By T.T. Furman (Eds.)
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Extra info for Approximate Engineering Methods Design
Xi) OEj = % ( P E j . d. d. 2. e. e. Gaussian, distribution of tolerance variations. 0% out of tolerance band Examples Apply Gladman’s design factors to the examples in preceding sections and comment on differences between results obtained. 1. 3 RELIABILITY OF FATIGUE CALCULATIONS Values of fatigue strength or endurance limit of materials given in technical publications generally represent results from tests on standard specimens. The endurance strength of a component made from such a material is then obtained from ( f, comp = f, .
The increase in local stress levels relative to the norminal value = Values for A , B, C , Q and K are to be found in most strength of materials reference books. The f, deterministic values published usually represent a mean value from a largish number of tests. Stullen et al. (1956) indicated that these values 3. STATISTICAL ERRORS 53 represented a 50% reliability level with a standard deviation of about 8%. 2. 2. , 1956). 4 DYNAMIC LIFE/LOAD CAPACITY OF ROLLING ELEMENT BEARINGS Manufacturers of rolling element bearings define the nominal or rated life of a bearing as the number of revolutions which will be reached or exceeded by 90% of a fairly large sample.
X" = (u+Au)" = a". 4 ERROR OF A FUNCTION Where functions other than the preceding forms arise, use is made of derivations and/or finite difference relationships. This is best illustrated by some typical examples. Example In a right-angled triangle the sides are (a k Aa) and (bk Ah). Find the accuracy of the angle 4, as shown: 4 is a function of a and b, expressed as tan 4 = (X) Using differentiation, we know that d tan 4 = (1 +tanz 4). da; a . db =-- Combining (i) and (ii) we get ~. db 2. THEORY OF ERRORS 37 or d4 = b.
Approximate Engineering Methods Design by T.T. Furman (Eds.)