コニカルギヤの歯面疲労におけるすべりの影響(S52-3 機素潤滑設計部門第10回卒業研究コンテスト(3),S52 機素潤滑設計部門第10回卒業研究コンテスト)

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.

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.

Vibration-based updating of wear prediction for spur gears

Sliding on gear teeth working surfaces has negative effects on the performances of gears, such as tooth surface wear, pitting, etc. In order to reduce the gear sliding during high speed and heavy load, a new type of pure rolling gear, named as an asymmetric logarithmic spiral gear, is designed referring to the characteristics of the Issus planthopper gear. To explore the meshing principle of this kind of gear, the equations of the teeth surfaces, their working lines, and contact lines are all derived. Then, the tooth profile parameters and slip rate are calculated. To ensure accurate gear engagement, the gear interferences are analyzed to build the gear models. Subsequently, the gear is performed to simulate its working condition by the finite element method. Furthermore, the results are compared with that of the pure rolling single arc gear. As a result, the asymmetric logarithmic spiral gear behaviors less contact and bending stresses than the pure rolling single arc gear under the same work condition.

Purpose Crossed helical gears have point contact and their surfaces are subject to high surface stress. Contact stress and root tooth stress are the most common sources of failure in crossed helical gear. This paper aims to study the load-carrying capacity and performance of crossed helical gear teeth with different gear tooth profiles. To overcome defects and reduce the sensitivity to small shaft angle changes. The combined tooth profile is designed to reduce the bending stresses, contact stresses and tooth deflection, and prevent pinion failure in the gearbox. Design/methodology/approach The principle of the method is a line contact is introduced instead of a point contact between two teeth in mesh with each other. The tooth surface of the helical gear is designed and cut by a modified tool. Higher normal pressure angles like 25° and 35° are used. The modified involute is accomplished to eliminate interference between the teeth. Engineering software packages have been applied to generate all crossed helical gears gear profiles. The modification is compounding curves consisting of an epicycloid-involute-hypocycloid gear teeth profile generated by the cutter modified. Findings The stresses in the crossed helical gear teeth profile were reduced by increasing the normal pressure angle values. Using a 35° pressure angle the enhancement percentage in contact stress and teeth fillet region will be about 29.345% and 15.421%, respectively. The best enhancement in a gear’s resistance is the epicycloid-involute-hypocycloid gear teeth profile. The enhancement was 32.610% and 18.588%. The skew in line of action in skewed helical gear will be sensitive when the crossing angles are small. Their teeth surface tends to be easily worn out; however, the wearing process will be reduced by using a proposed gear teeth profile. Practical implications The gear teeth to be modified are cut by a shaper process. The modifying rack cutter of this study can be used as a reference for creating a different helical gears sample. The helical teeth surface is modified to become an envelope of the other. This makes an original point contact change into a line contact. The epicycloid-involute-hypocycloid gear teeth profile is preferred for a higher contact ratio and a large load capacity. This work explicitly introduces a new method of kinematic consideration to improve the load capacity of crossed helical gear. Originality/value This paper showed some novel results by the unique shape of the rack-cutter designed to generate different helical angles and different gear positions. In the future, it will make valuable contributions to the further development of the dynamic performance of a crossed helical gear system through the study in the field of using asymmetric teeth profiles of helical gears with tip relief as the manner to enhance the crossed helical gear performance. Investigation of crossed helical gear by applying a predesigned parabolic function of transmission error enables the absorption of linear discontinuous functions caused by misalignment.

Since gears transmit motion by meshing teeth, it is hard to avoid problems which wear and damage to the tooth surface. Because Tooth surface wear is difficult to predict, the approach to the wear problem still often relies on empirical rules and symptomatic measures. If the undermining by wear can be predicted by mathematical formulas, it may allow engineers to solve wear issues in model-based development, or to consider wear resistance from the design state. Therefore, the development of wear prediction formulas seemed like a very valuable goal, so the authors decided to work on it. In this paper, as a step for the final goal, the gear driving test was conducted using multiple gears with different tooth surface roughness. Then to detect changes in tooth profile, the tooth profile error was measured, and wear depth was calculated. Moreover, surface roughness on teeth was measured, and the relationship between surface roughness and wear depth was investigated.

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.

In this paper, a study on calculating optimum gear ratios of mechanical driven systems using a chain drive and a two-step helical gearbox with the first step double gear sets is introduced. To determine the optimum ratios, an optimization problem was conducted with the selection of system cross section area as the objective function. Also, several input parameters consisting of the total system ratio, the wheel face width coefficients of the both helical gear sets, the allowable contact stress and the output torque were investigated. Furthermore, a simulation experiment was run to study the impacts of these parameters on the optimum ratios. The results show that the optimum ratios can be obtained with high accuracy by using recommended models.

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

Carburized gears with tooth surfaces in different states were prepared by changing surface treatments, and gear surface fatigue endurance tests were carried out to clarify the influence of running-in performance on the tooth surface strength. Furthermore the relation between the running-in ability and the surface properties was discussed.

Loaded tooth contact analysis (LTCA), deformation, and stress calculations of three types of thin-rimmed spur gears with inclined webs at the left side, the center, and the right side of the tooth are conducted in this paper with finite element methods (FEM) combined with a mathematical programming method when these gears are engaged with a solid mating gear. The contact stresses on the tooth surfaces, the bending stresses at the tooth roots, and the joint stresses of the rim and the web are analyzed as the web position and the web angle are changed. It was found that the web position and the web angle of the thin-rimmed gears have a significant effect on the tooth contact stresses, the root bending stresses, and the joint stresses. The maximum contact stress of the right web gear becomes very small when the web is inclined from 0 to 30 deg, and it increases again when the web angles are changed from 45 to 60 deg. This interesting relationship between the web angle and the tooth contact stresses of thin-rimmed right inclined web gears is used to absorb the misalignment errors in the gears and improve the partial tooth contact pattern resulting from the misalignment errors. A calculation example is provided to illustrate how to improve the partial tooth contact patterns in gears with misalignment errors.

This research employs finite element analysis for simulation and calculation to investigate the causes of tooth wear in coal mining machine transmission gears and how it affects gear transmission performance. Utilising Hertz theory, we calculated the maximum contact stress and Hertz half-width during the gear transmission process. A three-dimensional geometric model of the coal mining machine’s right rocker transmission system was created using Pro/E software, which was subsequently analyzed with ANSYS/LS-DYNA for gear meshing. The wear quantity on the gear tooth surface was determined using the Archard wear model, disregarding the effects of lubricant and gear tooth temperature rise. Our simulations revealed the wear distribution and changes in wear amount across various tooth surface wear models under different operating conditions. Notably, we found that wear quantity is directly correlated with tooth wear range and contact stress, with significant wear occurring at the top and root of the tooth. Furthermore, we conducted laser cladding remanufacturing experiments, optimizing process parameters to enhance wear resistance and fatigue strength. The microstructure of the remanufactured tooth face exhibited homogeneity and a lower friction factor than new surfaces. This study offers novel insights into the wear mechanisms of coal mining machine gears. It demonstrates the effectiveness of laser cladding technology in enhancing gear performance, providing practical implications for the design and maintenance of gear systems in harsh operating environments.

Based on the analysis of precision moulding mechanism for cylindrical gears with arcuate tooth trace (arc gear), the equation for tooth flank of arc gear was derived preliminarily and the ideal concave and convex tooth flanks were got by MATLAB simulation to achieve graphics rendering. On this basis, with UG NX8.0, the accurate three-dimensional modelling of arc gear was established to be used for the finite element analysis. Then, for the problem that there is no standardised bending strength calculation formula of arc gear, with the aid of finite element method (FEM) this paper studied the relationship between tooth line radius and bending strength. With FEM analysis performed, it was confirmed that under the same conditions, the bending strength of arc gear could be significantly improved compared with that of spur gear and helical gear, and that variation curve of tooth root stress was obtained under the different tooth line radius. Therefore, the analysis method provides engineering applications value under the high-speed and heavy-load working conditions and theoretical basis for the strength theory and design of arc gear.

In response to the new requirements for face gear transmissions in the latest heavy-load helicopters, this paper investigates the impact of pressure angle variations on the geometric contact and performance of asymmetric face gears. Firstly, using meshing theory, the tooth surface equations for asymmetric rack cutter, shaper, and face gear are derived, and the parameterized 3D models are created. Secondly, the line of action (LOA), contact ratio, contact point curvature, and load sharing ratio considering multi-pair contact (MPC) under different pressure angles are analyzed. Then, a wear calculation model based on the Archard wear equation is developed, detailing the tooth surface wear depth calculation. Finally, a case study calculates the contact stress and wear depth under different pressure angles is presented. The results indicate that appropriately increasing the pressure angle effectively lower the contact stress and wear depth on tooth surface, although further increases degrade meshing performance. The gear pair with a pressure angle of 30° in the case study exhibits optimal performance. This study provides a reference for optimizing asymmetric face gear meshing performance under various pressure angles.