Tooth Profile Design Research Articles

Tooth profile design and meshing characteristics analysis of internal meshing gears based on variable center meshing line

A design method of internal meshing gear based on variable center meshing line (VCML) is presented in this paper. The meshing line is an arc line connecting the intersection of the indexing circle connecting the inner and outer gears and the intersection of the tooth top circle, and the center of the line of engagement freely slides on the vertical bisection line of the line connecting the two intersection points. The top tooth profile equation of internal and external gears is derived by rack equation. According to the normal method of gear profile, the equation of gear root meshing line is derived by using the tooth top profile equation of the gear. According to the principle of plane meshing, the root profile equation of gear is derived by using the root meshing line equation of gear. The tooth profile of VCML gear can be deduced quickly by adjusting the center position of the meshing line. The stress, meshing stiffness, transmission error, contact ratio and sliding ratio of the VCML gears are analyzed by finite element method, and the area of significant performance improvement of the meshing line center of the VCML gears is found. The research results show that compared with involute gears, the maximum average stress of VCML gears is reduced by 64.99%, the meshing stiffness is increased by 193.67%, and the transmission error is reduced by 65.95%. This method improves the efficiency of new tooth profile design and transmission performance. By changing the center coordinates of the meshing line, the tooth profile of the VCML gear can be quickly redesigned, which greatly improves the efficiency of the new tooth profile design and transmission performance. This design method provides a new idea for the tooth profile design of internal meshing gear.

Effects of Profile Shifting of a Cosine Gear

Cosine gears are a special type of gear drive, in which the tooth profile of the theoretical generating rack is described by the cosine function. According to recent research results, the cosine gear drive has a lower slip coefficient and the contact and bending stresses supported by the teeth during the load are smaller than those occurring in involute gears. The main advantage of the cosine drive pair lies in the apparent higher rigidity of the gear tooth: this can reduce flank wear and increase gear life, especially in heavy load and highspeed applications. In contrast to involute profile gears, cosine gears do not show undercut root fillet, even with small teeth number. This paper deals with cosine gear tooth profile design and the meshing of the cylindrical cosine gear pair conceived without, or with the application of the profile shifting. The mathematical model of the meshing was implemented in a Mathcad environment, showing that there exists a significant difference compared to the well-known involute gears. The simulation of the motion during the rolling of the gear pairs was realized with the Autolisp programming interface. Solid models were created and tested in the Autodesk Inventor environment.

Design and fluid analysis of the microsegment gear tooth profile for pump operating at high speed and high pressure

In order to solve the problem of oil trapping in involute gear pumps, a new tooth profile based on the microsegment tooth profile and incorporating the circular arc tooth profile theory has been designed in this study. Firstly, the tooth profile equation of the microsegment gear profile for the pump has been derived. Then, the spatial tooth surface equation of the helical microsegment gear for the pump has been derived, and the feasibility of the new tooth profile has been verified using the contact spot experiment. The characteristics of the new gear profile without oil trapping and the closed “8” type mesh line have been analyzed, from which the output flow rate of the microsegment gear pump has been verified to be constant. A conclusion has been drawn on the applicability of the microsegment gear tooth profile for the pumps. Further, the fluid analysis model of the microsegment gear pump has been proposed to analyze the oil pressure distribution and state of fluid motion at high pressures in the microsegment gear pump. A comparison of the performances of the involute and the microsegment gear pumps shows that the output pressure and maximum pressures of the microsegment gear pump are smoother than that of the involute gear pump. Analysis of the effect of the high rotational speed on the output oil pressure and the maximum pressure shows that the former increases, whereas the latter varies very little with the rotational speed.

Investigation on high contact ratio harmonic two-dimensional tooth profile design based on mid-point meshing method

Investigation on high contact ratio harmonic two-dimensional tooth profile design based on mid-point meshing method

Tooth profile design of a novel helical gear mechanism with improved geometry for a parallel shaft transmission

Abstract. Based on the space curve meshing equation, a novel helical gear mechanism with improved geometry is presented. First, equations of the theoretical contact curves were derived based on the space curve meshing theory. Then, tooth surfaces with a concave–convex meshing form were constructed, depending on the contact curves. The tooth profiles were improved as the theoretical contact curves were corrected by predestining the designed transmission errors. The effect of the center distance error on the transmission errors was studied, and the effects of gear modifications on transmission errors and maximum contact stresses were also investigated. The results show that the transmission error curves of the improved gear drive become much smoother. Maximum contact stresses of the improved gear drive are decreased synchronously.

Design and extraction of tooth profile of denatured elliptical gear

Elliptical gear is a common type of non-circular gear; it’s theory and design methods are mature. But the research on denatured elliptical gear was not enough, the design method of tooth profile was single, low precision, and there may occur tooth overlap at the splice when the denatured elliptical gear is generated by the envelope method. The denatured elliptical gear design in the existing literature did not include tooth profile point extraction, so the denatured elliptical gear design only exists in theory, it can’t obtain the necessary data for processing and production. Given this situation, a design method is proposed to design denatured elliptical gear, and the tooth profile data are extracted. The main steps are as follows: firstly, the arc length of gear was calculated, and the arc length corresponding to the rotation angle is obtained. The piecewise interpolation of the gear with equal arc length was spliced together to get a complete envelope image, then, the image was binary processed. Finally, using the designed program, the tooth profile pixels were extracted by the eight-neighborhood algorithm. This method provides a new way of designing denatured elliptical gear, this method is stable and has a fast operation speed. The tooth profile data can be directly used for 3D modeling or wire cutting machining.

Investigation and optimization of hypoid gear micro-geometry parameters and axle deflections to improve the contact stress distribution and fatigue life of hypoid gears

The automotive industry always demands more torque per kilogramme of weight. On the other hand, there is always a growing demand for increased warranty kilometres for customers. This puts increased pressure on the life of the drive axle, which is the major load and torque-carrying member in commercial vehicles. Drive head unit is a crucial contributor to this aim. This paper focuses on the work done towards the above targets wherein advanced tools helped to achieve them in the minimum time. Due attention is given to the hypoid gear system to sustain higher stress because of the heavy torque demanded by the application. It is accomplished by the optimum design of the gear tooth profile and system design. Gear durability is a major concern in heavily loaded axles. To have an optimum design with higher performance torque is a key challenge. The paper talks about the challenges overcome during the design, development, and validation of a single-reduction large-size gear axle to replace the hub reduction rear axle. It demands a better understanding of gear tooth and system behavior, which was analyzed by advanced software tools and measurement machines. The same is validated on the test bench, and the results are discussed.

Design and Application of Non-Circular Gear with Cusp Pitch Curve

To solve the design problem of non-circular gears with cusp pitch curves, this paper proposed a new variable-involute and incomplete variable-cycloid composite tooth profile (VIIVC-CTF), deduced the new VIIVC-CTF mathematical model, and constructed the conjugate gear model based on the envelope method. The design software of the non-circular gear with a cusp pitch curve was developed based on MATLAB. The variation law of rolling radius on an incomplete cycloid profile and its characteristics such as pressure angle and radius of curvature were analyzed. The variation relationship of the rolling radius on the meshing line and the contact ratio of the VIIVC-CTF were studied. The variation relationship of incomplete variable-cycloid profile shape, pressure angle, and curvature radius corresponding to different elliptical eccentricities were analyzed. The meshing analysis of the non-circular gear transmission mechanism was carried out based on virtual software. A comparison of the consistency of the theoretical value and simulation value of the transmission ratio curve verified that the tooth profile design method was feasible, and the VIIVC-CTF was applied to the seedling pick-up mechanism of the non-circular gear planetary gear train. Through the seedling picking experiment of the seedling pick-up mechanism, the feasibility of the application of the VIIVC-CTF was verified.

Eliptik Dişli Tasarımı, İmalatı, Analizi ve Eliptik Dişlilerin Endüstriyel Uygulamaları

Eliptik dişliler üzerine yapılan çalışmaların diş profillerinin tasarımı üzerine yoğunlaştığı ve prototip imalatlarına yönelik araştırmaların arttığı görülmektedir. Eliptik dişlilerin diş profillerinin silindirik dişliler gibi özdeş olmayacağından hareketle geliştirilen eliptik dişlinin diş profili; kramayer veya silindirik düz dişli formlu kesicinin bölüm elipsi üzerinde yuvarlanma yöntemine uygun olarak evolvent eğriye sahip diş yanaklarının şekillendirilmesiyle elde edilmektedir. Eliptik dişlilerin imalatında CNC tel erozyon tezgahlarından faydalanmanın yaygınlaştığı, bununla birlikte azdırma tezgâhları için elektronik dişli kutuları geliştirilerek eliptik dişlilerin standart modülde imalatının da mümkün olduğu tespit edilmiştir. Eliptik dişli çiftleri farklı makine ve teçhizatta kullanılmakta, özellikle eliptik dişli çiftine sahip debimetre ve pompaların yaygınlaştığı görülmektedir. Enerji verimliliğinin son derece önem kazandığı günümüzde, yüksek akışkan miktarlarının doğru ve hassas ölçülmesi ve işletmelerin akışkan transferindeki kayıplarının giderilmesi de gerekmektedir. Bu genel değerlendirme çalışmasında eliptik dişlilerin tasarımı, geleneksel ve geleneksel olmayan imal usulleri ile imalatı, dayanım ve titreşim analizleri ve literatürde yer alan muhtelif endüstriyel uygulamaları gözen geçirilmiş ve çalışmanın ortak bulguları elde edilmiştir. Eliptik dişlilerin yakın gelecekte bünyesinde mekanik kısım barındıran birçok akıllı ürünün vazgeçilmez bir organı olacağı öngörülmektedir.

Computerized design, simulation of meshing and stress analysis of pure rolling internal helical gear drives with combined tooth profiles

The computerized design of non-generated pure rolling internal helical gear drives with combined transverse tooth profiles based on the active design of the meshing line function is presented. The application of different combinations of curves, namely circular arcs and involutes, to form the gear active tooth profiles is discussed. The parametric equations for tooth surfaces and the basic design parameters and equations of geometric sizing are proposed. The meshing performance and mechanical behavior are studied in terms of the contact patterns, maximum contact and bending stresses and peak-to-peak level of loaded transmission errors compared with a design of internal helical gear drive with corrected fillet. The combination of a circular arc and an involute connected at the pitch point to form the active tooth profile for both the pinion and the internal gear shows reduced maximum contact and bending stresses and lower peak-to-peak level of the loaded function of transmission errors. The proposed design of combined tooth profiles will contribute to lower the noise and vibration of the proposed gear drives, increase the endurance and life of the gear drive, and lower the heat generation due to pure rolling conditions of the achieved bearing contact.

Geometric Design of a Face Gear Drive with Low Sliding Ratio

A design method of low sliding ratio face gear drive is presented. The rack and gear meshing pair with a low sliding ratio is obtained by constructing the contact path. The face gear is then formed by this gear, and its tooth width characteristics are analyzed. Combined with the explicit solution of the meshing point of the tooth surface, a method to solve the sliding ratio of the proposed face gear pair is given, and the effects of relevant design parameters on the sliding ratio are analyzed. Moreover, the rationality of the tooth profile design is verified by 3D modeling and motion simulation. The proposed face gear pair has a lower sliding ratio, as well as larger tooth width, than those of traditional face gear drive (the pinion is involute spur gear) with the same basic parameters. The results of this study can provide points of reference for reducing friction and improving the mechanical efficiency of face gear drives.

Tooth Profile Design and Analysis Method of Harmonic Drive Driven by the Conjugate Parameter

Tooth Profile Design and Analysis Method of Harmonic Drive Driven by the Conjugate Parameter

基于图解法和Alpha shape算法设计带啮合间隙的双螺杆压缩机转子齿形

基于图解法和Alpha shape算法设计带啮合间隙的双螺杆压缩机转子齿形

A vectorial modification methodology based on an efficient and accurate cycloid tooth profile model

A cycloid gear is the central component of a rotate vector reducer, and cycloid profile design has served as the basis for manufacturing modification research. The previous cycloid tooth profile equations are complicated to derive and not efficient to calculate. Moreover, the current tooth modification method only allows for uniform correction of the overall profile. This work presents an efficient calculation and high accuracy model of the cycloid profile which is designed in dual quaternion space by introducing assembly and machining error parameters. Moreover, we propose a vectorial modification method to achieve a single-point partial modification instead of simultaneous modification of all tooth profile points. With the meshing characteristics as the optimization objective, the optimal solution of the error term is obtained by means of the response surface method, which is the maximum error tolerance in the design process. Finally, verification is carried out by the finite-element method. The new cycloid tooth profile model provides the basis for a modification vector calculation of large-scale scatter points. The synchronization of the design error tolerance maximum and tooth profile design will also effectively improve the manufacturing accuracy of the whole machine and shorten the design cycle.

Parameter design of double-circular-arc tooth profile and its influence on meshing characteristics of harmonic drive

In this paper, a design method of double-circular-arc tooth profile for harmonic gear based on curve mapping and bidirectional conjugation is proposed. By considering the kinematic principle of harmonic drive, the curve mapping is used to solve the addendum circular arc, and on this basis, the dedendum circular arc is solved by the bidirectional conjugation. The influence of design parameters on the tooth profile shape and meshing characteristics of harmonic gear drive are analyzed. The results show that the proposed tooth profile design method can not only construct the mathematical relationship between basic parameters (modulus, number of teeth, deformation, etc.) and tooth profile shape, but also realize the multi-tooth engagement of harmonic drive. The change of the scaling coefficient has a great effect on the tooth profile shape. The increase of flexure coefficient will reduce the pressure angle of the tooth profile, and the smaller flexure coefficient is beneficial to reduce the maximum Von-Mises stress of the flexspline during assembly and loading stage. The research results will provide a novel design method for the tooth profile and improving meshing characteristics of harmonic gear.

A Novel Approach to Calculating the Transmission Accuracy of a Cycloid-Pin Gear Pair Based on Error Tooth Surfaces

Transmission error (TE) and backlash are important parameters used to evaluate the transmission accuracy of cycloid-pin drives. Existing calculation methods are mostly based on two-dimensional tooth profile models, and these methods ignore the influence of some abnormal meshing phenomena caused by profile modifications (PMs), manufacturing errors (MEs), and assembly errors (AEs), such as the instantaneous mesh-apart of tooth pairs and the eccentric load on the tooth surface. To fill this gap, a novel approach to accurately calculating the TE and backlash of a cycloid-pin gear pair based on the error tooth surfaces is proposed, and its feasibility and effectiveness are validated by comparison with the theoretical analyses and the results from the literature. Based on this, the effects of the PMs, MEs, and AEs on the transmission accuracy are studied, which will be helpful in optimizing the tooth profile design of a cycloid gear and the tolerance allocation during the installation of a gear pair. The proposed method is also expected to provide accurate error excitation data for the dynamic analysis of cycloid-pin drives.

Design and modification of harmonic double circular arc tooth profile based on finite element method

Design and modification of harmonic double circular arc tooth profile based on finite element method

Geometry design and dynamic analysis of a modified cycloid reducer with epitrochoid tooth profile

This study proposes a design method for a modified cycloid reducer with an epitrochoid tooth profile. The reducer used here has one contact pattern and non-pin rollers like a planocentric reducer. This feature makes the designed reducer easier to be manufactured compared to conventional cycloid reducers, which are difficult to manufacture due to tolerances. The tooth profile characteristics for nine different design scenarios for the cycloid reducer were analyzed with respect to the tooth thickness ratio and the distance from the center of the rolling circle. It was observed that the inflection point, which was calculated from the radius of curvature, was a major factor influencing the design of the cycloidal tooth profiles. A mathematical model for the force analysis of the designed reducer was developed, and variations in force distribution between the internal and external gears as well as the efficiency of the cycloid reducer were calculated according to different coefficients of friction. Involute and cycloid gears with a difference of one tooth between the internal and external gears were designed and manufactured, and finite element analysis showed that the cycloid gear had higher rigidity than the involute gear.

The Structure and Optimal Gear Tooth Profile Design of Two-Speed Transmission for Electric Vehicles

As environmental regulations have been strengthened worldwide since the Paris Climate Agreement, the automobile industry is shifting its production paradigm to focus on eco-friendly vehicles such as electric vehicles and hydrogen-battery vehicles. Governments are banning fossil fuel vehicles by law and expanding the introduction of green vehicles. The energy efficiency of electric vehicles that use a limited power source called batteries depends on the driving environment. Applying a two-speed transmission to an electric vehicle can optimize average speed and performance efficiency at low speeds, and achieve maximum speed with minimal torque at high speeds. In this study, a two-speed transmission for an electric vehicle has been developed, to be used in a compact electric vehicle. This utilizes a planetary gear of a total of three pairs, made of a single module which was intended to enable two-speed. The ring gear was removed, and the carrier was used in common. When shifting, the energy used for the speed change is small, due to the use of the simple method of fixing the sun gear of each stage. Each gear was designed by calculating bending strength and surface durability, using JGMA standards, to secure stability. The safety factor of the gears used in the transmission is as follows: all gears have been verified for safety with a bending strength of 1.2 or higher and a surface pressure strength of 1.1 or higher. The design validity of the transmission was verified by calculating the gear meshing ratio and the reference efficiency of the gear. The transmission to be developed through the research results of this paper has a simple and compact structure optimized for electric vehicles, and has reduced shift shock. In addition, energy can be used more efficiently, which will help improve fuel economy and increase drive range.

Study on tooth profile design of harmonic drive with deformation model of flexspline

Study on tooth profile design of harmonic drive with deformation model of flexspline