Cylindrical Involute Gears Research Articles

Parameters impact analysis on contact characteristics of intersected beveloid gear and involute cylindrical gear

According to gear geometry and tooth contact analysis (TCA) theory, the TCA model of intersected beveloid gear and involute cylindrical gear pair is built. The formulas for calculating curvature and contact ellipse at contact points are derived, and the shape and region of contact ellipse are determined. Then, the impacts of cone angle, helix angle and installation errors on contact characteristics are studied by numerical examples. The finite element model of gear pair is established to carry out the loaded tooth contact analysis (LTCA) and verify the accuracy of theoretical TCA model. The results show that gear pair with small cone angle or big helix angle has wide contact area, large carrying capacity and high transmission quality. The shaft angle error may cause the edge contact of gear pair, while the axial position error has limited effect. The research can provide input parameters for the study of tooth surface wear mechanism and dynamics in the future work.

Geometric parameter design and contact characteristics of beveloid gear and involute cylindrical gear transmission with crossed axes

Geometric parameter design and contact characteristics of beveloid gear and involute cylindrical gear transmission with crossed axes

Effects of cutter modification on the meshing characteristics of intersected beveloid gear and involute cylindrical gear

The parabolic cutter is introduced into the design of intersected beveloid gear and involute cylindrical gear pair, and the numerical model of the normal section tooth profile of the parabolic cutter is established. Based on the hobbing theory, the equation of the beveloid gear face of tooth machining with a modification cutter is derived. The mesh characteristics analysis model of gear pair is established, and the impacts of modification coefficients on meshing characteristics that contact pattern, transmission error, meshing stiffness, contact force, and tooth root stress are studied.

Gear Transmission System Based on Cloud Platform

Based on the Amazon cloud platform, the development and application scenarios of industrial software for gear transmission systems are introduced. Taking the geometric dimension calculation transmission with involute cylindrical gear as an example, the design idea, development process and system architecture design of the transmission design software based on the cloud platform are expounded. Results show that the developed software of transmission system design based on the cloud platform can meet the requirements of accurate calculation, fast response and operation.

A Reliability-Enhanced Forming Grinding Method of Cylindrical Involute Gears for Electrical Vehicles

A new form-grinding method of cylindrical involute gears for electrical vehicles (EVs) is proposed to obtain stable contact performance of gear tooth surfaces and improve their reliability based on a predesigned controllable second-order transmission error function. The predesigned second-order transmission error function is assigned to a gear drive based on design specifications of EVs. Mathematical models of modified gear tooth surfaces of the gear pair can be obtained by the predesigned second-order trans-mission error function. Moreover, a section profile of a form-grinding wheel for cylindri-cal involute gears can be determined by a coordinate transformation matrix during form-grinding and settings of computer numerical control form-grinding programs for this active design method. This approach is ultimately conducted on three cylindrical involute gear pairs to demonstrate its feasibility and effectiveness.

3D involute gear evaluation - part II: deviations - basic algorithms for modern software validation

The fundamental equations for the evaluation of cylindrical involute gear measurements on 3D gear measuring instruments are provided. The computations are based on the principles of gear kinematics and use the system of involute gear coordinates introduced in a previous work of the authors. This holistic approach focuses on significant error sources that only appear since 3D measurement technology is used and that are almost unrecognized till today. The proposed algorithms are beneficial for the description of gear deviations as they allow the use of simple formulas covering profile, helix and pitch evaluation for internal or external and spur or helical gears. The presented equations contain the key fundamentals to complement existing standards. They will become part of reference algorithms used by the Physikalisch-Technische Bundesanstalt, the national metrology institute of Germany, to certify gear evaluation software.

Recent Progress and Prospect on Tooth Modification of Involute Cylindrical Gear

Background: Recent reviews on tooth modification of involute cylindrical gear are presented. Gear pairs are widely employed in motion and power transmission systems. Manufacturing and assembling errors of gear parts, time-varying mesh stiffness, and transmission error of gear pair usually induce vibration, noise, non-uniformly load distribution, and stress concentration, resulting in earlier failure of gear. Tooth modification is regarded as one of the most popular ways to suppress vibration, reduce the noise level, and improve the load distribution of gear pairs. Objective: The objective of this study was to provide an overview of recent research and patents on tooth modification methods and technology. Methods: This article reviews related research and patents on tooth modification. The modification method, evaluation, optimization, and machining technology are introduced. Results: Three types of modifications are compared and analyzed, and influences of each on both static and dynamic performances of gear pair are concluded. By summarizing a number of patents and research about tooth modification of cylindrical gears, the current and future development of research and patent are also discussed. Conclusion: Tooth modification is classified into the tip or root relief along with tooth profile, lead crown modification along tooth width, and compound modification. Each could be applied in different ways. In view of design, optimization under the given working condition to obtain optimal modification parameters is more practical. Machining technology and device for modified gear is a key to get high-quality performance of the geared transmission. More patents on tooth modification should be invented in the future.

GEOMETRIC SYNTHESIS OF INVOLUTE PLANETARY GEARS WITH CONNECTED GEAR WHEELS OF TYPE 2K-H

Based on the basic law of flat interlocking, the paper considers a possibility of increasing the gear ratio of low module involute cylindrical planetary gears by using asymmetric tooth profile for the purposes of measuring devices. An example of the synthesis of such reduction gearing by optimal choice of asymmetry between the profiles and Possibility of generation III is presented. Also presented is a planar matching of the unconditional existence areas in the field of independent coefficients of instrument displacement by the straight optimization method and pre-set qualitative indicators of the gearing.

Gear Cutting in a Globoid Pair with an Initial Cylindrical Involute Gear

The cutting of convex–concave conjugate surfaces of a globoid pair with an initial cylindrical gear is considered. Experimental assessment confirms the practical utility of the proposed approach. That permits the manufacture of globoid gears with increased load capacity when the hardness of the contacting surfaces is very different, without the need for globoid mills.

Expansion of the domain of existence of the cylindrical involute gears

The method for optimal geometric synthesis of gearing of cylindrical involute gears is proposed in this paper. A new geometry settlements system has been proposed. The technique developed on the basis of this settlements system can significantly expand the domain of existence of the solution to the synthesis problem, as well as the domain of existence of gear.

A general mathematical model for two-parameter generating machining of involute cylindrical gears

• A general mathematical model for two-parameter generating machining of involute gears is developed. • A general discrete assisted model for two-parameter generating machining is proposed. • The instant contact line is derived by implicated information during discrete enveloping. • The engaged cutting edge segments can be distinguished when multiple-cutting edge are adopted. Instead of the common analytical model for involute gears machining, a general mathematical model for two-parameter generating machining is developed in this study with adopting discrete enveloping to increase its robustness and generality for machined profile calculation and instant contact analysis. The geometric parameters and motion relationships are integrated according to the cross-axis gear meshing at first, and the enveloping theory for two-parameter generating process is analyzed briefly with involving middle gear rack. By transforming the multiple cutting edges relative to the gear blank according to the generating motions, a numerical algorithm is proposed to distinguish the external enveloping profile on the shaft section, then the derivation of instant contact points via the implied time sequences of profile points is introduced. Finally, the coordinate transformations for the spatial trajectory of instant contact points identifying and the engaged cutting edge segments distinguishing are investigated. At last, a non- involute profile skiving is performed to verify the generality and the robustness of proposed method, and several typically generating machining operations for cylindrical involute gear are simulated numerically to proof the accuracy of the proposed model by finding the deviations from the standard involute curves and the geometries of the instant contact points.

Mathematical approach to evaluate involute gear profile and helix deviations without using special gear software

The paper presents mathematical-geometrical approach to evaluate profile and helix deviations of cylindrical involute gear tooth flank without the usage of any specialised gear measurement software. The input data for the evaluation is represented by a set of Cartesian coordinates of surface points (points of contact between the measuring stylus and the measured surface) measured along the profile and flank curves by CAD based tactile gear measurement on coordinate measuring machine. This approach is based on deep study of ISO standards dealing with gear geometry, gear measurement and gear characteristics evaluation. Here, the development of general mathematical model of both helical and spur involute gear tooth flank surfaces is described and geometrical properties of these surfaces (important for corresponding CAD model generation) are mentioned. For practical application, mathematical formulas for calculation of profile and helix deviations from a set of measured points are derived. Due to the purely mathematical approach, no special gear measurement software is necessary for evaluation of profile and helix deviations. The required characteristics of involute gears can be evaluated by means of any general-purpose spreadsheet software. The presented method can be used not only in case of regular involute gear profile and helix inspection but mainly in case of those gear measurement standards that could not be measured as regular gears by commercial software because of unusual shape and design of the standards.

Geometric Modeling and Manufacturing Method for a few Teeth Involute Gear with Bilateral Modification

Aiming at the issue of undercutting and machining difficulties caused by gear with a few teeth, the geometric modeling method and processing method of bi-directional displacement less tooth number were studied. Based on the calculation formula of the involute cylindrical gear and the characteristics of the bi-directional gear, the calculation formula of the diameter of the variable tooth top circle is derived, and the modeling of the gear pair with bi-directional variable bit number is carried out. The research shows that the bidirectional displacement can solve the root cutting problem well and improve the transmission quality. In view of the problem that machining efficiency is not high at present, a method of machining with tangent and radial gear is proposed, and the same gear cutter is used to process different cutting and radial gears, and the feasibility of the above method is verified by the processing test. The research work laid a foundation for further promotion and application of small tooth number gear transmission.

Effects of Tooth Modifications on Mesh Characteristics of Intersected Beveloid and Cylindrical Involute Gear Pair with Small Shaft Angle

Effects of Tooth Modifications on Mesh Characteristics of Intersected Beveloid and Cylindrical Involute Gear Pair with Small Shaft Angle

3D involute gear evaluation – Part I: Workpiece coordinates

The definition of 3D workpiece coordinates for cylindrical involute gears, together with their formal relation to conventional cross sections, are prerequisites for an unambiguous and thus reliable evaluation of 3D measurement data. Both will be described in this article, as no corresponding information is currently available in national or international standards and guidelines. The definitions and calculation methods presented here are part of reference algorithms used by the Physikalisch-Technische Bundesanstalt (PTB), the national metrology institute of Germany, to certify gear evaluation software.

Laser line triangulation for fast 3D measurements on large gears

The causes of geometrical deviations from the production process and the prediction of application properties, such as noise behavior, wear or material fatigue, are only possible by having detailed information about the gear geometry. The gold standard for the gear quality inspection is represented by dimensional measurements with a tactile sensor system. As a result for industrial applications, the slow serial measurement leads to the compromise of a random inspection of the gear geometry. For the purpose of a faster and more extensive surface acquisition, a laser line triangulation sensor is investigated providing 1280 points at a line width of 25 mm with up to 200 lines/s. The results at the tooth of a large cylindrical involute gear with a pitch circle diameter of 922 mm and a face width of 246 mm show the qualification for fast three-dimensional measurements of the convex and reflective surface. The detection of the complete profile line at once is possible. It is shown that the measurement deviation of laser line triangulation can be minimized by increasing the dynamic threshold. The measurement deviations amount to ± 8.2 µm and can be attributed to random and systematic errors. Compared to the standard gear inspection, an acceleration factor of 5700 was attained. An optical scanning of the complete tooth flank provides the prerequisite for an identification of surface defects in the form of breakouts and blemish.

Calculating the Strength of K-H-V Planetary Gears

Рассмотрены вопросы расчета прочности планетарных зубчатых передач вида K-H-V с малой разностью чисел зубьев. При проведении расчетов внесены необходимые коррективы относительно ГОСТ 21354-87 «Передачи зубчатые цилиндрические эвольвентные внешнего зацепления. Расчет на прочность», чтобы использовать его для предупреждения пластического деформирования зубьев при оценке контактной прочности и для предупреждения поломки зубьев при расчете на изгибную выносливость, а также в расчетах на прочность при действии максимальной кратковременной нагрузки. Дополнительно приведен расчет вероятности безотказности работы передачи. На основе выполненных исследований разработана методика расчета планетарных зубчатых передач вида K-H-V на прочность, реализованная в виде интерактивной программы на ЭВМ. Приведены результаты ускоренных ресурсных испытаний передачи, которые были проведены по специально созданной методике и подтвердили основные положения методики расчета на прочность.

Method for the pre-dimensioning of beveloid gears

Conical involute gears – also referred to as beveloid gears – are based on cylindrical involute gears, as both gear geometries are based on a basic rack. They differ from cylindrical gears in that the beveloid gears’ addendum modification along the face width is not constant, but linearly variable. This allows beveloid gears to transfer mechanical power with parallel, intersecting or even skewed axes up to shaft angles of approximately 20°, whereas bevel or hypoid gears are applied with larger shaft angles. Compared with both cylindrical and bevel gears, there is less knowledge available concerning the design of beveloid gears. Existing tools for contact analysis are based on predetermined main gearing data. Therefore a method to pre-dimension main beveloid gearing data based on application requirements was developed. Initially, equivalent cylindrical gears are dimensioned and then transformed into beveloid gears with the required mounting positions. The method involves pre-optimizing of beveloid gears with several targets. Firstly, to comply with selected boundaries of the addendum modification coefficient, as well as to minimize ease-off between the tooth flanks achieved by a centric contact pattern and ensure adequate tip clearance by reducing tip circles. The method was implemented in a software environment for tooth contact analysis and applied to a wide range of data sets. The evaluation demonstrated the efficient design of the main data of beveloid gears including pre-optimization to achieve the objectives mentioned previously. In further optimizations, the microgeometry of beveloid gears must be adapted regarding the gap that occurs between the flanks.

Revisiting Generation and Meshing Properties of Beveloid Gears

The teeth of ordinary spur and helical gears are generated by a (virtual) rack provided with planar generating surfaces. The resulting tooth surface shapes are a circle-involute cylinder in the case of spur gears, and a circle-involute helicoid for helical gears. Advantages associated with involute geometry are well known. Beveloid gears are often regarded as a generalization of involute cylindrical gears involving one additional degree-of-freedom, in that the midplane of their (virtual) generating rack is inclined with respect to the axis of the gear being generated. A peculiarity of their generation process is that the motion of the generating planar surface, seen from the fixed space, is a rectilinear translation (while the gear blank is rotated about a fixed axis); the component of such translation that is orthogonal to the generating plane is the one that ultimately dictates the shape of the generated, envelope surface. Starting from this basic fact, we set out to revisit this type of generation-by-envelope process and to profitably use it to explore peculiar design layouts, in particular for the case of motion transmission between skew axes (and intersecting axes as a special case). Analytical derivations demonstrate the possibility of involute helicoid profiles (beveloids) transmitting motion between skew axes through line contact and, perhaps more importantly, they lead to the derivation of designs featuring insensitivity of the transmission ratio to all misalignments within relatively large limits. The theoretical developments are confirmed by various numerical examples.

A function-oriented active form-grinding method for cylindrical gears based on error sensitivity

This paper proposes a function-oriented form-grinding approach to obtain excellent and stable contact performance of cylindrical gears by designing modification forms based on a predesigned controllable fourth-order transmission error (TE) function and error sensitivity evaluation. First of all, a predesigned fourth-order TE polynomial function is assigned to the gear drive. Mathematical models of modified tooth surfaces that can describe their local deviation and ease-off topography are then obtained with the predesigned fourth-order TE function. The corresponding error sensitivity analysis is applied for investigation that reflects inherent relationships between contact attributes of modified tooth surfaces and misalignments. Moreover, the form-grinding wheel’s profile equation, the coordinate transformation matrix during form-grinding, and settings of computer numerical control (CNC) form-grinding programs for this active design method can be determined. This approach is ultimately conducted on three involute cylindrical gear pairs to demonstrate its feasibility and effectiveness.