Flank Form Research Articles

The Optimum Designing Method of Heavily Loaded Involute Spur Gear Tooth against Scuffing Failure.

A mathematical function of one variable is proposed that can express the reasonable transverse tooth form of a cylindrical involute gear with profile correction. The algorithm to obtain the optimum transverse tooth form of 2-dimensional involute spur gears in the term of minimum frictional heat generation on tooth flank is shown. The 3-dimensional tooth flank form of the gear with longitudinally crowned tooth lead correction is rather easily decided based on the transverse tooth form obtained. The tooth flank form of heavy-duty traction gears of big locomotives have been redesigned by this method. Several months of field operation has shown that the newly designed gears are fully free from the scuffing failure of tooth flank. By contrast, the gears designed by the old conventional method could not avoid tooth flank failure.

Laser Holographic Measurement of Tooth Flank Form of Cylindrical Involute Gear

The form deviations of tooth flanks of spur and helical gears obtained by using a laser holographic interferometer are compared with the results of the conventional measuring method using a contacting stylus. The objective tooth flank which has a rough finish compared with optical parts is irradiated with a laser beam in a large incident angle to obtain the reflected ray from it. Image patterns of the interference fringes for tooth flanks with various types of form deviation are obtained, and they are transformed to the form deviations from the target tooth flank form. The algorithm of this transformation is shown: the brightness information of the image of the interference fringe on the CRT is converted to the amplitude of form deviation defined on the plane of action of the gear according to the phase difference of light beam by using the phase stepping method. A partial measuring procedure for helical gears is proposed which achieves the same level of accuracy as the conventional method using a stylus.

Proper Setting of Form-Cutting Machine of Hypoid Gears using Measured Tooth Flank Form.

A new method to provid hypoid gears of high quality of tooth flank form is developed for the form cutting system of Gleason gears. Using the newly developed tooth-profile measuring machine, the relationships between the machine setting and the tooth flank form of gears are examined quantitatively. The proper setting values of the gear cutting machine can be determined by use of these relationships and by the differences between the target tooth flank form and the measured tooth flank form of the gears cut by the machine.

Development of a Grinding System for Sharpening the Cutter of Gear Shape and Evaluation of its Performance. 2nd Report. Construction of Gear Tooth Grinder and Examination of its Principle.

A grinding machine for involute helical gears is constructed that can generate arbitrarily three-dimensionally corrected tooth flank forms by using a grinding disc without transverse movement. Basic structures such as the coordinate system and the axes of the grinding machine are designed and a new antibacklash speed reducer using involute worm gears is invented to raise the Computer Numerical Control (CNC) performance for synchronous action between the axes for generating tooth flanks. An integrated procedure of action of the computer to simulate the tooth flank form to be generated and that of the actual grinding machine is proposed. This grinding system shows a good performance for achieving the intended three-dimensionally corrected tooth flank form.

Measurement of Three-Dimensional Curved Surface of Machine Part Using Holographic Interferometry. 2nd Report. Tooth Flank Form Deviation of Spur Gear.

Tooth flank form deviation of spur gears is measured by laser holographic interferometry. In order to get the diffracted ray from the objective tooth flank to be measured in definite directivity, a laser beam is irradiated with large incident angle to the surface which has a considerably rough surface finish. The conversion of the coordinates of the image figure of the objective surface, i. e. the gear tooth flank, on the CRT to the coordinate system of the gear is worked out by the fitting of contour form of simulated and observed images on the CRT. By using this method, image patterns of the interference fringe of some tooth flanks with various kinds of form deviation were measured. The algorithm of transformation from these fringe patterns to tooth flank form deviation by converting brightness of interference fringe images on the CRT to the amplitude of form deviation defined on the plane of action of the gear via phase difference of the light beam by a fringe scanning device is shown. The measured tooth flank form deviation is compared with the results of a conventional measuring method of tooth form using a contacting stylus.

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.

Acceptance Condition for Toothform- and Toothtrace Accuracy of Cylindrical Involute Gears and its Effect On Power Transmitting Characteristics : 1st Report, Acceptance of Gears with Bad Tooth Flank Form

To express the quality of the form of a gear tooth flank, the error surface defined as the difference between an ideal involute helicoid and an actual tooth flank of cylindricai involute gears expressed on the plane of action, is useful. Here, a method to illustrate the error surface for the form of a gear tooth flank from some tooth form- and tooth trace checking curves measured along some definite positions on a tooth flank is introduced. This method vas used in a simulation of power transmitting characteristics of cylindrical involute gears, and the problem of gear acceptance was discussed. It was found to be a problem to receive gears whose quality was actually out of tolerance and showed poor performances. The results of the state of tooth flank loading in the simulation suggested that this mistake occured due to the insufficiency of the test method of gear quality at acceptance.

Acceptance condition for toothform- and toothtrace accuracy of cylindrical involute gears and its effect on power transmitting characteristics. (2nd report. Difference between intended and actual performance of gears).

There is uncertainty about actual gear accuracy due to improper acceptance codes of gears. In this paper the magnitude of the influence of this uncertainty on the state of tooth fillet stress, contact stress of tooth flanks, flash temperature on tooth flank and exciting force of machine vibration caused by gear meshing are discussed. It is pointed out that there were some cases in which the deviation of the tooth flank form from the intended one, by which the maximum values of contact stress, flash temperature and gear vibrational excitation were strongly affected, could not be found by the normal gear accuracy checking procedure defined in current standard specifications. It was shown that the influence of the deviation of the tooth flank form was so large, that the reliability of the gears could not be guaranteed, and that the machine vibration or gear noise of the machine become far removed from the intended level or specification limit. Gear accuracy also changes the amount of gear alignment error, which affects the power transmitting characteristics of gears.