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Engineering Tribology Episode 2 Part 4

Tham khảo tài liệu 'engineering tribology episode 2 part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 300 Engineering Tribology derive simplified expressions for the elliptic integrals required for the stress and deflection calculations in Hertzian contacts. The derived formulae apply to any contact and eliminate the need to use numerical methods or charts such as those shown in Figures 7.12 and 7.13. The formulae are summarized in Table 7.4. Although they are only approximations the differences between the calculated values and the exact predictions from the Hertzian analysis are very small. This can easily be demonstrated by applying these formulae to the previously considered examples with the exception of the two parallel cylinders. in this case the contact is described by an elongated rectangle and these formulae cannot be used. in general these equations can be used in most of the practical engineering applications. k0 Figure 7.12 Chart for the determination of the contact coefficients k k2 and k3 13 . k4 line contact k2 kj point contact Figure 7.13 Chart for the determination of contact coefficients k4 and k5 13 . TEAM LRN Elastohydrodynamic Lubrication 301 table 7.4 Approximate formulae for contact parameters between two elastic bodies 7 . Contact area dimensions 6 k2 - WR Y 3 a - nE Maximum contact pressure n - 3W Pmax 2 n ab Average contact pressure W Paverage - nab Maximum deflection X - 7174.5 V W Y 1 3 L eR n kE . Simplified elliptical integrals - - 1.0003 0.5968Rx Ry I - 1.5277 0.6023ln R Rx Ellipticity parameter 0.636 Rd Rx b 6 e WR V 3 nkE where - and are the simplified elliptic integrals k is the simplified ellipticity parameter. The exact value of the ellipticity parameter is defined as the ratio of the semiaxis of the contact ellipse in the transverse direction to the semiaxis in the direction of motion i.e. k a b. The differences between the ellipticity parameter k calculated from the approximate formula Table 7.4 and the ellipticity parameter calculated from the exact formula k a b are very small 7 . The other parameters are as defined already.