the low discharge pressure.........................................................8 

4.1.4: Axial, radial, and tangential acceleration for four-cylinder 

reciprocating compressor at 45 Hz ............................................................................9 

4.1.5: Tangential acceleration for four-cylinder reciprocating compressor at 

three frequencies at the high discharge pressure .......................................................9 

4.1.6: Tangential acceleration for four-cylinder reciprocating compressor at 

45 Hz at the low and high discharge pressure ...........................................................10 

4.2.1: Axial acceleration for the scroll compressor at three frequencies at the 

low discharge pressure...............................................................................................11 

4.2.2: Radial acceleration for the scroll compressor at three frequencies at 

the low discharge pressure.........................................................................................11 

4.2.3: Tangential acceleration for the scroll compressor at three frequencies 

at the low discharge pressure .....................................................................................12 

4.2.4: Axial, radial, tangential acceleration for the scroll compressor at 30 

Hz at the low discharge pressure ...............................................................................12 

4.2.5: Axial and radial acceleration for the scroll compressor at 25 Hz at the 

high discharge pressure..............................................................................................13 

4.2.6: Radial acceleration for the scroll compressor at 25 Hz at the low and 

high discharge pressure..............................................................................................13 

iv
4.2.7: Axial acceleration for the scroll compressor failure at a drive 

frequency of 25 Hz and low pressure ........................................................................14 

4.3.1: Axial, radial, and tangential acceleration with two-cylinders loaded for 

the large reciprocating compressor............................................................................15 

4.3.2: Axial, radial, and tangential acceleration with four-cylinders loaded 

for the large reciprocating compressor ......................................................................15 

4.3.3: Axial, radial, and tangential acceleration with six-cylinders loaded for 

the large reciprocating compressor............................................................................16 

4.3.4: Axial acceleration with two-, four-, and six-cylinders loaded for the 

large reciprocating compressor..................................................................................16 

4.3.5: Radial acceleration with two-, four-, and six-cylinders loaded for the 

large reciprocating compressor..................................................................................17 

4.3.6: Tangential acceleration with two-, four-, and six-cylinders loaded for 

the large reciprocating compressor............................................................................17 

A1: Sketch of a bearing ........................................................................................................20 

v
Nomenclature 

fo rotational frequency of the compressor shaft (r/s or Hz) 

f/fo ratio of vibration frequency to the compressor shaft rotational frequency 

gn acceleration experienced by a unit of mass within earth’s gravity field, equivalent 

to 9.81 m/s

2 (32.2 ft/s2

) 

OD outside diameter, mm (in) 

RPM compressor shaft revolutions per minute 

VDC volts of direct current 

vi
Acknowledgment

The authors thank Mr. John Wamsley, Mr. Glenn Savage, and Mr. Glen Glaeser for their 

assistance with the testing of these compressors. 

vii
1: Introduction 

Vibration signatures of machinery contain a wealth of information regarding the interaction of 

all of the machine’s components. For this reason, it is practicable to use vibration monitoring to 

detect and diagnose compressor faults before they lead to catastrophic failure. In order to 

successfully implement vibration as a means of fault detection, it is necessary to acquire and 

evaluate the appropriate measurement equipment. 

Changes in the vibration signature over time may indicate that a defect has become present 

somewhere in the system. Therefore, it is possible to detect a fault by comparing the vibration 

signature of a faultless system to the signature of the same system after a period of operation. By 

continuously monitoring the vibration signature, it is possible to detect a fault before it becomes 

severe to the point of mechanical failure. Furthermore, Johnson (2000) reasoned that if a 

particular mode of failure were expected, one could expect to see enhanced excitation of specific 

frequencies while monitoring the vibration signature of a system (see Appendix A for detailed 

derivations regarding roller bearing failure). Therefore, it is not only possible to detect the 

presence of a problem, but also to diagnose problems as they arise. 

Commercially available accelerometers provide an excellent means for acquiring vibration 

information; however the cost associated with these sensors makes them unattractive for heating, 

ventilation, air conditioning and refrigeration (HVAC&R) applications. MEMS accelerometers 

offer a viable, low cost option for data acquisition, but they must first be evaluated for this 

application. In order to evaluate their feasibility, a series of vibration signatures for several 

compressors must be catalogued for a reference in evaluating the response of a vibration meter to 

known conditions. 

1
2: Experimental Setup 

2.1: Data acquisition equipment and uncertainty 

The vibrational signatures of each compressor were gathered using a triaxial quartz 

accelerometer and dynamic signal acquisition card located in the personal computer interface 

(PCI) bus of a personal computer. Table 2.1.1 lists the characteristics of the accelerometer and 

data acquisition card. Figure 2.1.1 shows the size of the triaxial accelerometer relative to a 

writing pen. The manufacturer of the accelerometer lists its 95 % confidence limit ( two sigma 

on the measured value) for acceleration to be ±5 % of the reading. In the table below, bias level 

is the voltage offset above 0 VDC; therefore, all acceleration waveforms will originate (or be 

centered around) the bias level voltage. The bias level voltage may be subtracted from the 

acceleration waveform to produce the raw acceleration waveform with zero bias. 

Table 2.1.1: Data acquisition card and accelerometer specifications 

Three-Axis Accelerometer with a ± 490 m/s

2

 (50 gn) range 

Model 356B07

x-axis, sensitivity 9.82 mV/(m/s

2

) [96.3 mV/gn] 

x-axis, bias level 11.6 VDC 

y-axis, sensitivity 10.04 mV/(m/s

2

) [98.5 mV/gn] 

y-axis, bias level 11.5 VDC 

z-axis, sensitivity 9.69 mV/(m/s

2

) [95.0 mV/gn] 

z-axis, bias level 11.3 VDC 

PCI Dynamic Signal Acquisition Card 

Sample Rate 5 to 205 thousands of samples per second 

Inputs 2 analog, 16 bit 

Bandwidth 0 kHz to 95 kHz 

Dynamic Range 90 dB 

2
Figure 2.1.1: Triaxial accelerometer 

Data acquisition code was written using commercial DAQ software. The vibrational waveforms 

were captured and analyzed using a Fast Fourier Transform (FFT) to clarify those frequencies 

experiencing the high amplitude vibration. 

2.2: Four cylinder, reciprocating compressor 

The open-drive R22 compressor shown in Figure 2.2.1 was connected to a 5.6 kW (7.5 hp) 

motor with full speed of 184.3 rad/s (1760 RPM) at 60 Hz. This compressor uses bronze bushed 

bearings. The picture on the right-hand side of Figure 2.2.1 uses arrows to indicate where the 

mounting fixtures for the accelerometer were located. Radial, axial, and tangential vibration 

measurements were taken for this compressor. 

 Figure 2.2.1: Four cylinder, open-drive, reciprocating compressor (the arrows on picture at the right

indicate the position of vibration sensor mounts)

2.3: Hermetic, scroll compressor 

The R410A scroll compressor shown in Figure 2.3.1 had a displacement of 10.13 m3/h 

(5.96 ft3

/min) at 366.5 rad/s (3500 RPM) operating at 230 V, 3-phase. Figure 2.3.1 uses arrows 

3
to indicate where the mounting fixtures for the accelerometer were located. Radial, axial, and 

tangential vibration measurements were taken for this compressor. 

Figure 2.3.1: Hermetic, scroll compressor (the arrows on the picture indicate the position of the vibration 

sensor mounts)

2.4: Six cylinder, reciprocating compressor 

The large, open-drive R404A compressor shown in Figure 2.4.1 has a displacement of 796 m3

/h 

(7.54 ft3

/s). The compressor can be operated with two, four, or six cylinders with various 

amount of hot-gas bypass for capacity control. The unit operates at constant shaft rotational 

speed. Motor shaft speed is 186.9 rad/s (1785 RPM) on a 26.0 cm OD (10.25 in OD) sheave 

connected to the driven sheave with an OD of 67.3 cm (26.5 in). This produces a compressor 

shaft rotational speed of approximately 72.3 rad/s (690 RPM). The compressor uses automotive 

style journal bearings fed by pressurized oil on its crankshaft. Figure 2.4.1 uses arrows to 

indicate where the mounting fixtures for the accelerometer were located. Radial, axial, and 

tangential vibration measurements were taken for this compressor. 

 Figure 2.4.1: Six cylinder, reciprocating compressor (the arrows on the picture at the right indicate the 

position of the vibration sensor mounts)

4
3: Experimental Procedure 

A triaxial accelerometer was mounted on each compressor in two locations; 1) close to the main 

axis of the compressor crank shaft for axial and radial acceleration measurements, and 2) 

tangential to the crank-axis for tangential acceleration measurements. Several scans were made 

at a rate of 100 000 scans per second for 1 s in the axial, radial, and tangential directions. Data 

were recorded as voltages with respect to sample time, and the data were also processed using 

FFT to reveal frequency characteristics of the vibration signals. 

To further aid in simplifying the data, the vibration frequencies were tabulated as multiples of

the rotational frequency (r/s, f0). Estimates of the rotational frequency for the four cylinder 

reciprocating compressor and the hermetic scroll compressor were based upon the drive 

frequency and the motor speed at 60 Hz. A simple linear relationship was assumed to give an 

estimate of the rotational frequency, i.e., Drive frequency / 60 Hz x Motor Rotational Velocity at 

60 Hz. The estimated rotational frequency of the six cylinder reciprocating compressor was 

72.3 rad/s (690 RPM). 

In all cases, the peaks of the various harmonics were typically within 2 % of the estimated 

rotational frequency, with the most extreme difference being less than 9 %. The exact rotational 

frequency was found by adjusting the frequency so that the harmonics aligned with integer 

multiples of the rotational frequency. 

3.1: Four cylinder, reciprocating compressor test procedure 

The compressor was tested with two discharge pressures and three different drive frequencies. 

Table 3.1.1 lists the pressures, drive frequencies, and resulting shaft rotational frequency for 

each test. 

Table 3.1.1: Four cylinder, reciprocating compressor test conditions 

True Shaft Rotational Speed Drive Frequency Estimated Shaft 

Rotational Speed 1724 kPa (250 psig) discharge 2413 kPa (350 psig) discharge 

25 Hz 76.8 rad/s 

(733 RPM) 

72.3 rad/s 

 (690 RPM) 

 70.7 rad/s 

 (675 RPM) 

35 Hz 107.4 rad/s 

(1026 RPM) 

 104.7 rad/s 

 (1000 RPM) 

 103.7 rad/s 

 (990 RPM) 

45 Hz 138.2 rad/s 

(1320 RPM) 

 136.7 rad/s 

 (1305 RPM) 

 136.1 rad/s 

 (1300 RPM) 

3.2: Hermetic, scroll compressor test procedure 

The scroll compressor had been part of an R410A variable speed condensing unit. Before the 

vibration tests, the scroll was operated between 40 Hz and 65 Hz during the system testing and at 

various operating conditions with the added protection of an oil separator on the compressor 

discharge. The compressor performed with almost no audible noise or vibration for several 

weeks while operating in the normal frequency range. The operator then began to notice the 

amperage draw of the compressor had increased over a several day period. This change in 

amperage caused him to observe the compressor more closely. During a normal test where the 

5
condensing unit compressor was operating at 45 Hz, a loud rattle was heard and the compressor 

over-amped, tripping the amperage limit on the variable speed drive. Subsequent attempts to 

operate the compressor above a 40 Hz drive frequency resulted in the same loud rattle and shutdown after less than 3 min of operation. 

In order to obtain some useful vibration data from this compressor, the compressor drive 

frequency was lowered until the compressor would operate for 10 min to 15 min without rattle or 

over-amping. Vibration data were recorded at two pressures and several drive frequencies below 

the rattling frequency. At higher pressures the compressor exhibited excessive noise and 

vibration due to an unknown failure of its internal components. The loud knock and excessive 

vibration data were also recorded and presented in this report. Table 3.2.1 shows the test matrix 

for this compressor. Tests at higher frequencies were not possible due to excessive vibrations 

and motor over-amping (high current draw). 

Table 3.2.1: Hermetic, scroll compressor test conditions 

True Shaft Rotational Speed Drive Frequency Estimated Shaft 

Rotational Speed 

1724 kPa (250 psig) discharge 2413 kPa (350 psig) discharge 

20 Hz 122.2 rad/s 

(1167 RPM) 

 119.4 rad/s 

 (1140 RPM) 

25 Hz 152.7 rad/s 

(1458 RPM) 

150.8 rad/s 

 (1440 RPM) 

141.4 rad/s 

 (1350 RPM) 

30 Hz 183.3 rad/s 

(1750 RPM) 

183.3 rad/s 

 (1750 RPM) 

3.3: Six cylinder, reciprocating compressor test procedure 

The large, open-drive reciprocating compressor was tested with different numbers of cylinder 

engaged. Pressure control and drive frequency control were not possible with this compressor. 

Table 3.3.1 lists the test matrix for this compressor. 

Table 3.3.1: Six cylinder, reciprocating compressor test conditions 

True Shaft Rotational Speed 

Estimated Drive 

RPM 

2 cylinders (with hot gas 

bypass) 4 cylinders 6 cylinders 

72.3 rad/s 

 (690 RPM) 

71.9 rad/s 

 (687 RPM) 

 71.6 rad/s 

 (684 RPM) 

 71.0 rad/s 

 (678 RPM) 

6
4: Experimental Results 

The following figures characterize the vibrational signatures of the three compressors operating 

under various load conditions. 

4.1: Four cylinder, reciprocating compressor vibration signatures 

This compressor was operated at two different discharge pressures and three drive frequencies. 

Figures 4.1.1, 4.1.2, and 4.1.3 show the axial, radial, and tangential components, respectively, of 

acceleration at multiples of the rotational speed for 1724 kPa (250 psig) discharge pressure and 

three different drive speeds. Figure 4.1.4 shows the axial, radial, and tangential vibration 

signatures at a 1724 kPa (250 psig) discharge pressure with a drive frequency of 45 Hz. Figure 

4.1.5 shows the tangential acceleration for 2413 kPa (350 psig) discharge pressure at drive 

frequencies of 25 Hz, 35 Hz, and 45 Hz. Figure 4.1.6 shows the tangential acceleration at a 

drive frequency of 45 Hz for both discharge pressures. 

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

f / fo

Acceleration (gn)

Low P, 25 Hz, Axial

Low P, 35 Hz, Axial

Low P, 45 Hz, Axial

Figure 4.1.1: Axial acceleration for four-cylinder reciprocating compressor at three frequencies 

at the low discharge pressure 

7
0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

f / fo

Acceleration (gn)

Low P, 25 Hz, Radial

Low P, 35 Hz, Radial

Low P, 45 Hz, Radial

Figure 4.1.2: Radial acceleration for four-cylinder reciprocating compressor at three frequencies 

at the low discharge pressure 

0

0.05

0.1

0.15

0.2

0.25

0.3

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

f / fo

Acceleration (gn)

Low P, 25 Hz, Tangential

Low P, 35 Hz, Tangential

Low P, 45 Hz, Tangential

Figure 4.1.3: Tangential acceleration for four-cylinder reciprocating compressor at three 

frequencies at the low discharge pressure 

8
0

0.05

0.1

0.15

0.2

0.25

0.3

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

f / fo

Acceleration (gn)

Low P, 45 Hz, Axial

Low P, 45 Hz, Radial

Low P, 45 Hz, Tangential

Figure 4.1.4: Axial, radial, and tangential acceleration for four-cylinder reciprocating 

compressor at 45 Hz 

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

f / fo

Acceleration (gn)

High P, 25 Hz, Tangential

High P, 35 Hz, Tangential

High P, 45 Hz, Tangential

Figure 4.1.5: Tangential acceleration for four-cylinder reciprocating compressor at three 

frequencies at the high discharge pressure 

9
0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

012 3456 7 8 9 10 11 12 13 14 15

f / fo

Acceleration (gn)

Low P, 45 Hz, Tangential

High P, 45 Hz, Tangential

Figure 4.1.6: Tangential acceleration for four-cylinder reciprocating compressor at 45 Hz at the 

low and high discharge pressure 

4.2: Hermetic, scroll compressor vibration signatures 

The scroll compressor was tested at 20 Hz, 25 Hz, and 30 Hz with a discharge pressure of 

1724 kPa (250 psig). The compressor was tested at 25 Hz and 2241 kPa (325 psig) as well, but 

only axial and radial acceleration were measured. Only one frequency was tested at the higher 

pressure due to excessive noise and over-amping of the variable speed drive. The figures below 

show the vibration amplitude with frequencies shown as multiples of the rotational frequency. 

Figures 4.2.1, 4.2.2, and 4.2.3 show the axial, radial, and tangential components, respectively, of 

acceleration at multiples of the rotational speed for 1724 kPa (250 psig) discharge pressure and 

three different drive speeds. Figure 4.2.4 shows the axial, radial, and tangential vibration 

signatures at a 1724 kPa (250 psig) discharge pressure with a drive frequency of 30 Hz. Figure 

4.2.5 shows the axial and radial acceleration for 2241 kPa (325 psig) discharge pressure at a 

drive frequency of 25 Hz. Figure 4.2.6 shows the radial acceleration at a drive frequency of 

25 Hz for both discharge pressures. 

Figure 4.2.7 shows the vibrations experienced by the scroll compressor during a failure. The 

system was immediately shut down by the technician when these vibrations occurred. The figure 

shows that acceleration in the axial direction approached 3 gn’s at a frequency ratio between 0.03 

and 0.05. This corresponds to approximately 8 Hz to 10 Hz in the frequency domain. This level 

of vibration is two to three orders of magnitude larger than vibrations seen during normal 

operation. 

10
0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0 1 2 3 456 7 8 9 10 11 12 13 14 15

f / fo

Acceleration (gn)

Low P, 20 Hz, Axial

Low P, 25 Hz, Axial

Low P, 30 Hz, Axial

Figure 4.2.1: Axial acceleration for the scroll compressor at three frequencies at the low 

discharge pressure 

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

f / fo

Acceleration (gn)

Low P, 20 Hz, Radial

Low P, 25 Hz, Radial

Low P, 30 Hz, Radial

Figure 4.2.2: Radial acceleration for the scroll compressor at three frequencies at the low 

discharge pressure 

11
0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

f / fo

Acceleration (g)

Low P, 20 Hz, Tangential

Low P, 25 Hz, Tangential

Low P, 30 Hz, Tangential

Figure 4.2.3: Tangential acceleration for the scroll compressor at three frequencies at the low 

discharge pressure 

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

f / fo

Acceleration (gn)

Low P, 30 Hz, Axial

Low P, 30 Hz, Radial

Low P, 30 Hz, Tangential

Figure 4.2.4: Axial, radial, tangential acceleration for the scroll compressor at 30 Hz at the low 

discharge pressure 

12
0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

f / fo

Acceleration (gn)

High P, 25 Hz, Axial

High P, 25 Hz, Radial

Figure 4.2.5: Axial and radial acceleration for the scroll compressor at 25 Hz at the high 

discharge pressure 

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

f / fo

Acceleration (gn)

Low P, 25 Hz, Axial

High P, 25 Hz, Axial

Figure 4.2.6: Radial acceleration for the scroll compressor at 25 Hz at the low and high 

discharge pressure 

13
0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 0.511.5 2 2.5

f / fo

Acceleration (gn)

3

Failure at Low P, 25 Hz, Axial

Figure 4.2.7: Axial acceleration for the scroll compressor failure at a drive frequency of 25 Hz 

and low pressure 

4.3: Six cylinder, reciprocating compressor vibration signatures 

The six cylinder reciprocating compressor was tested at three different levels of loading; 

operation with two, four, or six cylinders engaged. The figures below show the vibration 

amplitude with frequencies shown as multiples of the rotational frequency. 

Figures 4.3.1, 4.3.2, and 4.3.3 show all three components of acceleration at multiples of the 

rotational speed for two-cylinder, four-cylinder, and six-cylinder operation, respectively. 

Figures 4.3.4, 4.3.5, and 4.3.5 show the axial, radial, and tangential components, respectively, of 

acceleration at multiples of the rotational speed for the three different loading levels. It is 

interesting to note that a 1⁄2 fo component of acceleration was seen for each measurement, 

although this does not align with the shaft rotational frequency. This component is seen between 

the second and third harmonic, as well as multiples of 1⁄2 fo. Its magnitude was the smallest when 

the compressor was fully loaded and running on six cylinders. This 1⁄2 fo component of vibration 

had the largest magnitude in the axial direction (parallel with the compressor crank shaft). No 

obvious reason for this vibration was noted, and it may be a normal phenomenon that was part of 

the compressor’s no-fault vibration signature. 

14
0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

f / fo

Acceleration (gn)

2-cylinder Axial

2-cylinder Radial

2-cylinder Tangential

Figure 4.3.1: Axial, radial, and tangential acceleration with two cylinders loaded for the large 

reciprocating compressor 

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

f / fo

Acceleration (gn)

4-cylinder Axial

4-cylinder Radial

4-cylinder Tangential

Figure 4.3.2: Axial, radial, and tangential acceleration with four cylinders loaded for the large 

reciprocating compressor 

15
0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

01234567 8 9 10 11 12 13 14 15

f / fo

Acceleration (gn)

6-cylinder Axial

6-cylinder Radial

6-cylinder Tangential

Figure 4.3.3: Axial, radial, and tangential acceleration with six cylinders loaded for the large 

reciprocating compressor 

0

0.005

0.01

0.015

0.02

0.025

0.03

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

f / fo

Acceleration (gn)

2-cylinder Axial

4-cylinder Axial

6-cylinder Axial

Figure 4.3.4: Axial acceleration with two, four, and six cylinders loaded for the large 

reciprocating compressor 

16
0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

f / fo

Acceleration (gn)

2-cylinder Radial

4-cylinder Radial

6-cylinder Radial

Figure 4.3.5: Radial acceleration with two, four, and six cylinders loaded for the large 

reciprocating compressor 

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0123456 789 10 11 12 13 14 15

f / fo

Acceleration (gn)

2-cylinder Tangential

4-cylinder Tangential

6-cylinder Tangential

Figure 4.3.6: Tangential acceleration with two, four, and six cylinders loaded for the large 

reciprocating compressor 

17
5: Concluding Remarks 

The preceding figures document the vibration characteristics of three different compressors. 

These vibration signatures are useful in evaluating a vibration meter that may be applied to 

future test systems; any vibration meter should have sampling and response characteristics 

sufficient to capture the vibrations seen with these compressors. The vibration signatures 

presented here are not meant to detect a fault within the compressor, but serve only to indicate 

the range of vibrations seen during normal operation of these compressors. Long term

monitoring, trending, and fault simulations would need to be performed in order to diagnose a 

particular fault using vibration information. This document is intended to serve as a catalog for 

steady-state vibration information and help evaluation of future vibration measurement devices. 

The vibration tests included a scroll compressor that had a failure during testing. This failure 

allowed characterization of the vibration amplitude and frequency that would be seen in an 

actual field-installed system. The vibration meter meant to detect this failure should have a 

resolution of at least ±9.8 m/s

2

 (±1 gn). Normal operations of all the compressors tested here 

were below 4.9 m/s

2

 (0.5 gn) in all directions. Vibration meters with greater sensitivity may cost 

more to produce and may be less robust in a compressor system environment. At a minimum, all 

of these factors must be weighed against development and economic constraints when designing 

a workable vibration meter. 

18
References 

Johnson, Michael S. “Vibration Tests for Bearing Wear,” ASHRAE Journal, October 2000, pp. 

52-58. 

19
Appendix A: Vibration Analysis Derivations for Rolling Element Bearings 

Figure A.1 shows a schematic of a rolling element 

bearing. The inner race has a radius R, the roller has 

a radius r, and the shaft is rotating clockwise at a rate 

ωs. The position of the roller relative to the center of

the shaft is defined by the angle φ. There are n 

rollers distributed throughout the bearing. 

c r A 

R

φ

o Because the top of the roller is in contact with the 

fixed outer race, and the bottom of the roller is in 

contact with the inner race at point A, the velocity of 

point A is defined by: 

ωs 

2 VA r θ

•

= ×

Figure A.1 Sketch of bearing θ defines the angle of rotation of the roller. 

The velocity of this point is also defined by its position relative to the center of the shaft: 

V R A = − ×ωs

Therefore, the angular rate of rotation of the roller is related to the shaft rotation rate: 

2 s

R

r

θ ω •= −

The velocity of the center of the roller is defined by its path around the center of the shaft: 

V R c ( ) r φ

•

= − + ×

But since the top of the roller is the instantaneous center of rotation, the velocity of point C is 

also defined by: 

V r c θ

•

= ×

Therefore the rate at which the roller orbits the center of the shaft is related to the rotation rate of

the roller: 

( )

r

R r φ θ • •

= − ×

+

And therefore, it is related to the shaft rotation rate: 

( ) 2 2( ) s s

r R R

R r r R r

φ ω ω •     = −  × − =   + +    

This is the rate at which a fixed point on the outer race of the bearing will be in contact with a 

roller. If a defect were present on the surface of the outer race, it would be impacted by the 

20
roller at this rate. Since there are n rollers evenly spaced along this bearing, the rate at which 

rollers come into contact with this defect is related to the shaft rotation rate: 

( ) , 2 outer contact s

nR

R r

ω = ω

+

The rate of contact between an inner race surface defect and a roller is found as follows. The 

angle of rotation of the shaft, α (ωs is the time derivative of α), is related to the orbital rate of the 

roller. From the previous step: 

2( )

d R

dt R r dt

φ dα = +

The roller will be in contact with the same point on the inner race every time the inner race laps 

the roller: 

φ = − α π 2k

Therefore: 

( ) 2

2

R k

R r

φ = − α π = +α

( )

( )

( )

2

2 1

2 2

R R r

k

R r R r

π α α

  + = −   = + +  

Since there are n rollers, the rate at which rollers come into contact with a point on the inner race 

is: 

( )

( ) ,

2

2 inner contact s

n R r

R r

ω ω

+ = +

Finally, in order to find the impact rate for a defect on the surface of a roller itself, one must 

visualize the roller completing one full orbit: 

φ = 2π

During this orbit, the prior relationship shows that the roller will rotate through an angle of: 

( ) 2 R r

r

π θ = +

In other words, the roller will go through

(R r)

r

+

rotations as it completes one orbit. 

Since one contact with each race is added through each orbit because of the changing angle of 

contact, a point on the surface of the roller will be in contact 

(R 2r)

r

+

times with each race. 

21
Since there are an inner and an outer race, this point will be impacted a total 

of

2 2 ( ) R r

r

+

( )

times throughout each orbit. 

Since the orbital rate is related to the shaft rotation rate: 

2 s

R

R r φ ω •

= +

A point on the surface of a roller will be in contact with the races at the rate of: 

( )

( ) ,

2

roller impact s

R R r

r R r

ω ω

+ = +

22