Optimal design of paired tapered roller bearings under centred radial and axial static loads

Abstract

-Based on the relationships from the ISO 76 standard, this paper optimizes the internal dimensions of tapered roller bearings for maximum static load capacity. A bearing system formed by two identical bearings is assumed, subjected to whatever combination of centred radial and axial forces. It is shown that the static capacity increases linearly with the roller infill, with the ratio of roller length to roller diameter and with the square of the pitch diameter of the roller set. Further, given the ratio of axial to radial force, an optimal contact angle exists which maximizes the static capacity of the bearing pair, regardless of the actual bearing size and ratio of roller diameter to pitch diameter. The optimization procedure can either be used to design custom-made bearings or to pick from manufacturers' catalogues the bearing with the best contact angle for any assigned loading condition.

Optimal design of tapered roller bearings for maximum rating life under combined loads

“…In this range of operation, special supplies [31,32] or custom constructions are needed to achieve the maximum load capacity. Figure 8 compares the optimal angles from Table 3 (optimization for dynamic loading) with the corresponding optima (Table 3 of [21]) for the static loading of taper roller bearings. Figure 8 shows that the optimal dynamic contact angles are generally higher than their static counterparts for equal δ lim .…”

“…Within the wide range of dimensions and contact angles considered, the maximum error in Table 1 (see Appendix) is about 8% (bearings 301230-A and T7FC095) while the average absolute error is just 4%. Errors of the same order of magnitude were calculated by Dragoni [21] for the static load rating of the same bearings listed in Table 1.…”

“…Equation (19) shows that the basic rating life, L 10 , is proportional to the functions φ and ω 10 . From (21) we see that, for given radial load F r , function φ increases more than quadratically with the filling ratio, ζ, and the aspect ratio, λ, and goes up with the sixth power of the pitch diameter, D. Function φ can be regarded as a control factor through which the basic rating life, L 10 , can easily be made large at will by increasing the pitch diameter. Similarly, function ω 10 in Equation (19) can be interpreted as the intrinsic rating life of the bearing system obtained when the filling ratio, the aspect ratio, the pitch diameter and the radial load assume unit value.…”

“…Papers dealing with the optimization of bearing features have appeared only lately, aimed at maximizing one or several performance properties of ball bearings [5][6][7][8][9][10][11], cylindrical roller bearings [12,13] and tapered roller bearings [14][15][16][17][18][19]. For a detailed review of the literature on ball and cylindrical roller bearing optimization see [20,21].…”

“…Relying on easy step-by-step calculations and with no need for specific optimization backgrounds, that procedure gives the macro-geometry of the bearing (roller diameter, roller length, pitch diameter of roller set, number of rollers) which maximizes the static and the dynamic load ratings under realistic size constraints. A later paper by the author [21] has extended the research to radial bearings with tapered rollers under radial and axial static " X " " O "…”