Mechanical Engineering for the Green Transition

1. Introduction Definitions and Classifications Definition and classification of machines. Issues related to modeling. Description of machine assemblies. Definition of mechanisms. Definition and classification of kinematic pairs. Description and classification of kinematic chains. 2. Review of Kinematics Using Phasors Kinematics of the Point Review of point kinematics using phasors and examples. Kinematics of the Rigid Body Review of rigid body kinematics using phasors. Recall of rigid motion types and instantaneous center of rotation; definition of base and roulettes. Fundamental kinematic formulas for velocity and acceleration using phasors. Constraints Complete coordinate systems and constraint equations. Point constraints and reaction forces. Constraint equations in the presence of sliding velocity and pure rolling. 3. Kinematics of Mechanisms General Aspects Description and classification of mechanisms according to the kinematic chain and differences with structures. Examples of common applications of mechanisms. Formulation of kinematic equations according to the type of kinematic chain; closure equations. Example of modeling a bar constrained by rectilinear guides, using phasors and the instantaneous center of rotation. Planar RR Manipulator Fields of application. Degrees of freedom. Kinematic equations for position, velocity, and acceleration. Simple Centered Crank Mechanism Characteristics and applications. Degrees of freedom. Kinematic equations and graphs for position, velocity, and acceleration. Interpretation of the equation through the theorem of relative motion. First- and second-order approximation of the piston’s Jacobian. Four-Bar Linkage Characteristics, fields of use, and Grashof’s criterion. Degrees of freedom. Kinematic equations for position, velocity, and acceleration. Oscillating Slotted Link Fields of application and main features. Degrees of freedom. Kinematic equations for position, velocity, and acceleration. 4. Formulation of the Equations of Machine Dynamics Review: Dynamic Equilibrium Equations Material point. Rigid body. Equivalent systems of forces for rigid bodies. Equivalent systems for inertia forces. Systems of rigid bodies. Review: Extended Principle of Virtual Work Extension of the Principle of Virtual Work (PVW) to dynamics. Definition of Lagrangian variables and components. Example of a rigid body constrained to a frame by a revolute pair, solved using both dynamic equilibrium equations and the PVW. Power Balance Derivation of the power balance equation from the PVW. Kinetic energy of machines and König’s theorem. Power balance and kinetic energy theorem. 5. Tribology and Contact Actions Introduction History of tribology. Classical friction models: adhesion, limiting friction, and sliding. Friction Description of the phenomenon and its causes. Coulomb’s law for static friction: inequality for adhesion verification. Coulomb’s law for dynamic friction. Tribological triplet and third-body approach. Effect of roughness, hardness, and Hertzian theory. Wear Description of the wear process (simplified). Elementary wear model by Archard. Wear rate. Conceptual tools of the tribologist: tribological triplet, accommodation mechanisms. Example of a solved tribological problem. Generalities on Lubrication Boundary lubrication; fluid film lubrication: hydrodynamic and hydrostatic. Description of liquid, solid, grease, and gaseous lubricants. Elementary Theory of Hydrodynamic Lubrication Fields of application. Equilibrium equations for an elementary volume of lubricant. Integration of equations for the calculation of lubricant velocity components. Petroff’s law. Equations of the mass continuity principle. One-dimensional analysis of a lubricated pair: pressure gradient analysis; resultant forces, load capacity; example of a narrow clearance between flat plates. 6. Dynamics of Machine Groups with Single Degree of Freedom Models Model Formulation Modeling of a machine group composed of motor and driven system connected by a transmission. Application of the power balance. Motor Modeling Mechanical system considerations on the motor side: calculation of equivalent torque and equivalent moment of inertia reduced to the motor shaft; dependence on angular position and velocity. Example of equivalent inertia calculation for a simple crank mechanism. Mechanical characteristic and equivalent moment of inertia for internal combustion engines, DC motors, and three-phase asynchronous motors with and without inverter. Load Modeling General considerations on the mechanical system on the driven side. Constant and quadratic mechanical characteristics. Transmission Modeling Kinematic model of the transmission. Dynamic model: definition of forward and reverse motion and calculation of power losses in both conditions. Determination of power flow through the transmission in direct and inverse dynamic analysis. Series transmissions: kinematic and dynamic model. Operating Regimes of a Machine Group Steady-state regime: definition and conditions required for its occurrence. Variable motion: transients, start-up, and stopping; periodic motion as a condition analogous to steady-state for periodic machines. Dynamics of a Machine Group Allowing Steady-State Regime Determination of the general dynamic equation of a machine group through power balance, in direct and reverse motion. Special case of steady-state regime. Example: Start-Up Transient Analysis of the start-up transient of a group driven by a DC motor and a constant-resistance load. Dynamics of an Elevator Physical model. Dynamic equations in direct and reverse motion. Upward and downward motion. Steady-state regime. 7. Power Transmissions General Description Classification of transmissions and fields of application. Friction Wheels Kinematics. Dynamics. Advantages and disadvantages. 7.1 Gears and Gear Trains General Description and Nomenclature Definition and description of the most common types of wheels and gears. Reference primitive surfaces and operating principles. Spur Gears Pitch radii, number of teeth, pitch and module, transmission ratio. Tooth profile and smoothness of operation. Involute tooth profile: line of action, instantaneous center of relative rotation, sliding velocity, constancy of transmission ratio, dynamics of spur gears, modular sizing. Gear Trains Classification. Kinematics of simple gear trains, epicyclic gear trains, Willis’ formula. 7.2 Belts, Chains, and Ropes General Description General description and fields of application. Flat Belts Description of operation and fields of use. Kinematics and micro-slips. Calculation of frictional forces between belt and pulley and relation between tensions of driving and driven sides. Verification of transmitted torque. V-Belts, Toothed Belts, Chains: overview. 8. Mechanical Devices Operating by Friction Introduction to brakes and clutches. Rigid and free engagement motion. Types of brakes: shoe, band, disc, and drum brakes. Materials used. Detailed analysis of shoe brake (calculation of braking force) and disc brake (calculation of braking torque). Types of clutches: flat, multi-plate, and conical. 9. Vibrations of a Mechanical System 9.1 Single Degree of Freedom System Generalities Definition and relevance of the study field. Modeling of oscillating systems. Calculation of equivalent stiffness. Formulation of dynamic equations. Examples. Free Vibrations Undamped free vibrations. Natural frequency. Initial conditions. Damped free vibrations. Damping factor. Cases with damping factor less than, equal to, and greater than one. Forced Vibrations Complete solution and particular integral as steady-state motion for systems with and without damping. Harmonic excitation: complex exponential representation of excitation and response; dynamic amplification and phase shift of response. Periodic excitation: Fourier series, superposition principle. Step excitation with and without damping. General excitation: Duhamel’s integral and convolution integral. Frequency Response Function (FRF) Overview of the Fourier transform and definition of the frequency response curve (FRF). Calculation of complex response using complex excitation. Relationship between unit impulse response h(t) and H(ω). Frequency response curves: receptance, mobility, and inertance. Considerations on viscous and structural damping. Vibration Isolation Cases of base excitation and transmission to the base; definition, calculation, and analysis of transmissibility. Air springs. Example: rotor with eccentricity. 9.2 Two Degrees of Freedom System Undamped free vibrations. Natural frequencies and normal vibration modes: example. Coupling of static and dynamic coordinates. Application to a two-DOF system: dynamic vibration absorber. Solved Exam Exercises with Solutions

Basic knowledge of Mathematical Analysis, Geometry, General Physics, and Rational Mechanics. Prerequisites: Physics I, Rational Mechanics, Technical Drawing and CAD Methods.

Attendance not mandatory

Exam and Assessment Methods The in-person exam consists of a written test divided into two parts. Details of the written test: Part 1: One kinematics exercise and one dynamics exercise, similar to the exam problems shared and solved during the course. Note: Both exercises must be passed in order for the student to pass the exam. Failure in even one of the two exercises results in failure of the entire exam. Part 2: A set of theoretical and application-based questions covering all topics included in the exam program and explained in the instructor’s lecture notes. Instructions for the In-Person Written Exam Failure to comply with these rules will result in the cancellation of the exam. During the written exam, only pens, pencils, erasers, rulers, and similar writing or drawing tools are allowed. Answer sheets are provided together with the exam paper. No other sheets, notes, books, phones, calculators, smartwatches, or any other electronic devices are allowed. When requested by the instructor, the student must write their personal details on all submitted sheets. The entire test lasts approximately 180 minutes, divided into three periods of 60 minutes each. The exam is considered passed if the student provides satisfactory answers to each of the three main questions. Students may withdraw from the exam at any time; in such a case, the exam will be considered not taken. Exam papers with solutions are available on the instructor’s Classroom notice board: https://classroom.google.com/c/MjE2ODc1NDgzNDRa?cjc=dbirst6u

The teaching method includes lectures alternating with exercises carried out by the instructor with active student participation. During the lessons, there will be opportunities for discussion and exchange on the topics covered in class. Four exam-style assessments are scheduled throughout the course.