Machine construction II

Expected Learning Outcomes

This course aims to provide students with the fundamental concepts of the finite element method and of the structural mechanical design of mechanical components and systems.

Knowledge and Understanding

The course covers the theoretical foundations of the finite element method and the matrix method for the analysis of planar structures, as well as issues related to the mechanical design of systems and components subjected to dynamic loading, including rotating discs, shafts operating at critical speeds, torsional vibrations of shafts, mechanical engine components such as connecting rods, pistons and piston rings, straight- and helical-bevel gears, and helical cylindrical gears.

Applying Knowledge and Understanding

The course also promotes familiarity with numerical modelling issues through the development of matrix-based computational codes for the analysis of planar structures in MATLAB and the verification of the results using commercial finite element software.

Prerequisites

Students must have passed the prerequisite examinations specified in the regulations of the Degree Programme.

Course Delivery

The course consists of theoretical lectures and computer-based practical sessions held in the classroom. Should the course be delivered in blended or distance-learning mode, the necessary changes to the teaching activities described above may be introduced in order to ensure completion of the programme set out in this syllabus.

Assessment

The assessment consists of an oral examination. The assessment of learning outcomes may also be conducted remotely if circumstances so require.

To ensure equal opportunities and in compliance with applicable legislation, interested students may request an individual meeting to arrange any appropriate compensatory and/or exemption measures, based on the learning objectives and their specific needs. Students may also contact the departmental CInAP representative lecturer. CInAP is the Centre for Active and Participatory Inclusion, which provides services for students with disabilities and/or specific learning disorders: https://www.cinap.unict.it/content/referenti.

The skills acquired through the course may be applied to quality management activities within organisations operating in the civil, industrial and service sectors, in accordance with Goals 9, 11 and 12 of the United Nations 2030 Agenda for Sustainable Development.

Lessons and exercitations at the PC

MACHINE DESIGN – II (9 cfu)

Objectives and organization

This course is aimed at delivering the main concepts of finite elements and of structural dynamics in the design of engines, machines and their mechanical components. The familiarization with modeling issues is also promoted, together with the implementation of the above concepts to practical cases.

Class exercises will be organized for practising with both self-written computer programs as well as commercial f.e. codes.

CONTENT OF THE COURSE

1) Matrix method and Finite Elements for structural calculation:

Matrix method for monodimensional plane structures - Stiffness matrix for an element - Global /local reference rotation matrix - Structure stiffness matrix - Permutation of dof and stiffness partitioning - Nodal displacements and reaction loads - Internal and external constraints - Element geometry, nodal displacement approximating polynomials - Shape functions - Differentiation and strains - Stress-load relationship - Principle of virtual work, Rayleigh Ritz method - Truss elements - Euler beam - 4 nodes plane elements (plane stress / plane strain membrane, Kirchoff plate, axysimmetric solid) - 8 noded esahedric element - Isoparametric formulation - Gauss integration - Matrix Equations for dynamic equilibrium - Consistency and direct lumping for mass matrices -  Free undamped oscillatory solution - Rayleigh damping - State equations for damped oscillatory motion - Transitory and regimen damped oscillations.

References:

• “Belingardi”, Parte 1 cap. 1; Parte 2 capp. 1, 2, 3; Parte 3 chapt. 1, 2,3, 4, 6, 7, 9, 11; Appendice 2.
•  “Zienkiewicz-Taylor” chapt. 17, Dispensa Gavin x matrici

2) Rotors and rotating discs:

Fundamental equations - constant thickness disc - effect of shaft and blade supporting ring - Hyperbolic, conical and uniform stress profile discs - Grammel method for arbitrary shape discs - Thermal stresses in discs with arbirtary profile – Centrifugal stress due to radial blades - Stress concentation around holes

References:

Giovannozzi –II” chapt. 10.

3) Critical speed of shafts:

Shaft with a single lumped mass - Critical speed, eccentricity, oscillations - Effect of transverse inertia - Effect of axial stress - Shaft with multiple lumped masses - Equivalent shaft - Vibration modes, eigenvalues and eigenvectors.

References:

“Giovannozzi –II” chapt. 11.

4) Torsional vibrations of shafts:

Introduction to torsional vibrations - Equivalent system for a torsionally vibrating shaft - Free and forced solutions for torsional vibrations of a shaft - Frequencies of series and parallel shafts systems - Inertia reduction to crank axis for traslating and rotating components of piston engines - Armonic decomposition of torque compinents induced by pressure and inertia - Main and secondary armonics in multi cylinder engines - Resonating armonics -  Vibration amplitude of forced and resonating armonics - dynamic stress on crankshafts

References:

 “Giovannozzi –II” chapt. 12.

5) Main components of piston engines:

Typical cranshaft configurations - Pulsating and rotating forces and moments of 1^st and 2^nd order - Loads on crankcase and engine mounts - Approximations for calculating critical speed of crankshafts - Design of piston pins - Design of connecting rod arm and eyes - Design of piston rings – Dynamics of engine distribution system - Valve opening, speed and acceleration - Cam profile calculation - Loads on camshafts, springs, valves and seats.

References:

 “Giovannozzi –II” chapt. 17, 19.

6) Transmission gears:

Straight tooths conical gears - Tredgold model - Minimum number of teeth - Selection of gear parameters - Loads on conic gears - Helicoidal gears - front profile and normal profile - Minimum number of teeth - Helicoidal stub tooth profile - Loads on cylindrical gears with helicoidal teeth - Skew axes transmission - Arc of action and effective width - Loads and efficiency – Loads and efficiency – Conical gears with helicoidal teeth – Tipical shapes of inclined teeth – Planar/conical equivalent gear – Radial, tangential, axial loads.

References:

 “Giovannozzi –II” chapt. 2, 3.

Textbooks

See next section.

1. Lecture notes;
2. Giovannozzi R., “Costruzione di Macchine Vol. II”, Patron (in Italian);
3. Belingardi G.,  “Il Metodo degli Elementi Finiti nella Progettazione Meccanica”, Levrotto & Bella (in Italian);
4. Zienkiewicz & Taylor, The finite elements method V. 1, Butterworth & Heinemann; (Cap. 17);
5. Cophra A., “Dynamics of Structures Theory and Application”, Prentice Hall;
6. Software Manuals (MATLAB, MSC MARC) ;