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Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Includes bibliographical references (p. 227-233).

Torsional vibrations in differentials of Rear Wheel Drive vehicles are of major importance for the automotive industry. Hypoid transmissions, forming the motion transfer mechanism from the driveshaft to the wheels, suffer from severe vibration issues. The latter are attributed to improper mesh between the mating gear flanks due to misalignments, variation of contact load and shifting of the effective mesh position. For certain operating conditions, the gear pair exhibits high amplitude motions accompanied with separation of the mating surfaces. Ultimately, single or even double-sided vibro-impact phenomena evolve, which have been related to noise generation. This thesis attempts to address these issues by effectively analysing the dynamic behaviour of a hypoid gear pair under torsional motion. The case study considered is focused on a commercial light truck. The major difference of the employed mathematical model to prior formulations is the usage of an alternative expression for the dynamic transmission error so that the variation of contact radii and transmission error can be accounted for. This approach combined to a correlation of the resistive torque in terms of the angular velocity of the differential enables the achievement of steady state, stable periodic solutions. The dynamic complexity of systems with gears necessitates the identification of the various response regimes. A solution continuation method (software AUTO) is employed to determine the stable/unstable branches over the operating range of the differential. The ensuing parametric studies convey the importance of the main system parameters on the dynamic behaviour of the transmission yielding crucial design guidelines. A tribo-dynamic investigation aims at expanding the dynamic model from pure dry conditions to a more integrated elastohydrodynamic (EHL) approach. Analytical and extrapolated solutions are applied for the derivation of the film thickness magnitude based on the kinematic and loading characteristics of the dynamic model. The temperature rise is governed mainly by conduction due to the thin lubricant films. The generated friction is also computed as a function of the viscous shear and asperity interactions. The effective lubricant viscosity is greatly affected by the pressure increase due to the resonant behaviour of the contact load. The final part of this work is involved with a feasibility study concerning the application of Nonlinear Energy Sinks (NES) as vibration absorbers, exploiting their ability for broadband frequency interaction. Response regimes associated with effective energy absorption are identified and encouraging results are obtained, showing the potential of the method.

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Orientador: Anselmo Eduardo Diniz / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-03T20:42:19Z (GMT). No. of bitstreams: 1 Fontana_Douglas_M.pdf: 10116872 bytes, checksum: 3a8e7469b54d02c31d22b732a5021bb1 (MD5) Previous issue date: 2003 / Resumo: A transmissão de movimentos mecânicos através de engrenagens é muito utilizado em todos os segmentos industriais.O corte de dentes de engrenagens é uma operação bastante importante dentro da usinagem. Apesar de sua importância, este é um processo pouco estudado, pois esta é uma área bastante restrita de atuação. Emfunção disso,a maior parte dos desenvolvimentos relacionados à tecnologia de corte de dentes de engrenagens ocorre no meio industrial, geralmente de forma empírica. A determinação do fim de vida das lâminas de corte Gleasonsão feitas,no chão de fabrica,pelos preparadores ou mesmo pelos operadores das máquinas.Tal decisão é baseada em critérios altamente subjetivos e portanto, faz com que o tempo de utilização da ferramenta apresente uma grande variabilidade,ou seja, em determinados momentos, a ferramenta é utilizada além de sua vida efetiva e, em outros momentos, esta utilização se dá a quém da mesma. Caso a ferramenta ultrapasse sua utilização ótima, ocorrem vários problemas, dentre os quais: maior volume de material retirado na afiacão da ferramenta com conseqüente redução do númerode vidas desta, a rugosidademédia (Ra) das peças toma-se muito elevada,fazendo com que a japidação do dentado (operação posterior ao corte) seja muito demorada e portanto, anti-econômica.Por outro lado, se a ferramenta for sub-utilizada. ocorre um desperdício de lâmina,bem como um aumento do tempo de processamento pois um maior número de trocas da ferramenta vai ocorrer. Este trabalho procurou estabelecer um parâmetro objetivo de fim de vida da lamina de corte do tipo Hardac, utilizandoo processo de corte denominado Completo (Completing). Para tanto, foi feito um trabalho junto a um fubricante de auto-peças, que usina engrenagens cônicas e hipoidais, utilizada em diferenciais de caminhões e ônibus.O parâmetro escolhido foi a rugosidade média (Ra) do flancodos dentes das engrenagens. O comportamento e a dispersão da vida da ferramenta anterior e posterior à implantação do parâmetro proposto foram analisadas.Os resultados mostram uma maior uniformidade da vida das laminas de corte gleason,bem como dos tempos de afiação das mesmas e Iapidação do dentado. Além disso, as lâminas passaram a ser utilizadas de forma otimizadas em relação ao seu desgaste e à quantidades uperficial da peça. Um segundo objetivo do trabalho foi comparar a vida de ferramentas de aço rápido com algumas coberturas diferentes e também sem cobertura na superficie de saída, pois foram utilizadas após a afiação da ferramenta com cobertura total Pelo desempenho mostrado nos resultados a melhor cobertura foi aquela de nitreto de titânio originária do fabricante da ferramenta e do equipamento / Abstract: The transmission of mechanical motion through gears is very used in alI industrial segments.The cutting process of gears is a very important process in the manufacturing. Despiteits importance this is a process not so studied as it a very specific area. According to this, most part ofthe industrial field, usually in an empirical way. The determination to end the life of a Gleason Cutter Blade is made by machine operators. The decision is based on highly subjective criteria and as for this it makes the using time of this tool to presenta great variability. As resuh this tool is sometimes used longeror less than it should.If its use is longer exceedingits life time,many problems may occur, such as: bigger volume taken from the sharpening material of tools which results in a reduction of their lifetime, the average rougbness (Ra) of the parts becomes higher which makes lapping of the teeth (process which occurs after cutting) to take longer and as a resuh not economical.On the other hand,if the tool is used less there is a waste ofthe blade as well as an increasein the manutacturing process due to the change of tools. This work tried to establishan objetive parameteron the end ofthe life ofthe Hardac type ofblade, using a cutting process called Completing.For this reason this work was done together with an Automotive Company that produces beveland hypoidgears used on heavyduty drive axles for trucks and buses. The chosen parameter was the average rougtmess(Ra) ofthe teeth flankof the gears. The behavior and dispersion of the tool Jife before and after the setting of the proposed parameter were analized. The resuhs show a greater uniformity of the life the Gleason Cutter Blade as well as its sbarpeningtime and teeth lapping. Apart from it, the blades started to be used on an optimized way related to its wear and to the surlace quality of the piece. Another objetive of this work was to compare the high speed steel tool life with some different coats andalso no coating on theftont ceplane,as theywere used after the tool sharperning with total coat. For the result showed the best coating was the one with titanium nitrideoriginate dftom the tool and equipamentmanufacturer / Mestrado / Materiais e Processos de Fabricação / Mestre em Engenharia Mecânica

Die Kontaktgeometrie von Kegelrad- und Hypoidverzahnungen bestimmt wesentlich deren Betriebseigenschaften. Sie wird während des Prozessschritts der Hartfeinbearbeitung produziert. Als direkte Konkurrenz zum Schleifen stellt das Läppen ein flexibles und hoch effizientes Verfahren zur Hartfeinbearbeitung von Hypoidverzahnungen dar, das sich zudem meist günstig auf das Geräuschverhalten auswirkt. Allerdings ist der lokale Materialabtrag auf den Zahnflanken und damit die durch das Läppen erzielte Kontaktgeometrie von einer Vielzahl an Einflüssen abhängig, was eine praxisgerechte Vorhersage derselben bislang nicht gestattete. Gegenüber einer deterministischen Schleiffertigung im Closed Loop stellt dies einen erheblichen Nachteil dar. Hier setzt die vorliegende Arbeit an und stellt ein Simulationsverfahren für den lokalen Läppabtrag vor. Es basiert auf dem Archard-Ansatz zur Verschleißtiefenberechnung sowie einer hocheffizienten und validierten Zahnkontaktsimulation. Durch die Einführung eines virtuellen Bremsmoments kann dabei erstmals der Einfluss der Abrasivpartikel auf die Lastverteilung im Zahnkontakt simulativ berücksichtigt werden. Für die Simulation sind nur wenige Parameter erforderlich, die das tribologische System des Läppprozesses charakterisieren. Diese lassen sich aus einfachen Versuchen automatisiert bestimmen. Anhand von Praxisversuchen wird die gute Abbildungsgenauigkeit der Simulation nachgewiesen. Durch eine Invertierung des zeitlichen Ablaufs lässt sich die Läppsimulation in den gewohnten Prozess zur digitalen Auslegung von Kegelrad- und Hypoidverzahnungen integrieren.:1 Einleitung 1 2 Motivation 3 2.1 Vergleich zu konkurrierenden Hartfeinbearbeitungsverfahren 3 2.2 Anwendungspotenzial einer Läppsimulation in der Auslegung von Hypoidverzahnungen 5 3 Stand der Technik 7 3.1 Läppen 7 3.1.1 Tribologisches System 9 3.1.2 Verschleißmechanismen 10 3.1.3 Planläppen 12 3.1.4 Grundlagen des Verzahnungsläppens 13 3.1.5 Wissenschaftliche Arbeiten zum Verzahnungsläppen 15 3.2 Einflussgrößen auf den Läppabtrag 16 3.2.1 Einfluss von Grund- und Gegenkörper 16 3.2.2 Einfluss der Abrasivpartikel 20 3.2.3 Einfluss des Trägermediums 25 3.2.4 Einfluss der Maschineneinstellungen 26 3.3 Einfluss von losen Partikeln auf den Zahnkontakt 28 3.3.1 Einfluss auf die Lastverteilung 28 3.3.2 Bewegung von Abrasivpartikeln im Kontakt 30 3.4 Ansätze zur Verschleißberechnung 32 3.4.1 Ansatz nach Archard 33 3.4.2 Ansatz nach Rabinowicz 35 3.4.3 Ansatz nach Williams und Hyncica 36 3.5 Simulation des Verzahnungsläppens 37 3.5.1 Jiang und Gosselin 37 3.5.2 Park und Kahraman 39 3.6 Optimierung von Läppprozessen 41 4 Simulation des lokalen Läppabtrags 45 4.1 Diskretisierung des Zahnkontakts an Hypoidverzahnungen 45 4.2 Geschwindigkeitskomponenten im Zahnkontakt 47 4.3 Wahl des geeigneten Verschleißansatzes 49 4.4 Anwendung des Archard-Ansatzes auf Verzahnungen 50 4.5 Ablauf der Simulation 53 4.5.1 Ermittlung der Relativlage für die Haltepositionen 55 4.5.2 Diskretisierung des Läppprogramms 56 4.5.3 Geometriemodifikation 58 4.5.4 Glättung des simulierten Läppabtrags 59 4.6 Berücksichtigung von Läpppartikeln im Zahnkontakt 61 4.7 Invertierung der Läppsimulation 63 5 Analogieversuche 67 5.1 Vorgehen 67 5.2 Reproduzierbarkeit 69 5.3 Lastwechselzahl 70 5.4 Gleitgeschwindigkeit 71 5.5 Gleit-Wälz-Verhältnis 73 5.6 Kritik des Versuchsaufbaus 74 6 Verzahnungs-Läppversuche 77 6.1 Versuchsverzahnungen 77 6.2 Versuchsdurchführung 78 6.3 Messdatenausrichtung 80 6.4 Bestimmung des Läppabtrags 82 6.5 Reproduzierbarkeit der Läppversuche 84 6.6 Untersuchte Einflüsse auf den Läppabtrag 88 6.6.1 Hochlauf 88 6.6.2 Läppzeit 90 6.6.3 Drehzahl 93 6.6.4 Bremsmoment 94 6.6.5 Flankentopologie 95 7 Experimentelle Ermittlung des Läppkoeffizienten 97 7.1 Problemstellung 97 7.2 Vorgehen 97 7.3 Ergebnisse 101 8 Validierung der Simulation gegen Versuchsergebnisse 105 8.1 Läppzeit 105 8.2 Drehzahl 107 8.3 Bremsmoment 109 8.4 Flankentopologie 111 8.5 Validierungsversuche 113 8.5.1 Radsatz A, geschliffene Verzahnung 114 8.5.2 Radsatz B, seriennaher Läppprozess 118 8.5.3 Radsatz C, serienmäßiger Läppprozess 122 8.5.4 Grenzen der Läppsimulation 126 9 Zusammenfassung und Ausblick 129 10 Summary and outlook 133 11 Literaturverzeichnis 137 A Abtragsergebnisse der Verzahnungs-Läppversuche 151 A.1 Erläuterung zu den folgenden Darstellungen 151 A.2 Versuchsübersicht 152 A.3 Versuchsreihe 1 [Lu 18] 155 A.3.1 Drehmomenteinfluss 155 A.3.2 Drehzahleinfluss 156 A.3.3 Hochlaufversuche Radsatz A 158 A.3.4 Haltezeit 158 A.3.5 Serienversuch Radsatz A 159 A.4 Versuchsreihe 2 [We 20] 160 A.4.1 Wiederholversuche Drehmomenteinfluss 160 A.4.2 Drehmomentversuche ungeschliffene Verzahnung (Radsatz B) 161 A.4.3 Hochlaufversuche 162 A.4.4 Kurzzeitversuche 163 A.4.5 Serienähnliche Versuche Radsatz B 163 A.5 Zusätzliche Versuchsreihe zur Validierung 164 A.5.1 Wiederholversuche zu W501 164 A.5.2 Hochlaufversuche Radsatz C 164 A.5.3 Serienversuche Radsatz C 164 A.5.4 Versuch zur Topologiestreuung 165 / The contact geometry of bevel and hypoid gears determines their operating characteristics. It is finally produced during the process step of hard finishing. As a direct competitor to grinding, lapping is a flexible and highly efficient process for the hard finishing of hypoid gears, which also usually has a favourable effect on NVH behaviour. However, the local material removal on the tooth flanks and thus the contact geometry achieved by lapping depends on a multitude of influence factors, effectively preventing any practical predictions of the resulting geometry up until now. Compared to deterministic closed-loop grinding, this has been a considerable disadvantage. This work presents a simulation method for the local removal of material during lapping. It is based on the Archard equation and a highly efficient and well validated tooth contact simulation to calculate the wear depth distribution. By introducing a virtual braking torque, the influence of the abrasive particles on the load distribution can be considered in the simulation for the first time. The simulation requires only a few parameters to characterize the tribological system of the lapping process. These can be determined automatically from fairly simple experiments. Practical examples are used to prove the accuracy of the simulation. By inverting the time sequence, the lapping simulation can also be integrated into the established process for the digital design of bevel and hypoid gears.:1 Einleitung 1 2 Motivation 3 2.1 Vergleich zu konkurrierenden Hartfeinbearbeitungsverfahren 3 2.2 Anwendungspotenzial einer Läppsimulation in der Auslegung von Hypoidverzahnungen 5 3 Stand der Technik 7 3.1 Läppen 7 3.1.1 Tribologisches System 9 3.1.2 Verschleißmechanismen 10 3.1.3 Planläppen 12 3.1.4 Grundlagen des Verzahnungsläppens 13 3.1.5 Wissenschaftliche Arbeiten zum Verzahnungsläppen 15 3.2 Einflussgrößen auf den Läppabtrag 16 3.2.1 Einfluss von Grund- und Gegenkörper 16 3.2.2 Einfluss der Abrasivpartikel 20 3.2.3 Einfluss des Trägermediums 25 3.2.4 Einfluss der Maschineneinstellungen 26 3.3 Einfluss von losen Partikeln auf den Zahnkontakt 28 3.3.1 Einfluss auf die Lastverteilung 28 3.3.2 Bewegung von Abrasivpartikeln im Kontakt 30 3.4 Ansätze zur Verschleißberechnung 32 3.4.1 Ansatz nach Archard 33 3.4.2 Ansatz nach Rabinowicz 35 3.4.3 Ansatz nach Williams und Hyncica 36 3.5 Simulation des Verzahnungsläppens 37 3.5.1 Jiang und Gosselin 37 3.5.2 Park und Kahraman 39 3.6 Optimierung von Läppprozessen 41 4 Simulation des lokalen Läppabtrags 45 4.1 Diskretisierung des Zahnkontakts an Hypoidverzahnungen 45 4.2 Geschwindigkeitskomponenten im Zahnkontakt 47 4.3 Wahl des geeigneten Verschleißansatzes 49 4.4 Anwendung des Archard-Ansatzes auf Verzahnungen 50 4.5 Ablauf der Simulation 53 4.5.1 Ermittlung der Relativlage für die Haltepositionen 55 4.5.2 Diskretisierung des Läppprogramms 56 4.5.3 Geometriemodifikation 58 4.5.4 Glättung des simulierten Läppabtrags 59 4.6 Berücksichtigung von Läpppartikeln im Zahnkontakt 61 4.7 Invertierung der Läppsimulation 63 5 Analogieversuche 67 5.1 Vorgehen 67 5.2 Reproduzierbarkeit 69 5.3 Lastwechselzahl 70 5.4 Gleitgeschwindigkeit 71 5.5 Gleit-Wälz-Verhältnis 73 5.6 Kritik des Versuchsaufbaus 74 6 Verzahnungs-Läppversuche 77 6.1 Versuchsverzahnungen 77 6.2 Versuchsdurchführung 78 6.3 Messdatenausrichtung 80 6.4 Bestimmung des Läppabtrags 82 6.5 Reproduzierbarkeit der Läppversuche 84 6.6 Untersuchte Einflüsse auf den Läppabtrag 88 6.6.1 Hochlauf 88 6.6.2 Läppzeit 90 6.6.3 Drehzahl 93 6.6.4 Bremsmoment 94 6.6.5 Flankentopologie 95 7 Experimentelle Ermittlung des Läppkoeffizienten 97 7.1 Problemstellung 97 7.2 Vorgehen 97 7.3 Ergebnisse 101 8 Validierung der Simulation gegen Versuchsergebnisse 105 8.1 Läppzeit 105 8.2 Drehzahl 107 8.3 Bremsmoment 109 8.4 Flankentopologie 111 8.5 Validierungsversuche 113 8.5.1 Radsatz A, geschliffene Verzahnung 114 8.5.2 Radsatz B, seriennaher Läppprozess 118 8.5.3 Radsatz C, serienmäßiger Läppprozess 122 8.5.4 Grenzen der Läppsimulation 126 9 Zusammenfassung und Ausblick 129 10 Summary and outlook 133 11 Literaturverzeichnis 137 A Abtragsergebnisse der Verzahnungs-Läppversuche 151 A.1 Erläuterung zu den folgenden Darstellungen 151 A.2 Versuchsübersicht 152 A.3 Versuchsreihe 1 [Lu 18] 155 A.3.1 Drehmomenteinfluss 155 A.3.2 Drehzahleinfluss 156 A.3.3 Hochlaufversuche Radsatz A 158 A.3.4 Haltezeit 158 A.3.5 Serienversuch Radsatz A 159 A.4 Versuchsreihe 2 [We 20] 160 A.4.1 Wiederholversuche Drehmomenteinfluss 160 A.4.2 Drehmomentversuche ungeschliffene Verzahnung (Radsatz B) 161 A.4.3 Hochlaufversuche 162 A.4.4 Kurzzeitversuche 163 A.4.5 Serienähnliche Versuche Radsatz B 163 A.5 Zusätzliche Versuchsreihe zur Validierung 164 A.5.1 Wiederholversuche zu W501 164 A.5.2 Hochlaufversuche Radsatz C 164 A.5.3 Serienversuche Radsatz C 164 A.5.4 Versuch zur Topologiestreuung 165

Gears are an integral part of devices ranging from simple wrist watches to complex systems like automotive and wave energy converters. They play a very important role in the transfer of torque. There are several types of gears to be chosen from, depending on the application. This thesis work deals exclusively with hypoid gears. A hypoid gear is a type of bevel gear, that transmits torque between two non-parallel shafts. It is similar to a spiral bevel gear, except that the pinion axis can be oset. It is this ability to offset, that renders hypoidgears as highly sought-after gears for automotive applications. It is crucial that these hypoid gears are designed efficiently and that their life before failure is predictable, to a reasonable degree of accuracy. To enable such predictions, this thesis makes an effort to build a finite element (FE) model. With the developed FE model, a study of the effect of press-fit on the ring gear's root bending stresses, that is present in a hypoid gear set of a car's Rear-Drive Unit (RDU), was carried out. The FE model was built on three different software - Transmission 3D (T3D), Hypoid Face Milled (HFM) and MSC Marc (Marc). The effect of press-fit on root bending stresses of the ring gear was first analyzed on T3D. To determine if the press-fit was correctly induced, the model was rebuilt and analyzed on Marc. HFM was used to determine the effect of inclusion of different components on the root bending stresses. Additionally,the HFM model was also replicated on Marc and a press-fit of 100m was induced. This was done to see if modelling the press-fit on HFM gave similar results to that of T3D and if using HFM in conjunction with Marclead to a better modelling procedure. It was found that the maximum root bending stresses increased linearly with increasing press-fit dimension. It was also found that the inclusion of different parts does not cause a significant increase in root bending stresses, except for the inclusion of differential cage. The effect of press-fit could not be quantified despite knowing that it affects the root bending stresses. When the same analysis done on HFM or T3D was done on Marc, there wasa 10% increase in stresses at highly stressed zone in Marc model of T3D; there was 10-15% increase in stresse sat highly stressed zone in the HFM model of Marc. Hence, quantification remained an impediment. It was not possible to quantify the error that occurred during the migration of analysis from HFM or T3D to Marc. However, potential causes of these errors could be the error in computation of bearing forces and difference in the definition of contacts in the software. Owing to large computational time and limited working period, all the analysis on Marc was carried out for one position and for the first time step of the gear mesh. If the errors in migration of analysis from one software to another could be quantified, then this modelling can be used to estimate the contribution of press-fit to rootbending stresses on the ring-gear. Although the contact pattern comparison between the virtual models andthe physical test suggests that HFM is a more trustworthy software, it is recommended to conduct some straingauge measurements on different ring gear teeth and then compare the results with those of the virtual model. / Kugghjul är en integrerad del av utrustningar som sträcker sig fråan enkla armbandsur till komplexa system som bilar eller vågfrakftverkomvandlare. De spelar en mycket viktig roll vid överföring av vridmoment. Det finns flera typer av kugghjul som man kan välja från, beroende på applikationen. Detta projekt handlar exklusivt om hypoidväaxlar. En hypoidväxel är en typ av vinkelväxel som överför vridmoment mellan två icke parallella axlar. Det liknar ett spiralformat växel, förutom att kugghjulets axel kan förskjutas. Det är denna förmåga att kompensera, vilket gör hypoidväxlar en mycket eftertraktade redskap för fordonsapplikationer. Det är avgörande att dessa hypoid-redskap är konstrueras effektivt och att deras liv före misslyckande ar förutsägbart, i en rimlig grad av noggrannhet. För att möjliggöra sådana Förutsägelser gör denna avhandling ett försök att bygga en finita-element (FE) modell. Med den utvecklade FE-modellen utfördes en studie av effekten av presspassning pa ringvaxelns rotböjspänningar, som finns i en hypoid växelsats av en bilens Bakre enhet (RDU). FE-modellen byggdes på tre olika programvaror: Transmission 3D (T3D), Hypoid Face Milled (HFM) och MSCMarc (Marc). Effekten av presspassning på riggböjspänningarna hos ringväxeln analyserades först på T3D. För att bestämma om presspassningen var korrekt inducerad, byggdes modellen och analyserades på Marc. HFM användes för att bestämma effekten av inkludering av olika komponenter på rotböjspänningarna. Dessutom replikerades HFM-modellen också på Marc och en presspassning på 100 microns inducerades. Detta gjordes för att se om modellering av presspass på HFM gav liknande resultat som T3D och om man använde HFM i kombination med Marc leder det till ett bättre modelleringsförfarande. Det visade sig att de maximala rotböjspänningarna ökade linjärt med ökande presspassningsdimension. Det konstaterades ocksåa att införandet av olika delar inte orsakar en signifikant ökning av rotböjspänningar, utom införandet av differentialbur. Effekten av presspassning kunde inte kvantifieras trots att man vet det påverkar rotböjspänningarna. När samma analys gjord på HFM eller T3D gjordes på Marc, fanns det en 10% ökning av späanningar vid starkt stressad zon i Marc-modellen av T3D; det var 10-15% ökning av spänningar vid starkt stressad zon i HFM-modellen av Marc. Därför förblev kvantifiering ett hinder. Det var inte möjligt att kvantifiera felet som inträffade under analysanalysen från HFM eller T3D till Marc. Dock kan potentiella orsaker till dessa fel vara felet vid beräkning av bärkrafter och skillnad i definitionen av kontakter i programvaran. På grund av stor beräkningstid och begränsad arbetstid utfördes all analys på Marc för bara en position och för det forsta steget av växelns nät. Om felen i migration av analys från en programvara till en annan kunde kvantifieras, då kan denna modellering användas för att beräkna bidragen från presspassning till rotböjspänningar på ringväxeln. Även om kontaktmönstersjämforelsen mellan de virtuella modellerna och det fysiska testet föreslår att HFM är en mer pålitlig programvara, rekommenderas det att utföra en viss belastning Mätmätningar på olika ringväxeltänder och sedan jämföra sedan resultaten med dem från virtuella modellen.

Automotive industry is faced with numerous power train Noise, Vibration and Harshness issues. Particularly, in the driveline area of vehicles a noise commonly referred as differential axle whine which is a tonal response and becomes apparent under cruising conditions. This is one of the key concerns in rear wheel drive commercial vehicles. Although not a failure state, it is regarded as a quality issue and a source of annoyance, which can lead to warranty concerns. The associated cost of palliation to Ford Motor Company was estimated to be $25,000,000 in 2003. There have been several ways of studying axle whine through experimentation and numerical analysis. In this thesis, a new approach for investigating axle whine is highlighted, which is more integrative and detailed. Multi-body dynamics model of a light truck s driveline is developed with all the appropriate components, using constrained Lagrangian dynamics. Component flexibility is included for driveshaft pieces, rear axle half-shafts and the suspension elements. The connectivity of the components is accurately modelled such as the floating effect of rear half-shafts, linear bushings between driveline components to chassis connections, as well as the non-linear effect of tapered roller bearings, supporting the wheel hubs and gears. Furthermore, integrated to the previously described large scale model a detailed hypoid gear pair model is devised. This incorporates micro-scale physics for tooth contact analysis to predict geometric properties and deflections for the gear pair. At the same time thermo-elastohydrodynamic lubrication theory with non-Newtonian friction is applied. All these phenomena at different physical scales, such as large displacement rigid body dynamics and analytical equations for the detailed model are solved simultaneously, all within the same modelling environment. This multi-physics, multi-scale approach has not hitherto been reported in the literature, and constitutes a significant contribution to knowledge. Comparative studies of the model predictions and detailed vehicle tests are carried out, the combination of which points to resonant conditions in system responses and flexible component behaviour, coincident with the adverse conditions in the hypoid gear meshing. It is shown that vehicle drive and coast conditions, promoting teeth pair separations lead to irregular (improper) meshing of the differential gears. Such conditions induce impulsive actions that promote the axle whine phenomenon. This is a major finding of the research and contributes to a better understanding of the axle whine problem.

A hypoid gear optimization procedure using the method of feasible directions has been developed. The objective is to reduce the gear set weight with bending strength, contact strength and facewidth-diametral pitch ratio as constraints. The objective function weight, is calculated from the geometric approximation of the volume of the gear and pinion. The design variables selected are number of gear teeth, diametral pitch, and facewidth. The input parameters for starting the initial design phase are power to be transmitted, speed, gear ratio, type of application, mounting condition, type of loading, and the material to be used. In the initial design phase, design parameters are selected or calculated using the standard available procedures. These selected values of design parameters are passed on to the optimization routine as starting points.