Nicolò Vincenzi

A generalized theory for shaft—hub couplings

Abstract The design of compression-fit joints, based on the theory of thick-walled cylinders, is usually referred to shaft—hub couplings carried out between two elements that have an axial symmetric shape. The stress distributions both inside the elements and on the contact surfaces can be defined by the equilibrium and by the compatibility formulae once the total radial interference and the internal and external pressure (the boundary conditions) are known. The complete tensile state of the coupling is defined by two principal stresses: the radial and the hoop tensions. The present article aims at extending the analytic calculation valid for two elements to a number of n elements by means of a sequential solution of the governing equation system. The elements in contact can rotate at a generic angular velocity and can, also, be made of different materials. The overall solution has been derived starting from the hypothesis of the simultaneous presence of axial symmetric geometries and axial symmetric loads. The mathematical model has been verified by comparing the theoretical results with some finite-element analysis calculations performed on the same coupled elements.

Experimental Analysis of Static and Fatigue Strength Properties in Press-Fitted and Adhesively Bonded Steel–Aluminium Components

Press-fitted and adhesively bonded joints (Hybrid Joints) are increasingly used as an alternative way to traditional structural joining techniques. The main achievable benefits can be summarized in the possibility of maximizing the load transfer (torque or axial) and reducing both the weight and the stress field of the components, by taking advantage of the adhesive strength. Hybrid joints studies can be found in literature mainly on steel–steel components (Steel Hybrid Joints). The aim of this paper is to provide some relevant information on the static and fatigue strength properties in the case of steel–aluminium components (Mixed Hybrid Joints), from the experimental tests performed on a high strength, single-component adhesive which cures anaerobically. The use of the adhesive increases the press-fitted joint performances, with respect to its release force: the adhesive static shear strength is about 9 MPa, whereas the adhesive endurance limit is about 6 MPa, in presence of a stress ratio R = 0.1.

Normalization of the stress concentrations at the rounded edges of a shaft–hub interference fit: extension to the case of a hollow shaft

This work addresses the issue of stress concentrations at the rounded edges of shaft–hub interference fits. An infinitely long shaft, press fitted into a hollow hub with bore rounded edges is examined. Limited to interference fits involving a solid shaft, Strozzi and colleagues introduced a normalizing parameter, which accounts for the combined effects on the stress concentrations of the fillet radius, the shaft external radius and the interference level. The aim of this work is to extend the field of application of the said normalizing parameter, to the case of interference fits involving a hollow shaft. By means of finite element analysis, run-on geometries with different hub and shaft aspect ratios (ratio between internal and external diameters), charts for stress concentration factors as functions of the normalizing parameter were drawn. Appropriate functions are proposed, which allow obtaining the stress concentration factors valid for the case of hollow shaft, starting from the stress concentration factors valid for the case of solid shaft. The stress concentration factors predicted by means of this novel method are then compared with those provided by finite element analysis. Stress concentration factors in the presence of hollow shafts are demonstrated to be always higher than those evaluated for solid shafts. Finally, a numerical example illustrates the typical workflow to be followed in order to calculate the stress concentration factor for a defined joint.

Stress concentration factors in compression—fit couplings

Abstract The aim of the present work is to define the maximum stress generated by the coupling of axially symmetric and continuous shafts press-fitted into axially symmetric hubs. The theoretical stresses given by the well-known formulae of the thick-walled cylinders theory are constant on the whole coupling surface, but if the shaft extends beyond the hub there is a stress concentration factor on the boundary zone. This occurrence is confirmed by finite element analyses performed by the authors on several different shaft—hub couplings. The analysed couplings have the shaft extended beyond the hub, the shafts press-fitted into the hubs, and both shafts and hubs loaded by an external pressure and an internal pressure. The stress concentration factors have been calculated in this work and their expressions have been derived as a function of some tensile and geometrical parameters. By combining the thick-walled cylinders theory with the proposed formulae, it is possible to evaluate the maximum stress located at the end of the hub without performing any numerical investigations.

How to improve static and fatigue strength in press-fitted joints using anaerobic adhesive

This study is focused on the static and fatigue strength of interference-fitted connections supplemented with anaerobic adhesive (hybrid joints). Through axial release tests, it is demonstrated that the addition of the adhesive always improves the performance of the joint. The main achievable benefits can be summarized in (a) the possibility of increasing the load transfer capability with the same joint geometry and (b) reducing both the weight and the stress field of the joint with the same load transfer capability. The objective of the study is to provide some relevant information on the static and fatigue strength properties in case of both steel–aluminium components (mixed hybrid joints) and steel–steel components (steel hybrid joints). Furthermore, the authors provide some design formulae useful to predict the releasing force (the strength of the joints) both under static and dynamic conditions. Relevant improvements can be obtained using the anaerobic adhesive in terms of releasing force, which increases at least of 40 per cent. The proposed results derive from a collection of 200 experimental tests performed by the authors on a high-strength, single-component adhesive, which cures anaerobically (LOCTITE 648®).

An analytical approach to the structural design and optimization of motorbike forks

From a structural standpoint, motorbike forks must withstand the most diverse loading conditions that the normal use of the vehicle implies. By means of experimental analyses, the authors found the emergency braking to be the most severe loading case. This contribution presents a novel analytical model that, given a few geometric parameters of the motorbike and of the fork, allows calculation of the stress field on the legs under braking. The analytical model was designed to account for the unequal stress distribution on the two legs that arises from the geometrical asymmetry of single brake disc architectures. The model accuracy was tested by comparison with finite element analysis (FEA) and experimental stress analyses. Finally, the possibility of balancing the loads on the legs of single disc architectures was examined and some structural optimization strategies were proposed.

Experimental Analysis on the Tightening Torque - Preloading Force Relationship in Threaded Fasteners

The aim of this study is to provide an experimental methodology useful to determine the friction coefficients in bolted joints and, therefore, to relate precisely the tightening torque to the preloading force. The components under investigation are some clamped joints made of aluminium alloy and used in front motorbike suspensions to connect the steering plate (fork) to the legs and the legs to the wheel pin. The aluminium alloy is realised by a casting or a forging process afterwards anodized or spry-painted in surface. Some specific specimens have been appropriately designed and realised with the same process of the actual components. The bolt torque is given by a torque wrench whereas the preloading force has been evaluated by means of a strain gauge. Thread and underhead friction coefficients have been studied separately, by applying an axial bearing located between the bolt head and the flange of the specimen. The overall friction coefficient and the torque coefficient (nut factor) have been calculated. Experimental tests have been carried out by applying the Design of Experiment (DOE) method in order to obtain an accurate mathematical model that involves the significant friction variables and their interactions. The results of this preliminary study have been, then, applied to those connections used in front motorbike suspensions to lock the steering plates with the legs and the legs with the wheel pin, by means of one or two bolts. The preloading force, produced during the tightening process, should be evaluated accurately, since it must lock safely the shaft, without overcoming the yielding point of the hub. Firstly, the applied tightening torque has been precisely related to the imposed preloading force by means of the friction coefficients definition. The tensile state of clamps, have been evaluated both via FEM and by leveraging some design formulae proposed by the Authors as functions of the preloading force and of the clamp geometry. Finally the results have been compared to those given by some strain gauges applied on the tested clamps: the discrepancies between numerical analyses, design formulae and experimental results remains under a threshold of 10%.Copyright

Analytical, Numerical and Experimental Study of the Effects of Braking on Single Disc Motorcycle Forks

This work deals with the development of an analytical model which allows to describe the tensile state arising in single-disc motorcycle forks, during the brake. Stress and strain trends are computed as functions of some key parameters of the motorcycle (mass and centre of gravity location) and of the fork (lengths and diameters). The fork geometry is represented by a portal frame loaded out of its plane, whose axisymmetric elements represent the legs (pillars) and the wheel pin (transverse beam). Each of the three elements has material and inertia parameters variable along their axis, allowing for the actual mechanical properties of the component. Finally, the stress state of several fork models has been investigated either via Finite Element Analysis and with field tests, in order to support the validity of the proposed model.

Structural Analysis and Loads Distribution in Motorbike Forks During the Braking Phase

This work deals with the development of an analytical model, which allows to describe the tensile state arising in single-disc motorcycle suspensions, during the brake. Stress and strain trends are computed as functions of some key parameters of the motorcycle (mass and centre of gravity location) and of the fork (lengths and diameters). A portal frame loaded out of its plane represents the suspension geometry, whose axisymmetric elements represent the pillars (legs) and the wheel pin is the transverse beam. Each of the three elements has material and inertia parameters variable along its axis depending on the actual mechanical properties of the component. Finally, the stress field of several fork models has been investigated both via FEA and via in field tests, in order to support the effectiveness of the proposed model.© 2010 ASME

The Structural Design of Front Motorbike Suspensions

The fundamental goal of this paper is to provide a methodology useful for the structural design and optimization of front motorbike suspensions. Two different types of shaft-hub couplings are normally used to assembly the whole suspension: (i) an interference-fit coupling (between the fork and the steering pin) and (ii) a clamped joint (between the fork and the leg and between the leg and the wheel pin). Firstly the Design of Experiment method has been applied in order to evaluate the static friction coefficient μll . Secondly a mathematical model, based on the thick-wall cylinder theory, has been developed in order to calculate the tensile state in the fork-pin couplings. Finally other mathematical models have been defined with the aim to calculate the maximum bending stress and the mean coupling pressure generated in the fork-leg and in the wheel-clamp couplings. The research results have been used to realize an innovative software (Leg Design©) that is useful to design and to verify the whole front motorbike suspensions with correct and effective results obtained for different geometries and material combinations.Copyright