Gear Analysis Formulas For Vibration Analysis Diagnostics ppsx

Manufacturing problems in the gears, damage to the gears from contamination traveling through the mesh or from reorienting the gear during overhaul operations can cause this fault.. The

Gear Analysis Formulas For Vibration Analysis Diagnostics The gear is usually characterized by the larger, slower gear in the set The pinion is characterized by the mating faster, smaller gear in the set An accurate count of the gear teeth in the mesh is what gear analysis relies on This information must be attained by first-hand inspection of the teeth, or by consultation with the original gearbox manufacturer

Tooth counts can not be determined from the (input: output) speed ratio given on the gearbox

nameplate

Gear Meshing Frequency Calculations

GMF = (#TeethGEAR x RPMGEAR)

GMF = (#TeethPINION x RPMPINION)

(#TeethGEAR x RPMGEAR) = (#TeethPINION x RPMPINION)

RPMGEAR = (#TeethPINION x RPMPINION) / (#TeethGEAR)

RPMPINION = (#TeethGEAR x RPMGEAR) / (#TeethPINION)

Gear Assembly Phase Frequency Problems

GAPF = GMF / NA

Hunting Tooth Frequency (Tooth Repeat Problem)

FHT = (GMF x NA) / (TGEAR x TPINION)

NA= Assembly Phase Factor is described as the product of the common prime factors of the tooth counts of the mating gears

A number that can only be divided by itself and one is a prime number A factorable number is called composite The prime factors of a gear tooth count establish the assembly phase factor for the gear set

Prime Factors For Gear Tooth Count

1 = 1 x 1

2 = 1 x 2

3 = 1 x 3

4 = 1 x 2 x 2

5 = 1 x 5

6 = 1 x 2 x 3

7 = 1 x 7

8 = 1 x 2 x 2 x 2

9 = 1 x 3 x 3

10 = 1 x 2 x 5

11 = 1 x 11

12 = 1 x 2 x 2 x 3

13 = 1 x 13

14 = 1 x 7 x 2

15 = 1 x 3 x 5

16 = 1 x 2 x 2 x 2 x 2

17 = 1 x 17

18 = 1 x 2 x 3 x 3

19 = 1 x 19

20 = 1 x 2 x 2 x 5

21 = 1 x 3 x 7

22 = 1 x 2 x 11

23 = 1 x 23

24 = 1 x 2 x 2 x 2 x 3

25 = 1 x 5 x 5

26 = 1 x 2 x 13

27 = 1 x 3 x 3 x 3

28 = 1 x 2 x 2 x 7

29 = 1 x 29

30 = 1 x 2 x 3 x 5

31 = 1 x 31

32 = 1 x 2 x 2 x 2 x 2 x 2

33 = 1 x 3 x 11

34 = 1 x 2 x 17

35 = 1 x 5 x 7

36 = 1 x 2 x 2 x 3 x 3

37 = 1 x 37

38 = 1 x 2 x 19

39 = 1 x 3 x 13

40 = 1 x 2 x 2 x 2 x 5

41 = 1 x 41

42 = 1 x 2 x 3 x 7

43 = 1 x 43

44 = 1 x 2 x 2 x 11

45 = 1 x 3 x 3 x 5

46 = 1 x 2 x 23

47 = 1 x 47

48 = 1 x 2 x 2 x 2 x 2 x 3

49 = 1 x 7 x 7

50 = 1 x 2 x 5 x 5

51 = 1 x 3 x 17

52 = 1 x 2 x 2 x 13

53 = 1 x 53

54 = 1 x 2 x 3 x 3 x 3

55 = 1 x 5 x 11

56 = 1 x 2 x 2 x 2 x 7

57 = 1 x 3 x 19

58 = 1 x 2 x 29

59 = 1 x 59

60 = 1 x 2 x 2 x 3 x 5

61 = 1 x 61

62 = 1 x 2 x 31

63 = 1 x 3 x 3 x 7

64 = 1 x 2 x 2 x 2 x 2 x 2 x 2

65 = 1 x 5 x 13

66 = 1 x 2 x 3 x 11

67 = 1 x 67

68 = 1 x 2 x 2 x 17

69 = 1 x 3 x 23

70 = 1 x 2 x 5 x 7

71 = 1 x 71

72 = 1 x 2 x 2 x 2 x 3 x 3

73 = 1 x 73

74 = 1 x 2 x 37

75 = 1 x 3 x 5 x 5

76 = 1 x 2 x 2 x 19

77 = 1 x 7 x 11

78 = 1 x 2 x 3 x 13

79 = 1 x 79

80 = 1 x 2 x 2 x 2 x 2 x 5

Gear Assembly Phase Problems For Vibration Analysis Diagnostics

Gear assembly phase problems are a gear wear pattern induced fault that outcomes in the

generation of fractional sub-harmonics of gear mesh frequency in the vibration spectrum

Manufacturing problems in the gears, damage to the gears from contamination traveling through the mesh or from reorienting the gear during overhaul operations can cause this fault What usually results from this type of problem is accelerated wear

For any gear, the assemble phase factor (NA) defines the groups of gear teeth that will come in contact during meshing The product of the common prime factors of the tooth counts in the meshing gears is NA

For example:

TGEAR = 21 Prime factors: 1 x 3 x 7

TPIMION = 9 Prime factors: 1 x 3 x 3

NA = product of Common prime factors, 1 x 3 = 3

The gear seat will have 3 unique groups or phases of teeth that will mesh The spectral frequency

produced is the gear assembly phase frequency will be equal to (GMF/NA) An example for a spectrum is shown below

Gear Eccentricity & Backlash For Vibration Analysis Diagnostics

Eccentricity faults create a radial unbalance like response at 1x RPM of the eccentric component or

part Such as eccentric gears in mesh, the effect (wobble) of the eccentric part is felt on the

“coupled” component

The vibration frequency spectrum of eccentric gear sets will create amplified modulation at 1x RPM of the eccentrics part and produce sidebands at this frequency around gear mesh frequency harmonics The amplitudes and number of sidebands sets indicate severity Numerous times the

sidebands will not be even (symmetry) The 3x and 1x GMF harmonics are likely to increase in amplitude because of the change in the “sliding” contact as the teeth move in and out of mesh

Impact caused by increased clearance and backlash in the gear teeth may also excite the gear natural frequencies Spacing of the sideband sets normally identifies the eccentric gear Increasing load on the gears will usually reduce backlash amplitude response

Gear Hunting Tooth Problems For Vibration Analysis Diagnostics

This problem is a special tooth repeat problem in gear sets Due to a flaw on both a gear tooth and mating pinion tooth, a unique frequency is generated Manufacturing problems, mishandling, or damage from operating in the field can be the cause of the gear faults

When both faults enter the mesh at the same time, the maximum vibratory response occurs This will not occur on every revolution The tooth counts of the meshing gears and the gear set assembly factor is what the rate of occurrence depends on

The group of gear teeth that will come in contact during meshing is defined by the assembly phase factor (NA) for any gear The product of the common prime factors of the tooth counts in the

meshing gears is NA

FHT = GMF x Na

(TGEAR x TPIMION)

The hunting tooth frequency, FHT can be indicated by itself as a very low frequency in the

vibration spectrum, or more frequently as a sideband frequency surrounding 1x RPM and/or gear mesh frequency harmonics.

Gear Loose Fit Problem For Vibration Analysis Diagnostics

A loose fit problem in a gear train is not in fact a gear fault, but operation of a gearbox with

condition can cause gear damage

Excessive clearances in bearings supporting the gear shafts themselves can cause the looseness Or can also be caused from loss of press fits or loose keyways locking the gear hub to the shaft

Mechanical looseness type C response with increased running speed harmonics and raised noise

floor is what usually indicates by vibration spectrum, but the gear mesh frequency harmonics are also affected Increased amplitudes of GMF harmonics and amplitude trends that increase with higher GMF orders is the result

Gear Misalignment For Vibration Analysis Diagnostics

Misaligned gear sets (Gearbox) tend to create higher 2x GMF amplitudes because of a change in

the “rolling” contact between the gear teeth about the pitch circle Like in most gear faults, the basis

of the problem is indicated by the spacing of the sidebands around the Gear Mess Frequency

harmonics

Misaligned gears will create dominant sidebands spaced at 2x RPM of the misaligned gear in the

frequency spectrum Numerous times these sidebands won’t be even (symmetry) with the higher amplitudes on the lower frequency side of the GMF harmonics Uneven or skewed wear pattern on the circumference may be shown by visual inspection of the gears Prior to spectral indications, gearbox oil analysis is helpful in offering early evidence of gear wear

General Amplitude Conversion Factors

(Only Simple Sinusoids Waveforms)

For Vibration Analysis Diagnostics

Peak 2.000 Peak-to-Peak

mili-seconds x 1,000 = seconds

micro-seconds x 1,000,000 = seconds

seconds / 1,000 = mili-seconds

seconds / 1,000,000 = micro-seconds

CPM/60 = Hz

Hz x 60 = CPM

Hertz = Cycles/Second (CPS)

CPM = Cycles/Minute

RPM = Revolutions/Minute

Orders = CPM/(1x RPM)

General Natural Frequency Equations For Vibration Analysis Diagnostics

FNAT = FNAT =

K = Stiffness (psi)

M = Mass, pounds force (lbf)

W = Weight, pounds mass (lbm)

g = Gravity constant (32.2 ft/s2, 386.09 in/s2)

The Normal Gear Spectrum Waveform For Vibration Analysis Diagnostics

Vibration analysis of gear problems is appropriately addressed by spectral analysis covering the

range of frequencies where bearing defects typically occur, likewise, a higher frequency range the spans as least the first three gear mesh frequency harmonics The rolling element bearing analysis range is usually the higher of 50x RPM or 120,000 CPM (2kHz) The gear analysis frequency range

is usually 3.25x GMF Gear Mess Frequency The analysis needs to know the tooth counts of the

gears on each shaft for the accurate calculation of GMF

The normal vibration spectrum for gear analysis will point out: low noise floor, low-level 1x RPM

amplitudes for each gear shaft, low amplitude GMF harmonics that diminish at higher frequency, and low amplitude running speed sidebands surrounding the GMF harmonics

Sinusoidal GMF response should dominate the normal gear time waveform with minor modulation and no distinct transient events The model analysis time waveform ought to be limited to 6 to 10 shaft revolutions (each rotor)

Excessive Gear Tooth Load For Vibration Analysis Diagnostics

Tooth-load is not a real gear fault, but the gear meshing frequencies are usually very sensitive to

load The load ought to be set in the same conditions for each condition monitoring survey, for meaningful vibration trending Nearly all sources recommend at least 80% of maximum load ought

to be maintained Construct separate “routes” for each process to maintain repeatable loads for each trend, if the gearbox application involves a series of processes or load conditions

The problems are usually indicated when running speed sidebands sets augment in number and/or

when gear natural frequencies show up in the spectrum.

Do not forget to capture a time waveform to check for broken, cracked, or distressed gear teeth that can be induced from severely overloaded conditions