Hiroshige Fujio

Design of laser interferometric measuring device of involute profile

The vibration and noise of gears is one of the serious problems for devices, such as vehicles and wind turbines. The characteristics of the vibration and noise of gears are considerably affected by the tooth flank form deviation of micrometer order. The quality of product gears is controlled using a gear measuring instrument and calibrated with an involute artifact. However, the conventional calibration of the involute artifact cannot achieve a sufficient accuracy. In this report, a direct method of measuring the involute artifact using a laser interferometer is proposed. Fundamental experiments are carried out, in which the effects of the surface condition of the measured object and the effect of the driving of the artifact are investigated. It is confirmed that the proposed method enables the measurement of the detailed form of an involute tooth flank and has the potential of accomplishing a highly precise measurement of an involute artifact.

Laser Interferometric Measurement of Involute Profile by Rolling of Artifact

The vibration of gear is one of the serious problems for vehicles. The characteristics of vibration are influenced by tooth flank form of sub micron meter order and therefore strict quality control of tooth flank form is demanded. However, involute artifact, which is used to calibrate the measuring machine of tooth flank form of gear, must be measured with extreme precision. In this report, the method to measure the profile of involute artifact by laser interferometer is proposed. Fundamental research is carried out and it is confirmed that highly precise measurement is possible.

Effects of Heating Conditions on Residual Stresses, Hardened Layers and Bending Fatigue Strength of Induction Hardened Gears

This paper presents a study on effects of heating conditions on residual stresses, hardened layers and bending fatigue strengths of induction hardened gears. Residual stresses and hardened layers of gears induction hardened under various heating conditions were calculated by means of the induction-hardening simulator, which had been developed by authors. Measurements of hardened layers and bending fatigue tests of gears induction hardened under various heating conditions were carried out. Calculated hardened layers were compared with measured ones. The optimum heating condition for the bending fatigue strength of induction-hardened gears was examined.© 2003 ASME

Effects of Gear-Side Case-Hardening on Residual Stress of Case-Hardened Gears.

This paper presents a study on effects of gear-side case-hardening on residual stresses of case-hardened gears. The carbon content of each element of the FEM models due to carburizing was computed on the basis of the relation between carburizing condition and carbon content distribution. A heat conduction analysis and an elastic-plastic stress analysis during the case-hardening process of spur gears were carried out for various case-hardening conditions by the three-dimensional finite-element method (3D-FEM), considering changes of the thermal expansion coefficient and the yield stress with the temperature and the carbon content distribution, and then residual stresses were obtained. The effects of the case depth, the case-hardened part (tooth surface, gear-side and bore), the face width, the rim thickness and the standard pressure angle on the residual stress were determined.

F-0334 Simulation of Induction Hardening Process of Sintered Metal Shafts

Abstract. A FEM simulation program for induction hardening of sintered metal shafts was made up. Physical properties of the sintered metal were measured. An electromagnetic field analysis, a heat conduction analysis and an elastic-plastic stress analysis during the induction hardening process of sintered metal shafts were carried out for various hardening conditions by using the measured material data and the simulation program. The effects of the electric power and the frequency on the temperature and the stress during the induction hardening process of the sintered metal shaft and the residual stress were examined. The map for selecting the optimum heating condition (P, f) for the residual stress of the sintered metal shaft due to the induction hardening was indicated.

Residual Stress and Hardened Layer of Shouldered Shafts Due to Dual Frequency Induction Hardening.

This paper presents a study on residual stress and hardened layer of shouldered shafts due to dual frequency induction hardening (using both high- and low-frequency heat sources). Amounts of heat due to eddy current induced in the shouldered shaft were calculated by the FEM electromagnetic field analysis method, and the effect of the frequency on the amounts of heat was examined. An electromagnetic field analysis, a heat conduction analysis, and an elastic-plastic stress analysis during the single and the dual frequency induction hardening process of the shouldered shaft were carried out by the FEM, considering changes of the magnetic permeability, the resistivity, the thermal expansion coefficient and the yield stress with the temperature. The effects of the induction hardening method on the temperature and the stress changes during the induction hardening process, the residual stress and the hardened layer were determined. The validity of the dual frequency induction hardening method for the shouldered shaft was confirmed. Furthermore, a method of determining optimum coil configuration and hardening condition was indicated.

New Optical System for Reduction of Interference Fringe Density in Laser Interferometric Measurement of Tooth Flank Form of a Gear.

In interferometry measurement, it is important to obtain a clear interference fringe pattern. High density of fringes in interferometric measurement of involute gear tooth induces noises in measuring signal and makes the analysis difficult. In this paper, a new optical system to obtain an interference fringe pattern of low density is proposed. A spherical concave lens is added in the optical path of reference beam to deform the curved figure of the phase of the reference beam over the CCD plane. Selecting the focal length of the concave lens inserted, the phase difference between reference beam and object beam becomes fairly small over the CCD plane and the fringe density of the interference fringe pattern becomes lower. The effect of this new optical system is investigated.

Contact Free Measurement of Tooth Flank Form Deviation of Cylindrical Involute Helical Gears.

Interferometry using laser holography is applied for the purpose of measuring gear tooth flank form deviation of involute helical gear. The accuracy of the measurement by this method is comparable with that of the conventional measuring method using a contacting stylus. One problem with this method is that the curved tooth according to the helix angle of a helical gear interferes with the region of the flank to which the laser beam can be irradiated. The main reason for this interference is not due only to the existence of neighbouring tooth flank, but also to the fact that the incidence side of the objective tooth flank itself intercepts the beam irradiation upon the flank. To solve this problem, a method is proposed: As the first step, the objective tooth flank to be measured is divided into separate regions, and the contact free measuring is worked out. The measured values for the form deviation of tooth flank in each region are then concatenated into one on the whole plane of action, which results in a curved surface for the form deviation of the whole tooth flank of a helical gear.

Effects of rim thickness and standard pressure angle on residual stress of case-hardened internal spur gear.

This paper presents a study on the residual stresses of case-hardened internal spur gears with various rim thicknesses and standard pressure angles. A heat conduction analysis of the temperature and an elastic-plastic analysis of the stress in a cooling process for the case-hardened internal spur gear are carried out by finite element method (FEM). The effects of the case depth, the rim thickness and the standard pressure angle on the residual stress are examined. The optimum case depth for the residual stress is also clarified.

Accuracy of individual errors of spur gear measured by a single flank meshing test.

In order to obtain all individual errors which are defined in JIS, a master gear which is composed of two parts, is used for a single flank meshing test. Also, each tooth of the master gear has an effectual flank with a modified face width, which is geometrically arranged at a position in the direction of the gear axis. The experiment with the master gear was attempted for some test gears demonstrating characteristic errors. The first one has lead error and the second shows the modified curved, such as sine curve, in the meshing direction. The rest of the gears is eccentrically ground for pitch error between neighbouring teeth. Individual errors computed from the record of single flank meshing test between the master and the test gears give a good coincidence with the results from a conventional method, except for lead error.