S1103-3-4 表面改質による歯面のなじみ性の変化が浸炭歯車の歯面強度に及ぼす影響([S1103-3]伝動装置の基礎と応用(3):強度)

Fine particle bombarding (denoted as FPB) is one of the surface modification processes that makes fine (20-200μm in diameter) and hard (Hv 750-1000) particles impact with the metal surface at a high speed (more than 100 m/s), which is similar to shot peening. Although FPB has been already applied to extend lifetimes of a die and a metal cutting tool, and to reduce friction on the contact surface, the influence on the tooth surface strength of gears has not been clarified. The purpose of this study is to determine quantitatively the effect of FPB on the tooth surface strength of carburized gears and to clarify the factors caused by FPB that influence on the tooth surface strength. First, the author examined the tooth surface properties such as residual stress, roughness, hardness, surface texture, etc. using test gears processed by the FPB under three different conditions of arc height. A test gear performed by conventional impeller-type shot-peening was also used for comparison with the FPB. Next, durability tests were carried out using the gears to measure the tooth surface strength. The results showed that the FPB is effective to increase the tooth surface strength compared to conventional shot-peening. In the 1st report, the effect of the FPB on the tooth surface properties is described.

Because the life of power transmission gears has come to be greatly affected by the tooth surface strength, it is an important problem to clarify the influence of tooth profile and helix deviation on the tooth surface strength of carburized helical gears in a practical design. In this research, first, the experiments were carried out to measure the tooth surface strength using the test gears with six kinds of different tooth surface deviation. Next, this experimental result was arranged as S-N diagram by using Hertzian contact stress calculated in consideration of the tooth surface deviation. The influence of the tooth surface deviation on the tooth surface fatigue life was quantitatively shown by the empirical formula. Using the obtained result, the influence which the kind and the amount of the tooth profile and helix deviation exerted on the tooth surface fatigue life was considered. In addition, the effect of crowning was discussed.

The contact between tooth surfaces of the conical involute gear is a point contact. Therefore, tooth surface strength of the conical involute gear is smaller than the cylindrical gear. In the design of the conical involute gear, the evaluation of tooth surface strength is more important than bending strength. Tooth surface strength is evaluated at the allowable contact stress of tooth surface. A fatigue test is performed in order to evaluate this allowable contact stress. But, tooth surface is worn out during this test. Therefore, it is difficult to calculate the contact stress. Wear of tooth surface is influenced slip. Slip is evaluated the spesific sliding. But, there is no theoretical formula of the conical involute gear's spesific sliding now, so this theoretical formula is asked on an approximation target in this research. The relation between wear of the test gear and the spesific sliding is considered.

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.

A design guide for very small power transmission gears considering tooth surface strength and manufacturing cost

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 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.

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.

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.

Nowadays, infrared imaging technologies have been developing in various industrial fields. We therefore focus on the infrared ray imagery as a novel method to estimate the gear tooth meshing. In the present report, a high response infrared thermography, which could take a middle infrared ray image of around 4 μm wavelength, was used to investigate the temperature hysteresis on the tooth contact surface of hypoid gear under running conditions. We installed the high reflective mirror of infrared ray at the opposite side of the gear tooth meshing point to obtain the tooth surface images around the entire gear, and estimated the variation of tooth surface temperature at the duration from a tooth meshing to the next tooth meshing. As a result, it is clear that the temperature on the tooth surface after meshing can be modeled by first order time delay and the maximum temperature is affected by contact pressure, relative sliding speed between tooth surfaces and average peripheral speed of tooth surface. This proposed method is effective to evaluate the temperature hysteresis on the tooth contact surface of hypoid gear.

To control the meshing performance of hypoid gear drive, current local conjugate theory and local synthesis method establish a relationship between the relative motion and local geometrical properties of the mating surfaces at one reference point. Theoretically, both local conjugate theory and local synthesis method cannot ensure the contact performance on the entire tooth surface resulting in uncontrolled contact pattern and undesirable transmission error. A global synthesis approach consisting of a machine-tool settings calculation model, a tooth contact analysis model, a meshing quality assessment function, and a swarm intelligence algorithm are proposed. The direction, area, and shape of the contact pattern and the amplitude of the intersection of two adjacent transmission error curves are taken as the evaluation indexes. Three curvatures of the design pitch cone of the pinion are taken as the control variables. A global selection space is then established within the reasonable range of the curvatures. An improved multiple population genetic algorithm is employed to find the optimal set of the curvatures to achieve the target values of the evaluation indexes. To avoid the edge contact and corner contact condition, a feasible region is defined on tooth surface and the contact patterns on the gear and pinion surfaces are all confined within the area. The optimized contact patterns obtained by the loaded tooth contact analysis method are similar to those obtained by the proposed approach, thus demonstrating the effectiveness of this methodology. The main novelty of this approach is to translate the derivation of the mathematical relation between the curvatures of the mating surfaces and the contact properties to solving a multi-objective optimization problem of the meshing quality indexes by the intelligence algorithm.

Purpose During the oil lubrication process of aviation herringbone gears, lubricating oil is injected into and spreads around the tooth surface. Its spreading characteristics directly affect the lubrication state and transmission efficiency of gears. This study aims to investigate the effect of changing the injection parameters and gear operating conditions on the oil film deposition during injection lubrication. Design/methodology/approach The computational fluid dynamics method was used to establish the computational domain for the simulation and optimization using an orthogonal test. The oil film spreading and thickness of the tooth surface were calculated with the change in gear speed, fuel injection distance and fuel injection speed. Optimized oil injection lubrication parameters were obtained, and design ideas were provided for the oil injection lubrication analysis of aviation herringbone gears. Findings Under different operating conditions, such as varying the injection speed, gear rotational speed and injection distance, there were differences in the distribution of the lubricating oil film formed on the tooth surface. The thickness of the oil film decreases as the distance from the injection port increases. The thickness of the oil film deposition can be increased by increasing the injection velocity and reducing the gear rotation speed. The injection distance had a relatively small effect on the spreading thickness of the deposited oil film, affecting only the dynamic spreading process of oil film deposition. Furthermore, the simulation results are compared with the analytical calculation results, and finally the experimental verification is carried out. Originality/value Oil spray lubrication characteristics are important for achieving precise gear lubrication designs in the aerospace field. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-08-2023-0250/

In mixed lubrication, the interplay of lubricant flows, solid asperity contact, and material wear between tooth surfaces creates complex and unpredictable contact states on tooth surface. To comprehensively understand the interaction between the lubrication and wear characteristics of the rough tooth surfaces of helical gears, this study established a mixed lubrication sliding wear calculation model for helical gears based on the mixed elastohydrodynamic lubrication model and Archard’s model. Specifically, the study aimed to examine the effects of surface topography features on average film thickness, contact area ratio, and accumulated wear at the meshing point. The findings demonstrated that the texture and power spectral density distributions of a non-Gaussian reconstructed surface closely resembled those of the actual ground surface. Furthermore, for non-Gaussian rough surfaces, a larger wavelength ratio enhanced microwedge motion, which increased film thickness and reduced wear. Additionally, a negatively skewed surface demonstrated better lubrication performance compared to both positively skewed and Gaussian surfaces. This improved performance is evident in the smaller contact area ratio and lower accumulated wear value of the negatively skewed surface.

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.