Design method for controlling gear surface cutting textures to reduce noise

The advantages of the five-axis flank milling of (developable) ruled surfaces include that (1) the machined surfaces could be very accurate and smooth and (2) the machining efficiency is high. Currently, spiral bevel gears are machined on the machine tools specially used for gear manufacturing. The disadvantages are that the cost is high for small batch, prototype, or repair. If a small group of spiral bevel gears are needed, the current methods are not valid. Thus, it is expected to machine the gears on five-axis computer numerical control (CNC) milling centers. Unfortunately, when tooth surfaces are designed based on the conventional gear manufacturing methods, they cannot be accurately machined in five-axis flank milling. This work is to develop the new technique for the five-axis flank milling of spiral bevel gears. First, a new method of designing the tooth surface of spiral bevel gears with ruled surface is proposed. Second, the cutter locations and orientations are calculated for five-axis flank milling the tooth surfaces. Third, the actual tooth surfaces are accurately represented with the cutter envelope surface in five-axis flank milling. It is confirmed that the difference of the actual tooth surface and the designed tooth surface is within the tolerance. Then, a pinion is generated to mesh with the gear, and the tooth contact analysis (TCA) is conducted. The good result demonstrates that the proposed method is valid, thus it can be used in industry.

In order to resolve the issues of low efficiency and poor precision in the traditional finishing process of hardened internal gears, a method is proposed for calculating the profile curves of a drum-shaped grinding tool suitable for mass finishing of hardened internal gears. Additionally, the impact of drum-shaped grinding tool installation errors on the tooth surface deviation of internal gears is analyzed. Firstly, the processing principle for the generation grinding of internal gears by the drum-shaped grinding tool is introduced. Based on differential geometry, meshing theory, and two-degree-of-freedom enveloping method, a mathematical model is developed for the generation grinding of internal gears. Profile curves of the drum-shaped grinding tool are obtained by solving the meshing equation between the drum-shaped grinding tool and the internal gear. Then, the tooth surface equation for the internal gear is derived in the presence of drum-shaped grinding tool installation errors. By discretizing the error tooth surface of the internal gear, the average normal deviation of the tooth surface is calculated. In the end, the distribution of normal deviation on the tooth surface of the internal gear with different drum-shaped grinding tool installation errors is acquired, and the influence of four kinds of installation errors on the tooth surface of the internal gear is analyzed. The sensitive direction is identified for drum-shaped grinding tool installation errors on the tooth surface of the internal gear. Consequently, this research provides a calculation method for the drum-shaped grinding tool fit for high-precision and high-efficiency finishing of mass-produced hardened internal gear and offers a reference for correcting deviation in the tooth surface of internal gear with installation errors of the drum-shaped grinding tool.

A general mathematical model for the generated gear tooth surfaces of spiral bevel and hypoid gears is established based on the three-axis CNC bevel gear machine. According to the principle and the method for the function-oriented design of point-contact tooth surfaces, the locus of spatial tooth contact points on the tooth surface is described on the axial plane of the gear, and then the detailed formulae for the design with the generated gear are derived from the mathematical model. The mathematical model and the formulae can be used in the function-oriented design of point-contact tooth surfaces of spiral bevel and hypoid gears with the gear generated in different types on both the three-axis CNC bevel gear machine and the conventional cradle one.

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.

The manufacturing error of spiral bevel gear tooth surface has a great influence on transmission efficiency and gear life. The error of the gear tooth surface needs to be measured accurately and fed back to the machine tool to adjust the parameters. When measuring the spiral bevel gear using a gear measuring machine, combined with the measurement theory of the tooth flank of spiral bevel gear, this paper proposed a method to compensate the inclination error in the measurement result precisely. Based on the iterative search method, a precision matching method for the theoretical and the measured tooth surface of the spiral bevel gear was designed to calculate the compensation results. The experimental results show that the inclination errors included in tooth surface measurement results reduced from more than 3 μm to less than 0.5 μm, and more than 70% of the errors are compensated by the proposed method. The accuracy of the measurement results improved significantly after compensation, and furthermore, it can provide a more accurate basis for the adjustment of machine tool parameters in the manufacturing process.

Low noise and vibration in the gearing operation is always required. Inspection by measuring gear tooth surface is a common way to investigate the source of noise and vibration. However many problems probably occur during assembling procedure, or are attributed to the bearing condition of the tooth pairs that certainly cannot be detected when inspecting each gear separately. In this paper, the newly developed method to evaluate gear tooth surface geometry based on vibration measurement is proposed. This method can be done in field. Moreover measured vibration also relates directly with the tooth bearing condition. In this method, vibration of the gear pair is measured and processed by the synchronous averaging technique to extract only the signal of interest. Then the system transfer function obtained experimentally is applied to the averaged-meshing vibration to estimate vibration excitation. Consequently tooth surface geometry directly relating with the vibration excitation can be inversely evaluated. The effectiveness of this method was verified by many experiments done by measuring the vibration of helical gears with various kinds of tooth surface forms at various operating conditions. The evaluated vibration excitations were plotted in the polar coordinate. The changes of amplitude and phase angle of the second order components were found to be suitable and could be used as an indicator to evaluate gear tooth surface form.

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 ensure the transmission precision of spur face gears whose surfaces are a kind of complex space curved surface and their representation accuracy of meshing engagement, a section lofting method to establish exact tooth surface model based on complex tooth surface grid planning principle is proposed. First, the coordinates on the tooth surface are planned. Then, a tooth surface model is established with two different types of section lofting methods according to the planned coordinates. Meanwhile, the maximal chord error of each lofted tooth facial line is measured so as to quantitatively describe the precision of the tooth facial lines and surface model. Experimental results demonstrate that an exact tooth surface model could be constructed with the methods. Moreover, it would be better to utilize the section lofting method that lofts along tooth root or tooth top.

Investigation of diagonal shaving of an involute pinion and optimization of parameters for the pinion finishing operation and of the shaving cutter design are the objectives of the current research. The paper covers the following topics: (1) analysis of the local topology of the pinion tooth surface and shaving cutter; (2) exploration of the parameters of geometry of contact between the involute tooth surfaces of the pinion and the shaving cutter; (3) determination of the optimum parameters of the shaving cutter design and of the kinematics of the diagonal shaving operation. An approach for the computation of the optimum parameters for the diagonal shaving operation of an involute pinion is developed. The approach is based on fundamental results in the theory of gearing obtained by Buckingham (Analytical mechanics of gears, Dover Publications, New York). The developed approach enables the computation of the optimum parameters for the gear finishing operation. Its application can be easily extended to and employed for the optimization of parameters for other methods of rotary shaving operations of involute and non-involute pinions, i.e., axial (transverse or conventional) shaving, tangential (or underpass) shaving, and plunge shaving operations. Computer simulation of the diagonal shaving operation proves that application of the developed approach enables shaving time reduction or reduction of the actual pinion tooth surface deviation from the true involute tooth surface.

In the measurement process of the large, complex surface, due to the errors of the installation, the errors of the machine bed itself and other factors, the probe can be over pressed. The situation of measuring interruption can be occurred. In the paper, take the measurement of the spiral bevel gear for example, by using of the gear meshing theory and differential geometry, through a series of coordinate transformations, the coordinates of the tooth surface grid nodes are calculated. Through measuring the tooth surface of the spiral bevel gear by using of Gear Measuring Center(GMC) and 3D scanning probe system, the follow-up control strategy of continuous scanning measurement based on the constant measuring force was proposed. The measurement and evaluation of the tooth surface were achieved through continuous scanning motion along the measurement path planned. In the measurement process, the measurement path was planned according to the theoretical models. The offset values of the probe were real-time detected, the constant deformation of the probe was ensured through controlling the motion of X,Y,Z axes. The mathematical model of the relationship between the velocity of each axis and the deformation vector of the probe was established. The continuous scanning measurement along the path planned based on the constant measuring force can be implemented. The requirement of the steady-state errors and real-time were meted by using of PID control strategy of subsection variable parameters. The method was finally simulated and experimented. The results showed that the occurrence of unexpected interruption in the measuring process can be effectively solved. It plays an important role for the highly-efficient and highly-precise measurements of the tooth surface.

This paper investigates the geometrical design principal of the spiral bevel gears with two contact paths from spatial conjugate curve theory. Differential geometry and gearing kinematics are introduced to derive this model. In this process, the calculation method of contact paths and tooth surface generating method are presented. According to the arguments in this paper, a process of designing the tooth surface of logarithmic spiral bevel gears with two contact paths is investigated. Then, through this process, the design of a pair of logarithmic spiral bevel gears with two contact paths is completed. Besides, the prototype is manufactured and the performance experiment is completed. Results show the maximum contact stress of spiral bevel gears with two contact paths is reduced compared to those with one contact path. Besides, the transmission efficiency of the spiral bevel gears with two contact paths can reach 98.2%.

Conical gear is an involute gear having a cone angle. When the conical gears are meshed on the intersecting axis or nonintersecting- nonparallel axis, the contact between tooth surfaces is a point contact. So the tooth surface strength is generally small. It is the Concave conical gear that was developed in order to overcome this weak point. Its tooth surface is a curved surface having the reverse crowning on the tooth surface of the conical gear. Conventionally, this tooth surface has been generated by the conical shaped wheel. By this method, however, it is not necessarily easy to make an ideal tooth surface. Therefore, we devised a new rack for generating the concave conical gear. This is the rack in which the tooth thickness of normal rack is corrected in the direction of the tooth trace. We obtained the theoretical tooth surface generated by the new rack. And, we made the gear having the theoretical tooth surface by the five axis machining center. In this research, first we developed a coordinate calculation method of the theoretical tooth surface, and next a 3D model, and finally an optimal tool path by using CAM. And we measured the curved line of the tooth surface in the plane of principal radii of curvature of the test gear and confirmed that this line agrees well with the ideal curved line. From the above results, the validity of this design and production system is confirmed.

<div class="htmlview paragraph">This paper describes and discusses the result of a comprehensive simulation analysis we have carried out to clarify the effects of gear dimensions, tooth surface modification, and manufacturing error on the static transmission error of automotive hypoid gears. Three representative factors have been analyzed contact ratio, crowning and pitch error because these characteristics play the most important role in tooth dimensions, tooth surface modification and manufacturing error. The analysis has clarified the effect of each factor on gear noise, making it possible to prepare a guideline for optimal design of gear dimensions and tooth surface modification under various conditions.</div>

Conical involute gears used for marine transmissions are mostly helical conical involute gears. Besides these gears are not intersecting axis gears but also nonintersecting-nonparallel axis gears. The contact between tooth surfaces of a pair of gears is the point contact. Hence the tooth surface durability is generally small. In order to overcome this weak point, one of the authors invented a new type of conical gear, which is called conical Concave conical gear has higher tooth durability than the conventional conical involute gear. In this research, a new method to generate the helical Concave conical gear is presented. First the principle of generating method is introduced. Theoretical tooth surface is analyzed. Secondly test gears are ground. Tooth surfaces of the test gears are measured and compared with theoretical ones. Two tooth surfaces are in good agreement.

In many situations, the polymer gears are the perfect replacement for traditional metal gears. Compared to metal gears, the polymer gears will generate more heat at the gear tooth contact surface and more wear loss. Hence, this study aims to decrease the wear loss and increase the load-carrying capacity of the polymer gears. To achieve this, the reinforcement materials were added to the base polymer gear material. In this study, Nylon-66 was chosen as the polymer matrix material and an isolated glass fibre and steel grid were used as the reinforcement materials. Three different types of polymer spur gears such as Polyamide Gear (Nylon-66), Reinforced Polyamide Gear (Nylon-66+Glass Fibre), and Hybrid Glass Fiber Steel Grid Gear (Nylon-66+Glass Fibre+Steel Grid) named PG, RPG and HGFSGG were fabricated using injection moulding machine and each type of gears were compared for wear loss and specific wear rate under the similar testing conditions. The wear test was performed in the Forschungsstelle fur Zahnrader und Getriebebau (FZG) test rig at 1500 rpm with an applied load of 20 N for 12.5 h continuously. From the test results, it was identified that HGFSGG polymer spur gears have exhibited a lower surface temperature and better wear properties compared to the other two types of spur gears. From the Scanning Electron Microscope (SEM) analysis, it was noticed that the PG spur gear exhibited deep and uniform wear at the gear tooth surface. In contrast, RPG spur gear exhibited glass fibre distortion and abrasive-type wear. The SEM micrograph of the HGFSGG spur gear reveals the presence of very few surface flaws in the gear tooth surface.