The concept of reliability is greater importance in the design of various machine members. As reliability is now an exceedingly important aspect of competitiveness, there is need to design reliability into products. Conventional engineering design uses a deterministic approach. It disregards the fact that the material properties, dimensions of components and the externally applied loads are statistical in nature. In conventional design these uncertainties are covered with factor of safety, which is not always successful. Probabilistic design is a concept where by engineering variables are treated statistically. Each variable is modeled to reflect a spectrum of possible values. The growing trend towards uncertainty is to use the probabilistic approach. In the present work three types of gears namely spur, helical and bevel gears are designed using the reliability principles and their results are compared with those obtained by the deterministic procedure. Design is considered to be safe and adequate if the probability of failure is less than or equal to specified quantity.
[...] Even if the variables follow other than normal distribution, the basic approach applied here will not change. The probabilistic design procedure is quite general and can be applied to any machine elements. We can also avoid over designing of the elements. As the reliability increases, the face width of gear pair also increases. For the same reliability, as the coefficient of variation [...]
[...] Since safety factors are not performance related measures, there is no way by which an engineer can know whether this designs are near optimum or over conservative. A. Failure due to bending stress The allowable stress in bending is I. INTRODUCTION sb = Sb F .S Gears constitute an important element in the design of machines. Being an important element the gears are to be designed for a failure free operation for a given period of time and under given working conditions. The above need cannot be fulfilled by deterministic design. These conditions force to follow reliability based design. [...]
[...] Failure due to wear stress The relationship between induced wear stress and tooth thickness is γ2 sw = where Mt t2 A IV DETERMINISTIC DESIGN OF HELICAL GEARS A Failure due to bending stress Induced bending stress assuming the tooth as cantilever beam with end load is γ2 = 0.59 + + E k c k d cos β i sin 2α M = 2 2t A sw 2 The face width due to wear is calculated as sb = where β2 Mt At1 t2 ( 4.2 ) The greater of t1, t2 is taken as the face width of the gear pair. [...]
[...] DETERMINISTIC DESIGN OF BEVEL GEARS A. Failure due to bending stress Induced bending stress assuming the tooth as cantilever beam with end load is γ3 = 0.64 2 + 2 + E k c k d i 2 + 1 i i sin 2 Ae = L (ψ L 0.5 ) ψL L = mS t w 1 + i 2 2i where The face width due to wear is calculated as t2 = 3 e 2 Mt 2 w ( 6.2 ) The greater of t1, t2 is taken as face width of the gear pair. [...]
[...] The work surface of the tooth wears out considerably, this is called surface wear failure In the present work a spur, helical and bevel gear pair are designed for the face width of the gear using reliability principles. All the parameters affecting the Induced bending stress assuming the tooth as cantilever beam with end load is[2] sb = β1 M t At1 ( 2.1 ) The face width due to bending is calculated as t1 = Where β1 M t As b M t = 9548 P nw β = c k d + / imy cos α A = w + t p ) m 2 20 y = 0.52 + tw B. [...]
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