


Politecnico di Torino  
Academic Year 2015/16  
14ALPNC Machine Design 

Master of sciencelevel of the Bologna process in Electrical Engineering  Torino 





Subject fundamentals
The course aims at giving the students advanced knowledge and understanding of the design of mechanical components relevant to electrical applications, resorting for computational purposes to the finite element method, due to its generality and wide range of application in engineering. Specifically, one deals with the static and the dynamic analysis of shafts and rotating disks. The mastering of the technical language characteristic of the mechanical design is emphasized.

Expected learning outcomes
The knowledge and understanding capabilities the students must acquire in this course are meant to improve their interdisciplinary background with reference to subjects characterizing the design of mechanical components such as stress and strain in threedimensional and axisymmetric elastic bodies, vibrations of discrete systems, rotordynamics, finite elements. The applying knowledge and understanding capabilities concern the use of the language of the mechanical design in the framework of electromechanical systems through an interdisciplinary approach as well as the modelling, calculation and results analysis through finite element codes as regards the static and dynamic analysis of mechanical components. As for the communication skills, the course gives the students the potential capabilities to interact with people from other technical fields, e.g., mechanical engineering, improving the effectiveness of a mixed professional team.

Prerequisites / Assumed knowledge
The students are required to possess the basic ideas and facts regarding the static and dynamic equilibrium of a mechanical system and the stress and strain in an elastic solid, especially the SaintVenant solid (beam). In particular, this implies that the students should be conversant with topics such as the mechanical behaviour of materials, principal stresses, yielding criteria, free and forced vibrations of onedegree systems. The following abilities are also required: stress analysis of simple structures composed of beams, analysis of vibrating mechanical systems which can be reduced to the harmonic oscillator.

Contents
Stress and strain in threedimensional bodies. Differential equations of equilibrium and compatibility [4 h]. Stress and strain in axisymmetric bodies, rotating disks of uniform thickness subjected to centrifugal field, radial temperature gradient, radial loads. Grammel's method for disks of arbitrary profile [6 h].
Static equilibrium of discrete systems, stiffness and flexibility matrices, stiffness matrices and equivalent load vectors of bar and beam elements, procedures for assembling, constraining and solving chain systems [5 h]. General formulation of the finite elements through the virtual work principle. Three and fournodes plane elements, higherorder plane elements, definition of finite element models, hconvergence [6 h]. Free and forced of discrete systems. Eigenvalue problem: natural frequencies and modes, solution by bar and beam models, lumped and consistent approaches [7 h]. Rotor dynamics: free and forced response of the Jeffcott rotor, critical speed. Rotating shafts with many degrees of freedom, gyroscopic effects [4 h]. 
Delivery modes
In addition to lectures, the course programme includes exercise sessions.
As for Statics, exercise sessions deal with the stress analysis of both rotating disks, through integration of the relevant elasticity equations, and shafts through matrix methods; both components are analyzed for various combinations of mechanical and thermal loads [10 h]. Machine dynamics entails exercises on the free and forced response of oscillating shafts, which are solved resorting to simple beam element models. Such approach is then applied to the lateral oscillations of rotating shafts with particular attention to the phenomenon of critical speeds [8 h]. 
Texts, readings, handouts and other learning resources
For a review of the basic concepts of Structural mechanics the students can utilize: F. A. Raffa, Fondamenti di meccanica strutturale, CLUT, 2008.
Further readings on Finite elements and Mechanical vibrations are: G. Belingardi, Il metodo degli elementi finiti nella progettazione meccanica, Levrotto & Bella, Torino, 1996. A. Fasana, S. Marchesiello, Meccanica delle vibrazioni, CLUT, 2006. Texts and other learning resources are also available. Specifically, the students find online notes written by the instructor on elasticity theory, stress analysis of axisymmetric solids, finite elements and elements of mechanical vibrations. Texts and solutions of the exercises are available as well. 
Assessment and grading criteria
The assessment of the students’ skills is based on a two hours written examination divided in two parts (numerical exercises and theoretical questions) which must be solve separately. In order to pass the written examination the students must obtain a score of at least 18/30; the score is given by the arithmetic average of the evaluations of the single exercises and theoretical questions. During the oral examination the students go through the corrections reported on their texts. In general, the final score coincides with the evaluation of the written examination.

