Nonlinear dynamic modeling and analysis of helical gear system with time-varying backlash caused by mixed modification

A new internal meshing gear transmission with curve element is put forward in this paper. The mathematical principle of tooth profile generation is described based on conjugate curves theory. For a given spatial curve, the meshing equation and its conjugated spatial curve under the motion law were derived. Considering the equidistant kinematic method, general internal tooth profiles models were established by the conjugate-curve pair. Numerical example of the internal gear pair was developed according to gear parameters and gear solid models were established by MATLAB and UG software. Motion simulation result shows that the gear pair satisfies point contact condition and design requirements. Meshing analysis of tooth profiles using FEA method was carried out. Stress analysis results of tooth profiles with single point contact and two points contact were, respectively, obtained. The conclusions lay the foundation for multi-point contact generation and tooth profile design. Also, further studies on transmission characteristics and manufacturing technology of the new gear drive will be carried out.

Mathematical model and meshing analysis of internal meshing gear transmission with curve element

Vibration control of commercial vehicle drive axles based on modification of helical gears

Abstract For the development of high power density gearboxes the knowledge of the gear mesh behavior is important. Especially, the tooth deflection influences flank load distribution and is the basis for the design of flank modifications. Analytical and numerical approaches are suitable to evaluate the behavior. Since numerical methods are complex, elaborate and time-consuming, fast and accurate analytical methods are still important and are worth to be further developed and assessed. An analytical method for calculating tooth deformation for gears goes back to Weber and Banaschek from 1953. In the initial work the final equations are given without many intermediate steps in the plane strain assumption for materials with Poisson’s ratio ν = 0.3. This paper derives the tooth deflection equations in a more detailed and general manner for any linear material. The final equations are valid for the plane stress and plane strain state in one new closed representation and are therefore suitable for an efficient implementation. While the plane strain state is typical for gears, the plane stress state is significant for a thin slice model or special gearings. The presented method captures the shear influence with a more detailed calculation of the shear correction factor. A calculation study validates the results from the derived analytical tooth deflection calculation method with a plane Finite Element Model. In the study the point of application of force and the gear body are varied to cover the influence of different variants (size and mesh position). Finally limits of the analytical modeling and the validation are discussed. 

/pdf/fast-tooth-deflection-calculation-method-and-its-validation-4f33bzco.pdf

Fast tooth deflection calculation method and its validation

Neck injuries caused by low-speed rear-end collisions are a worldwide problem. The reasonable design of car seat can effectively prevent or reduce the passenger neck injuries. In this paper, the finite element analysis (FEA) and whiplash test are combined to optimize the seat structure parameters to enhance the safety. The whiplash test results of the existing car seats according to C-NCAP (2015) were matched with FEA, and the optimization scheme was developed by computer simulation. For the improvement of seat safety, the optimizations are applied to determine backrest stiffness, backrest rotational stiffness, headrest rotational stiffness and headrest stiffness. The retest results of optimized seat show that its safety performance is greatly improved. Furthermore, it shows that the combination of finite element analysis and whiplash test can optimize seat structure to improve safety performance.

Combined with finite element analysis of car seat safety performance improvement

This work developed an efficient model for calculating the mesh stiffness of spur/helical internal gear pairs by combining the finite element method (FEM) and analytical formula. The tooth global deformation is obtained by separation of the deformation of a full finite element model and a partial model, and the local contact deformation is derived by an analytical line contact formula based on Hertz contact theory. The transmission error and mesh stiffness of the gear pair can be acquired after solving the nonlinear contact equilibrium equations. Compared with the conventional FEM, the proposed method has much smaller computational consumption. Furthermore, it also overcomes the disadvantage that the analytical method is difficult to consider different ring gear structures. Then the influences of ring thicknesses and the number of support pins of the ring gear on the mesh stiffness are discussed. The results show that the ring flexibility will change the amplitude-frequency components of the mesh stiffness a lot.

A hybrid finite element and analytical model for determining the mesh stiffness of internal gear pairs

The invention discloses a high-contact-ratio gleason spiral bevel gear design method. The high-contact-ratio gleason spiral bevel gear design method comprises the steps of presetting a geometrical transmission error curve, and deriving a relational expression of large and small gear meshing rotation angles; by means of the principles of transformation of homogeneous coordinates and space meshing,obtaining a small gear auxiliary tooth surface making line contact with a large gear; according to the small gear meshing rotation angles generated when entering meshing and exiting from meshing, computing the largest design contact ratio of a gear pair; computing the profiling length and the profiling quantity on the tangent plane of the contact point, superposing the profiling length and the profiling quantity on the small gear auxiliary tooth surface, and obtaining the small gear target tooth face which can meet the preset meshing performance and can make point contact with the paired largegear; building an optimization model in which the small gear processing parameter serves as the optimization variable, the optimization objective is that the sum of squares of the normal errors of the small gear tooth surface corresponding to the processing parameter and the target tooth surface is minimum, and by using a genetic algorithm, inversely solving the processing parameter, meeting thepreset performance, of the small gear of the high-contact-ratio gleason spiral bevel gear. By means of the method, the transmission efficiency of the gear pair can be improved, and the probability oftooth surface scratching and gluing failure is reduced.

High-contact-ratio gleason spiral bevel gear design method

The invention discloses a gear pair design method based on a clothoid rack cutter. The gear pair design method based on the clothoid rack cutter comprises the steps that a clothoid blade is adopted toreplace a linear blade and an arc blade of the rack cutter, and by means of the involute profile generating theory, the tooth profile of a conjugate gear pair is obtained; geometric constraint conditions are established with gear tooth basic parameters, and the shape parameter of the clothoid is calculated; a tooth profile coordinate system and a moving coordinate system of the rack cutter are established, and the position vector and a normal vector of the rack cutter are obtained; and by controlling the motion relationship between movement speed along a pitch line of the rack cutter and thespeed of rotation of the workpiece around the axis of the workpiece, by means of homogeneous coordinate transformation and a plane engagement theory, the tooth surface equations of a big gear and a pinion are deduced, and a gear pair model is established. According to the gear pair design method based on the clothoid rack cutter, by means of a concave-convex rack cutter, concave-convex contact ofthe gear pair is obtained, and the contact strength of tooth surfaces is improved; each tooth root is machined through a concave tooth crest of the rack cutter, the thickness of the tooth roots of gear teeth is increased, the bending strength of the gear teeth is improved, and the minimum number of the teeth without undercutting is reduced.

Gear pair design method based on clothoid rack cutter

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A hybrid finite element and analytical model for determining the mesh stiffness of internal gear pairs

High-contact-ratio gleason spiral bevel gear design method

Gear pair design method based on clothoid rack cutter