Case Study Analysis of wo Stage Planetary Gearbox Vibration KSC Consulting LLC Ken Singleton Manager Abstract: A two stage planetary gearbox used in underground coal mining experienced an overload in service which caused bearing and bolting failures. he gearbox was repaired and underwent a no load spin test. A very audible noise was present in the vicinity of the st stage gear set. Vibration analysis was used to determine the source of the vibration. he equations for calculating the planetary gear shaft speeds, gear meshing frequencies, and bearing frequencies in the gearbox are provided. Background: Gearboxes used in underground coal mining are of compact design. A typical two stage planetary gearbox, 8 HP, 4.7: Ratio with 8 RPM input is shown in Figure. he unit was received by a repair facility for rebuild following failure from an overload incident. It was reported that the bearings were replaced and that one bearing had broken into many fragments. Following repairs a no load spin test of the gearbox was performed as a check for bearing faults, Figure. here was an audible impacting type noise from the input planetary section. Analysis: During the spin test, vibration data were measured using an accelerometer with rare earth magnetic mount. Initial inspection of the data indicated impacting and ringing of natural frequencies of the gearbox, Figure. he impacts measured a.87 msec period or 4.57 Hz ~ 74.6 CPM. he FF of the time domain data showed harmonics of 74.6 CPM and indication of excitation of several natural frequencies of the gearbox. Figure. Cutaway View of -Stage Planetary Gearbox, 4.7: Reduction. Figure. Gearbox On est Stand For No Load Spin est. of Case Study wo Stage Planetary Gearbox - Ken Singleton Sept 4, 6
Before a determination of the source of the vibration could be made, an understanding of the gearbox design was required and calculation of the excitation frequencies. Based on the information provided by the drawing shown in Figure, several calculations were made to obtain the shaft speeds, bearing fault frequencies and gear meshing frequencies. RMS Acceleration in G-s..9.6. LW - Joy L7EP 4.7 SN-8586 -PH Pt Hor Input Shaft Resonance at about 66, CPM Route Spectrum 6-Mar-6 8:48:6 OVERALL=.8 V-AN RMS =.89 LOAD =. RPM = 56. (8.44 Hz) Acceleration in G-s 4 6 8 Frequency in CPM.87 msec ~ 4.57 Hz ~ 74.6 CPM Route Waveform 6-Mar-6 8:48:6 RMS =.74 PK(+/-) =.7/.5 CRESF= 5.8 - - - 4 5 6 7 8 9 Revolution Number Figure. Vibration Signal Measured at Gearbox Input Section Showed Impacts at.87 msec Interval ~ 4.57 Hz ~ 74.6 CPM. he FF (op Plot) Indicated Excitation of Several Resonant Frequencies Including A Very Response One at About 66, CPM ~, Hz. Epicyclic gear boxes derive their name from the epicyclodial curves that the planet gears produce during rotation. here are three general types of epicyclic arrangements, ) planetary which consists of a stationary ring gear combined with a rotating sun gear and moving planet carrier, ) star configuration which consists of a stationary planet carrier coupled with a rotating sun gear, and ) solar gear that has a fixed sun gear combined with a moving ring gear and planet carrier. he planetary arrangement is most common and is shown by the schematic in Figure 4. he subject gearbox had the planetary arrangement for the st and nd stages. Input was from the sun with three planets supported by a carrier revolving about the sun pinion and the ring gear fixed. of Case Study wo Stage Planetary Gearbox - Ken Singleton Sept 4, 6
st Stage nd Stage S S Sun Gear RPM (Input Speed) 78-4.88 R Ring Gear eeth 7 P Planet Gear eeth 47 7 S Sun Gear eeth 7 7 value rain Value.5786.8767 C S Carrier RPM -4.88-44.58 P S Planet RPM 559.6 9.9 P Sabsolute Planet RPM Absolute -4.775-75.57 R S Ring Gear RPM P GMF Planet Gear Meshing Freq 6,.76,8.4 CPM F GMF-Sun Sun Gear Meshing Freq CPM,94.,99. Ratio Stage Ratio 7.588 5.94 able : Summary of he Gearbox Shaft Speeds and Gear Meshing frequencies. Figure 4. Gear Arrangement Of st Stage Planetary Input Section. Step : Carrier Speed he st stage carrier speed can be calculated as follows: rain value: Value S P 7 47 = = =.5786 P R 47 he st stage Carrier Speed then calculates to: C S RS value SS.5786 78 7.4865 = = = = 4.876 RPM (.5786).5786 value he negative sign - indicates the carrier is rotating in the opposite direction to the sun gear. he nd stage carrier speed which is also the output of the gearbox calculated to: Value S P 7 7 = = =.8767 P R 7 7 C S RS value SS.8767 4.876 54.688 = = = = 44.58 RPM (.8767).8767 value he gearbox ratio calculated to: InputRPM 78 Ratio = = = 4.7 Output 44.586 RPM he calculated ratio agreed with the ratio provided by the gearbox manufacture of 4.7. of Case Study wo Stage Planetary Gearbox - Ken Singleton Sept 4, 6
he carrier speeds can also be calculated as follows: he st stage carrier speed: R O Rt + St + 7 = = = 7.588 S 7 t C S SS 78 = = = 4.88 RPM R 7.588 O he nd stage carrier speed: R O Rt + St 7 + 7 = = = 5.94 S 7 t SS 4.88 CS = = = 44.58RPM R 5.94 O 4 of Case Study wo Stage Planetary Gearbox - Ken Singleton Sept 4, 6
Step : Planet Speed he st stage planet rotational frequency or planet spin speed was calculated as follows: R PS = CS = 4.88 = 559.6RPM P 47 he st stage absolute planet rotational frequency can be determined by summing the carrier and planet rotational frequencies algebraically. Note that this frequency seldom appears in vibration data. P = C + P = 4.88 + 559.6 = 4.775 RPM S Absolute s s he nd stage planet spin speed calculated as follows: R 7 PS = CS = 44.594 = 9.95 RPM P 7 he nd stage absolute planet rotational frequency is then determined: P = C + P = 44.58 + 9.95 = 75.577 RPM s s s Absolute he planet speed can also be calculated as follows: st stage planet RPM: Rt PR = ( RS CS) = ( 4.88) = 559.64 RPM P 47 t nd stage planet RPM: Rt 7 PR = ( RS CS) = ( 44.594) = 9.95 RPM P 7 t 5 of Case Study wo Stage Planetary Gearbox - Ken Singleton Sept 4, 6
Step : Gear Meshing Frequencies he planet gear meshing frequencies were then determined for stage as follows: P = P P = 559.6 47 = 6,.76CPM GMF S he higher frequency sun gear meshing frequency was calculated: S = S S = 78 7 =,94 CPM GMF s he nd stage planet gear meshing frequencies were then determined as follows: P = P P = 9.9 7 =,8.4 CPM GMF S he nd stage sun gear meshing frequency was then calculated: S = S S = 4.876 7 =,99.4 CPM GMF s 6 of Case Study wo Stage Planetary Gearbox - Ken Singleton Sept 4, 6
Step 4: Bearing Fault Frequencies After the gearbox shaft speeds were determined, the bearing fault frequencies were calculated and listed in able. For purposes of calculating the bearing fault frequencies of the planet bearings, the spin frequency of the planets must be summed to the carrier rotational frequency. Since the outer race was turning faster the calculations were made as if the bearing inner race was not rotating. Stage Planet Spin Freq 559.6 + 4.88 = 794.45 RPM Stage Planet Spin Freq 9.9 + 44.59 = 64.9 RPM Note that dimensions were not located in the time allowed for the cylindrical roller bearing NUP 97. X Brg Fault Frequencies CPM Component Brg Inner Race RPM (Relative to Outer Race) FF BSF BPFO BPFI Sun NU8E 78. 764.48 64.55 45. 94.7 Sun 66 78. 746.66 56.4 7459.45 6.55 st Stage Planet NJ4 794.45 45.6 78. 6474.5 869.6 Output Carrier NCF 864B 44.6.89 8.4 8. 67. Output Carrier NUP 97 44.6.... nd Stage Planet JN8 64.9 65.88 98.89 856.6 79.6 able : Listing of Gearbox Bearings and Fault Frequencies CPM. he bearing fault frequencies were calculated using Machinery Health Manager software (CSI RBMware). Equations from Reference are provided below. Cage Hz Ball Spin Ball Pass Ball Pass n d = ( ) cosα PD.. Hz PD.. n d = d PD. Outer Race Hz Inner Race Hz { ( ) cos } α n d = Z { ( ) cos α} PD.. n d = Z { + ( ) cos α} PD.. Where: d = Rolling Element Diameter Cycles RPM n = Shaft Freqeuncy or ( ), Hz sec 6 O. D. + bore P. D. = Pitch Diameter ( For ball bearings P. D. = ) Z = Number of balls or rollers ( per row) α = Bearing contact angledegree for pure radial load α = 5to deg ( thinner sec tionbearings) α = 7to 4deg (7,74 Series) α = to5deg spherical roller typical range 7 of Case Study wo Stage Planetary Gearbox - Ken Singleton Sept 4, 6
Step 5: Determination of Vibration Source Referring to the data plots in Figure, it was readily determined using the vibration software cursors that the impulse frequency was 4.47 Hz ~ 74.6 CPM. A check of the frequencies in able showed that this frequency does not match any of the bearing fault frequencies. A check of the gearbox shaft speeds and gear meshing frequencies in able also did not immediately identify a forcing frequency. he pulses in the time domain measured 85.4 msec ~.7 Hz ~ 7.4 CPM. Since the gearbox has three planets in each stage an impulse could occur at three times the st stage carrier frequency of 4.88 CPM if there were damage to the ring gear teeth. his frequency was calculated as follows: 4.88 = 74.5 CPM ~.74 Hz. =.857 Sec ~ 85.7mSec.74 he source of the pulses was related to rotation of the carrier and the three planets in the st stage also called the planet passing frequency. Updating able to include the planet passing frequency, able A: st Stage nd Stage S S Sun Gear RPM (Input Speed) 78-4.88 R Ring Gear eeth 7 P Planet Gear eeth 47 7 S Sun Gear eeth 7 7 value rain Value.5786.8767 C S Carrier RPM -4.88-44.59 P S Planet RPM 559.6 9.9 P Sabsolute Planet RPM Absolute -4.775-75.57 R S Ring Gear RPM P GMF Planet Gear Meshing Freq 6,.77,8.4 CPM F GMF-Sun Sun Gear Meshing Freq CPM,94.,99. P Pass Planet Passing Freq 74.54 6.79 Ratio Stage Ratio 7.588 5.94 able A: Summary of he Gearbox Shaft Speeds, Gear Meshing and Planet Passing Frequencies. 8 of Case Study wo Stage Planetary Gearbox - Ken Singleton Sept 4, 6
Expanding the time domain plot to show only two pulses, Figure 5, the pulses ring down which is typical response of structural resonance. he spectrum data also provided clear indication of resonance excitation. RMS Acceleration in G-s Acceleration in G-s.8.7.6.5.4... 4 - - - -4 LW - Joy L7EP 4.7 SN-8586 -PH Pt Hor st Stage Planet Structural resonance of gearbox excited by impacting. 4 6 8 Frequency in CPM 4 6 8 4 6 ime in msecs Route Spectrum 9-Mar-6 :6:54 OVERALL=.786 V-AN RMS =.446 LOAD =. RPM = 56. (8.44 Hz) Route Waveform 9-Mar-6 :6:54 RMS =.66 PK(+/-) =.4/.5 CRESF= 7.6 ime: Ampl: Dtim: Freq:.7 -.555 85.4 7.45 Figure 5. ime Data Expanded o Show Impacting and Ring Down. Plotting a single pulse in Figure 6 showed more clearly the time between oscillations was about.4 msec or 57,6 CPM. Note that spectrum analyzers don t make good oscilloscopes due to the rather course sampling at.56 times the maximum frequency to be displayed in the frequency spectrum. Acceleration in G-s 4 - LW - Joy L7EP 4.7 SN-8586 -PH Pt Hor st Stage Planet Route Waveform 9-Mar-6 :6:54 RMS =.7497 LOAD =. RPM = 56. (8.44 Hz) PK(+) =.4 PK(-) =.5 CRESF= 7.6 - - -4 4 5 6 7 8 9 ime in msecs ime: Ampl: Dtim: Freq: 48.7.8.4 576. Figure 6. Expanded Plot of One of he Impact Events in he ime Domain Shows he Ring Down Frequency Is About 57,6 CPM. 9 of Case Study wo Stage Planetary Gearbox - Ken Singleton Sept 4, 6
Plotting the time data in a circular plot, Figure 7, clearly shows three periodic impacts per revolution of the carrier. he impacts occurred as each planet rolled over a damaged ring gear tooth. Peakvue spectrum and time domain data are plotted in Figure 8 and shows impacting to about 5g s with the same frequency content as the normal vibration data. he auto correlation plot of Peakvue time data is plotted in Figure 9 in a circular plot format. Acceleration in G-s 4 - - - -4 7 LW - Joy L7EP 4.7 SN-8586 -PH Pt Hor st Stage Planet 9 Route Waveform 9-Mar-6 :6:54 RMS =.4867 LOAD =. RPM = 4. RPS =.9 PK(+) =.4 PK(-) =.5 CRESF= 7.6 ime in msecs Phas: 7.6 ime:. Rev :.9 Ampl:.66 8 Revolution Number:. -. RMS Acceleration in G-s Acceleration in G-s.4..6..8.4 LW - Joy L7EP 4.7 SN-8586 -PP Pt Hor Peakvue st Planet Analyze Spectrum 6-Mar-6 8:5:55 (PkVue-HP Hz) RMS =.455 LOAD =. RPM = 56. (8.44 Hz) 4 6 Frequency in CPM 6 Analyze W aveform 5 6-Mar-6 8:5:55 (PkVue-HP Hz) 4 RMS =.985 PK(+) = 5.7 CRESF= 5.4 DCoff =. Figure 7. ime Domain Data Plotted in Circular Format. Correlation Factor..5 -.5 -. 9 LW - Joy L7EP 4.7 SN-8586 -PP Pt Hor Peakvue st Planet Analyze ACorr(W f) 6-Mar-6 8:5:55 (PkVue-HP Hz) RMS =.46 LOAD =. RPM = 5. RPS =.9 PK(+) =.684 PK(-) =.664 CRESF= 4.8 7.4.8..6 ime in Seconds 8 Revolution Number:. -. Figure 8. PeakVue Data Also Contained Impacting Data At the X the Carrier RPM. Figure 9. Auto Correlation of Peakvue ime Data. After reviewing the data and calculations, the conclusions were: ) he st stage carrier was impacting a stationary object three times each revolution, or ) Each planet gear in the st stage was rolling over damaged teeth on the ring gear. No gear meshing frequencies were evident in the data. Opening of the gearbox for inspection of the st stage was recommended. of Case Study wo Stage Planetary Gearbox - Ken Singleton Sept 4, 6
Gearbox Inspection: With the likely problem area in the gearbox identified, the gearbox was dissembled for inspection. A small fragment of the disintegrated bearing was found imbedded in the unloaded side of one tooth of the ring gear. he bearing fragment was removed, the damaged tooth dressed, the gearbox reassembled and spin tested again. Before and after vibration data are plotted in Figure 9 &. he periodic impacting caused by the planet teeth rolling over the damaged ring gear tooth was reduced. RMSAccelerationinG-s AccelerationinG-s..5..5 4 - - - -4 LW - Joy L7EP 4.7 SN-8586 -PH Pt Hor st Stage Planet 4 6 8 Frequency in CPM..6.9. ime in Seconds Route Spectrum 6-Mar-6 8:5:6 OVERALL=.87 V-AN RMS =.4798 LOAD =. RPM = 56. (8.44 Hz) Route Waveform 6-Mar-6 8:5:6 RMS =.48 PK(+/-) =.6/.6 CRESF= 7.46 Figure 9. Initial Spectrum And ime Domain Data With Brg Fragment Imbedded In he Ring Gear. RMSAccelerationinG-s AccelerationinG-s..5..5 LW - Joy L7EP 4.7 SN-8586 -PH Pt Hor st Stage Planet 4 6 8 Frequency in CPM 4 - - - -4..6.9. ime in Seconds Route Spectrum 8-Apr-6 :5:56 OVERALL=.546 V-AN RMS =.958 LOAD =. RPM = 56. (8.44 Hz) Route Waveform 8-Apr-6 :5:56 RMS =.5 PK(+/-) =./. CRESF= 6. Figure. Spectrum And ime Domain Data After Dressing Ring Gear Damaged ooth. of Case Study wo Stage Planetary Gearbox - Ken Singleton Sept 4, 6
A photo of the damaged ring gear tooth is shown in Figure after dressing. Indentations can be seen where the tooth material was compressed by the bearing fragments. Conclusions: Figure. Ring Gear ooth Afer Removing Brg Fragment & Dressing Raised Metal. his article describes the process that was used to analyze impacting type vibration of a two stage epicyclic planetary gearbox during a post-repair unloaded spin test. he forcing frequencies were calculated and identified the probably source of the vibration. Inspection of the ring gear identified fragments of a bearing race embedded in the unloaded side of a ring gear tooth. References:. Eisenmann, Sr., P.E., Eisenmann, Robert, C., Jr. Machinery Malfunction Diagnosis and Correction, Prentice Hall PR, ISBN --4946-, PP 47-477.. Guyer, Raymond A. Jr., Rolling Bearings Handbook And roubleshooting Guide, ISBN -89-8876-, PP 8. Author Ken Singleton is Manager of KSC Consulting LLC with over 4 years industrial experience. He retired from Eastman Chemical Company in 999 as a Senior Engineering echnologist in the Rotating Machinery echnology Group after years service. He has presented technical papers at the Vibration Institute National Meetings, P/PM Conferences, ASME Joint Power Conferences, and Piedmont Chapter of the Vibration Institute. Education includes an AAS Electronic Engineering echnology, Mechanical Engineering ICS, Journeyman Machinist, Washington Co echnical School. of Case Study wo Stage Planetary Gearbox - Ken Singleton Sept 4, 6