Gear Analysis Formulas For Vibration Analysis Diagnostics ppsx

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 = (#Teeth GEAR x RPM GEAR ) GMF = (#Teeth PINION x RPM PINION ) (#TeethGEAR x RPM GEAR ) = (#Teeth PINION x RPM PINION ) RPMGEAR = (#Teeth PINION x RPM PINION ) / (#Teeth GEAR ) RPMPINION = (#Teeth GEAR x RPM GEAR ) / (#Teeth PINION ) Gear Assembly Phase Frequency Problems GAPF = GMF / N A Hunting Tooth Frequency (Tooth Repeat Problem) F HT = (GMF x N A ) / (T GEAR x T PINION ) N A = 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 (N A ) 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: T GEAR = 21 Prime factors: 1 x 3 x 7 T PIMION = 9 Prime factors: 1 x 3 x 3 N A = 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 (N A ) for any gear. The product of the common prime factors of the tooth counts in the meshing gears is N A . F HT = GMF x Na (T GEAR x T PIMION ) 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 Value Multiply To Obtain Peak 2.000 Peak-to-Peak RMS 2.828 Peak-to-Peak Peak-to-Peak 0.500 Peak RMS 1.414 Peak Peak 0.707 RMS Peak-to-Peak 0.353 RMS 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 F NAT = F NAT = K = Stiffness (psi) M = Mass, pounds force (lbf) [...]... 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... 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... 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... 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... 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 . 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. 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. 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