Deformations and Stresses in Face-Hobbed Spiral Bevel Gears

2011 ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Nodal Point ◽  
Design Parameters ◽  
Element Discretization ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Spiral Bevel ◽  
Element Method

In this study an attempt is made to predict displacements and stresses in face-hobbed spiral bevel gears by using the finite element method. A displacement type finite element method is applied with curved, 20-node isoparametric elements. A method is developed for the automatic finite element discretization of the pinion and the gear. The full theory of the generation of tooth surfaces of face-hobbed spiral bevel gears is applied to determine the nodal point coordinates on tooth surfaces. The boundary conditions for the pinion and the gear are set automatically as well. A computer program was developed to implement the formulation provided above. By using this program the influence of design parameters and load position on tooth deflections and fillet stresses is investigated. On the basis of the results, obtained by performing a big number of computer runs, by using regression analysis and interpolation functions, equations for the calculation of tooth deflections and fillet stresses are derived.

scholarly journals Tooth Fracture Detection in Spiral Bevel Gears System by Harmonic Response Based on Finite Element Method

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Yuan Chen ◽  
Rupeng Zhu ◽  
Guanghu Jin ◽  
Yeping Xiong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Bevel Gear ◽  
Spiral Bevel Gear ◽  
Spiral Bevel Gears ◽  
Harmonic Response ◽  
Bevel Gears ◽  
Tooth Fracture ◽  
Spiral Bevel ◽  
Element Method

Spiral bevel gears occupy several advantages such as high contact ratio, strong carrying capacity, and smooth operation, which become one of the most widely used components in high-speed stage of the aeronautical transmission system. Its dynamic characteristics are addressed by many scholars. However, spiral bevel gears, especially tooth fracture occurrence and monitoring, are not to be investigated, according to the limited published issues. Therefore, this paper establishes a three-dimensional model and finite element model of the Gleason spiral bevel gear pair. The model considers the effect of tooth root fracture on the system due to fatigue. Finite element method is used to compute the mesh generation, set the boundary condition, and carry out the dynamic load. The harmonic response spectra of the base under tooth fracture are calculated and the influence of main parameters on monitoring failure is investigated as well. The results show that the change of torque affects insignificantly the determination of whether or not the system has tooth fracture. The intermediate frequency interval (200 Hz–1000 Hz) is the best interval to judge tooth fracture occurrence. The best fault test region is located in the working area where the system is going through meshing. The simulation calculation provides a theoretical reference for spiral bevel gear system test and fault diagnosis.

Method for Generation of Spiral Bevel Gears With Conjugate Gear Tooth Surfaces

1987 ◽  
Vol 109 (2) ◽  
pp. 163-170 ◽  
Author(s):  
F. L. Litvin ◽  
Wei-Jiung Tsung ◽  
J. J. Coy ◽  
C. Heine
Keyword(s):  
Gear Tooth ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Straight Line ◽  
Parallel Motion ◽  
Tooth Surfaces ◽  
Spiral Bevel

The authors proposed a method for generation of spiral bevel gears that provides conjugate gear tooth surfaces. This method is based on a new principle for the performance of parallel motion of a straight line that slides along two mating ellispses with related dimensions and parameters of orientation. The parallel motion of the straight line, that is the contact normal, is performed parallel to the line which passes through the foci of symmetry of the related ellipses. The manufacturing of gears can be performed with the existing Gleason’s equipment.

Assembly interference and its avoidance of spiral bevel gears in cyclo-palloid system

2019 ◽  
Vol 234 (2) ◽  
pp. 704-717
Author(s):  
Isamu Tsuji ◽  
Kazumasa Kawasaki
Keyword(s):  
Contact Analysis ◽  
Experimental Results ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Spiral Bevel ◽  
Good Agreement

In this article, the assembly interference of spiral bevel gears in a Klingelnberg cyclo-palloid system is analyzed based upon tooth contact analysis and is investigated experimentally. Each backlash in increasing mounting distance of the pinion is calculated step by step, using developed tooth contact analysis. When the backlash increases, the assembly interference does not occur based upon the calculated results. When the backlash decreases and is less than zero, the assembly interference occurs. When the assembly interference occurs, the tooth surfaces should be modified in order to prevent the assembly interference. In this case, a method of the modification is proposed. The experimental results showed a good agreement with the analyzed ones. As a result, the validity of the analysis and avoidance of the assembly interference in this method was confirmed.

Spiral Bevel Gears CNC Milled by Disc Cutter with Concave End

2013 ◽  
Vol 415 ◽  
pp. 636-641
Author(s):  
Xiao Zhong Deng ◽  
Geng Geng Li ◽  
Bing Yang Wei
Keyword(s):  
Face Milling ◽  
Strip Width ◽  
Disc Cutter ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Cutter Orientation ◽  
End Mills ◽  
Spiral Bevel ◽  
Yaw Angle

In order to solve the small cutting strip width and poor surface quality problems when spiral bevel gears are CNC machined by ball-end mills£¬a machining method of face milling spiral bevel gears by using a disc cutter with a concave end is presented. Based on the researches of spiral bevel gears geometry structure, through a bigger diameter disc cutter with a concave end selected, the setting order of cutter orientation angles changed, and the functions of cutter tilt and yaw angle separated, tooth surfaces machined with big cutting strip width and no bottom land gouge can be expected. Finally, taking a spiral bevel gear pair as an example, through machining and measurement experiments, the method feasibility and correctness are verified

Advanced Design and Manufacture of Face-Hobbed Spiral Bevel Gears

2009 ◽  
Author(s):  
V. Simon
Keyword(s):  
Gear Tooth ◽  
Numerical Control ◽  
Mutual Position ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Pinion Gear ◽  
Tooth Surfaces ◽  
Spiral Bevel ◽  
Tooth Flank ◽  
Crown Gear

The design and advanced manufacture of face-hobbed spiral bevel gears on computer numerical control (CNC) hypoid generating machines is presented. The concept of face-hobbed bevel gear generation by an imaginary generating crown gear is established. In order to reduce the sensitivity of the gear pair to errors in tooth-surfaces and to the mutual position of the mating members, modifications are introduced into the teeth of both members. The lengthwise crowning of teeth is achieved by applying a slightly bigger lengthwise tooth flank curvature of the crown gear generating the concave side of pinion/gear tooth-surfaces, and/or by using tilt angle of the head-cutter in the manufacture of pinion/gear teeth. The tooth profile modification is introduced by the circular profile of the cutting edge of head-cutter blades. An algorithm is developed for the execution of motions on the CNC hypoid generating machine using the relations on the cradle-type machine. The algorithm is based on the condition that since the tool is a rotary surface and the pinion/gear blank is also related to a rotary surface, it is necessary to ensure the same relative position of the head cutter and the pinion on both machines.

Sensitivity of Stress Intensity Factors with Respect to the Crack Geometry by the Scaled Boundary Finite Element Method

2014 ◽  
Vol 553 ◽  
pp. 737-742
Author(s):  
Morsaleen Shehzad Chowdhury ◽  
Chong Ming Song ◽  
Wei Gao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Shape Sensitivity ◽  
Intensity Factors ◽  
Element Discretization ◽  
Crack Geometry ◽  
Scaled Boundary Finite Element ◽  
Element Method

The sensitivity of the stress intensity factors (SIFs) with respect to the crack geometry, shape sensitivity, plays an important role in the reliability analysis of cracked structures and many other fracture mechanics applications. This paper presents a numerical technique to evaluate the shape sensitivity using the scaled boundary finite element method. It combines the finite element formulations with the boundary element discretization. The crack surface remains meshless. The variation in crack geometry is modelled by applying direct differentiation with respect to the crack geometry, without remeshing. The sensitivity of the stress modes are not required for the calculation of the sensitivity of the SIFs. A numerical example demonstrates the efficiency, accuracy and simplicity of the technique.

A POSTERIORI ERROR ESTIMATION FOR THE FINITE ELEMENT METHOD-OF-LINES SOLUTION OF PARABOLIC PROBLEMS

1999 ◽  
Vol 09 (02) ◽  
pp. 261-286 ◽  
Author(s):  
SLIMANE ADJERID ◽  
JOSEPH E. FLAHERTY ◽  
IVO BABUŠKA
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Method Of Lines ◽  
Posteriori Error ◽  
Parabolic Problems ◽  
A Posteriori ◽  
Element Discretization ◽  
Mesh Spacing ◽  
A Posteriori Estimates ◽  
Element Method

Babuška and Yu constructed a posteriori estimates for finite element discretization errors of linear elliptic problems utilizing a dichotomy principal stating that the errors of odd-order approximations arise near element edges as mesh spacing decreases while those of even-order approximations arise in element interiors. We construct similar a posteriori estimates for the spatial errors of finite element method-of-lines solutions of linear parabolic partial differential equations on square-element meshes. Error estimates computed in this manner are proven to be asymptotically correct; thus, they converge in strain energy under mesh refinement at the same rate as the actual errors.

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