Mathematical model for design and analysis of power skiving tool for involute gear cutting

2016 ◽  
Vol 101 ◽  
pp. 195-208 ◽  
Author(s):  
Chung-Yu Tsai
Keyword(s):  
Mathematical Model ◽  
Gear Cutting ◽  
Power Skiving ◽  
Involute Gear

scholarly journals About the Profile Accuracy of the Involute Gear Hob

2017 ◽  
Vol 9 (1) ◽  
pp. 5-18 ◽  
Author(s):  
Márton Máté ◽  
Dénes Hollanda
Keyword(s):  
Mathematical Model ◽  
Cutting Tools ◽  
Helical Gear ◽  
Gear Cutting ◽  
Involute Gear ◽  
Edge Profile ◽  
Design Solutions ◽  
The Moment ◽  
Profile Accuracy

Abstract Gear hobs are the most widely and frequently used gear cutting tools. During the time passed between the moment of invention (Schiele, 1876) and the present, gear hobs reached a considerable evolution regarding the geometry, the profile of the edge, the relieving technologies finalizing in the latest constructive and design solutions. This paper deals with the calculus of the edge profile in the case the basic worm of the hob has involute helicoid surfaces. In order to obtain a constant grinding allowance on the relief faces of the gear hob teeth it is necessary to compute the edge of the roughing relieving cutter. The equations are deduced considering that the provenience involute worm is a one teethed helical gear with shifted profile. The presented mathematical model proves that linearizing the relieving cutter profile is not an adequate solution if aspiring to higher precision.

Research on the profile modification of power skiving tool for internal gears

2021 ◽  
Author(s):  
Han ZHENGYANG ◽  
Jiang CHUANG ◽  
Deng Xiaozhong
Keyword(s):  
Mathematical Model ◽  
Rake Angle ◽  
Correction Method ◽  
Profile Error ◽  
Power Skiving ◽  
Tool Profile ◽  
Profile Correction ◽  
Order Of Magnitude ◽  
Fifth Order ◽  
Gear Profile

Abstract Power skiving provides an effective solution and considerable machining efficiency for the machining of internal gears. The tool profile design and the reusability after resharpening is critical in gear machining. In this paper, a tool profile correction method based on the error inverse complement of involute profile is proposed. The mathematical model of involute cutter with rake angle and relief angle is established, and the profile error relative to the target gear is calculated by using the tool of this mathematical model. The distribution of gear profile error is fitted by fifth-order multinomial, and the multinomial function of fitting was attached to the cutter profile. The theoretical error of the target gear profile is in 10e-7mm order of magnitude through the calculation of fewer iterations. The distribution of the coefficient of the error multinomial along the resharpening direction is obtained by linear programming. The result shows that the tool designed by this method has almost negligible error accuracy and good repeatability.

scholarly journals Mathematical Modelling of Power Skiving for General Profile based on Numerical Enveloping

2021 ◽  
Author(s):  
Kang Jia ◽  
Junkang Guo ◽  
Tao Ma ◽  
Shaoke Wan
Keyword(s):  
Surface Topography ◽  
Cutting Tools ◽  
Mathematic Model ◽  
Machining Process ◽  
Machined Surface ◽  
High Productivity ◽  
Power Skiving ◽  
Involute Gear ◽  
Motion Speed ◽  
General Profile

Abstract Power skiving is an effective generating machining method for internal parts like gears with respect its high productivity. The general mathematic modelling for power skiving is the basis for cutting tools design, machining precision evaluation, and machining process optimization. Currently, mainly studies are focus on the involute gear machining with adopting the analytical enveloping equation. However, these analytical methods have failed to deal with overcutting for general profile skiving tasks. Moreover, little attention has been devoted to investigate the power skiving process with taking variable configuration parameters, which is significant to control the machined surface topography. Herein, we introduce a mathematic modelling method for power skiving with general profile based on the numerical discrete enveloping. Firstly, the basic mathematic model of power skiving is established, in which the center distance is formulated as polynomial of time. With transforming the power skiving into a forming machining of the swept volume of cutting edge, a numerical algorithm is designed to distinguish the machined transverse profile via the discrete enveloping ideology. Especially, the precise instant contact curve is extracted according to the feed motion speed inversely. Finally, simulations for involute gear and cycloid wheel are carried out to verify the effectiveness of this method and investigate the influence of variable radial motions on the machined slot surface topography. The results show this method is capable to simulate the dynamic power skiving process with general profiles and to evaluate the machined results.

A Study on the Tooth Geometry and Cutting Machine Mechanisms of Spiral Bevel Gears

1991 ◽  
Vol 113 (3) ◽  
pp. 346-351 ◽  
Author(s):  
Z. H. Fong ◽  
Bill Chung-Biau Tsay
Keyword(s):  
Mathematical Model ◽  
Bevel Gear ◽  
Spiral Bevel Gear ◽  
Helical Motion ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Gear Cutting ◽  
Cutting Machine ◽  
The Matrix ◽  
Spiral Bevel

The tooth geometry and cutting machine mechanisms of spiral bevel gears are investigated. Based on the kinematics of titled head cutter, machine cradle, sliding base and work head, the matrix presentation of spiral bevel gear’s tooth geometry are developed. The relations between the parameters of the proposed mathematical model and the machine settings of existing spiral bevel gear cutting machines are also investigated. The tilt of head cutter axis, motion of generation, helical motion of sliding base, and nongenerating cutting of spiral bevel gears are taken into consideration. An example is given to illustrate the application of the proposed mathematical model.

A General Mathematical Model for Gears Cut by CNC Hobbing Machines

1997 ◽  
Vol 119 (1) ◽  
pp. 108-113 ◽  
Author(s):  
Shinn-Liang Chang ◽  
Chung-Biau Tsay ◽  
Shigeyoshi Nagata
Keyword(s):  
Mathematical Model ◽  
Degree Of Freedom ◽  
Cutting Process ◽  
Generation Process ◽  
Cutting Mechanism ◽  
Gear Cutting ◽  
Different Types ◽  
General Mathematical Model ◽  
Crossed Axes ◽  
The Mathematical Model

A hobbing machine’s cutting mechanism is a mechanism with multi-degree of freedom during the cutting process. In this paper, we propose a general gear mathematical model simulating the generation process of a 6-axis CNC hobbing machine based on the cutting mechanism of CNC hobbing machine and worm-type hob cutter. The proposed gear mathematical model can be applied to simulate different types of gear cutting. Some examples are included to verify the mathematical model. Also, a novel type of gear named “Helipoid” which can be used in crossed axes transmission is proposed. The proposed general gear mathematical model can facilitate a more thorough understanding of generation processes and toward the development of novel types of gears.

Small Module Involute Gear Precise Modeling and NC Machining

2014 ◽  
Vol 496-500 ◽  
pp. 1348-1351
Author(s):  
Hong Sun
Keyword(s):  
Mathematical Model ◽  
Three Dimensional ◽  
Nc Machining ◽  
Numerical Control ◽  
Processing Problem ◽  
Point Approximation ◽  
Processing Node ◽  
Involute Gear ◽  
Data Points ◽  
Wire Cutting

We can take the approach of mathematical model by establishing accurate mathematical model of small module gear, and will get the data point approximation file to import into UG, and we can realize the precise three-dimensional modelling of small module gear through UG calling data points. We can take the close data as CNC wire-cutting processing node coordinates of programming, and program CNC wire-cutting processing. This can be a very good solution to the small module gear precise modeling and numerical control processing problem.

Meshing analysis of a gear with a ring-involute gear

2003 ◽  
Vol 217 (12) ◽  
pp. 1287-1299 ◽  
Author(s):  
S-C Yang
Keyword(s):  
Mathematical Model ◽  
Stress Analysis ◽  
Geometric Model ◽  
Gear Ratio ◽  
Geometric Modelling ◽  
Numerical Example ◽  
Involute Gear ◽  
The Family ◽  
New Type ◽  
Kinematic Errors

The surface of a gear with ring-involute teeth generated by a rack cutter with ring-involute teeth is a new type of gear. This paper describes a method developed from gear theory for deriving a pinion and a gear with ring-involute teeth. A gear with ring-involute teeth is regarded as an envelope to the family of rack cutter surfaces when the pinion and gear rotate for a cycle. Using a developed mathematical model, the investigation on the undercutting analysis of the proposed gear is studied. Here the kinematic errors are investigated according to the obtained geometric modelling of the designed gear meshing when assembly errors were present. Stress analysis for the proposed gear was performed. Finally, a numerical example is presented to demonstrate the geometric model of a gear with ring-involute teeth and a gear ratio of 3:2.

Gear Cutting in a Globoid Pair with an Initial Cylindrical Involute Gear

2020 ◽  
Vol 40 (12) ◽  
pp. 1087-1090
Author(s):  
L. S. Mal’ko ◽  
A. V. Sutyagin ◽  
I. V. Trifanov ◽  
N. V. Zakharova ◽  
O. A. Sukhanova
Keyword(s):  
Gear Cutting ◽  
Involute Gear

scholarly journals Research On Machining Non-Orthogonal Face Gears By Power Skiving With Tooth Flank Modification Based On Six-Axis Machine Tool

2021 ◽  
Author(s):  
Han ZHENGYANG ◽  
Jiang CHUANG ◽  
Deng Xiaozhong
Keyword(s):  
Mathematical Model ◽  
Machine Tool ◽  
Relative Position ◽  
Experimental Results ◽  
Machining Parameters ◽  
Face Gear ◽  
Power Skiving ◽  
Tooth Flank ◽  
The Mathematical Model

Abstract To solve the manufacturing difficulties of non-orthogonal face gear, an efficient gear machining method referred to as power skiving is proposed. The machining principle of the power skiving and the relative position between the cutter tool and the workpiece are analyzed. Then, the mathematical model of machining non-orthogonal face gears by power skiving is established and the tooth flank equation is obtained. The installation and movement mode of non-orthogonal face gears on six-axis machine tool are analyzed and the machining parameters are calculated precisely. A method of tooth flank modification on the six-axis machine tool is presented by changing the machining parameters. The meshing performance of the obtained non-orthogonal face gear is analyzed by an example. Finally, the processing test and the tooth flank measurement are carried out. The experimental results show that the non-orthogonal face gear can be machined and modified by power skiving on the proposed six-axis machine tool.

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