5 軸マシニングセンタによるコンケーブコニカルギヤの設計製造システムの構築

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.

A control method of finishing dimensions of a helical concave conical gear, called center-ball measurement, is newly developed. The tooth surface of the concave conical gear is different from that of the conical involute gear, which is concave compared to the tooth surface of the conical involute gear. So the over-ball measurement of the conical involute gear can not be used at it is, but can be applied to a special measuring conditions. This center-ball measurement is based on the over-ball measurement of the helical conical gear. But in this method, the measuring ball, which is composed of two hemispheres, must be used. So the over-ball diameter can not be measured, but a center-ball diameter, which is the distance between two ball centers, can be measured instead. In this research, first the measuring condition is established. Second the center-ball diameter is obtained analytically. Finally, the center-ball diameter is verified through experiments. The experiments prove that this method has opened a door to the control of finishing dimensions in hobbing and grinding of the helical concave conical gear.

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.

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.

In this study, we call an internal gear having conical angle as the internal conical gear. In the case of conjugating with spur gear, this gear can transmit rotational motion between intersecting shafts. Also in the case of conjugating with conical gear, there is possibility of adjusting backlash by axial movement. Therefore, as a first step of the study we obtain theoretical tooth surface of the internal conical gear cut by gear shaper. Next we measured tooth surface of the test gears and compared them with theoretical one. Finally the tooth-bearing test confirms that theoretical analyses holds true.

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.

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.

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.

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.

Conical involute gears (beveloids) are used in transmissions with intersecting or skew axes and for backlash-free transmissions with parallel axes. Conical gears are spur or helical gears with variable addendum modification (tooth thickness) across the face width. They can mesh with all gears made with the same tool. The geometry of such gears is generally known, but applications in power transmissions are more or less exceptional. ZF applications so far include marine transmissions with inclined output shafts and low backlash robot transmissions. The latest development has been realized for the AWD version of a six-speed automatic transmission. Here, the torque must be transmitted from a center differential to a front-axle bevel gear. By means of conical spur gears, it has been possible to realize an inclined drive shaft which offers considerable advantages in terms of installation space. This lecture deals with the development of conical gears for vehicle transmissions: basic geometry, design, production and testing.

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.

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.

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.

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.

Based on the homogeneous coordinate transformation method and finite element simulation method of a whole hobbing machine, this paper proposes a highly applicable force-induced error model for a high-speed dry hobbing machine. The number of parameters needed in the error estimation can be effectively reduced by using this model, which has great value in industry application. According to the engagement features of the conjugating surface and the principle of two-degrees-of-freedom hobbing, the meshing equation was deduced and the force-induced errors of the system were mapped to the normal errors of gear surface. In this way, the mapping relationship between different kinds of force-induced errors and hobbing precision can be obtained. Then, the theoretical tooth surface and the real tooth surface under the influence of force-induced errors were respectively calculated by using a numerical simulation method. Based on numerical simulation results, the mathematical relationship between the tooth profile root-mean-square error (RMSE) and the compensation variables was obtained, as well as the optimal value of the compensation variables. The following experimental results validate the feasibility and accuracy of this error compensation method. This study has an important guiding role in the improvement of dry gear hobbing precision.