Flank Correction for Spiral Bevel and Hypoid Gears on a Six-Axis CNC Hypoid Generator

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Yi-Pei Shih ◽  
Zhang-Hua Fong
Keyword(s):  
Correction Method ◽  
Numerical Control ◽  
Cnc Machine ◽  
Hypoid Gears ◽  
Nc Code ◽  
Machine Errors ◽  
Contact Patterns ◽  
Spiral Bevel ◽  
Tooth Flank ◽  
Cutter Head

Because the contact patterns of spiral bevel and hypoid gears are highly sensitive to tooth flank geometry, it is desirable to reduce the flank deviations caused by machine errors and heat treatment deformation. Several methods already proposed for flank correction are based on the cutter parameters, machine settings, and kinematical flank motion parameters of a cradle-type universal generator, which are modulated according to the measured flank topographic deviations. However, because of the recently developed six-axis Cartesian-type computer numerical control (CNC) hypoid generator, both face-milling and face-hobbing cutting methods can be implemented on the same machine using a corresponding cutter head and NC code. Nevertheless, the machine settings and flank corrections of most commercial Cartesian-type machines are still translated from the virtual cradle-type universal hypoid generator. In contrast, this paper proposes a flank-correction methodology derived directly from the six-axis Cartesian-type CNC hypoid generator in which high-order correction is easily achieved through direct control of the CNC axis motion. The validity of this flank-correction method is demonstrated using a numerical example of Oerlikon Spirac face-hobbing hypoid gears made by the proposed Cartesian-type CNC machine.

Flank Correction for Spiral Bevel and Hypoid Gears on a Six-Axis CNC Hypoid Generator

2007 ◽  
Author(s):  
Yi-Pei Shih ◽  
Zhang-Hua Fong
Keyword(s):  
Correction Method ◽  
Numerical Control ◽  
Cnc Machine ◽  
Hypoid Gears ◽  
Nc Code ◽  
Machine Errors ◽  
Highly Sensitive ◽  
Spiral Bevel ◽  
Tooth Flank ◽  
Cutter Head

Because the contact bearings of spiral bevel and hypoid gears are highly sensitive to tooth flank geometry, it is desirable to reduce the flank deviations caused by machine errors and heat treatment deformation. Several methods already proposed for flank correction are based on the cutter parameters, machine settings, and kinematical flank motion parameters of a cradle-type universal generator, which are modulated according to the measured flank topographic deviations. However, because of the recently developed six-axis Cartesian-type computer numerical control (CNC) hypoid generator, both face-milling and face-hobbing cutting methods can be implemented on the same machine using a corresponding cutter head and NC code. Nevertheless, the machine settings and flank corrections of most commercial Cartesian-type machines are still translated from the virtual cradle-type universal hypoid generator. In contrast, this paper proposes a flank-correction methodology derived directly from the six-axis Cartesian-type CNC hypoid generator in which high-order correction is easily achieved through direct control of the CNC axis motion. The validity of this flank correction method is demonstrated using a numerical example of Oerlikon Spirac face-hobbing hypoid gears made by the proposed Cartesian-type CNC machine.

Enhanced Algorithms of Contact Simulation for Hypoid Gear Drives Produced by Face-Milling and Face-Hobbing Processes

2006 ◽  
Vol 129 (1) ◽  
pp. 31-37 ◽  
Author(s):  
Qi Fan
Keyword(s):  
Face Milling ◽  
Numerical Control ◽  
Surface Generation ◽  
Tooth Surface ◽  
Free Form ◽  
Generic Model ◽  
Hypoid Gear ◽  
Hypoid Gears ◽  
Contact Patterns ◽  
Spiral Bevel

Modeling of tooth surface generation and simulation of contact is an important part of computerized design and manufacturing of spiral bevel and hypoid gears. This paper presents new developments in this subject. Specifically, the paper covers: (i) development of a generic model of tooth surface generation for spiral bevel and hypoid gears produced by face-milling and face-hobbing processes conducted on free-form computer numerical control (CNC) hypoid gear generators which are incorporated with the Universal Motions Concept (UMC); (ii) a modified algorithm of tooth contact simulation with reduced number of equations of the nonlinear iterations and stabilized iteration convergence; and (iii) an algorithm of numerical determination of contact lines that form the contact patterns. The enhanced approach of contact simulation can be generally applied to other forms of gearings. Two examples, a face-hobbing design and a face-milling design, are illustrated to verify the implementation of the developed algorithms.

Cutter Interchangeability for Spiral-Bevel and Hypoid Gear Manufacturing

2003 ◽  
Author(s):  
Claude Gosselin ◽  
Jack Masseth ◽  
Wei Liang
Keyword(s):  
Test Case ◽  
Hypoid Gear ◽  
Hypoid Gears ◽  
Manufacturing Operations ◽  
Before And After ◽  
Gear Manufacturing ◽  
Spiral Bevel ◽  
Tooth Flank ◽  
Tooth Flank Surface Topography ◽  
Flank Surface

In the manufacturing of spiral-bevel and hypoid gears, circular cutter dimensions are usually based on the desired performance of a gear set. In large manufacturing operations, where several hundred gear geometries may have been cut over the years, the necessary cutter inventory may become quite large since the cutter diameters will differ from one geometry to another, which results in used storage space and associated costs in purchasing and maintaining the cutter parts. Interchangeability of cutters is therefore of significant interest to reduce cost while maintaining approved tooth geometries. An algorithm is presented which allows the use of a different cutter, either in diameter and/or pressure angle, to obtain the same tooth flank surface topography. A test case is presented to illustrate the usefulness of the method: the OB cutter diameter of an hypoid pinion is changed from 8.9500" to 9.1000". CMM results and the comparison of the bearing patterns before and after change show excellent correlation, and indicate that the new pinion can be used in place of the original pinion without performance or quality problems. Significant cost reductions may be obtained with the application of the method.

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.

Accurate modification methodology of universal machine tool settings for spiral bevel and hypoid gears

2016 ◽  
Vol 232 (2) ◽  
pp. 339-349 ◽  
Author(s):  
Zhen-yu Zhou ◽  
Jin-yuan Tang ◽  
Han Ding
Keyword(s):  
Machine Tool ◽  
Error Compensation ◽  
Geometric Error ◽  
Higher Order ◽  
Experimental Result ◽  
Form Error ◽  
Hypoid Gears ◽  
Universal Machine ◽  
Spiral Bevel ◽  
Tooth Flank

Universal machine tool settings with higher-order motion coefficients are developed to make accurate modification considering the actual machine geometric error compensation for spiral bevel and hypoid gears. First, the universal machine tool settings are exploited for the identification of the real tooth flank form error. Furthermore, the error sensitivity analysis method and an improved Levenberg–Marquardt algorithm with a trust-region strategy are utilized to obtain the solution of modification amount. Finally, a higher-order modification methodology for the universal machine tool settings is proposed which mainly covers three vital parts: (a) optimized selection of the modification settings, (b) modification of universal machine tool settings, and (c) machine geometric error compensation. Especially, a higher-accuracy fitting method for the form error tooth flank is investigated. Some numerical examples verify that the tooth flank form error after higher-order modification can reach less than 0.5 µm or even a smaller one, and the position error after compensating process spindle can be reduced from 0.0044861° to 0.0009232°. In addition, given experimental result can validate the feasibility of the proposed methodology.

scholarly journals Closed-Loop Feedback Flank Errors Correction of Topographic Modification of Helical Gears Based on Form Grinding

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Huiliang Wang ◽  
Jubo Li ◽  
Yang Gao ◽  
Jianjun Yang
Keyword(s):  
Closed Loop ◽  
Correction Method ◽  
Numerical Control ◽  
Grinding Wheel ◽  
Helical Gears ◽  
Form Grinding ◽  
Loop Feedback ◽  
Feedback Correction ◽  
Closed Loop Feedback ◽  
Tooth Flank

To increase quality, reduce heavy-duty gear noise, and avoid edge contact in manufacturing helical gears, a closed-loop feedback correction method in topographic modification tooth flank is proposed based on the gear form grinding. Equations of grinding wheel profile and grinding wheel additional radial motion are derived according to tooth segmented profile modification and longitudinal modification. Combined with gear form grinding kinematics principles, the equations of motion for each axis of five-axis computer numerical control forming grinding machine are established. Such topographical modification is achieved in gear form grinding with on-machine measurement. Based on a sensitivity analysis of polynomial coefficients of axis motion and the topographic flank errors by on-machine measuring, the corrections are determined through an optimization process that targets minimization of the tooth flank errors. A numerical example of gear grinding, including on-machine measurement and closed-loop feedback correction completing process, is presented. The validity of this flank correction method is demonstrated for tooth flank errors that are reduced. The approach is useful to precision manufacturing of spiral bevel and hypoid gears, too.

Higher-Order Tooth Flank Form Error Correction for Face-Milled Spiral Bevel and Hypoid Gears

2007 ◽  
Author(s):  
Qi Fan ◽  
Ronald S. DaFoe ◽  
John W. Swanger
Keyword(s):  
Higher Order ◽  
Hypoid Gear ◽  
Form Error ◽  
New Approach ◽  
Hypoid Gears ◽  
Form Errors ◽  
The Face ◽  
Spiral Bevel ◽  
Universal Motion ◽  
Tooth Flank

The increasing demand for low noise and high strength leads to higher quality requirements in manufacturing spiral bevel and hypoid gears. Due to heat treatment distortions, machine tolerances, variation of cutting forces and other unpredictable factors, the real tooth flank form geometry may deviate from the theoretical or master target geometry. This will cause unfavorable displacement of tooth contact and increased transmission errors, resulting in noisy operation and premature failure due to edge contact and highly concentrated stresses. In the hypoid gear development process, a corrective machine setting technique is usually employed to modify the machine settings, compensating for the tooth flank form errors. Existing published works described the corrective machine setting technique based on the use of mechanical hypoid gear generators, and the second order approximation of error surfaces. Today, Computer Numerically Controlled (CNC) hypoid gear generators have been widely employed by the gear industry. The Universal Motion Concept (UMC) has been implemented on most CNC hypoid generators, providing additional freedoms for the corrections of tooth flank form errors. Higher order components of the error surfaces may be corrected by using the higher order universal motions. This paper describes a new method of tooth flank form error correction utilizing the universal motions for spiral bevel and hypoid gears produced by the face-milling process. The sensitivity of the changes of tooth flank form geometry to the changes of universal motion coefficients is investigated. The corrective universal motion coefficients are determined through an optimization process with the target of minimization of the tooth flank form errors. A numerical example of a face-mill completing process is presented. The developed new approach has been implemented with computer software. The new approach can also be applied to the face-hobbing process.

Mathematical Model for a Universal Face Hobbing Hypoid Gear Generator

2006 ◽  
Vol 129 (1) ◽  
pp. 38-47 ◽  
Author(s):  
Yi-Pei Shih ◽  
Zhang-Hua Fong ◽  
Grandle C. Y. Lin
Keyword(s):  
Mathematical Model ◽  
Object Oriented ◽  
Face Milling ◽  
Object Oriented Programming ◽  
Hypoid Gear ◽  
Hypoid Gears ◽  
Proposed Model ◽  
Spiral Bevel ◽  
Cutter Head ◽  
Cutting System

Based on the theory of gearing and differential geometry, a universal hypoid generator mathematical model for face hobbing spiral bevel and hypoid gears has been developed. This model can be used to simulate existing face hobbing processes, such as Oerlikon’s Spiroflex© and Spirac© methods, Klingelnberg’s Cyclo-Palloid© cutting system, and Gleason’s face hobbing nongenerated and generated cutting systems. The proposed model is divided into three modules: the cutter head, the imaginary generating gear, and the relative motion between the imaginary generating gear and the work gear. With such a modular arrangement, the model is suitable for development of object-oriented programming (OOP) code. In addition, it can be easily simplified to simulate face milling cutting and includes most existing flank modification features. A numerical example for simulation of the Klingelnberg Cyclo-Palloid© hypoid is presented to validate the proposed model, which can be used as a basis for developing a universal cutting simulation OOP engine for both face milling and face hobbing spiral bevel and hypoid gears.

scholarly journals Cutter Head Approximation Machining Method of Line Contact Spiral Bevel Gear Pairs Based On Controlling Topological Deviations

2021 ◽  
Author(s):  
Mingyang Wang ◽  
Yuehai Sun
Keyword(s):  
Simulation Analysis ◽  
Gear Tooth ◽  
Bevel Gear ◽  
Spiral Bevel Gear ◽  
Line Contact ◽  
Bevel Gears ◽  
Spiral Bevel ◽  
Tooth Flank ◽  
Cutter Head ◽  
The Mathematical Model

Abstract To improve the meshing performance and increase the bearing capacity and service life of spiral gear pairs, the cutter head approximation machining method based on controlling topological deviations was proposed to solve the problem where line contact spiral bevel gears with tapered teeth depth cannot be directly machined by cutter heads. First, the mathematical model of line contact conjugate flanks was established, and meshing equations and conjugate flank equations of bevel gear pairs were derived. Second, the gear tooth flank was set as the datum tooth flank for priority machining, and the pinion theoretical tooth flank which is fully conjugate with the gear tooth flank and the pinion machining tooth flank matching with the gear were solved. Then, the geometric topological deviations model of the comparison between the pinion machining tooth flank and its theoretical tooth flank can be established. Finally, with the pinion machining tooth flank approaching its theoretical tooth flank as the modification, the additional cutting motions and machining compensation parameters of cutter heads were obtained to control the pinion machining tooth flank deviations and reduce them to the allowable deviations of its theoretical tooth flank. The contact simulation analysis and rolling test verified the correctness of the line contact conjugate flank model and feasibility of the cutter head approximation machining method.

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