Cylindrical Involute Gears Research Articles

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.

Estimation of Transmission Error of Cylindrical Involute Gears by Tooth Contact Pattern.

The correlation between the transmission error of gears and some factors which are usually considered to express characteristics of a tooth contact pattern, such as areal percentage and total length of simultaneous contact lines, is examined, but very poor correlation is found. A new method of estimating the transmission error from a tooth contact pattern is introduced. This is a method of supposing a triangular shape for the composite error on the actual contact line, which results in the ridge figure of the composite error surface as a function of the tooth contact pattern. The transmission error is derived as a function of this ridge figure. The results estimated by this method showed fairly good correlation with the actual transmission error, especially for a low transmitting load. Based on this method, an index value to estimate the amplitude of transmission error of a gear pair by the observation of tooth contact pattern is also introduced.

Estimation of transmission error of cylindrical involute gears by tooth contact pattern.

The correlation between transmission error of gears and some factors which are usually considered to express characteristics of tooth contactt pattern, such as areal percentage and total length of simultaneous contact lines, is examined, but very poor correlation is found. A new method of estimating the transmission error from a tooth contact pattern is introduced. This is a method of supposing a triangular shape for composite error on actual contact line which results in the ridge figure of the composite error surface as a function of tooth contact pattern. The transmission error is derived as a function of this ridge figure. The results estimated by this method showed fairly good correlation with the actual transmission error, especially for low transmitting load. Based on this method, an index value for the magnitude of transmission error is also introduced.

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.

Power Transmission Efficiencies and Friction Coefficients at Teeth of Novikov-Wildhaber and Involute Gears

New equations have been derived to calculate the power transmission efficiencies, at the meshing teeth, of two kinds of representative cylindrical gears, Novikov-Wildhaber and involute gears. The efficiencies could be calculated from the equations and the friction coefficients obtained by simple experiments with test rollers. In order to show clearly the difference in the power transmission efficiencies of the two kinds of gears, the authors designed and made two interesting gear pairs with a small number of pinion teeth (Z1 = 3) and with a high gear ratio (Z2/Z1 = 9) by applying new techniques developed by them. The effects of gear speed, tooth load, type of lubricant, etc. upon the power transmission efficiencies were clarified using two interesting techniques to measure the efficiency. The experimental results indicated that the efficiency of the Novikov-Wildhaber gears was appreciably higher at high speeds, while it was lower than the involute gears at the start of rotation and also at low speeds.

Changing of Power Transmitting Characteristics of Cylindrical Involute Gears owing to Scoring Failure

When a scoring failure occurs on involute spur or helical gears, their power transmitting characteristics become different from those before scoring initiation. Measured and analyzed states of tooth fillet stress show, that it increases considerably with progress of scoring. The increase of the maximum contact stress stays at somewhat lower level than that of the maximum fillet stress. The analysis on the thermal and lubricating conditions on or between tooth flanks shows, that the rise of frictional coefficients and bulk temperature owing to initiation of scoring is responsible for the progress of scoring. When the state of scoring is very severe, the gear vibrational excitation becomes generally very strong, but at the beginning stage of scoring the changing of gear vibrational excitation receives strong influence from gear dimensions : in some gears the initiation of scoring makes gear noise and vibration stronger, but in some other gears it makes them weaker.

Changing of Power Transmitting Characteristics of Cylindrical Involute Gears Owing to Scoring Failure

Changing of Power Transmitting Characteristics of Cylindrical Involute Gears Owing to Scoring Failure

Initiation and Progress of Scoring Failure on Cylindrical Involute Gears

Distributions of flash temperature Tf of on tooth flanks of spur and helical gears were calculated. The concentration of Tf at the beginning point of contact on leading side edge of tooth and at the ending point of contact on trailing side edge of tooth was found on helical gears, and the maximum Tf appeared on helical gears of small overlap ratio. By computer simulation for progress of scoring and by tooth flank observation of gears scored on test bench, the fashion of scoring progress on tooth and it proceeds in longitudinal direction on tooth flank of approaching contact, and then it occurs at the ending point of contact on trailing side edge of tooth and it proceeds on tooth flank of recess-contact in counter longitudinal direction.

Vibrational Excitation of Cylindrical Involute Gears Due to Tooth Form Error

A method is shown to estimate the degree of vibrational excitation of involute helical gears due to transverse and longitudinal tooth form errors and periodical change of tooth stiffness with progress of meshing. Some charts and a table are shown to give the results of this analysis for the combinations of four gear pairs of different dimensions and four different kinds of tooth form errors. The analysis shows, that the convex tooth form error is the most harmless among different kinds of tooth form error shapes such as concave, waving tooth form error, pressure angle error and so on. The effect of convex tooth form correction for helical gears is recognized the same as the case for spur gears. With increase of total contact ratio or of helix angle, the magnitude of vibrational excitation becomes strongly weakened.