tailieunhanh - Mechanical Engineers Data Handbook Episode 2

Tham khảo tài liệu 'mechanical engineers data handbook episode 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | STRENGTHS OF MATERIALS 8 Z 2M d2 3 t J 2b3 6bd2 d3 t 6 - X 9 Z 7ĩD2t 4 J nD3t 4 p density Solid disk Maximum tangential and radial stress ơr ơ ơr pp2 3 v 8 at r 0 where v Poisson s ratio v ra . X 7 z 45J J2 i 3 at top J 3 40 1 3 6 b d 6 4bd2 d3 t d2 z at bottom x 65 3d 2 b d Stresses due to rotation Flywheels are used to store large amounts of energy and are therefore usually very highly stressed. It is necessary to be able to calculate the stresses accurately. Formulae are given for the thin ring solid disk annular wheel and spoked wheel and also the rotating thick cylinder. Thin ring Symbols used p density r mean radius V tangential velocity rcu Tangential stress Ơ pv2 pr2 D2 6 Z bd d2 3 t J t b d 3 6 16 MECHANICAL ENGINEER s DATA HANDBOOK No. of spokes Value of constant c Annular wheel For axial length assumed small AJA AJA T . _ _j24r .2 Tensile stress in spokes -pv Long thick cylinder Maximum tangential stress pv2 1 2v 3 2v 4 1 v L 2 at rj Spoked wheel . pv2 3 2v r. Maximum radial stress ơr .- 1 L 8 1-v V r2 2 Greatest tangential stress ĩt pv2 cos Ớ 2r I _ c o 1 -777-7 3c sin a Ct sin a cos at angle 0 . pt 2 v Maximum axial stress 7 14 1 -v L .r2. 2 where r mean radius of rim. tensile at rt compressive at r2 STRENGTHS OF MATERIALS 17 Fatigue and stress concentration In most cases failure of machine parts is caused by fatigue usually at a point of high stress concentration due to fluctuating stress. Failure occurs suddenly i as a result of crack propagation without plastic deformation at a stress well below the elastic limit. The stress may be alternating repeated or a combina- tion of these. Test specimens are subjected to a very large number of stress reversals to determine the i endurance limit . Typical values are given. At a discontinuity such as a notch hole or step the stress is much higher than the average value by a factor K which is known as the stress concentration factor . The Soderberg diagram shows the alternating and steady .