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The processing and design of point-contact gears have attracted the interest of many scholars. The point-contact gears are usually processed by specialized machines (face-milling and face-hobbing) or five-axes machines (forming milling). In this paper, a new type of point-contact gear formed by double-arc milling cutter on four-axes machine is proposed. Firstly, the meshing equation is proposed to obtain a pair of processing traces that satisfy the law of gearing, and the processing traces are also contact traces. Considering the important role of traces in obtaining the proposed gear, this gear is called as TG. Then, six pairs of contact traces for parallel-axes, crossing-axes, and skewing-axes TGs are solved. Furthermore, the tooth surface models are studied and the obtained models are used for tooth contact analysis and stress analysis, and then the instantaneous contact areas, the contact stresses, and transmission errors are obtained, respectively. Lastly, the TG pair with cross-axes is processed, and then, the measurement and rolling experiments are conducted. The obtained results indicate the meshing equation, tooth surface models, and milling method are feasible. The proposed milling method provides a new way for flexible and diversified manufacturing of point-contact gears. [ABSTRACT FROM AUTHOR]

Inspired by the inherent properties of logarithmic spiral in nature, a new cylindrical spur gear drives using logarithmic spiral as a gear tooth profile is proposed. The logarithmic spiral property is explored, and then the equation of meshing, conjugate tooth profile and contact path of the proposed gear pairs are derived. The meshing characteristics of the new pair are investigated, such as pressure angle, contact ratio and sliding ratio. Simulation analysis of the strength, transmission error and transmission efficiency are used to validate the performance of the gear pairs before production of the proposed gear, followed by gluing load capacity and bending fatigue strength testing of the fabricated gear pairs. The results show that the pressure angle at any point of the tooth profile on the proposed gear is constant and equal to the logarithmic spiral strike angle. The contact ratio of the gear decreases with the increase of the strike angle. Compared with that of involute gears, logarithmic spiral gears have better performance in terms of strength, transmission error, transmission efficiency and lifetime. [ABSTRACT FROM AUTHOR]

Face gear drives are special angular gears in which an involute pinion and face gear wheel mesh. They enable high transmission ratios in small construction spaces. The face gear is typically manufactured by gear hobbing or gear shaping using an involute pinion-type cutter. Face gear drives with identical pinion and cutter parameters form a conjugated pairing. Conjugate pairings tend to have unfavourable edge contact, which is usually counteracted by geometric flank modifications during manufacture. A common modification technique is the crowning of the flanks. This usually requires changes to the machine kinematics. Due to their geometry and manufacturing process, face gear drives offer an easy way to achieve a crowned contact pattern in the facewidth direction without changing the machine kinematics, making them promising for multiple applications. Using a pinion with fewer teeth than the cutter results in a crowned contact pattern (lead crowning). The position of the contact point along the facewidth can be adjusted by varying the profile shift coefficient of the pinion or the cutter. This paper presents a straightforward method for selecting proper design parameters depending on the contact distances. The contact distances can be estimated analytically to evaluate the chosen design parameters. Example calculations are given as proof of the developed method presented in this paper. Overall, this study offers a novel evaluation strategy for an ideal cutter/pinion design for manufacturing durable face gear drives with optimised contact patterns. [ABSTRACT FROM AUTHOR]

Rack-and-pinion gear sets with variable transmission ratios have gradually become a standard core component in steering systems, as the harmony between portability and sensitivity in vehicle steering can be achieved with such applications. When the conventional meshing theory is adopted to calculate point clouds of variable-ratio tooth surfaces, drawbacks will occur with respect to unevenness in point cloud density, inaccessible tooth surface boundaries, and point cloud fusion at the interface between the working tooth surface and fillet. Thus, the generated point cloud of variable ratio tooth surfaces is inapplicable for computer-aided engineering (CAE) and plastic forming. In this study, the point cloud reconstruction of pinion tooth surfaces with variable transmission ratio was investigated. Meanwhile, based on the analysis of transient length in contact lines that occur during gear meshing, various criteria were proposed to determine the validity of the variable-ratio rack-and-pinion design in terms of whether continuous and reverse driving can be achieved. By adopting the proposed methods, the designed variable-ratio pinion tooth surfaces demonstrate point clouds with equidistant distributions and clear boundaries. CAE analysis results also indicate a good quality in gear meshing. The real-time gear meshing status of variable-ratio rack-and-pinion sets is characterized by the transient length of contact lines. The measured variation curves for the transmission ratios of a prototype demonstrate significant consistency with the theoretical curves, indicated by attaining transmission ratio errors within a reasonable range. The validity of the design methods proposed in this study has been verified by the aforementioned results. [ABSTRACT FROM AUTHOR]

The contact quality between geometric features significantly affects the assembly accuracy and dynamic performance of mechanical products. However, accurate and efficient contact problem solving is currently a common challenge in the fields of tolerance analysis and tooth contact analysis (TCA). In this paper, a tolerance analysis method for gear mechanisms considering form deviations and elastic-plastic contact behaviors is proposed. Specifically, tolerance modeling of systematic and random deviations on tooth surfaces is represented by skin model shapes (SMS). Elastic-plastic contact behaviors including contact deformation, status, and stress distribution are modeled and calculated by a modified boundary element method (BEM). The accuracy and efficiency of this BEM algorithm are verified by comparing with the finite element method (FEM), indicating that the BEM can greatly improve the computational efficiency while maintaining high solution accuracy. A case study for a pair of spur gears demonstrates the significant effects of contact behaviors on transmission performance. This research provides an effective method to introduce mechanical contact behaviors in tolerance analysis of gear mechanisms. In addition, the contact simulation results can also be adopted in the analysis of vibration, reliability, and other aspects. • An accurate and efficient tolerance analysis method for gear mechanisms is proposed. • Real tooth surface topography and elastic-plastic contact behaviors are considered. • Systematic and random tooth surface deviations are represented by skin model shapes. • Elastic-plastic contact behaviors are modeled by a modified boundary element method. [ABSTRACT FROM AUTHOR]

In order to accurately calculate the meshing efficiency of the new internal S-gears, a time-varying friction model of the elastohydrodynamic lubrication is established considering the surface sliding of the gear tooth, lubricating oil condition and load. The lubrication mechanism of the meshing tooth surface is analyzed, and the sliding friction coefficient and friction loss power are calculated by tooth contact analysis (TCA) and loaded tooth contact analysis. On this basis, instantaneous meshing efficiency and average meshing efficiency of internal S-gears within one meshing cycle are obtained. The results show that the new internal S-gears have higher meshing efficiency than the involute gears under the same design parameters. The meshing efficiency of the new internal S-gears is improved after the tooth direction modification and increases positively with the tooth direction modification.

In response to the problem that the error value is usually set as a constant value in the tooth contact analysis (TCA) model of cycloidal needle tooth transmission, which makes the calculation results unreasonable, and the calculation does not converge in the calculation process, an analysis model of cycloidal pinwheel transmission error including multi-factors such as shaping modification and processing error is established. After analyzing the vector equation of the meshing point, a method to solve the problem of numerical non-convergence is proposed, that is, to find the meshing point with equal normal vector in the obtained point with equal ordinate and abscissa on the cycloid wheel and the needle tooth. After analyzing the form of the rotary body error, a method to solve the unreasonable calculation results is proposed, that is, the cycloid circumferential joint error, the cycloid tooth profile radial runout error and the needle tooth center circle radius error change periodically in the tolerance band. RV-80E reducer is taken as the test object, and the correctness of the theoretical model is verified by comparing the test results. The influence of each error on the transmission error is studied, and the sensitivity analysis of each error is carried out. The results show that the needle tooth radius error and the normal clearance under the comprehensive action of the needle tooth and the needle tooth shell gap are the important factors affecting the transmission error.

Machine tool error is one of the most important research contents in gear transmission error, and contact characteristics are important factors affecting gear transmission performance. The establishment of tooth contact analysis (TCA) model of gear pair plays a guiding role in analyzing contact characteristics of gear pair. Based on the forming principle of variable hyperbolic circular-arc-tooth-trace cylindrical gear (VH-CATT gear), the structure model and coordinate system of VH-CATT gear machine tool are established. Based on the gear meshing conditions, the tooth surface mathematical model of the VH-CATT gear with machine tool error are established, and the TCA model with machine tool error is established. The influence of different machine tool errors on the geometric contact characteristics of the gear pair is analyzed. The results show that the pressure angle error, rotation error in y direction, and rotation error in z direction, translation error in y direction, and rotation error in z direction have a significant impact on the contact characteristics of tooth profile of VH-CATT gear. [ABSTRACT FROM AUTHOR]

In response to the imperative for precise static transmission error (STE) calculations crucial for evaluating gearbox vibroacoustic responses, this paper conducts a rigorous comparative study, utilizing diverse software tools and exploring critical factors such as gear type, gearbox complexity, microgeometry modification, mounting defects, and geometrical cutouts for lightweight gears. The study systematically dissects modeling principles and assumptions, delving into detailed case studies and outcome comparisons, including the Peak-to-Peak Transmission Error (PPTE). Revealing substantial amplitude variations exceeding 66% in standard spur gear cases with different software and escalating to 200% with microgeometry alterations, the introduction of parallelism defects induced variations of up to 42% between ROMAX and MASTA. The variations were comparatively lower for involute helical gears, hovering around 48%. However, the examination of the impact of a crowning modification paired with tip relief revealed significant discrepancies, ranging from a decrease of −42% for the most standard model VIBRAGEAR to a substantial increase of 867% in GENOM FE. Notably, for complex gearboxes, variations extend to 150%, emphasizing the intricate stacking effects of micro and system-scale influences on calculation errors. Examining lightweight gears in MASTA, ANSYS, and MARC revealed variations in tooth-level PPTE that correlate with the magnitude orders observed in the single-tooth analysis and a commendable agreement in the fluctuating part of the STE.This research fills a gap in comparative studies on transmission error calculations, enhancing our understanding of gear contact mechanisms and factors influencing their estimation. It also serves as a practical guide for selecting tools tailored to specific cases and positions itself as a benchmark for the future development of more sophisticated numerical tools, contributing significantly to the ongoing evolution of methodologies within this field.

In order to use the concave cutter to process the straight bevel gear on the domestic CNC spiral bevel gear machine tool, the principle of using the concave cutter to process the straight bevel gear and the TCA method of tooth surface contact analysis are studied. Based on the machining principle and structural characteristics of the concave cutter, the tooth surface mathematical model of the straight bevel gear machined by the concave cutter is established, and the corresponding tooth surface contact analysis method is given. The tooth contact analysis program is compiled, and the contact pattern and transmission error curve of the gear pair are calculated. The correctness of the tooth surface mathematical model and the TCA method of tooth surface contact analysis are verified by the actual tooth cutting and contact spot inspection. It provides a theoretical basis for the determination of bevel gear machining parameters, tool parameters and the meshing quality control.

This paper presents an ultimate motion methodology of a face-milling spiral bevel gear pair to synthesize the mating tooth surfaces with a predesigned fourth-order motion curve. The methodology is to control some contact points along the contact path in the process of tooth contact analysis via application of an extended local synthesis which permits some transmission errors rather than zero at the concerned contact point. The modified offset motion correction is selected to demonstrate the proposed methodology. Applied torque corresponding to an elastic approach of 0.00635 mm at the mean contact point is calculated and the loaded tooth contact analysis is performed. Numerical results show that the extended local synthesis can effectively control the transmission errors on the predesigned fourth-order motion curve at arbitrarily predesigned contact points along the contact path of the spiral bevel gear pair. The tooth contact pattern for the actual tooth pair is scattered into three segments since the rotational motion of the driven gear at any instant angular position is dependent on the tooth pair with the least transmission error among the three adjacent tooth pairs. The actual tooth contact patterns of the spiral bevel gear pair become continuous when meshing tooth surfaces are elastically deformed. [ABSTRACT FROM AUTHOR]

This study proposes a double-crown tooth surface modification technology that improves the load-carrying capacity of non-orthogonal helical tooth surface gears. The tooth modification is determined by a modified rack-cutter, and its feed motion is related to an intentionally designed transmission error. The novelty of the tooth modification design is that the transmission error can be pre-designed. First, changing the tooth profile of the tool enables preliminary modification along the tooth profile direction; second, by modifying the interaction between the tool and the machined gear, subsequent fine adjustments are made to the contact path. This two-stage tooth modification strategy not only retains the advantages of the traditional method but also significantly improves the balance of the load distribution on the tooth surface through an original contact path modification strategy. Through systematic tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA), it was verified that the new method reduces contact stress and tooth root bending stress and improves the gear's resistance to misalignment errors. This research provides the basis and motivation for further exploring and improving this tooth profile modification technology to solve the challenges faced by more complex gear systems. [ABSTRACT FROM AUTHOR]

Aiming at the elliptical cylinder gear pair in the reversing device of the new drum pumping unit, the dynamic meshing process of tooth was simulated by LS-PREPOST software. The distribution law of effective plastic strain, effective stress, tooth surface pressure, tooth surface displacement and meshing force in the direction of tooth lines and tooth profiles under different rotational speeds were obtained. The results show that the effective plastic strain, the effective stress and the surface pressure in the tooth lines direction will decrease as the center position of the elliptical contact area of the tooth surface expands to both sides. The effective plastic strain, the effective stress and the surface pressure in the tooth profiles direction will increase with the increase of the rotational speed, and the rotational speed will affect the changing period of the tooth surface displacement and the meshing force. The research results can provide theoretical basis and certain guiding significance for the dynamic design, meshing analysis, modification and engineering application of non-cylindrical gears. [ABSTRACT FROM AUTHOR]

Due to the special meshing of convex and concave tooth profiles, an S-shaped tooth profile gear with a few teeth has the advantage of reducing the contact stress and improving the contact ratio. However, the theoretical inseparability of the center distance of an S-shaped tooth profile and shaft misalignments, including center distance errors and axis parallelism errors caused by manufacturing or installation errors, can easily cause tip contact and produce transmission errors. Accordingly, it is necessary to analyze the influence of shaft misalignments on the meshing performance. In this paper, a unified mathematical model of spur and helical gears with an S-shaped tooth profile is established and an analytic method for determination of the contact pattern, meshing path, and transmission error of a gear pair with shaft misalignments is proposed. Then, the validity of the analytic method is proved by practical examples and the influence of shaft misalignments on the contact pattern of an S-shaped tooth profile gear pair is obtained. Through comparison with an involute gear with the same parameters, it is found that shaft misalignments within a certain range result in an acceptable transmission error and contact area migration of the S-shaped tooth profile gear pair similar to that of the involute gear pair. [ABSTRACT FROM AUTHOR]

Copyright of China Mechanical Engineering is the property of Editorial Board of China Mechanical Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Large cylindrical worm gear set of ISO type I are manufactured using endmill tools on universal CNC machine tools. This manufacturing method requires neither special gear-generating machines nor special tools. The tooth flank forms of ISO type I cylindrical worm gears are involute helicoids as a standard. The targeted theoretical tooth flanks of the worm and the mating worm wheel are determined based on a tooth contact analysis (TCA) of such worm gear set. The cutting conditions of the worm are determined after the offset distance between the worm axis, and the central axis of the endmill tool is calculated. Afterward, the worm is manufactured by controlling only two axes on machine tools using a swarf milling method by use of the side of the endmill tool under the determined conditions. Meanwhile, the targeted theoretical tooth flanks of the mating worm wheel are modeled in 3-dimensional computer-aided design software, and the worm wheel is manufactured by a swarf milling method in a computer-aided manufacturing process. The comparison of experimental and analytical tooth contact patterns indicates almost no difference between the two tooth contact patterns. [ABSTRACT FROM AUTHOR]

Spiral bevel gears are key components in many mechanical transmission systems, and their production is always of great interest to industry, and hence, subjected to intensive research widely. The present machining methods for manufacturing spiral bevel gears, including the so called five-cut method and completing method, have drawbacks such as low processing efficiency, requiring complex calculations and high requirements on the machine-tool performance, respectively. To solve the above problems, the duplex spread blade method is proposed. Firstly, geometric parameters and machine setting parameters were comprehensively considered, and then a modified reference point was selected to deduce the machine setting parameters. Tooth contact analysis (TCA) model considering misalignment was established to check meshing performance, the influence of cutter parameters and misalignment on meshing performance was studied. As the research reveals that the cutter radius has an effect on the bias of contact trace, cutter number has an impact on the position of contact pattern. The experimental results are consistent with the theoretical which verified the effectiveness and feasibility of the proposed method. The results of this paper have a guiding significance and enrich the machining method for spiral bevel gear.

This paper presents an ultimate motion methodology of a face-milling spiral bevel gear pair to synthesize the mating tooth surfaces with a predesigned fourth-order motion curve. The methodology is to control some contact points along the contact path in the process of tooth contact analysis via application of an extended local synthesis which permits some transmission errors rather than zero at the concerned contact point. The modified offset motion correction is selected to demonstrate the proposed methodology. Applied torque corresponding to an elastic approach of 0.00635 mm at the mean contact point is calculated and the loaded tooth contact analysis is performed. Numerical results show that the extended local synthesis can effectively control the transmission errors on the predesigned fourth-order motion curve at arbitrarily predesigned contact points along the contact path of the spiral bevel gear pair. The tooth contact pattern for the actual tooth pair is scattered into three segments since the rotational motion of the driven gear at any instant angular position is dependent on the tooth pair with the least transmission error among the three adjacent tooth pairs. The actual tooth contact patterns of the spiral bevel gear pair become continuous when meshing tooth surfaces are elastically deformed.

This study proposes a double-crown tooth surface modification technology that improves the load-carrying capacity of non-orthogonal helical tooth surface gears. The tooth modification is determined by a modified rack-cutter, and its feed motion is related to an intentionally designed transmission error. The novelty of the tooth modification design is that the transmission error can be pre-designed. First, changing the tooth profile of the tool enables preliminary modification along the tooth profile direction; second, by modifying the interaction between the tool and the machined gear, subsequent fine adjustments are made to the contact path. This two-stage tooth modification strategy not only retains the advantages of the traditional method but also significantly improves the balance of the load distribution on the tooth surface through an original contact path modification strategy. Through systematic tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA), it was verified that the new method reduces contact stress and tooth root bending stress and improves the gear’s resistance to misalignment errors. This research provides the basis and motivation for further exploring and improving this tooth profile modification technology to solve the challenges faced by more complex gear systems.

Copyright of Machine Tool & Hydraulics is the property of Guangzhou Mechanical Engineering Research Institute (GMERI) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The traditional geometry of non-circular cylindrical gears provides a contact line between tooth surfaces. In a misaligned non-circular cylindrical gear drive, causing edge contacts that result in noise and vibration. The point contact of the tooth surface is achieved by modification of the driving gear in the longitudinal direction, in order to reduce the sensitivity of tooth surface contact to installation errors. The proposed longitudinal modification method is based on the application of a grinding worm by controlling the center distance of non-circular cylindrical gear and worm. Based on the gear meshing principle, a mathematical model of the tooth surfaces of non-circular cylindrical gears is established, and a parametric tooth surface equation with a unified expression is obtained. Tooth contact analysis (TCA) of non-circular cylindrical gears shows that the contact path and contact area on the tooth surface are shifted with the change of installation error, but still distributed in the middle of the tooth surface without creating edge contact. The transmission error is increased with the growth of installation error. Tooth modification in a longitudinal direction has an obvious improvement effect on the bad tooth contact condition, but too large a tooth modification parameter will make the tooth surface load distribution concentrated in a smaller area, which results in the decrease of gear load capacity. [ABSTRACT FROM AUTHOR]

The contact path and transmission error are key indexes for evaluating the meshing performance of spiral bevel gears. The contact path is offset by misalignment，and symmetry and fluctuation amplitude of transmission error change. Therefore，based on installation adjustment，an optimization method for the contact path and transmission error of spiral bevel gears is proposed. The equations are established by the constraining assembly conditions and the initial transmission ratio，and then the theoretical installation adjustment is solved. A tooth contact analysis （TCA） algorithm with the misalignment is built by introducing gear pair misalignment. Taking the misalignment as the design variable and presetting the characteristic parameters of contact path and the transmission error，an objective function is built and solved by the nonlinear optimization algorithm. The optimization results show that the contact path is moved to the small end and the loaded contact area is expanded to the middle of the tooth flank，load bearing contact performance is improved. That the droop deviation and fluctuation amplitude of the transmission error curve are decreased，whichis beneficial to avoid edge contact and improve dynamic performance.

The traditional modification design has some disadvantages such as complex calculation，uncontrollable tooth profile curve shape and unstable meshing performance，the pressure angle of the gear tooth profile has a great influence on the meshing force transmission performance. Therefore，a new tooth profile modification design method is proposed based on the distribution law of the pressure angle of the cycloid tooth profile. Based on the pressure angle distribution trend obtained by calculation and analysis，the mathematical model of tooth profile modification with straight-line method is established，and the function representation between the tooth profile pressure angle and the modification amount is deduced，the tooth contact analysis model is constructed，and the transmission error of modified cycloid-pin gear is obtained. Through the comparative measurement experiment of the tooth profile shape and transmission error of the cycloid，the correctness and effectiveness of the method proposed in the article are verified. This method considers the mutual influence between the pressure angle of the cycloidal gear tooth profile and the modification amount，and the technical problems of traditional modification method in calculation，processing，and active design are solved，and the trend of modification amount can be flexibly controlled，while ensuring the meshing performance，it obtains the design tooth profile that is closer to the theoretical cycloid.

Due to the special meshing of convex and concave tooth profiles, an S-shaped tooth profile gear with a few teeth has the advantage of reducing the contact stress and improving the contact ratio. However, the theoretical inseparability of the center distance of an S-shaped tooth profile and shaft misalignments, including center distance errors and axis parallelism errors caused by manufacturing or installation errors, can easily cause tip contact and produce transmission errors. Accordingly, it is necessary to analyze the influence of shaft misalignments on the meshing performance. In this paper, a unified mathematical model of spur and helical gears with an S-shaped tooth profile is established and an analytic method for determination of the contact pattern, meshing path, and transmission error of a gear pair with shaft misalignments is proposed. Then, the validity of the analytic method is proved by practical examples and the influence of shaft misalignments on the contact pattern of an S-shaped tooth profile gear pair is obtained. Through comparison with an involute gear with the same parameters, it is found that shaft misalignments within a certain range result in an acceptable transmission error and contact area migration of the S-shaped tooth profile gear pair similar to that of the involute gear pair.

A jack-up is an off-shore platform that, thanks to the capability of lowering its legs, is capable to elevate its hull from the water. Typically, the movement of the leg and the subsequent emersion of the jack-up is ruled by a rack-pinion system in which the pinion is a low number of teeth (typically 7 ÷ 8) spur gear. Recently, in order to reduce the contact pressure, it has been proposed to substitute the classical Involute (INV) profile of the pinion by a Multi Radius (MR) one. However, due to their intrinsic differences, the classical INV theory cannot be adopted directly as means to study the behaviour of the MR profile. Therefore, a Tooth Contact Analysis (TCA) procedure for the initial evaluation of a rack and MR pinion system is presented here. The aforementioned TCA enables to calculate relevant gear quantities (e.g. forces, velocities and contact pressure). Furthermore, thanks to the concept of coupled Transmission Error functions, it allows to evaluate, in the initial design phase, if the rack and pinion mesh occurs without impacts. [ABSTRACT FROM AUTHOR]

This study proposed a method of designing and modeling a modified parabolic face gear and analyzed its tooth contact characteristics. First, a parabola curve is introduced into the rack profile according to differential geometry and meshing theory and derived the equations of the generating gear, diamond wheel, worm, and modified face gear. Second, a method for modeling the tooth surface of the modified face gear is proposed. Then, the influence of the modified parameters on the face gear is studied. Moreover, the contact equations of the modified face gear and the cylindrical gear were combined to obtain the contact trace. Meanwhile, a coordinate analysis system with installation errors is established to obtain the contact traces and transmission error curves. Finally, the influence of the installation errors on the transmission error of the modified face gear under different modified parameters is analyzed. The results show that the modified face gear is susceptible to installation errors in the tooth width and tooth thickness direction. [ABSTRACT FROM AUTHOR]

The paper proposed a new asymmetrical offset face-gear transmission, applied meshing theory to derive the tooth surface mathematical model, and used discrete numerical methods to obtain the tooth model. Subsequently, the limitation of pointing and undercutting on effective tooth width of asymmetric offset face-gear were studied, and the influence of the eccentricity on the effective tooth width was analyzed. Finally, the finite element method was used to analyze the tooth surface contact stress of four groups of asymmetric offset gear pairs with different working pressure angles. The conclusion shows that the tooth surface contact stress takes the minimum value when the working side pressure angle is 30°, and the contact stress significantly reduced compared to the face-gear pair that does not adopt an asymmetric structure. The research provides a reference to the design of asymmetric offset face-gear. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Henan University of Science & Technology, Natural Science is the property of Editorial Office of Journal of Henan University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Helical gears are widely used in powertrain systems. The computerized design of a new type of non-generated external helical gears based on critical control points at the transverse tooth profile is presented. The entire tooth profile is divided into different parts including the active tooth profile and fillet by control points. Involutes, circular arcs and Hermite curves are defined between two critical control points and smoothly connected with each other at those control points. The parametric equations for the tooth surfaces are derived considering the position of the mentioned control points. The basic design parameters and equations of the geometric sizing are proposed. The contact patterns, variation of the maximum stresses and peak-to-peak level of loaded transmission errors for six cases of design of the proposed new geometry of helical gear drives are studied with two cases of traditional helical gear drives as a reference, including gears with and without micro-geometry modifications. One case of an external helical gear drive designed with a combination of a circular arc and an involute to form the active tooth profile for both the pinion and the gear shows a much lower maximum bending stress and similar lower peak-to-peak level of loaded transmission errors with respect to the other cases of design. The proposed design method of tooth profiles based on critical control points lays the foundation for the topological optimization of helical gear drives. [ABSTRACT FROM AUTHOR]

Finite element based tooth contact analysis of a rack and pinion system of an impulse continuously variable transmission is performed in this study. The rack and pinion system are designed with involute profile herringbone tooth profiles. The involute profile herringbone tooth profile is a type of concave-convex pro-files, which can be used for heavy load conditions. A contact load distribution model of the rack gear with involute profile herringbone tooth profiles is devel-oped to analyze normal loads of any mashing position of the rack pinion system based on the minimum elastic potential energy theory. With the aim of improving the rack and pinion system design, the actual operation of gears under the terms of the three-dimensional tooth contact analysis is conducted. A rack gear with herringbone tooth profiles and a pinion are used to tooth contact analysis. Based on comparing the results of this analysis, a new type of rack gears with concave-convex involute tooth profile are advantages and disadvantages in terms of the contact stress.

An exact system of generation for face-milled hypoid gears with uniform depth taper is proposed. This system defines the location of pinion and wheel, their respective cutting (or grinding) cutters, and the relations of motion in their respective reference coordinate systems attached to the cutting machine. As a result, the grinding cutter geometric parameters and basic machine-tool settings are analytically determined without the need of any further optimization process. The appropriate selection of the mean cutter radius is addressed following the recommendations of the Information Sheet AGMA ISO 22849-A12. The tooth contact analysis of the gear drive shows a localized bearing contact with no unloaded transmission errors in the absence of misalignments. A lower sensitivity of the contact pattern to errors of alignment is observed as the mean cutter radius is decreased. Stress analysis shows that only the application of a tip relief is needed to avoid edge contacts at the tip of the gear tooth surfaces, being the point width of the cutting blades a key parameter to balance bending stresses in the pinion and the wheel. • An exact system of generation is proposed for face-milled hypoid gears. • Basic machine-tool settings of pinion and wheel are analytically determined. • The mean cutter radius is selected according to AGMA ISO 22849-A12. • TCA shows a localized bearing contact with no unloaded transmission errors. • Stress analysis shows that some tip relief is required to avoid edge contacts. [Display omitted] [ABSTRACT FROM AUTHOR]

Variable transmission ratio gears have shown considerable potential as key components of variable speed transmission steering boxes that balance steering portability and sensitivity. The objective of this study is to develop a novel method for designing variable transmission ratio tooth surfaces to circumvent the shortcomings of the meshing theory method. The involute rack of the variable transmission ratio pinion-and-rack pair is considered as a set of countless and infinitely close transverse sections, each of which is referred to as a gear element. Assuming evenly distributed circles in the physical domain of the variable transmission ratio tooth surfaces of the pinion, the problem of generating a tooth surface point is transformed into solving the specific geometric feature intersection point of each circle and corresponding gear element during variable transmission ratio meshing. Thereafter, a mathematical model and algorithm are developed to generate tooth surface points in an approximately even pattern. The normal deviations of the gear-element–generated tooth surface points and the corresponding tooth surface points calculated using meshing theory show that the proposed design method has a sufficiently high accuracy. Finite element models are employed analyzing the contact pattern, contact stress, bending stress, and transmission ratio error. The results indicate that the layout of approximately even tooth surface points using the gear element method is beneficial for improving the fitting precision of tooth surfaces and reducing the contact stress and transmission ratio error. Further, the same derived law of the flank and fillet tooth surfaces is conducive to the continuity of the tooth surfaces, which contributes toward reducing the bending stress. Finally, a prototype is manufactured via CNC end milling. The major contributions lie in a robust and efficient modeling method for variable transmission ratio tooth surfaces, which combined forms a solid foundation for their application. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Central South University is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Based on the principles of common-generating conjugation mapping of pinion-rank-gear meshing, the constructing of ease-off surface has been done by means of the topology modification of the 4-order polynomial surface. The simulation method of tooth surface mesh is purposed based on the ease-off surface. By analyzing topological structure characteristics of ease-off surface such as modification gradient curves, contact line-off and contact path-off, the meshing characteristics such as the contact area, the contact line and transmission error are determined. It is stated on the interaction relations of coefficients of the 4-order polynomial to the topological construction of surface. The methods for reconstruction and analysis of ease-off surface with considering axis misalignments are presented by the direct transformation of coordinate systems. Taking the topological construction of four kinds of surfaces as examples, characteristics parameters such as modification gradient of tooth surface, contact path and transmission errors are simulated. They are expounded on the corresponding parameters of controlling form and adjusting methods for tooth surface. These methods take goals of adjusting-modification and controlling-property for tooth surface mesh. It is improved and developed the meshing analysis method of ease-off surface of tooth. The presented method is liable to provide the basis data for the further loaded contact analysis of complicated tooth surface and the more direct technical for the 3-D topological optimization of tooth surface.

Large cylindrical worm gear set of ISO type I are manufactured using endmill tools on universal CNC machine tools. This manufacturing method requires neither special gear-generating machines nor special tools. The tooth flank forms of ISO type I cylindrical worm gears are involute helicoids as a standard. The targeted theoretical tooth flanks of the worm and the mating worm wheel are determined based on a tooth contact analysis (TCA) of such worm gear set. The cutting conditions of the worm are determined after the offset distance between the worm axis, and the central axis of the endmill tool is calculated. Afterward, the worm is manufactured by controlling only two axes on machine tools using a swarf milling method by use of the side of the endmill tool under the determined conditions. Meanwhile, the targeted theoretical tooth flanks of the mating worm wheel are modeled in 3-dimensional computer-aided design software, and the worm wheel is manufactured by a swarf milling method in a computer-aided manufacturing process. The comparison of experimental and analytical tooth contact patterns indicates almost no difference between the two tooth contact patterns.

Purpose: Transmission error is an important excitation source of gear transmission system. In many previous dynamic models, the transmission error is often treated as a simple harmonic function, ignoring the difference among transmission errors caused by different deviations. In fact, each kinds of gear deviation may lead to transmission error with different characteristics, which has different influence on the dynamic characteristics of the system. To analyze the effect of different deviations on dynamic characteristics, it is necessary to explore the characteristics of each deviation and transmission error. Methods: This paper takes the profile deviation as the research object and, by analyzing its characteristics, builds the mathematical model of spur gear tooth surface including tooth profile deviation. Based on tooth contact analysis (TCA), the characteristics of transmission errors caused by different factors of tooth profile deviation are analyzed and then the influence of different factors of tooth profile deviation on the dynamic characteristics of spur gear system is discussed. To verify the rationality of the dynamic model, the simulation results are compared with the results in the previous literature. Results: The simulation results show that the effect of these factors of tooth profile deviation on the system is obviously different and it is necessary to consider their comprehensive effect for improving the accuracy of dynamic models. The modelling and analysis method based on TCA in this paper has practical guiding significance for analyzing the influence of different deviations caused by manufacturing and assembling on the dynamic characteristics of gear system. [ABSTRACT FROM AUTHOR]

Due to the involute worm and helical gear drive is different from the parallel shaft helical gear drive and the worm drive, the plane meshing theory and the space enveloping principle cannot be directly applied for this worm drive when the meshing analysis is performed, there has been no good analysis method to accurately calculate the meshing situation. To satisfy the increasing requirements of low-noise and long-lifetime in the service robots and the modern intelligent house systems, especially the intelligent shading system in the modern intelligent house system, a novel meshing performance analysis method is proposed for the involute worm and helical gear drive based on the counterpart rack. By calculating the contact line between the counterpart rack and helical gear and the contact line between the counterpart rack and involute worm, we can get the contact point of involute worm and helical gear finally. This novel meshing performance analysis makes it possible to use the plane meshing theory and the space enveloping principle to analyze involute worm and helical gear drive. The meshing relationship between the involute worm and the counterpart rack, as well as the counterpart rack and the helical gear are presented, and the computational model of contact ratio and contact ellipse are obtained through the counterpart rack. The mathematic model for the instantaneous contact point and contacts trace of the worm drive with different assembly errors is established, and the meshing performances are investigated through the numerical analysis, simulation analysis and performance testing. The results show that this worm drive is insensitively to the assembly errors, and it is beneficial for reducing the vibration-noise and extending the service life. This theoretical research provides theoretical support for further optimizing the vibration and noise of involute worm and helical gear drive and improving the fatigue life. [ABSTRACT FROM AUTHOR]