# FUNDAMENTALS OF MECHANICAL ENGINEERING

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- Versione italiana
- Academic year
- 2017/2018
- Teacher
- RAFFAELE DI GREGORIO
- Credits
- 6
- Didactic period
- Primo Semestre
- SSD
- ING-IND/13

#### Training objectives

- This is a basic course in the mechanical field: starting from the principles of mechanics, it provides the basic knowledge and methods required to perform the kinematic and dynamic analysis of mechanical systems and it introduces to some typical applications in automatic machines.

During the course, the student will develop skills in analyzing and modelling mechanical systems by applying the above-mentioned knowledge to typical mechanical systems. #### Prerequisites

- Basic knowledge in Mathematics, and Physics.
#### Course programme

- ALGEBRA AND GEOMETRY REVIEWS: Free and Applied vectors; Rotation matrices; Tensors (Ref. [1], Chs. I and II)

POINT KINEMATICS: Parametric functions of points and vectors; Trajectory; Velocity; Acceleration; Planar motion. (Ref. [1], Ch. V)

KINEMATICS OF RIGID BODY (cr): pose (position + orientation) of a cr; Angular velocity; Poisson formula; Scalar invariant; Characteristic vectors of the velocity field of a cr; Equivalence and composition of velocity fields; Instantaneous screw axis; Accelerations: Rivals’ theorem; Relative motions; Planar motion (mp) (Ref. [1], Chs. VI and VII; Ref. [3], Ch. V)

KINEMATICS OF CONSTRAINED SYSTEMS: Constraints; Degrees of freedom (dof); Lagrangian coordinates; displacements. (Ref. [1], Ch. VIII)

SYSTEMS OF FORCES (sf): Concept of force; Moment of a force; Resultant and resultant moment of a sf; Moment transport theorem; Equivalence of sf; Reduction of a sf to a single force plus a single moment; Scalar invariant of a sf; Central axis of a sf; Equilibrated sf; Planar sf (Ref. [1], Ch. III)

POINT DYNAMICS: Motion laws; Reference systems (absolute and relative); Impulse; Linear momentum; Angular momentum; Work and power; Kinetic energy; Energy theorem. (Ref. [1], Ch. X)

MECHANICAL SYSTEM DYNAMICS: Center of gravity; Linear momentum; Angular moment; Inertia forces; Equations of motion; Kinetic energy; Energy conservation (Ref. [1], Capp. XI and XII)

RIGID BODY’S INERTIA PROPERTIES: Center of mass; Inertia moment; Product of inertia; Inertia tensor; Huygens theorem; Principal axes of inertia and central axes of inertia; Inertia moments of solids with simple geometries (Ref. [1], Ch. IV; Ref. [2]).

RIGID BODY’S DYNAMICS: Linear momentum; Angular momentum; Resultant of inertia forces; Resultant moment of inertia forces; Newton-Euler equations; Kinetic energy; Equivalent system of point masses; Dynamic model of a cr constrained to perform planar motion. (Ref. [1], Chs. XI and XII; Ref. [2]; Ref. [3], Ch. 11)

MECHANISMS’ DYNAMICS: Classification of constraints according to their mathematical model; Constraint reactions; Grubler formula; Free body diagrams; Principle of virtual work (PLV); Lagrange equations; Using the PLV for the solution of statics problems on mechanisms with one dof; Dynamics of one-dof mechanisms; Dynamics of the slider-crank mechanism (Ref. [1], Chs. XI and XII; Ref. [2]; Ref. [3], Ch. 6 (Sec. 6.6) and Ch. 12)

VIBRATIONS OF ONE-DOF SYSTEMS: Springs; dampers; Free vibrations; Forced vibrations. (Ref. [3], Ch. 14: Secs. 14.1 - 14.2 - 14.3; Ref. [2])

ROTOR DYNAMICS: Static and dynamic unbalance; Rotor balancing; Flexural critical speeds (Ref. [3], Ch. 15: Secs. 15.1 - 15.2 - 15.3 (points (a), (b) and (c)) - 15.4 - 15.5; Ref. [2])

GEARS: Spur gears: involute, contact line and action arc, non-interference condition, gear cut, correction; Helical gears; Bevel gears; Couple worm-helical gear. (Ref. [3], Ch. 7: Secs. 7.1 - 7.2 - 7.4 - 7.5 - 7.6 -7.7 - 7.8 - 7.9 - 7:10 to 7:11 - 7:12 to 7:14 (outline) - 7.15; Ref. [2])

GREAR TRAINS: Ordinary gearings; Planetary gearings; Differential; Relationship between the external torques applied to a gearing (Ref. [3], Ch. 8, Ref. [2])

(°)THE DETAILED PROGRAM CAN BE DOWNLOADED FROM THE SECTION “DISPENSE” OF THE COURSE WEBSITE. #### Didactic methods

- During the course, the subjects are addressed both from a theoretical and from a practical point of view. In particular, a number of exercises, whose solution is partly addressed in class and partly left to the student as a tool for self-training, are proposed for each topic.
#### Learning assessment procedures

- The examination will evaluate the student skill in modeling mechanical systems and the systematic knowledge of the subjects presented during the course. In practical, the student is required to answer to a number (two/three) of queries on the subjects listed in the program and to show his skill in applying the theoretical tools to the analysis/modeling of a mechanical system.

Passing the final exam is the proof that knowledge and abilities outlined in the training objectives of the course have been achieved. #### Reference texts

- All the subjects addressed during the lessons are dealt in the following texts/files which the program refers to

[1] M.S. Mongiovì, “Appunti di Meccanica Razionale”, Ed. 2011.

[2] File “Materiale Didattico Integrativo (fotocopie, lucidi, note su argomenti specifici)” dowloadable from the section “Dispense (DM 270/04)” del sito del corso (http://www.unife.it/ing/informazione/Fond-mecc-tecnica/dispense-dm-270-04/ )

[3] Funaioli, E., Maggiore, A. e Meneghetti, U., "Lezioni di MECCANICA APPLICATA ALLE MACCHINE – Prima Parte: Fondamenti di Meccanica delle Macchine", Ed. Patron, Bologna, Edizione del 2005.

Also, in the section “Dispense (DM 270/04)” of the website (http://www.unife.it/ing/informazione/Fond-mecc-tecnica/dispense-dm-270-04/ ) are available in the directory “Testi di Approfondimento” the following freely downloadable textbooks:

[4] G. De Cecco, R. Vitolo, “Note di Calcolo Matriciale”, Ed. 2007

[5] G. De Cecco, R. Vitolo, “Note di Geometria ed Algebra”, Ed. 2007

[6] R. Esposito, “Appunti dalle Lezioni di Meccanica Razionale”, Ed. 1998

[7] T.R. Kane, D.A. Levinson, “Dynamics: Theory and Applications”, Ed. 1985

[8] A. Marzocchi, “Lezioni di Meccanica Razionale”, Ed. 2010

Eventually, in the net, there are websites that provide legal download of some textbooks. For instance, from the website of Prof. Alberto Strumia (http://www.albertostrumia.it/libri/didattica.html) the following textbook is dowloadable:

[9] A. Strumia, “Meccanica Razionale”, Casa Editrice Nautilus, 2a Ed. 1996

Other textbooks are available in UNIFE library, among which

[10] V. Franceschini, C. Vernia, “Meccanica Razionale per Ingegneria”, Ed. Pitagora, 2011

[11] T. Levi-Civita, U. Amaldi, “Lezioni di Meccanica Razionale”, Ed. Zanichelli

[12] S. Nocilla, “Lezioni di Meccanica Razionale”, Ed. Levrotto & Bella