Theoretical Validation of an Analytical Design Method for Beveloid Gears With Non-Parallel Non-Intersecting Axes

2019 ◽  
Author(s):  
Daniel Marino ◽  
Matthias Bachmann ◽  
Hansgeorg Binz
Keyword(s):  
Design Method ◽  
Analytical Calculation ◽  
Transmission Error ◽  
Spur Gear ◽  
Helical Gear ◽  
Fractional Factorial ◽  
Parameter Study ◽  
Beveloid Gears ◽  
Wide Range ◽  
Shaft Angle

Abstract An analytical calculation method was developed to determine the main gearing data for beveloid gears with non-parallel non-intersecting axes. To validate the method and identify its limits, a parameter study was to be conducted. A two-stage fractional factorial experimental design was therefore devised to deliberately vary the gearing parameters. For each gearing, an unloaded contact simulation was carried out using the position of the contact pattern, the transmission error and the predefined gear backlash as quality characteristics. The results of the simulation were subsequently classified in three evaluation categories. Due to the generalizability of the method proposed, it can also be used for the design of other involute gearings. A modification of the equations revealed its applicability for spur gear pairs with no shaft angle and for crossed helical gear pairs with shaft angles up to 90°. The results for the beveloid gear pairs investigated using a wide range of parameters as well as those for the cylindrical and crossed helical gear pairs proved the validity of the method. In the case of outliers in the evaluation, the causes were identified and corrective actions were presented.

scholarly journals Research on the Design and Modification of Asymmetric Spur Gear

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Xiaohe Deng ◽  
Lin Hua ◽  
Xinghui Han
Keyword(s):  
Computer Aided Design ◽  
Design Method ◽  
Geometric Model ◽  
Simulation Method ◽  
Transmission Error ◽  
Spur Gear ◽  
Geometric Shape ◽  
Spur Gears ◽  
Gear Design ◽  
Aided Design

A design method for the geometric shape and modification of asymmetric spur gear was proposed, in which the geometric shape and modification of the gear can be obtained directly according to the rack-cutter profile. In the geometric design process of the gear, a rack-cutter with different pressure angles and fillet radius in the driving side and coast side was selected, and the generated asymmetric spur gear profiles also had different pressure angles and fillets accordingly. In the modification design of the gear, the pressure angle modification of rack-cutter was conducted firstly and then the corresponding modified involute gear profile was obtained. The geometric model of spur gears was developed using computer-aided design, and the meshing process was analyzed using finite element simulation method. Furthermore, the transmission error and load sharing ratio of unmodified and modified asymmetric spur gears were investigated. Research results showed that the proposed gear design method was feasible and desired spur gear can be obtained through one time rapid machining by the method. Asymmetric spur gear with better transmission characteristic can be obtained via involute modification.

Four-Order Parabolic Transmission Error Design of Helical Gear Based on Meshing Area

2013 ◽  
Vol 842 ◽  
pp. 410-414
Author(s):  
Jian Jun Yang ◽  
Jian Jun Wang
Keyword(s):  
Contact Stress ◽  
Transition Point ◽  
Design Method ◽  
Transmission Error ◽  
Helical Gear ◽  
Transmission Curve ◽  
Tooth Contact Analysis ◽  
Contact Conditions ◽  
Helical Gears ◽  
Alignment Errors

In the paper, a new transmission error design method for helical gears is presented. According to transition point position of the contact area in one meshing cycle, the proposed four-order transmission curve is able to diminish contact stress and edge contact, decrease transmission error as well. Tooth contact analysis is used to simulate contact conditions of helical gear driver with four-order parabolic modification curve. The results show that the meshing area is non-sensitive to the alignment errors.

Research on Gear Cutter Tooth Profile for Semi-Topping: A Case of a Helical Gear

1992 ◽  
Author(s):  
Y. Ariga ◽  
Shiyeyoshi Nagata
Keyword(s):  
Design Method ◽  
Gear Tooth ◽  
Helical Gear ◽  
Tooth Profile ◽  
Tooth Surface ◽  
Gear Cutting ◽  
Gear Cutter ◽  
Conventional Design ◽  
Wide Range ◽  
Tooth Number

Abstract Gear tooth tips are frequently chamfered to prevent nicks or scuffing on the tooth surface. Some of the hob cutters and pinion cutters can be chamfered but many types of cutters should be used for a particular range of tooth numbers since the amount chamfering largely varies depending on the tooth number. However, intensive efforts in the design have made it possible to produce cutters with little variation of chamfering amount for a wide range of tooth numbers. The error in the amount of chamfering by a single cutter designed by the above method can be maintained within ±10 % for gears with tooth numbers ranging from 16 to 94. It was found that three cutters of the conventional design are required for keeping the error within the same range for cutting gears within a given range of tooth numbers. The paper describes the tooth design method of the hob cutter with little variation of chamfering amount along changes in number of teeth to be machined and demonstrates that chamfering errors are maintained within practically allowable ranges for profile shift cutting or helical gear cutting with the use of this cutter.

Analytical design method for beveloid gears with a small shaft angle and offset

2019 ◽  
Vol 83 (3) ◽  
pp. 611-620 ◽  
Author(s):  
Daniel Marino ◽  
Hansgeorg Binz ◽  
Matthias Bachmann
Keyword(s):  
Design Method ◽  
Analytical Design ◽  
Beveloid Gears ◽  
Shaft Angle

A Study of the Relationship Between the Dynamic Factors and the Dynamic Transmission Error of Spur Gear Pairs

2006 ◽  
Vol 129 (1) ◽  
pp. 75-84 ◽  
Author(s):  
V. K. Tamminana ◽  
A. Kahraman ◽  
S. Vijayakar
Keyword(s):  
Dynamic Models ◽  
Deformable Body ◽  
Nonlinear Behavior ◽  
Transmission Error ◽  
Spur Gear ◽  
Gear Mesh ◽  
Dynamic Factors ◽  
Wide Range ◽  
Dynamic Transmission Error ◽  
Torque Values

In this study, two different dynamic models, a finite-element-based deformable-body model and a simplified discrete model, are developed to predict dynamic behavior of spur gear pairs. Dynamic transmission error (DTE) and dynamic factors (DF) defined based on the gear mesh loads, tooth loads and bending stresses are computed for a number of unmodified and modified spur gears within a wide range of rotational speed for different involute contact ratios and torque values. Although similar models were proposed in the past, they were neither fully validated nor equipped to predict both DTE and different forms of DF. Accordingly, this study focuses on (i) validation of both models through an extensive set of experimental data obtained from a set of tests using spur gear having unmodified and modified tooth profiles, and (ii) establishment of a direct link between DTE and different forms of DF, especially the ones based on tooth forces and the root stresses. The predicted DF and DTE values are related to each other through simplified formulas. Impact of nonlinear behavior, such as tooth separations and jump discontinuities on DF, is also quantified.

Mathematical Modeling and Dynamic Contact Analysis of Beveloid Gear Pairs in Marine Gearbox With Small Shaft Angle

2017 ◽  
Author(s):  
Tengjiao Lin ◽  
Hang Li ◽  
Wen Liu ◽  
Jun Zhao
Keyword(s):  
Finite Element ◽  
Dynamic Contact ◽  
Transmission Error ◽  
Parametric Modeling ◽  
Tooth Surface ◽  
Element Analysis ◽  
Solid Models ◽  
Beveloid Gears ◽  
Spatial Geometry ◽  
Shaft Angle

The research objective of this study is involute beveloid gears in marine gearbox with small shaft angle. Based on the theory of gear geometry and the generation mechanism, the mathematical models of beveloid gear pairs are derived according to the tooth surface equations of the imaginary counterpart rack. Then a parametric modeling programs of beveloid gears are developed to automatically generate exact model of tooth surface, so as to establish gear solid models. Subsequently, the assembly models are established according to the spatial geometry relation of beveloid gear pairs with intersected axis and crossed axis respectively. On this basis, the finite element models of beveloid gear pairs with intersected axis and crossed axis are established, and the dynamic contact force, dynamic stress distribution and dynamic transmission error are obtained by dynamic contact finite element analysis.

Finite Element/Contact Mechanics Analysis of Spur Gear Pairs With Tooth Root Cracks

2021 ◽  
Author(s):  
Yaosen Wang ◽  
Adrian A. Hood ◽  
Christopher G. Cooley
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Contact Mechanics ◽  
Transmission Error ◽  
Spur Gear ◽  
Tooth Root ◽  
Transmission Errors ◽  
Wide Range ◽  
Dynamic Transmission Error ◽  
Root Crack

Abstract This study analyzes the nonlinear static and dynamic response in spur gear pairs with tooth root crack damage. A finite element/contact mechanics (FE/CM) model is used that accurately captures the elastic deformations on the gear teeth due to kinematic motion, tooth and rim deformations, vibration, and localized increases in compliance due to a tooth root crack. The damage is modeled by releasing the connectivity of the finite element mesh at select nodes near a tooth crack. The sensitivity of the calculated static transmission errors and tooth mesh stiffnesses is determined for varying crack initial locations, final locations, and the path from the initial to final location. Gear tooth mesh stiffness is calculated for a wide range of tooth root crack lengths, including large cracks that extend through nearly all of the tooth. Mesh stiffnesses are meaningfully reduced due to tooth root crack damage. The dynamic response is calculated for cracks of varying length. Larger cracks result in increased peak dynamic transmission errors. For small tooth root cracks the spectrum of dynamic transmission error contains components near the natural frequency of the gear pair. The spectrum of dynamic transmission error has broadband frequency response for large tooth root cracks that extend further than one-half of the tooth’s thickness.

Modeling the Nonlinear Vibration of a Spur Gear Pair

2000 ◽  
Author(s):  
R. G. Parker ◽  
S. M. Vijayakar ◽  
T. Imajou
Keyword(s):  
Finite Element ◽  
Transmission Error ◽  
Spur Gear ◽  
Tooth Surface ◽  
Nonlinear Phenomena ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Time Step ◽  
Mechanics Model ◽  
Wide Range

Abstract The dynamic response of a spur gear pair is investigated using a finite element/contact mechanics model that offers significant advantages for dynamic gear analyses. The gear pair is analyzed across a wide range of operating speeds and torques. Comparisons are made to other researchers’ published experiments that reveal complex nonlinear phenomena. The nonlinearity source is contact loss of the meshing teeth, which, in contrast to the prevailing understanding, occurs even for large torques despite use of high-precision gears. A primary feature of the modeling is that dynamic mesh forces are calculated using detailed contact analysis at each time step as the gears roll through mesh; there is no need to externally specify the excitation in the form of time-varying mesh stiffness, static transmission error input, or the like. A semi-analytical model near the tooth surface is matched to a finite element solution away from the tooth surface, and the computational efficiency that results permits dynamic analysis. Two single degree of freedom models are discussed briefly. While one gives encouragingly good results, the second, which appears to have better mesh stiffness modeling, gives poor comparisons with experiments. The results indicate the sensitivity of such models to changing mesh stiffness representations.

Effect of Contact Ratio on Spur Gear Dynamic Load With No Tooth Profile Modifications

1996 ◽  
Vol 118 (3) ◽  
pp. 439-443 ◽  
Author(s):  
Chuen-Huei Liou ◽  
Hsiang Hsi Lin ◽  
F. B. Oswald ◽  
D. P. Townsend
Keyword(s):  
Dynamic Load ◽  
Spur Gear ◽  
Tooth Size ◽  
Contact Ratio ◽  
Gear Dynamics ◽  
Wide Range ◽  
Gear Contact ◽  
Center Distance ◽  
Selection Of ◽  
Better Than

This paper presents a computer simulation showing how the gear contact ratio affects the dynamic load on a spur gear transmission. The contact ratio can be affected by the tooth addendum, the pressure angle, the tooth size (diametral pitch), and the center distance. The analysis presented in this paper was performed by using the NASA gear dynamics code DANST. In the analysis, the contact ratio was varied over the range 1.20 to 2.40 by changing the length of the tooth addendum. In order to simplify the analysis, other parameters related to contact ratio were held constant. The contact ratio was found to have a significant influence on gear dynamics. Over a wide range of operating speeds, a contact ratio close to 2.0 minimized dynamic load. For low-contact-ratio gears (contact ratio less than two), increasing the contact ratio reduced gear dynamic load. For high-contact-ratio gears (contact ratio equal to or greater than 2.0), the selection of contact ratio should take into consideration the intended operating speeds. In general, high-contact-ratio gears minimized dynamic load better than low-contact-ratio gears.

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