This is the first of a series of papers on the design of the tooth profile relief of both low and high contact ratio spur gears and its effects on transmission error (TE ) and tooth loads. A systematic approach to profile relief design is introduced. The process of profile relief analysis is based on a number of simplifying assumptions to ease the understanding of the relief design. Useful relief cases determined during the simplified analysis are further investigated, with realistic parameter values such as variable stiffness, manufacturing tolerances and so on, in other papers of the series. Experimental validation of the cases proven to be good are also given in forthcoming papers.In the present paper, the systematic approach is applied to low contact ratio (LCR) spur gears first with some design regions and to high contact ratio (HCR) spur gears with some new and promising design regions and rules. Several smooth transmission error curves at different loads are shown to be possible for the relief designed, hence allowing a range of loads with uniform motion transfer. The advantages of HCRG over LCRG in terms of smooth TE curves and tooth load values are noted.

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The design of shrink-fit precision gear forging dies based on strength considerations using an analytical (thick-wall cylinders) approach and the finite element method are compared. While the two methods, analytical and finite element, agree well for the dies with no irregularities (gear teeth), the finite element method predicts much higher stress values than those of the analytical approach for the dies with gear teeth. These high stresses are considerably reduced by reoptimizing the geometric parameters, such as the interference between the die and the ring.

This is a design/development study on helicopter transmission that had improved performance in terms of vibration and noise behaviour, in compliance with surface durability requirement, compared with what was achievable with previous designs. Different spur gears of both low and high contact ratios (HCRs) have previously been designed and tested in helicopter transmissions with different profile modifications but with limited performance improvement. The desired performance, however, was achieved through the use of a suitable profile modification for the HCR spur gears in mesh. Profile modification type of ‘double relief’ was applied for the first time to two sets of helicopter transmission spur gears, both with HCRs. Possibility of corner contact was avoided while achieving a relatively low value of peak-to-peak transmission error in ‘full load range of gears operating conditions’, which was not usually satisfied by conventional profile designs. With the new profile modification design, a measured noise level reduction of 7—11 dBA and a casing vibration reduction of two to four times were achieved at teeth meshing frequency. The new design philosophy presented in this article is pending worldwide patent by the authors.

With reference to the previous articles of the author(s) based on the systematic approach to the profile relief design of both low contact ratio and high contact ratio spur gears, some guidelines are drawn for the use of short and double reliefs of the HCRG profile design under the effect of realistic parameters like variable tooth stiffness and manufacturing errors regarding the profile relief values. Root stress of the double relief can be minimized by optimizing the maximum tooth load value, hence the tooth load diagram with constant and variable tooth stiffness. Interaction of the manufacturing errors with the relief parameters is put into a form of analytical relation between manufacturing grades, hence the manufacturing tolerance and some gear parameters such as contact ratio, base pitch, and the load at which the smooth transmission error curve is required. In case of double relief, design load plays a major role in its selection. A relation and also a tabular form of guideline are given: for the required manufacturing grade if the contact ratio and other gear parameters are known and for the minimum contact ratio required if the manufacturing grade of the gears are known for either of the two cases short and double reliefs.