APPLIED MECHANICS FOR MACHINERY AND MACHINERY

Teaching is divided into three parts. In the first part the basic concepts of mechanics applied to machinery are provided; in the second part the mechanical vibrations of systems with one and two degrees of freedom are studied. Finally, the third part describes the hydraulic machines

Frontal lessons with projector and blackboard.

Exam:

Written exercises (3 exercises on the 3 parts of the course)
Oral examination

1. GENERALITY ON MECHANISMS Machines and mechanisms, kinematic pairs, degrees of freedom of the kinematic pairs, degrees of freedom of planar and spatial mechanisms. 2. EFFICIENCY. Definition of mechanism efficiency, in series and in parallel efficiency, inverse motion. 3. FRICTION AND WEAR. Coefficient of friction and work, notes on the theory of sliding friction, rolling friction, friction circle. Examples: revolute pair, inclined plane. Contact pressures distribution and Reye's hypothesis. Applications: flat sliding pair, turning pair, disc brake, contact brake-pulley and brake drum. 4. GEAR WHEELS. Friction gears, conjugate profiles, primitive and fundamental circles, definition of involute of a circle. Spur gears and relative dimensioning, determination of the arc of action, non-interference condition. 5. Gearboxes. Ordinary gearboxes, planetary gears and Willis’ formula, automotive differential. Examples and exercises on gearboxes. 6. FLEXIBLES. Lifting devices, elastic and inelastic stiffness, friction in the pivots, lifting hoists, pulley block. 7. BELTS. Type of belts: flat, rounded, V-shaped, ribbed, with teeth. Belt transmission between parallel axes, transmission efficiency, belt forcing, maximum transmissible power. Ordinary and differential belt brakes.

MECHANICAL VIBRATIONS

1. ONE DEGREE OF FREEDOM VIBRATING SYSTEMS: FREE OSCILLATIONS. General information on mechanical vibrations, free elementary oscillator, equivalent systems, springs in series and in parallel. Examples. 2. ONE DEGREE OF FREEDOM VIBRATING SYSTEMS: DAMPED OSCILLATIONS. Elementary damped oscillator, critical, hyper-critical and sub-critical damping, method of the logarithmic decrement. Examples. 3. ONE DEGREE OF FREEDOM VIBRATING SYSTEMS: FORCED OSCILLATIONS. Elementary forced oscillator, amplification factor, Argand-Gauss plane representation with rotating vectors. Applications: Foundations, constraints displacement, seismographs and accelerometers. 4. ONE DEGREE OF FREEDOM VIBRATING SYSTEMS: TORSION OSCILLATOR. Elementary torsional oscillator, trees arranged in series and parallel, reduction of the rotating masses. Examples. 5. VIBRATING SYSTEMS WITH TWO DEGREES OF FREEDOM: FREE AND FORCED OSCILLATIONS. Free oscillations of 2-dof systems, determination of the equations of motion. Forced oscillations of 2-dof systems, determination of the equations of motion. Dynamic absorber.

HYDRAULIC MACHINES

1. RECALLS ON FLUIDS AND THEIR PROPERTIES. Dynamic and kinematic viscosity, Reynolds number, Mass conservation, Bernoulli equation, distributed and concentrated pressure losses. 2. TURBOMACHINES. General characteristics, velocity triangles, fundamental turbomachine or Euler equation and internal work, organic, hydraulic and volumetric efficiency, fluid dynamics similarity and dimensionless coefficients, Balje diagram. 3. TURBOPUMPS. Characteristic curves, centrifugal pumps, mixed-flow and axial pumps, dimensioning of a turbo pump. Examples. 4. VOLUMETRIC PUMPS. Classification, Piston pumps, displacement, capacity and volumetric efficiency, power and efficiency. 5. MATCHING OF PUMP AND SYSTEM. Operation point of a plant, cavitation, NPSH and Thoma parameter, pump choice and rotation speed. 6. ACTION HYDRAULIC TURBINES. Pelton turbine, speed triangles, internal work, efficiency and losses, specific speed and diameter and design. 7. REACTION HYDRAULIC TURBINES. Francis turbine, axial flow and Kaplan turbine, reaction rate, speed triangles, internal work, efficiency and loss, sizing, regulation, diffuser. Examples.

1. Massimo Callegari, Pietro Fanghella, Francesco Pellicano, “Meccanica applicata alle macchine”, UTET Università

2. Diana G., Cheli F., “Dinamica e vibrazione dei sistemi”, Utet Libreria.

3. G. Cornetti, "Macchine Idrauliche", Edizioni il Capitello Torino.

Insights:

1. Funaioli E., Maggiore A., Meneghetti U., “Lezioni di Meccanica Applicata alle Macchine – Vol. 1”, Pàtron Editore.
2. Jacazio G., Piombo B., “Meccanica Applicata alle Macchine – Vol.2”, Levrotto & Bella Torino.

course lecture notes