A tooth surface section lofting method of exact spur face gear model based on complex tooth surface grid planning principle

Multi-objective optimal design of modification for helical gear

According to generating principle of spiral bevel gear and space meshing theory, formation theory of generation line of tooth surface about skew bevel gears is studied. A new processing method of tooth surface with the generation line as chord of face circular cutters is put forward. Moving process model of milling processing with skew bevel gears is built, and profile of the gears can be machined using three axes linkage method based on the model. Machining test of the gears is carried out on experiment platform designed. Furthermore, 3D points cloud model of tooth surface are calculated in light of mathematical model of the tooth surface which has been established, and datum of mesh nodes on actual tooth surface are collected. Then surface errors is evaluated by normal vector equation of the tooth surface which has been developed. Finally, this method is proved to be effective and feasible.

Face gear drives exhibit smooth transmission, low noise, and insensitivity to pinion axial installation error. Nonorthogonal face gear pairs enable torque transmission and speed variation under diverse shaft intersection angles, thus expanding their engineering applicability. At present, mathematical modeling of face gears generally considers only the tooth flank surface, while neglecting the tooth bottom surface. This leads to missing data in partial regions of the accurate tooth geometry of face gears. This paper focuses on the precise modeling algorithm and grinding methodology for the full tooth surface of nonorthogonal face gears. The tooth surface generation principle is analyzed, and the meshing kinematics between the grinding wheel (acting as the generating gear) and the nonorthogonal face gear are established. The full tooth surface is divided into five regions, and boundary conditions are defined separately for each region. Mathematical expressions for the generating gear and the full tooth surface of the nonorthogonal face gear are derived. The parameter boundaries for dish-wheel grinding are determined to guarantee full-tooth-surface completion. According to the common gear grinding machine configuration, the kinematic coordinate system for dish-wheel grinding is formulated, and virtual machining and grinding test are implemented. Comparative results demonstrate that the theoretical tooth surface matches the virtual machining outcome without noticeable deviation, validating the accuracy of the full tooth surface modeling and grinding motion. In this study, the proposed grinding method overcomes the limitation that non-orthogonal face gear grinding can only be performed on a few dedicated machine tools, thereby further expanding the application scope of face gear grinding technologies.

In order to reduce the sensitivity of straight bevel gear drives to misalignment, a new geometry of such gear drives is proposed in longitudinal direction. Point contact instead of line contact of tooth surfaces is achieved by longitudinal crowning of pinion tooth surface. The tooth surface modeling and tooth contact analysis (TCA) of straight bevel gear drives have been established. TCA program of a pair of straight bevel gears was performed in MATLAB and tooth bearing contact and transmission errors were obtained.

It takes distinguishing the two beveloid tooth surface as starting point and compares the differences of tooth profile from some aspects, such as forming process, sectional profile and the shape of the contact line.According to the tilting processing principles of the rack cutter and slotting cutter, the author analyzes whether the outline of the beveloid gear's transverse plane is involute, and makes definition of the involute and non-involute beveloid tooth surface; and in the same coordinate system, the author establishes mathematical model of the cutter envelope beveloid tooth surface.Though describing the relationship between the parameter, corner and displacement distance of the cutter tooth surface, the author uses the methods of vector transformation and mesh equation, and expresses the vector transformation of the beveloid tooth surface; and compares the differences of transverse plane and normal plane of gear along the normal direction, and the results of numerical calculations show that the two kinds of beveloid gears are so similar that can replace each other; what's more, the author discusses shape of the beveloid tooth surface's contact line, studies the formation principle of cutter tooth surface's point contact and the flow track, and has supplementary instruction about the differences of the two kinds of beveloid gears.

To address the issue of cutting textures formed on gear tooth surfaces during the manufacturing process, a design method is proposed where the cutting textures are distributed according to a sine function. Initially, a simplified mathematical model of the actual gear tooth surface cutting texture was constructed based on a four-axis machining center and cylindrical milling cutter. Ten design cases were created with different sine function phases, aiming to minimize angular acceleration. These cases were compared with normally processed gear pairs to identify the optimal design. Subsequently, using the established actual tooth surface model, the optimal design gear pair was compared with normally processed gear pairs through noise simulation experiments. The correctness of the simulation results was verified through vibration and noise testing experiments. The results indicated that the maximum amplitude of the first-order frequency of vibration and noise sound pressure levels decreased by 14.93% and 11.16%, respectively, validating the effectiveness of the surface cutting texture optimization method. This method provides a novel solution for reducing vibration and noise in gears.

Research on spur face gear by electrochemical machining based on the complex surface mesh

Study on nonlinear dynamic characteristics of gear system with 3D anisotropic rough tooth surface based on fractal theory

To further develop the advantages of face gear drives and improve their anti-sticking performance and wear resistance, a novel method using laser cladding as the primary process is proposed; here, grinding processing is used as the secondary process, i.e., achieving tooth surface strengthening of the orthogonal offset face gear using two types of materials to form a material gradient based on a laser cladding technology. Then, grinding processing is performed using a five-axis grinding machining. First, according to the forming principle of the face gear tooth surface, we establish the coordinate system of the orthogonal offset face gear and the gear cutter coordinate system; we also derive the tooth surface equation of the virtual gear cutter and the tooth surface equation of the orthogonal offset face gear. Second, we research the principles of the laser cladding and establish a laser cladding test bed for the orthogonal offset face gear. Based on the analysis of the design of the cladding layer and the process parameters of the face gear, the selection of the scanning path, the heat accumulation during the laser cladding process, and the accuracy control of the scanning position, we perform a laser cladding experiment on the offset orthogonal face gear. Third, we establish the machining coordinate system of the face gear based on the machine tool structure and conduct a grinding experiment for the face gear after the cladding process. Finally, we analyze the morphology and hardness of the face gear after grinding. A bench test verification of the axle face gear transmission system is completed. The results show that the precision and surface hardness of the tooth surface are significantly improved after grinding. Meanwhile, the accuracy and feasibility of the laser cladding surface of the face gear are verified.

Under high speeds and heavy loads, gear tooth surfaces will be worn, which will lead to accidents. The current wear prediction model is not comprehensive, but the wear prediction model that considers the temperature field and dynamic response can provide more accurate gear wear fault early warning than previous methods. Therefore, according to the Archard model, the discrete wear prediction model of the tooth surface is deduced in this paper, and the wear evolution trend of the tooth surface is predicted and analyzed in each operation stage. The tooth surface temperature field was simulated by the finite-element method, and the tooth surface wear prediction model was improved considering its influence on materials. In addition, the dynamic model of the compound planetary transmission system was established, and the wear prediction model was improved again by using its nonlinear meshing force. Finally, the tooth wear prediction model under the interaction of the dynamic response and temperature field was obtained. A wear measurement method based on duplicate adhesive film was proposed. The wear evolution trend along the tooth length direction and the tooth width direction were measured, and the accuracy of the wear prediction model was verified. The results show that the wear depth along the tooth width direction is larger in the middle part and smaller on both sides under the influence of temperature. After the interference of the dynamic response, the wear depth along the tooth rectangle fluctuates, which is very similar to the results of the theoretical prediction model. It provides a theoretical basis for the early warning of gear health status in practical engineering.

Design of pure rolling line gear mechanisms for an arbitrary angle intersecting shafts was presented in this article. Based on the active design method of meshing line function for orthogonal shafts, three meshing types of conjugated tooth surfaces for an arbitrary angle intersecting shafts were discussed, including the parametric equations of different generatrix circles, the mathematical models of tooth surfaces, and central curves to be constructed, respectively. The validity of the active designed meshing line function was verified according to meshing equations, and the theoretical sliding rations were analyzed to prove pure rolling meshing. Then basic design parameters of pure rolling line gear mechanisms for the geometry design were determined, and the main structural parameters were obtained therefrom. Lastly, three groups of numerical examples were proposed according to mathematical models. Resin samples of line gears were processed by rapid prototyping technology and the kinematic performance of the pure rolling line gear mechanisms were validated. This paper laid the foundation of geometry and parameter design for pure rolling line gear mechanisms for an arbitrary angle intersecting shafts.

Effects of geometric design parameters and misalignments on contact ellipse of crossed beveloid gears

摘要： 为了深入研究20CrMnTi钢的磨削力生成机制与规律，基于Lawn压痕模型接触变形区和三角形截面切屑的基础上，构建立了单颗磨粒的磨削力、最大未变形切屑厚度、齿面磨削力的理论数学模型。磨削力主要源于切屑变形和摩擦，且存在磨削尺寸效应。磨削力随着磨削深度、进给速度、材料硬度和磨粒顶锥角等因素的增大而增大，然而却随着磨削速度与砂轮直径等因素的增大而减小。在砂轮磨损过程中，砂轮特性参数改变对磨削力产生较大影响。结合理论模型分析，开展了齿面局部磨削试验研究，详细分析了不同α常数情况下磨削力随磨削用量变化拟合曲线的残差和拟合优度F值。

PurposeThis study aims to research the time-varying mesh stiffness (TVMS) model for orthogonal face gear drives considering elastohydrodynamic lubrication (EHL) and provide a theoretical basis for understanding the dynamic characteristics of face gear drives.Design/methodology/approachConsidering EHL, a novel model is proposed to calculate the TVMS of orthogonal face gears using the deformation compatibility condition. First, the tooth surface equations of orthogonal face gears are derived according to the tooth surface generation principle. Then, the oil film thickness on the tooth surface of face gears is obtained by solving the governing equations of EHL. Furthermore, the proposed model is used to calculate the TVMS of face gears along the mesh cycle and is verified. Finally, the effects of module, tooth number of shaper cutter and pressure angle on mesh stiffness are analyzed.FindingsThe results indicate that when the contact ratio is greater than 1 and less than or equal to 2, the TVMS of face gears exhibits a phenomenon of double-single tooth alternating meshing where sudden changes occur. As the module increases, the overall mesh stiffness of face gears increases, and the magnitude of the sudden change at the moment of single-double tooth alternating meshing gradually increases. As the tooth number of shaper cutter and pressure angle increase, so does the TVMS of face gears. When the effect of oil film is considered, the calculated TVMS of face gears slightly increases overall and the increase in average oil film thickness leads to a rise in the TVMS. This study provides a theoretical basis for understanding the dynamic characteristics of face gear drives.Originality/valueThis study’s originality and value lie in its comprehensive approach, which includes conducting analysis based on loaded tooth contact, considering the influence of elastohydrodynamic lubrication, proposing a novel analytical–finite–element model, calculating TVMS of face gears, verifying the proposed model and analyzing the effects of typical structural parameters and oil film thickness.

Tooth surface wear is an essential factor that affects gear transmission system dynamic characteristics and must be considered in monitoring the health status of gear systems. In this study, a coupled bending and torsion dynamic model is first established. The internal excitation changes under the influence of tooth surface wear and geometric errors, including the time‐varying meshing stiffness and comprehensive meshing error, are calculated using the method proposed by the authors in a previously published paper. Subsequently, a quasi‐static wear model of a tooth surface is established based on the Archard wear formula. The two proposed models are combined to simulate the changes in the wear area and depth of involute gear pairs and to investigate the influence of tooth surface wear on gear system dynamic characteristics. Several sets of simulation results are used to demonstrate the relationship between the tooth surface wear and gear system dynamic characteristics. The coupled analysis method and findings presented in this study are of great significance for the fault diagnosis and health monitoring of gear transmission systems.