Issue34

R. Citarella et alii, Frattura ed Integrità Strutturale, 34 (2015) 554-563; DOI: 10.3221/IGF-ESIS.34.61 556 The nature of the external applied load (torsional) requires for the remaining part of the surfaces a discretization with quadratic elements. In the application that follows, an interference fit is assumed, with the global stresses resulting from the superposition of interference fit and torsional load. P ROBLEM DESCRIPTION he problem relates to the optimal choice of the following design parameters of the coupling: 1. P3G profile of the coupling in terms of the eccentricity of the lobes ( e ); 2. type of lubricant interposed between the coupling surfaces, influencing the design friction coefficient ( f ); 3. coupling tolerances. The objective is to minimize the effects of uncontrolled variability of the so called “noise factors” on the performance of the coupling while maximizing the performance parameters. A DoE (Design of Experiments) approach was adopted, to define different configurations to be tested in the structural simulations, based on the use of so-called “orthogonal matrices”. These simulations allow evaluating the performance parameters of the product, with particular reference to: 1. shaft-hub reciprocal circumferential sliding after loading, since limiting such sliding considerably increases the fatigue life of the joint; 2. maximum radial deformation of the hub, since excessive values could, for example, create malfunctioning if the hub is part of a kinematic chain (an alternative parameter may be the maximum error of circularity); 3. stress peaks in the hub (normally more stressed than the shaft), which must be limited in order to reduce its size and consequently the overall dimensions of the joint; 4. press fit force, since reduced values facilitate a possible isothermal assembly; this force ( F press fit ) is evaluated as: F press fit = p m *A*f where p m is the pressure at interface, assumed to be independent from the friction coefficient ( f ) and A is the contact surface. It is also worth noting that the aforesaid mean pressure is just slightly influenced by the eccentricity value, depending substantially on the interference value. Corresponding to the two profiles with e=2.05mm and e=3mm , the perimeters are respectively p 1 =201 mm and p 2 =207 mm. The identified performance parameters should be limited as much as possible in absolute value (lower is better) but above all in terms of sensitivity to the varying “environmental” conditions (noise factors), so as to be able to predict with a reduced margin of uncertainty, the value that they will assume under operational conditions. The noise factors, suitably simulated in each numerical analysis, are related to: • the precision of the machining, which manifests itself through an interference fit value that is variable within the chosen tolerance zone; • the variability of torque (torque peaks or overload in general); • the variability of the friction coefficient compared to the nominal design value. Finally, a series of numerical experiments L 4 (2 3 ) were carried out, based on three independent control variables and three noise factors, each with two possible levels. In order to quantify the variability of the torque and the friction coefficient, a normal distribution was assumed, centred at the respective nominal values and with a variation coefficient  of nearly 7%. For the effective dimensions of shaft and hub the concept of “natural tolerance” was used, according to which the width of the tolerance zone is equal to 6  and the mean value of the analysed dimension, which is also distributed according to a Gaussian function, is at the centre of the tolerance zone. The adopted tolerance bands were IT7 (30  m) for the hub and IT6 (19  m) for the shaft and the corresponding standard deviations  were equal to 30/6=5  m and 19/6=3.17  m respectively. The normal distribution of the interferences ( i ) was obtained by composing the distributions of the size of the shaft ( d a ) and hub ( d m ) as follows: i = d a -d m   i =  da -  dm  i 2 =  da 2 +  dm 2 = 25+10 = 35  m 2 T