1、C I Bending Fatigue Investigation Under Variable Load Conditions on Case Carburized Gears by: B.-R. Hhn, P. Ostre, K. Michaelis, Th. Suchandt and K. Stahl, Gear Research Center (FZG) J e American I I - TECHNICAL PAPER Bending Fatigue Investigation Under Variable Load Conditions on Case Carburized Ge
2、ars Bernd-Robert Hhn, P. Oster, Klaus Michaelis, Th. Suchandt and K. Stahl, Gear Research Center (FZG), Technical University of Munich The statements and opinions contained herein are those of the author and should not be construed as an official action or opinion of the American Gear Manufacturers
3、Association. Abstract Carburized spur gears were tested to determine bending fatigue life under variable loads. Fatigue life in random tests is shorter than in block programmed tests. However, chronological order of loads in block programmed tests has insignificant influence. Fatigue life in block p
4、rogrammed tests is decreased, if sequence length is shortened. Fatigue life is similar to random load tests, if a few hundred sequences are repeated until tooth breakage. Loads below 50% of the fatigue limit can be eliminated without changing test results. Fatigue life can be calculated by Miners Ru
5、le as modified by Haibach using a damage ratio of D = 0,s. Single loads applied early decrease fatigue life up to 65%. The greater the single load the greater the life reduction. Even single loads on reverse sides of teeth significantly reduce fatigue life. Copyright O 2000 American Gear Manufacture
6、rs Association 1500 King Street, Suite 201 Alexandria, Virginia, 22314 October, 2000 ISBN: 1-55589-771-1 BENDING FATIGUE INVESTIGATIONS UNDER VARIABLE LOAD CONDITIONS ON CASE CARBURIZED GEARS B.-R. Hhn, Professor; P. Oster, Chief Engineer; K. Michaelis, Chief Engineer; Th. Suchandt, Research Enginee
7、r; K. Stahl, Research Engineer Gear Research Center (FZG), Technical University of Munich, Boltzmannstr. 15, 85748 Garching, Germany Nomenclature gear face width mm pitch circle diameter mm base diameter . mm lever height at clamping in the pulsator . mm gradient of S-N-curve - normal module mm load
8、 cycle number on level i - damage parameter by Haibach - logarithmic standard deviation - chordal tooth thickness at 30“ mm addendum modification factor . - number of teeth - cumulative damage ratio . - casedepth . mm normal load on tooth flank N nominal tangential load N achieved load cycle number
9、at load level i - roughness pm stress correction factor - helix angle factor . - normal pressure angle . O pressure angle in pulsator O . actual fatigue limit . N/mm2 fatigue limit . N/mm2 nominal tooth root stress (DIN 3990) . N/mm2 1 Introduction Gears in practice are mostly operated under variabl
10、e loads. Even in a continuous process the load can fluctuate due to acceleration, malfunction, emergency stops or operating errors. Under these variable loads a tooth breakage, which mostly results in a total gear failure, must be avoided with high reliability. Additionally, demands on modern gears,
11、 regarding costs and weight, are increasing. With classic sizing of gears, where loads above the fatigue limit are not allowed, the above goals cannot be achieved. Using a calculation method, where loads above the fatigue limit are taken adequately into account, the operational stability without too
12、th breakage can be ensured with predictable safety. To evaluate tooth root fatigue tests with variable load amplitude, the applied spectrum of load levels and the tooth strength in terms of the S-N-curve is required. The expected spectrum of load levels during the life cycle can be evaluated by meas
13、urement, simulation or estimation. The S-N- curve can either be experimentally derived or stan- dardized curves as IS0 6336 lo can be used. For safe and operational stable sizing of variably loaded gears an experimentally verified and easily applicable calculation method is required. Therefore tooth
14、 breakage fatigue tests on spur, case carburized gears are carried out in hydraulic pulsators. Influence of load sequence and load distribution on the life cycle is examined. 1 O Additionally, a possible damaging influence of load high cycle fatigue. levels below fatigue limit is evaluated. Influenc
15、e of the load sequence is determined in Besides fluctuations of gear load, which appear block programmed tests, where one single sequence during standard operation and are recorded in the is repeated until tooth breakage. The chronological load distribution, singular events, due to order of the load
16、 levels in the sequence is varied to malfunctions or operating errors, can occur and ascending, descending and mixed load order. cause additional loads on gears. In several test Results of these tests are compared to results of series singular events are applied on the test gears, random tests with
17、stochastic load sequence. The in addition to the variable amplitude load according number of repeated sequences until tooth breakage to the standard load distribution. The influence of is varied by variation of the seauence lenath in block load level and temporal occurrence of singular programmed te
18、sts. Results are compared to the events is examined. results of random tests as well. 2 Test conditions 2.1 Test program The omission level is determined in block pro- grammed tests. Below this load level, cycles can be left out without an influence on test results. Running time of variable load amp
19、litude tests can be considerably shortened, if loads below the omission level with high cycle numbers are left out. Influence of the load distribution on fatigue life is examined with three different load distributions. Load distribution “B2“ is derived from measurements of Fig. 1 shows the test pro
20、gram for the constant amplitude and variable load amplitude tests within the scope of the present investigations. O S-N-curve load sequence LI Is L I l I !oad distributions omission level Fig. 1 : Test program: tooth root bending fatigue under constant and variable load amplitude The tooth bending s
21、trength of the test gears in terms of the S-N-curve is needed to evaluate variable load amplitude tests. The S-N-curve is determined in constant load amplitude tests with an adequate statistical verification in the range of low cycle and tooth root stress in practical gears and is typical for large
22、scale gear units 18. Load collective type “EK“ has a load spectrum, according to the Gaussian normal distribution 5, 81, which can be found in applications with continuous processes l 1. Load collective type “C2“ is a high load distribution and corresponds to the load spectrum of vehicle gear units.
23、 Achieved fatigue life with these three different load distributions is evaluated with different calculation methods based on linear fatigue accumulation according to Miners theorem 14. Sinaular events due to malfunctions or operating errors can cause additional loads on gears. In- fluence of load l
24、evel and temporal occurrence in a chronological sequence of singular events on tooth root fatigue are examined. 2 2.2 Test rigs a helix angle face width b addendum mod. factor x d pitch circle diameter base diameter d, tip diameter da The objective of this project is experimental investigations of c
25、arburized gears with regard to tooth root fatigue under variable loads. If tooth root fatigue O“ 14mm 0,172 108mm 101,5mm 118,4 mm tests are performed in running tests in gear test rigs, only one test result is obtained with each gear pair. Considering the great number of required tests, the Dolan,
26、T.J.: Cumulative fatigue da- mage. Proc. Int. Conf. Fatigue of Metals, Inst. Mech. London. New York (1956), S. 235-246. 3 DIN 3990 Teil 6: Tragfhigkeitsberechnung von Stirnrdern - Betriebsfestigkeitsberechnung. Beuth Verlag (1994). 4 Fischer, R.; Hck, M.; Kbler, H.; Schtz, W.: Eine dem stationren Ga
27、uproze verwandte Beanspruchungs-Zeit-Funktion fr Betriebs- festigkeitsversuche. Fortschritt-Berichte der VDI Zeitschriften Reihe 5 Nr. 30 (1 977). 5 Ganer, E.; Griese, F.W.; Haibach, E.: Ertragba- re Spannungen und Lebensdauer einer Schweiverbindung aus Stahl St 37 bei verschie- denen Formen des Bea
28、nspruchungskollektives, Archiv f. d. Eisenhttenwesen 35 Nr. 3, S. 255- 267 Verlag Stahleisen, Dsseldorf (1964). 6 Haibach, E.: Betriebsfestigkeit; Verfahren und Daten zur Bauteilberechnung. VDI-Verlag, Ds- seldorf (1989). 7 Haibach, E.: Modifizierte Schadensakkumula- Bending fatigue life of case car
29、burized gears can be calculated by modified Palmgren-Miner- rule by Haibach. Accumulation of damage ratio is only allowed up to D = 0,5. For comparison, according to DIN 3990 T6 3 respectively IS0 10495 l 11 using Palmgren-Miner-rule the accumulation of damaae ratio is allowed UD to D a - = 1,o. 5 A
30、cknowledgement This research project was sponsored by the Arbeitsgemeinschaft industrieller Forschungsvereini- gungen e.V. (AiF) by funds of the Bundesministerium fr Wirtschaft (BMWi) with an equity ratio by the Forschungsvereinigung Antriebstechnik (FVA) and the Verein zur Frderung der Forschung un
31、d der Anwendung von Betriebsfestigkeitskenntnissen in der Eisenhttenindustrie (VBFEh). tions-Hypothese zur Bercksichtigung des Dau- erestigkeitsabfalls mit fortschreitender Schdi- gung. Technische Mitteilungen Fraunhofer- Institut fr Betriebsfestigkeit Darmstadt (1 970), Nr. 50/70. 8 Hanke, M.: Eine
32、 Methode zur Beschreibung der Betriebslastkollektive als Grundlage fr Be- triebsfestigkeitsversuche. Automobiltechnische Zeitschrift 72 (1970) Nr. 3, S. 91-97. 9 Hck, M.: Ein verbessertes Verfahren fr die Auswertung von Treppenstufenversuchen. Be- richtsband der 6. Sitzung des DVM Arbeitskrei- ses B
33、etriebsfestigkeit, Berlin (1981), S. 147-176. lo IS0 6336: Calculation of Load Capacity of Spur and Helical Gears. International Organization for 13 Standardization (1 996). l 11 IS0 10495: Cylindrical gears - Calculation of service life under variable loads - Conditions for cylindrical gears accord
34、ing to IS0 6336. lnter- national Organization for Standardization (1997). 12 Jacoby, G.: Beitrag zum Vergleich der Aussage- fhigkeit von Programm- und Random-Ver- suchen. Zeitschrift fr Flugwissenschaften 18 (1 970) Heft 7, Seite 253-258. 13 Lipp, W.: Zuverlssigere Lebensdauerangaben durch bessere V
35、ermischung der Lasten im 8- Stufen-Programmversuch. Materialprfung Bd. 12 (1970) Nr. 11, S. 381/382. 14 Miner, M.A.: Cumulative Damage in Fatigue. J. Appl. Mech. 12 (1945). Heft 3, S. 159-164. 15 Palmgren, A.: Die Lebensdauer von Kugella- gern. Z.d. VDI 68 (1 924) Heft 14, S. 339-341. 16 Stahl, K.:
36、Zahnfubetriebsfestigkeitsuntersu- chungen an einsatzgehrteten Zahnrdern. FVA Forschungsvorhaben Nr. 188/11, Hefi 502 (1 996). 17 Suchandt, Th.: Zahnfubetriebsfestigkeitsunter- suchungen an einsatzgehrteten Zahnrdern. FVA Forschungsvorhaben Nr. 188/1, Heft 408 (1 993). 18 Zenner, H.; Griese, F.-W.; R
37、acker, R.; Schne, G.: Steigerung der Zuverlssigkeit von Gro- getrieben durch gezielte Auswertung vorhan- dener Betriebsuntersuchungen. VBVEh Nr. ABF 31 (1986). 19 Zenner, H.; Schtz, W.: Betriebsfestigkeit von Schweiverbindungen - Lebensdauerabschtz- ung mit Schadensakkumulationshypothesen. Schweien und Schneiden 26 (1974) Heft 2, S. 41 -45. 14 15
