Browsing by Author "Tsay, CB"

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A general mathematical model for gears cut by CNC hobbing machines
(1997-03-01)
Chang, SL
;
Tsay, CB
;
Nagata, S
;
機械工程學系
;
Department of Mechanical Engineering
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.
A general mathematical model for gears cut by CNC hobbing machines
(1997-03-01)
Chang, SL
;
Tsay, CB
;
Nagata, S
;
機械工程學系
;
Department of Mechanical Engineering
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.
A study on the bearing contact of roller gear cams
(2001)
Lo, JS
;
Tseng, CH
;
Tsay, CB
;
機械工程學系
;
Department of Mechanical Engineering
This study presents contact ellipse characteristics of the roller gear cams consisting of cambered rollers and screw cam surfaces. Principal curvatures and directions of generated cam surfaces are studied. The dimensions and the directions of contact ellipses are also evaluated. The investigation results are most helpful to understand contact nature, and contact stresses of the roller gear cam, which may be considered as design indices for performance consideration. (C) 2001 Elsevier Science B.V. All rights reserved.
A study on the Hertzian stress of the roller gear cam
(2000)
Lo, JS
;
Tseng, CH
;
Tsay, CB
;
機械工程學系
;
Department of Mechanical Engineering
This study presented the characteristics of Hertzian stress of roller gear cams that are composed of a cambered roller and a screwed 3D, cam surface. Based on the principal curvatures and directions of the generated cam surfaces and its cambered mating followers, pressure angle and contact force, the contact ellipses were derived. The investigated results are most helpful to the understanding of the contact nature and the contact stress of the roller gear cam which may be considered as design indices for further design consideration.
Bearing contact analysis of the involute spur planetary gear train
(2001)
Chen, JL
;
Tseng, CH
;
Tsay, CB
;
機械工程學系
;
Department of Mechanical Engineering
The goal of this study is to determine the dimensions and orientations of instant contact ellipses of gear surfaces in the meshing of the planetary gear train in order to recommend the proper amount of the crowning radii. The mathematical model for the surface profiles of the simple planetary gear train with the crowned planet gear is developed to simulate gear-meshing conditions and obtain the contact points. Principal curvatures and directions of the planetary gear train are derived and investigated based on the theory of gearing. The dimensions and orientations of the contact ellipses of the planetary gear train due to the assembly errors of different kinds of axial misalignments in different crowning radii can further be developed from the principal curvatures and directions of gear surfaces. Examples are presented to illustrate the above-mentioned investigations.
Bearing contact of a helical gear pair with involute teeth pinion and modified circular-arc teeth gear
(2001)
Chen, YC
;
Tsay, CB
;
機械工程學系
;
Department of Mechanical Engineering
This paper investigates the contact ellipse of a helical gear set, composed of an involute pinion and a modified circular-arc gear based on curvature analysis. This gear drive exhibits point contact and parabolic transmission error due to the double crowning effect of the gear, i.e. crowning in both profile and longitudinal directions. The principal directions and curvatures of the generating tool surfaces were derived by means of differential geometry and Rodrigues' equation. The principal directions and curvatures of the pinion and gear surfaces were obtained directly from the generating surfaces. Finally, the determination of the contact ellipses of the mating tooth surfaces was achieved. Numerical examples are also provided to demonstrate the computational results.
Computer-aided manufacturing of spiral bevel and hypoid gears by applying optimization techniques
(2001-07-04)
Lin, CY
;
Tsay, CB
;
Fong, ZH
;
機械工程學系
;
Department of Mechanical Engineering
A mathematical model of an ideal spiral bevel and hypoid gear-tooth surfaces based on the GIeason hypoid gear generator mechanism is proposed. Using the proposed mathematical model, the tooth surface sensitivity matrix to the variations in machine-tool settings is investigated. Surface deviations of a real cut pinion and gear with respect to the theoretical tooth surfaces are also investigated. An optimization procedure for finding corrective machine-tool settings is then proposed to minimize surface deviations of real cut pinion and gear-tooth surfaces. The results reveal that surface deviations of real cut gear-tooth surfaces with respect to the ideal ones can be reduced to only a few microns. Therefore, the proposed method for obtaining corrective machine-tool settings can improve the conventional development process and can also be applied to different manufacturing machines and methods for spiral bevel and hypoid gear generation. An example is presented to demonstrate the application of the proposed optimization model. (C) 2001 Elsevier Science B.V. All rights reserved.
Computer-aided manufacturing of spiral bevel and hypoid gears with minimum surface-deviation
(1998-08-01)
Lin, CY
;
Tsay, CB
;
Fong, ZH
;
機械工程學系
;
Department of Mechanical Engineering
The linear regression method to minimize the deviations of a real cut gear-tooth-surface is investigated in this paper. Based on the Gleason hypoid gear generator, a mathematical model of the tooth surface is proposed. Applying the proposed mathematical model, the sensitivities of tooth surface due to the variations of machine-tool setting are also investigated. The corrective machine-tool settings, calculated by using the sensitivity matrix and the linear regression method, are used to minimize the tooth-surface deviations. The minimization problem was solved by using the singular value decomposition (SVD) method. The result of this paper can improve the conventional development process and be also applied to different manufacturing machines and methods. Two examples are presented to demonstrate the proposed methodology. (C) 1998 Elsevier Science Ltd. All rights reserved.
Computerized tooth profile generation and analysis of characteristics of elliptical gears with circular-arc teeth
(2004-05-15)
Chen, CF
;
Tsay, CB
;
機械工程學系
;
Department of Mechanical Engineering
This study describes rack cutters with circular-arc profile teeth to generate elliptical gears which rotate about one of their foci. A mathematical model for elliptical gears with circular-arc teeth is developed according to gear theory. The influence of the design parameters, such as the number of teeth, gear module, pressure angle at the pitch point and the major-axis, are investigated. The effects of the circular-arc radius of the rack cutter on both the undercutting of teeth and on pointed teeth of the generated circular-arc elliptical gear are also studied. Three numerical examples are presented to elucidate the generation of gear tooth profiles using the proposed mathematical model, and to investigate the phenomena of tooth undercutting and pointed teeth. (C) 2003 Published by Elsevier B.V.
Computerized tooth profile generation and undercut analysis of noncircular gears manufactured with shaper cutters
(1998-03-01)
Chang, SL
;
Tsay, CB
;
機械工程學系
;
Department of Mechanical Engineering
Pitch curves of a conjugate noncircular gear pair are derived based on kinematic considerations. A method for considering the inverse mechanism relationship and the equation of meshing, is proposed here to derive a complete mathematical model of noncircular gears manufactured with involute-shaped shaper-cutters. The proposed method is similar to the contact line method and the envelope method but is easier to apply to the determination of tooth profiles. A computer program is developed for generation the tooth profile with backlashes. Undercutting analysis is also investigated by considering the relative velocity and equation of meshing. Finally modified elliptical gears are presented to illustrate the tooth profile generation when the proposed mathematical model is applied and to investigate the phenomenon of tooth undercutting.
Contact characteristics of beveloid gears
(2002-04-01)
Liu, CC
;
Tsay, CB
;
機械工程學系
;
Department of Mechanical Engineering
This study investigates the contact characteristics of beveloid gear pairs with intersected. crossed and parallel axes. Tooth contact analysis (TCA) is performed to examine the meshing and bearing contact of the beveloid gear pairs composed of a pinion and a gear. In addition, the principal directions and curvatures of the pinion and gear surfaces are investigated and the contact ellipses of the mating tooth surfaces are also studied. Numerical illustrative examples are provided to demonstrate the computational results. (C) 2002 Elsevier Science Ltd. All rights reserved.
Contact characteristics of cylindrical gears with curvilinear shaped teeth
(2004-09-01)
Tseng, RT
;
Tsay, CB
;
機械工程學系
;
Department of Mechanical Engineering
Transmission errors and bearing contacts of a curvilinear-tooth gear under different assembly conditions are investigated by applying the tooth contact analysis and the surface topology methods. Four numerical examples are presented to illustrate the influence of gear assembly errors on transmission errors and the directions and orientations of the contact ellipses. The numerical results reveal that the transmission error of the curvilinear-tooth gear pair is small and the bearing contacts are located in the middle region of the curvilinear-tooth surface even under axial misalignments. (C) 2004 Published by Elsevier Ltd.
Contact ratios and transmission errors of a helical gear set with involute-teeth pinion and modified-circular-arc-teeth gear
(2001-09-01)
Chen, YC
;
Tsay, CB
;
機械工程學系
;
Department of Mechanical Engineering
Contact ratio (CR) and transmission error (TE) are two significant indices for gear tooth strength and dynamics. This work investigated the CR, contact teeth (CT) and TE of a helical gear pair, composed of an involute pinion and a modified circular-arc gear. Point contact and built-in parabolic TE are obtained due to the modification of the gear's tooth profile. Tooth contact analysis (TCA) is applied to determine the TE as well as the CR of the proposed helical gear set under various assembly condition. The effect of gear design parameters on the CRs and TEs are also investigated in numerical examples.
Effects of profile shifted factor and pressure angle on the ZK-type dual-lead worm gear drives
(2001-05-03)
Bair, BW
;
Tsay, CB
;
機械工程學系
;
Department of Mechanical Engineering
In the light of a mathematical model of the ZK-type dual-lead worm gear set proposed in the authors' recent work, this study adopts tooth contact analysis to compute the kinematic errors, instantaneous contact teeth (ICT) and average contact ratios (ACR). An elastic deformation of 3 mum is allowed while calculating ICT and ACR. In addition, increasing the ICT from three to four or from four to five reduces the root stress of the gear set due to its multiple contact teeth. Although a worm gear driven with a small pressure angle can increase the ICT. a worm gear with a small pressure angle incurs a more serious undercutting phenomena. Undercutting can also be averted by applying a positive-shifted modification of the hob cutter during the worm gear generation. Moreover, the boundary of conjugate and nonconjugate surface regions appears on the worm gear tooth surface when the worm gear has a low pressure angle. The non-conjugate region also influences the transmission efficiency, operational life time and noise of the worm gear drive. Furthermore, worm gear generation with a negative-shifted modification can decrease the unfavorable non-conjugate region. (C) 2001 Elsevier Science B.V. All rights reserved.
Effects of the hob cutter regrinding and setting on ZE-type worm gear manufacture
(1996-10-01)
Fang, HS
;
Tsay, CB
;
機械工程學系
;
Department of Mechanical Engineering
A mathematical model for a ZE-type worm gear set is proposed. The characteristics of a ZE-type worm gear cut with an oversize hob cutter are investigated. Bearing contacts and kinematic errors in the ZE-type worm gear set due to regrinding of oversize hob cutters are also studied. Bearing contacts in the worm gear set were obtained using surface separation topology techniques and tooth contact analysis. It was found that bearing contact locations are sensitive to the hob cutter setting angle and setting distance. Kinematic error minimization was achieved modifying worm normal tooth angle. By applying the optimization theorem and computer simulation programs, optimum hob cutter settings and worm normal tooth angle were determined to improve bearing contact location and minimize the worm gear set kinematic errors. A numerical example is given to demonstrate the results of the investigation. The developed computer-aided manufacture program has successfully been applied to the worm gear manufacture and hob cutter design. Copyright (C) 1996.
Kinematic optimization of a modified helical gear train
(1997-06-01)
Chang, SL
;
Tsay, CB
;
Tseng, CH
;
交大名義發表
;
機械工程學系
A mathematical model of a modified helical gear train (MHGT), manufactured with a practical hobbing machine using a curved-template guide, and which takes considerations of center-distance variation and axial misalignment into account, is developed. Tooth contact analysis (TCA) and kinematic errors of a MHGT due to mis-assembly are investigated. A multiple optimization method is applied to reduce the level of MHGT kinematic errors, and to investigate optimal gear tooth modifications. Computer simulation programs for TCA and optimization are also developed. Two numerical examples are presented to illustrate the kinematic optimization of the proposed helical gear train. The results of this study are most helpful in designing and analyzing a MHGT.
Kinematic optimization of a modified helical gear train
(1997-06-01)
Chang, SL
;
Tsay, CB
;
Tseng, CH
;
機械工程學系
;
Department of Mechanical Engineering
A mathematical model of a modified helical gear train (MHGT), manufactured with a practical hobbing machine using a curved-template guide, and which takes considerations of center-distance variation and axial misalignment into account, is developed. Tooth contact analysis (TCA) and kinematic errors of a MHGT due to mis-assembly are investigated. A multiple optimization method is applied to reduce the level of MHGT kinematic errors, and to investigate optimal gear tooth modifications. Computer simulation programs for TCA and optimization are also developed. Two numerical examples are presented to illustrate the kinematic optimization of the proposed helical gear train. The results of this study are most helpful in designing and analyzing a MHGT.
Mathematical model and bearing contacts of the ZK-type worm gear set cut by oversize hob cutters
(1996-04-01)
Fang, HS
;
Tsay, CB
;
交大名義發表
;
機械工程學系
;
National Chiao Tung University
An oversize worm-type hob cutter is used to cut worm gears in this study. A mathematical model of the ZK-type worm gear set is developed based on the cutting mechanism and its tool parameters. Variations in bearing contact due to pitch diameter variations of oversize hob cutters and center distance variations of worm gear sets are also investigated. A numerical example is given to demonstrate the paths and dimensions of the bearing contacts of worm gear sets.
Mathematical model and bearing contacts of the ZN-type worm gear set cut by oversize hob cutters
(2000-12-01)
Fang, HS
;
Tsay, CB
;
機械工程學系
;
Department of Mechanical Engineering
The ZN-tyye oversize hob cutter for cutting of worm gears is investigated. The mathematical model of the ZN-type worm gear set is developed based on the cutting mechanism and hob cutter parameters, Influences of oversize hob cutter regrinding, worm-thread number and assembly errors on the bearing contacts and kinematical errors of the ZN-type worm gear set are investigated. A numerical example is given to demonstrate the bearing contacts and kinematical errors of the worm gear set. (C) 2000 Elsevier Science Ltd. All rights reserved.
Mathematical model and surface deviation of cylindrical gears with curvilinear shaped teeth cut by a hob cutter
(2005-09-01)
Tseng, JT
;
Tsay, CB
;
機械工程學系
;
Department of Mechanical Engineering
The generating motion of a cylindrical gear with curvilinear shaped teeth cut by a CNC hobbing machine is proposed. On the basis of the cutting mechanism and the gear theory, the surface equation of this type of gear is developed as a function of hob cutter design parameters. Computer graphs of the curvilinear-tooth gear are presented based on the developed gear's mathematical model, and the tooth surface deviations due to machine-tool settings with nominal radius of circular tooth traces are also investigated