ING-IND/14 - 9 CFU - 1° Semester

Teaching Staff


Detailed Course Content

Effect of high strain rates on materials response:

Basic concepts of time-independent plasticity – Yielding, Hardening, consistency condition and normality rule – Path-dependent response in elastoplasticity – Triaxial and Deviatoric parameters – Basics of ductile damage mechanisms – Wierzbicki-based damage models - Time-dependent plasticity of materials – Dynamic hardening - Johnson-Cook, Zerilli-Armstrong and Cowper-Symonds models – basic concepts of wave propagation in elastic solids – test methods at high strain rates – Hopkinson bar, working principles and practical problems.

Finite elements method and matrix methods for statics and dynamics:

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, - Truss element - Euler beam - - 4 nodes plane membrane element - 4 nodes plane shell element - Isoparametric formulation - Gauss integration - Consistency and direct lumping for mass matrices - Matrix Equations for dynamic equilibrium - Free undamped oscillatory solution - Rayleigh damping - State equations for damped oscillatory motion - Transitory and regimen damped oscillations

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

Critical speed of shafts:

Shaft with a single lumped mass - Critical speed, eccentricity, oscillations - Effect of transverse inertia - Effect of axial stress - Effect of shear stress - Shaft with multiple lumped masses - Equivalent shaft - Dunkerley formula - Shaft with distributed mass - Stodola method for 1st critical speed – Koch, Giovannozzi and Risitano methods for 2nd ctitical speed - Vibration modes, eigenvalues and eigenvectors.


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 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


Main components of piston engines:

Design of piston pins - Design of connecting rod arm and eyes - Design of piston rings.


Transmission gears:

Straight teeth conical gears - Tredgold model - Selection of gear parameters - Loads on conical gears - Helicoidal gears - front profile and normal profile - Arc of action and effective width - Selection of gear parameters - Loads on cylindrical gears with helicoidal teeth– Conical gears with helicoidal teeth – Tipical shapes of inclined teeth – Planar/conical equivalent gear - Selection of gear parameters - Loads on conical gears with helicoidal teeth.

Textbook Information

1) Appunti delle lezioni
2) Giovannozzi R., “Costruzione di Macchine Vol. II”, Patron;
3) Belingardi G., “Il Metodo degli Elementi Finiti nella Progettazione Meccanica”, Levrotto & Bella;
4) Dispensa K. R. Gurley, CES 4141 Notes,
5) Dispensa H. Gavin, CE 283 Notes,
6) Estratto Diana – Cheli – Dinamica dei sistemi meccanici,
7) Estratto Bocchi G. “Motori a quattro tempi”, Hoepli;
8) Estratto Vignocchi D. “Elementi di progettazione del motore”, Athena;
9) Estratto Cophra A., “Dynamics of Structures Theory and Application”;
10) Estratto Zienkiewicz O. C., Taylor R. L., “The finite elements method”;
11) Lecture Notes (draft);

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