Gear Tooth Profile Research Articles

Research on Mapping Rules of Hob Geometric Errors and Gear Geometric Precision

High precision gear is an necessary support of high-end equipment to meet the requirements of high-speed, heavy-duty,impact, low noise(mute) and other extreme environments. In order to improve the accuracy of hobbing manufacture, to partly achieve"replacing grinding with rolling", and to reduce processing costs, focusing on the insufficient quantitative mapping rules between hob geometry errors and gear geometric error, the quantitative mapping rule research between gear hob tooth profile error, helix error, gear hob installation angle of the radial runout error and the gear tooth profile error, base pitch error with the consideration of machine tool movement error are carried out respectively. Utilizing the counterpart rack law, the gear tooth profile equation enveloping from involute curve hob tooth profile equation is generated, quantitative mapping relational model of hob pitch error and pitch deviation based on differential geometry and envelope principle is builded. At the same time quantitative mapping relational model between hob helix error,radial runout error of hob installation angle and the gear tooth profile error are established respectively. According to the geometric relations between gear tooth profile error and gear base pitch error, the mapping rule of base pitch error is calculated based on the factors mentioned above. A joint equation model between the above three main errors of gear hob and the tooth profile error based on Gaussian distribution with the consideration of machine tool movement error are builded. At last the correctness of the above model by comparing the result of model simulation method with empirical data is verified, so the essential mapping rules of hob error and the main factors which affect tooth geometric precision such as tooth profile error, base pitch error with the consideration of machine tool movement error are revealed, thus a theoretical foundation for roll cutting gear with higher precision is layed.

Research on Tooth Profile Design of Spur Gears Based on Line of Action

This paper aims to propose a design method for tooth profiles of spur gears based on given line of action. A simplified derivation of the mathematical model of tooth profiles is introduced according to the meshing theory. Tooth profiles of spur gears, using a parabola as line of action, is established. The result shows that it will be better to control the performances of a gear set by specifying the shape of the line of action rather than specifying tooth profiles of mating gear.

Status and Problem research on Gear Study

The history of the gear drive and development of the gear industry is briefy reviewed. The development and application status of gear technology is more systematically introduced in recent years, focuses on three study aspects of gear tooth figure and transmission structure, application of some new theories, and development and application of computer software. Gear tooth profile,performance, tooth correction and transmission structure are researched in the part of gear tooth figure. The current combined application such as fractal theory and elastic fluid theory is mainly introduced. Computer research of gear develops rapidly and application and development of the domestic situation is briefly combed from computer-aided design, analysis, testing and manufacturing processes perspective. Standards and testing issues need to be addressed in the gear research, knowledge to solidify and marketing problems are required to solve in the new theory application, and knowledge mining and generalized problem need to be solved in the computer software applications are proposed and related solutions are given.

3203 ポリアミド歯車の膨潤が歯車精度および騒音に及ぼす影響(OS-10 プラスチック歯車)

We investigated the effect of swelling of polyamide gear on the gear accuracy and noise generation. For the influence of swelling on the gear accuracy, we examined the changes in the tooth profile and tooth trace of test gear by water immersion test. Gear swelling caused large negative pressure angle errors on the tooth profiles of test gear and the error increased with the immersion time. Changes in the tooth profile were approximately similar in each tooth of the test gear. For the influence of swelling on the gear noise, we examined by comparing the noise of swelled gear and that of non-swelled gear using a gear tester. In this study, we attached a polyamide gear to the driven shaft and a steel gear to the driving shaft, and carried out gear tests under the conditions of tangential force F/b = 6.5, 13.0, 19.6 N/mm (the nominal load torque = 19.6, 39.2, 58.8 Nm). The change in tooth profile due to swelling influenced the noise generation, however the influence was limitative and swelling had no very influence on the gear noise generation except for the case operated under low load condition.

S112011 サイクロイド歯形歯車の摩耗([S112-01]伝動装置の基礎と応用(1))

At present, many gears have involute tooth profiles which are easy to manufacture and are able to maintain constant gear speed even when the center distance changes. However the involute tooth profile has some disadvantages: it causes a high contact stress by meshing with two convex surfaces, and it also generates an undercut when gears have a small number of teeth. On the other hand, a cycloid tooth profile gear is also able to transmit a uniform motion. The cycloid tooth profile gear has greater tooth surface strength (except at the pitch point) due to the mesh with the convex and the concave surfaces, and it also has high bending strength. In this study, we investigated the wear of a cycloid tooth profile gear, using a power circulating-type gear testing machine, and measure the change in tooth profile of the test gears. Furthermore, we develop a computer program to predict the amount of the wear on the tooth surface for the spur gears. The method employs two equations: one based on Soda's wear model under lubricated condition; the other derived from the ploughing wear model. Using these equations, the wear depth on the tooth surface was calculated with changing of the contact stress, the sliding velocity, the oil film thickness, etc. The calculated value of the wear agreed with the experimental result.

Reverse Design of Non-Circular Planetary Gears Train Beating-Up Mechanism

A non-circular planetary gears train beating-up mechanism was proposed, the ideal kinematic curve of beating-up rockshaft was constructed and the reverse model of the pitch curve of non-circular gears was established based on the ideal kinematic curve. When the first-level non-circular gears were set as elliptical gears, the maximum swinging angle of the sley and the influence of the elliptical gears' eccentricity on the concavo-convex characteristic of the second-level non-circular gears were analyzed. Provided with a set of parameters, the pitch curves and tooth profiles of the second-level non-circular gears were determined by reverse method. The result has shown that non-circular planetary gears train beating-up mechanism can meet the requirements of beating-up process.

1212 新型の円弧歯すじ歯車の設計・製作に関する研究(OS-01 歯車の設計)

Typically, the circular-arc tooth-trace (CATT) gears are considered as a special type of spiral bevel gears whose shaft-angle is zero. Conventional circular face-mill gear-cutters are used to make these gears. In this paper, the characteristic of the new CATT gears designed by the author with 3D-CAD/CAM were studied; the tooth profile of pinion gears have the same involute curve at the any section through the face-width. Similarly the tooth profile of the CATT's rack is a straight line at the both ends of the face-width.

Study of electrochemical-mechanical finishing of bevel gears

This study discusses the performance assessment of high precision finishing of bevel gears by electrochemical-mechanical finishing (ECMF) process. In the present study, experimental investigation has been carried out on an indigenously developed experimental setup for ECMF of bevel gears of AISI 1040 steel to evaluate the process capability in improving the surface quality of gear teeth profile. Surface integrity of ECMFed surface was analysed and it was found that the process has capability to enhance the surface quality of gear teeth profile by minimising the irregularities. The emphatic features of the newly developed experimental setup have also been discussed.

Stress optimization and study of the sensitivity to geometric variations of a spur gear tooth profile

This paper presents an approach for obtaining an optimized geometry for the flank of a tooth by minimizing the equivalent contact stress. The stress calculation method is based on Hertz theory. As the majority of tooth profiles are involute, the geometric variation of the flank of the tooth is achieved variationally relative to the involute profile. The optimum profile is obtained by Monte Carlo simulation. During this optimization, a polynomial expression of the tooth geometry is used. The parameters influencing the simulation are the four characteristic contact points. The approach presented has been applied in a representative case. A study of the geometric sensitivity was conducted on the optimized tooth profile. Two different approaches were considered: by Monte Carlo simulation and analytical propagation. The robust and linear nature of the behavior of the tooth profile was demonstrated when it was subjected to geometric variations.

Finite Element Residual Stress Analysis of Planetary Gear Tooth

A method to simulate residual stress field of planetary gear is proposed. In this method, the finite element model of planetary gear is established and divided to tooth zone and profile zone, whose different temperature field is set. The gear's residual stress simulation is realized by the thermal compression stress generated by the temperature difference. Based on the simulation, the finite element model of planetary gear train is established, the dynamic meshing process is simulated, and influence of residual stress on equivalent stress of addendum, pitch circle, and dedendum of internal and external meshing planetary gear tooth profile is analyzed, according to non-linear contact theory, thermodynamic theory, and finite element theory. The results show that the equivalent stresses of planetary gear at both meshing and nonmeshing surface are significantly and differently reduced by residual stress. The study benefits fatigue cracking analysis and dynamic optimization design of planetary gear train.

Study of Time Dependent Behaviour of ECH of Bevel Gears

Electrochemical honing (ECH) is emerging as a potential gear finishing technique in which achieved surface finish and material removal are significantly influenced by the processing time. This paper comprises the findings of experimental investigation to explore the influence of processing time on process performance parameters: surface quality of gear teeth profile, tribological performance of the teeth surface and process capability and thus, to estimate the optimum processing time by graphical analysis. The emphatic characteristics of developed machine setup and guidelines for future research have also been discussed to stimulate the research community to carry out further research in this field to mature the process.

Parametric Optimization of Electrochemical Honing of Helical Gears by Response Surface Methodology and Genetic Algorithm

Finishing is crucial for maximizing the service life and overall in-service performance of gears. This paper presents the parametric optimization of Electrochemical Honing (ECH) of helical gears using Response Surface Methodology (RSM) and Genetic Algorithm (GA) to predict the surface quality of gear teeth profile. A three factors three levels Box Behnken Design (BBD) of Response Surface Methodology (RSM) has been designed to investigate and analyze the effects of input variables: voltage, rotating speed and electrolyte concentration on measures of process performances: percentage improvement in average and maximum surface roughness (PIRa / PIRtm) value. Typical ranges of input parameters were investigated and regression models were developed and used respectively as constraints and objective function for parametric optimization using GA. The results established the feasibility of using the process to improve the surface quality of gear teeth profile.

Influencia de la geometría en la resistencia a la flexión de los engranajes plásticos

En el presente trabajo se analiza el tema relacionado con las modificaciones geométricas del perfil del diente de engranajes plásticos cilíndricos de dientes rectos mediante el método de los elementos finitos y su influencia en la resistencia a la flexión. El objetivo fundamental del estudio es, desarrollar un procedimiento para determinar la influencia de la asimetría y la corrección del dentado en la resistencia a la flexión de los dientes de los engranajes plásticos. En esta investigación se ha desarrollado el cálculo de los esfuerzos de flexión, mediante procedimientos matemáticos y el uso del software con el que se ha logrado incrementar la resistencia a la flexión debido a la corrección del dentado (para un factor de corrección de 0 a 0,7) y asimismo la determinación del factor de forma en los engranajes cilíndricos de dientes rectos asimétricos que constituye una innovación científica. Los resultados alcanzados satisfacen a los objetivos generales y específicos del estudio, con el cual se demuestra que las innovaciones contribuirán a una mejorar el desarrollo tecnológico de la industria y del país.

Research on the Parametric Design of Involute Helical Gear Based on Pro/Program

Involute helical gear has advantages of larger overlap coefficient, steady transmission, lower impact and noise, higher load bearing capacity, longer life, so it is widely used in machinery, mining, metallurgy, aerospace and other fields. However, due to the involute helical gear tooth profile shape is more complex, and some low-level CAD software is difficult to directly generate a three-dimensional helical gear tooth profile. According to involute helical gear formation principle, this paper presents an effective method to establish the three-dimensional model for involute helical gear .In this paper, a parametric design method of realizing involute helical gear 3D model by using Pro/E modeling functions and Pro/Program programming is discussed. This method can enable designers to obtain helical gear 3D solid model quickly and accurately by inputting a little geometry characteristic parameters. It can also enables designers quickly update design based on the existing 3D gear model, so as to improve the design efficiency.

New Tooth Profile Design of Spiral Bevel Gears with Spherical Involute

Based on the generating line principle of spiral bevel gear, this paper researches the conjugation meshing mechanism of line contact between the meshing surfaces, and proposes a new theory for designing the tooth profile of spiral bevel gear. A certain tooth surface design of spiral bevel gear with spherical involute is analyzed deeply as an example. Key parameters of spiral bevel gear tooth profile are calculated by using space geometry principle, which include helix angle, generating line radius, modules and so on. Then the 3D solid model of spiral bevel gear is built by using the modeling software of CATIA, and key parameters are measured from the model. The measured values are equal to calculated values. It can be indicated that the teeth profile designed in this paper can mesh correctly. And the tooth surface can be generated with more simple movement.

On Martin Disteli's spatial cycloidal gearing

The modeling of the tooth flanks of gears with skew axes still represents a challenge to geometers. This paper is a contribution along these lines, as pertaining to gears with skew axes and cycloidal teeth. To this end, the authors follow and extend the results reported by Martin Disteli at the turn of the 20th century concerning the general synthesis of gears with skew axes. The main goal is the rendering of the tooth profiles of cycloidal gears with skew axes. This is done by means of the dualization of the geometric relations proposed by Disteli for bevel gears with cycloidal teeth, which leads to ruled surfaces as conjugate tooth flanks such that at any instant the contact points are located on a straight line. All results are proven by means of a consistent use of dual vectors representing directed lines and rigid-body twists.

Numerical Algorithm of Tooth Profile of Noncircular Gear Pair

According to the generating method theory, noncircular gear with all convex pitch curve can be processed by generating, author designed noncircular gear tooth profile, described a method of precisely calculating noncircular gear tooth profile. And proposed automatically optimizes the noncircular gear tooth profile meshing curve part separately by the identical rack cutting tool different side envelope. Through rack cutting tool along two gear center of rotation segment deviation pitch curve change modified quantity to avoid tooth undercut, realization nonzero modified. The driving gear and the driven gear tooth profile meshing curve part separately by the identical rack cutting tool different side envelope, guarantees when meshing zero clearance. The noncircular gear machined by this method has been used in real machine, which verifies the feasibility of the method.

Free-Form Conjugation Modeling and Gear Tooth Profile Design

The paper presents the first theory and practice of free-form conjugation modeling. It introduces the concept of master-slave that broadens the traditional computer aided single geometry modeling to dual geometry modeling. The concept is then applied to gear geometry to establish the first free-form conjugation modeling technique, in which a fictitious free-form rack-cutter or free-form contact path is proposed as the master geometry. Simple geometric relationship suitable for conjugation modeling and undercutting analysis is found between the master and the conjugate profiles. With a free-form master geometry, free-form conjugation modeling has desirable properties of guaranteed continuity, flexibility, and controllability. It offers unlimited representation capability crucial for conjugation modification and optimization. Undercutting is examined rigorously and extensively under the free-form technique via differential geometry. For general planar conjugation, including noncircular gearing, necessary and sufficient undercutting conditions in terms of the master geometry are obtained. Simple geometric explanation of undercutting is demonstrated in terms of the distance between a contact path and two centrode centers. The technique is demonstrated with B-spline as the master geometry.

Analysis of mixed model in gear transmission based on ADAMS

The traditional method of mechanical gear driving simulation includes gear pair method and solid to solid contact method. The former has higher solving efficiency but lower results accuracy; the latter usually obtains higher precision of results while the calculation process is complex, also it is not easy to converge. Currently, most of the researches are focused on the description of geometric models and the definition of boundary conditions. However, none of them can solve the problems fundamentally. To improve the simulation efficiency while ensure the results with high accuracy, a mixed model method which uses gear tooth profiles to take the place of the solid gear to simulate gear movement is presented under these circumstances. In the process of modeling, build the solid models of the mechanism in the SolidWorks firstly; Then collect the point coordinates of outline curves of the gear using SolidWorks API and create fit curves in Adams based on the point coordinates; Next, adjust the position of those fitting curves according to the position of the contact area; Finally, define the loading conditions, boundary conditions and simulation parameters. The method provides gear shape information by tooth profile curves; simulates the mesh process through tooth profile curve to curve contact and offer mass as well as inertia data via solid gear models. This simulation process combines the two models to complete the gear driving analysis. In order to verify the validity of the method presented, both theoretical derivation and numerical simulation on a runaway escapement are conducted. The results show that the computational efficiency of the mixed model method is 1.4 times over the traditional method which contains solid to solid contact. Meanwhile, the simulation results are more closely to theoretical calculations. Consequently, mixed model method has a high application value regarding to the study of the dynamics of gear mechanism.

The Research on Variety of Instantaneous Transmission-Ratio of Gear Pump with Circular-Arc Tooth Profile

According to basic law of tooth profile meshing and principle of higher pair to be replaced with lower pair of planar mechanism, the calculating formula which is used for calculation of transmission ratio of gear pump with circular-arc tooth profile is obtained. The calculating results indicate that stability of transmission ratio of gear pump are very effected by the difference between concave arc radius of tooth profile of pinion and convex arc radius of tooth profile of wheel gear. The smaller the difference of radiuses, the more severe the wave of velocity while meshing.