By T.T. Furman (Eds.)
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A) or = 300007). 000 233. (b) 40 APPROXIMATE METHODS IN ENGINEERING DESIGN Case 2 Errors of a and b are in the same direction and of equal magnitude, we have A4=+ -3Aa-Ab 10a :. ha = 5 . e. relative errors will be constant. 2. e. no effect on accuracy of angle @ at all. 60. e. OOOO 29 = 0 . 6 0 . 8 Determine the variation in stiffness of a cantilever leaf spring resulting from tolerances of its dimensions and the Young’s modulus of the material. 9 Wallingford Spring Pressings Ltd produce Belleville disc springs and recommend the formulae below for calculations of suitable springs for functions required: P = axial load (newtons) Pflat= load to flatten disc f = deflection (mm) f / h = ratio deflectionlfree height s(xl = stress at (x) in (N mm-’) K , , K,, K , C = factors = factor depending on ( D / d ) and E depending on (h/t)and (f) tDt3) Pflat= K , .
Case A 16 square grid, h, and since we have for point (1) and since = $a. 21) we get for point (0) 28 APPROXIMATE METHODS IN ENGINEERING DESIGN 1. 375h; GO 4% = 0 (for a 16 square matrix) (Aiv) Case B 36 square matrix h, = 4 6 . 1925 2 . . e. 7% higher. 2. Approximate computations. 3. Relationships between trigonometric and exponential functions. sin x - ,xi - -xi 2i exi+e-xi cos x - sinh x -~ - 2 ex-e--y 2 REFERENCES Balfour, A. and McTernan, A. J. (1967). ” Heinemann Educational Books, London.
1 Rated life. The International Standards Organization (ISO) definition of rated life is the number of revolutions that 90% of all bearings will complete or exceed before first evidence of fatigue failure develops. e. where the axes of the inner and outer races are “perfectly parallel”. Misalignment can be caused by errors in manufacture and/or assembly and also by deflections from external loads. e. nonself-aligning bearings act as elastic fixture points which experience built-in bending moments with consequent internal eccentric load distributions and reduced bearing life.
Approximate Engineering Methods Design by T.T. Furman (Eds.)