| Gear transmission, as a key mechanical part, may affect the performance andreliability of machinery and equipment, which relate to gear design and manufacture.The theoretical and experimental researches on gear strength and friction have asignificant meaning for increasing the carrying capacity, improved fatigue life, andto reduce friction and wear, to improve the transmission performance.Many researches are devoted to gear bending strength and friction by usingtheoretical and experimental methods. However, there are many intractabilityproblems about exactly calculating or testing the bending strength and friction, andneed to be studied further:(1) Accurate finite element model and numericalsimulation method for calculating root stress and tooth compliance under differentloads;(2) the realistic model for describing the friction and lubrication states andchange rules on the tooth surface, and pervasive calculating methods for toothfriction parameters;(3) Impact friction mechanism and quantitative calculationbased on interdisciplinary such as theory of gear, tribology, contact dynamics.Above all, the main motivations of the present paper are:(1) Accurate finiteelement model and numerical simulation method for bending strength;(2)polymorphism model and calculating method of gear friction and lubrication;(3)pervasive calculating methods for friction force and coefficient of tooth surface.Main works and innovation points are listed as follows.1. The research is about the accurate FEM modeling of gear pair and thecalculation method of bending, which are validated by comparative research. Thetooth curve is deduced based on the gear generating method and coordinatetransformation, and the accurate geometrical modeling of gear profile isaccomplished by the co-modeling method of APDL and MATLAB with text data files.Due to the calculation model including error and deformation, the calculationequation of bending strength is deduced, which may be a criterion to determine theselection of calculation points. The effective loads are studied with the FEM of gearbending strength. The peak stress value of dedendum and deformation of gear toothunder varying loads are compared and conclude that the accuracy of calculation isincreased along with the order of concentrated force, line loads, distribution force onHertz contact interface and static contact force. Dynamic characteristic analyses of moving load cannot exhibit the impact effects easily.2. The additive effects of tooth load, load distribution in the direction of toothdepth and tooth width are exhibited in the research. Moreover, the deformation ofgear tooth and the distribution discipline of maximum pull/press force are deserved.The research shows:(1) the additive effect of adjacent gear tooth meshing cannot beignored in the accurate calculation of gear strength, press sides are more affectedthan pull sides, eventually the maximum deformation of gear tooth is increased.Under the influence of even load, triangular distribution and cubic parabola loaddistribution, the varying disciplines of peak stress of dedendum in the gear widthdirection and tooth deformation in the contact zones are displayed. Moreover, it isvalidated about the gear end stiffness effect, gear tooth deformation and continuationof stress. Overall, the maximum press or pull stress of dedendum is increasedaccording to the irregularity of tooth load and effect of gear end stiffness, whereasthe maximum deformation of contact zones is decreased.3. Based on the virtual integration platform, a new method of stress is conductedcombined with wireless strain acquisition card and stress data transmitted by router.Further, the wireless test rig of dynamic strain in dedendum is designed. The dataunmeasured is acquired with the elimination of random electrical noise by averagemethod. And the input and output of speeds and torques are averaged to be regard asworking conditions, which can be coordinated with the boundary of calculatingmodel and experimental conditions. The tested variation curve of strain ondedendum reflect the phenomenon of single and double tooth gear meshing, gearmeshing impact and the impact of adjacent gear tooth. The measured maximumstrain on dedendum is coordinated with the results of FEM model and conclusionsderived by other researchers, which means the reliability and correction of methodreferred in the thesis and the FEM model as well as the results deduced. At last, thetest samples, namely measuring stresses, used in the fiction coefficient reverse ofgear tooth are acquired reliable.4. The polymorphism model of gear friction and lubrication is proposed. Theforming-mechanisms, characteristics and existing conditions of multiple gearfriction and lubrication behaviors (including elastohydrodynamic lubrication,boundary lubrication, mixed lubrication, dry friction, impact friction) in drivingprocess are investigated combining mesh theory with tribology. Then thepolymorphism model is proposed in consideration of the tribology systemcomplexity of gear drive and the friction transient phenomenon of teeth contact. The mixed lubrication can be devided into typeⅠ(not including local dry friction) andtype Ⅱ (including local dry friction). Finally, the composition model of mixedlubricationⅠand calculating method of friction coefficient are studied.5. The reverse method for coefficient of friction on surfaces on gear teeth isproposed by IP-uGA based on the numerical solution and test value of maximumtooth root stress. The sensibility of the tooth root stress to profile friction force andcoefficient is investigated when loaded on the upper point of single gear engagement.The sensitivity of the maximum tensile stress is twice as much as the maximumcompressive stress. The objective function considering calculating stress, testingstress and friction force as variables is gained and the dry friction coefficient isreversed by the genetic algorithm and FEM program. The effects of tooth surfacefriction on tooth root stress and tooth deformation are studied based on the frictioncoefficient reversed.6. Corner contact is devided into impact, scrape and normal engagement stages.Combining gear theory with numerical backstepping, the method for modelling andcalculating of impact friction caused by corner contact in gear transmissionconsidering the system error and tooth deformation is proposed. Main conclusionsinclude:(1) The work law of the main system errors, teeth deformation and loads onthe line of action is studied, which influences corner contact. Then the calculationmodel including gear equivalent error—combined deformation is established on theline of action.(2) According to the distributive rule, gear equivalent error issynthesized by base pitch error, normal backlash and tooth profile modification onthe line of action, and combined deformation is synthesized by bending, compressive,shearing and contact compliances. Combining the secondarily equivalent error withthe combined deformation, the position standard of the point situated at cornercontact is established.(3) The combined tooth compliance of the first point lying incorner contact before the normal path is backstepped, on basis of the curve of toothsynthetic compliance&load-history curve. After the impact position and force arecalculated accurately, the impact friction model is estabilshed and the impact frictioncoefficient is calculated. |
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