Static and dynamic analysis of spur and bevel gears using FEM
Section snippets
Nomenclature
ajk force acting on the kth degree of freedom of jth substructure fpk pth Fourier harmonic of forces m number of degrees of freedom in each substructure N number of sectors [K] stiffness matrix {δ} displacement vector {δj} displacement vector of jth substructure {δ′p} displacement of the first substructure of pth harmonic
Static analysis
A gear wheel is made of substructures which have identical geometry and material properties and are connected to each other in the circumferential direction. Thus, a gear may be considered a rotationally periodic structure. If cyclic symmetry concept is used in the analysis of such structures, a significant reduction in computational effort can be effected.
In the present analysis, only one substructure (tooth) is assumed to have a contact line load. A line load on one substructure and zero load
Frequency analysis
The mathematical approach to the concept of cyclic symmetry used in the frequency analysis of rotationally periodic structures has been discussed in[7]. The use of cyclic symmetry concept effects a large saving in memory and reduction in computational effort. The method proposed by Balasubramanian and Ramamurti[8] is extended to the free vibration of the spur gear tooth. The simultaneous iteration scheme is modified to compute the Hermitian eigen value problem. An out of core technique is
Spur gear
A load of 500 N per mm width is applied first at the tip of the tooth and then at two other points along the profile. The stress distribution along the profile of the tooth for the three load cases is shown in Fig. 3. The points M and N indicate the stress concentration at the point of application of load. The stress distribution along the root section is shown in Fig. 4. As can be seen the nature of radial stress changes from tension on the loaded side to compression on the unloaded side along
Conclusion
This analysis demonstrates the use of cyclic symmetry concept in the finite element analysis of a rotationally periodic structure like spur gear. Application of this approach results in large saving in computer memory and reduction of computational effort. This efficient approach can also be used in the dynamic analysis of gear tooth utilising the geometrical periodicity and the submatrices elimination scheme.
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2011, Applied Mathematical ModellingCitation Excerpt :Fujii et al. [2] also studied the analysis of dynamic behaviors of straight bevel-geared shaft supported on tapered roller and angular bearings. Ramamurti et al. [3] used FEM and the so-called submatrices elimination scheme to study three-dimensional stress analysis of spur and bevel-gear teeth. Li et al. [4,5] performed dynamic analysis of spur and spiral bevel-geared rotor-bearing system by means of linear vibration models with the effects of systematic parameters.
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2000, Computer Methods in Applied Mechanics and EngineeringCitation Excerpt :However, only one geometric model of the contact pair was used (for the pinion tooth) and the action of the other contacting tooth (of the mating gear) was simulated by application of a contact force to the pinion model. Therefore, the research performed in [2,11] could provide with good accuracy only the bending stresses in the root area. Developed geometric models: The finite element models are shown in Fig. 19.
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