Mechanical Engineering

Introduction to PDEs and Classification

• Prerequisites in linear algebra.
• Prerequisites in integration.
• Prerequisites in solving ordinary differential equations.
• Prerequisites in multivariable functions.
• Terminology and Examples of PDEs.
• Classification of second-order linear PDEs.

Fourier Series

• Physical motivation.
• Space of square-integrable periodic functions.
• Trigonometric series.
• Fourier coefficients.
• Fourier series in L¹ (Dirichlet's Theorem) then in L² (Parseval's Identity).

Fourier Transform

• Analysis and Synthesis of the Fourier transform on L¹.
• Algebraic and differentiation properties.
• Inverse transform and Plancherel formula.
• Convolution.
• Transform on L² and illustrative examples.

Sturm-Liouville Theory

• Definition.
• Examples and properties of solutions.

Solving PDEs by Separation of Variables

• Well-posed problem and Boundary conditions.
• Homogeneous 1D heat equation.
• Homogeneous 1D wave equation.
• General overview of the separation of variables method (Homogeneous equations, then with source term, then with non-homogeneous boundary conditions, and the relevance of knowing the associated Sturm-Liouville problem).

Fluid Statics

• Introductory definitions and general properties of a fluid.
• Forces acting on a fluid particle.
• Statics of incompressible and compressible fluids.
• Manometry.
• Buoyancy force.
• Forces and moments exerted by a fluid on plane and curved surfaces.
• Pressure distribution in rigid-body motion.

Fluid Dynamics

• Dynamics and kinematics of fluids.
• Euler's equation.
• Bernoulli's equation.
• Conservation of mass.
• Control volume and Reynolds transport theorem.
• Linear momentum equation.

• Fundamental concepts of signals and systems.
• Transfer functions of linear time-invariant systems.
• First-order systems.
• Generalized first-order systems.
• Second-order systems.
• Time-delay systems.
• Transfer locus in Bode plots and asymptotic sketching.
• Introduction to state-space representation.

Mechanical Design

• Mechanism modeling.
• Design of removable complete joints (fasteners).
• Design of pivot joints: friction and bearings.
• Analyzing performance and deviations.

Geometric Dimensioning and Tolerancing (GD&T)

• Geometric: ISO method.

Manufacturing Analysis

Tolerancing

• Basic concepts and principles of dimensioning, notation rules, types of features.
• Zone-based specification.
  • Symbols.
  • Definition of different geometric tolerances (Form, Orientation, Location, Runout).
• Datums.
  • Types of features.
  • Single datum.
  • Common datum.
  • Datum system.
• Gauge specification: Modifiers.
  • Maximum Material Condition (MMC) M and Least Material Condition (LMC) L.
  • Envelope requirement E.
  • Projected tolerance zone P.
• Concept of favorable / unfavorable clearance in a joint.
• Dynamic tolerance diagram.
• Order of magnitude of tolerance intervals obtained with different manufacturing processes.
• Reading table for dimensional and/or geometric specifications.
• CLIC method.

Objectives

• Being comfortable with fundamental concepts related to GHG (greenhouse gas) emissions, and being able to perform simple calculations on the matter.
• Knowing the order of magnitude of key variables.
• Being able to retrieve emission values from the ADEME database and use them appropriately.
• Understanding ecological challenges in all their complexity and studying a specific issue.
• Gaining notions of life-cycle assessment (LCA) and implementing it.
• Being able to conduct research in scientific literature.
• Being able to understand and analyze figures/data.
• Drawing political conclusions from scientific facts and personal values.
• Debating, discussing, and confronting different viewpoints.

Objectives

• Developing skills to look for internships or jobs (personal assessment, search tools, tailored resumes and cover letters, analyzing job offers in French, interview preparation, intercultural communication).

Introduction to Heat Transfer

Fundamental Principles of Conduction

Steady-State One-Dimensional Conduction

Fundamental Principles of Convection

Forced Convection in External Flow (over a flat plate, around a cylinder or a sphere)

Fundamental Principles of Radiation

Analysis of Control Systems

• Open-loop and closed-loop transfer loci.
• The accuracy-stability dilemma.
• Statics of incompressible and compressible fluids.
• Responsiveness.

Design of Control Systems

• Series compensation.
• Parallel compensation.
• Feedforward compensation.
• State-feedback compensation.

Combinational Logic

• Boolean Algebra.
• Function representations and minimization.

Sequential Logic

• Design of sequential systems in the field of production.
• Detailed study of a specification language: Grafcet.
• Study of the Statechart language.
• Definition of operating and shutdown modes through the joint use of both languages.

Implementation of Control Systems using Programmable Logic Controllers (PLCs)

Main Concepts Introduced

• Requirements analysis and preliminary design.
• Dynamic modeling and identification of multiphysics technological systems.
• PID control and digital implementation.

Case Studies

• Thermal control and attitude control of Cubesats.

Modeling a Mechanical Architecture using Multiphysics Simulation Software

• Linking model to reality.
• Parameter configuration.
• Model validation.
• Exploitation of results.

Kinematic Modeling of a Complex System

• Blueprint reading.
• Kinematic diagram.
• Overconstraint (Hyperstatism).
• Equivalent joints.

Design and Dimensioning of Mechanical Systems

• Actuators.
  • Cylinders.
  • Motors.
• Pivot joints.

Project

• Modeling a leg of a quadruped robot.

Disassembly of gearboxes and differentials.

Objectives

• Explain the main concepts of Computer-Aided Manufacturing (CAM).
• Explain the main concepts of Computer Numerical Control (CNC) for turning and milling machine tools as well as the main concepts of digitization (DIG) associated with reverse engineering.

Objectives

• Adopt a methodology to successfully carry out product development within a quality assurance approach.
• Understand who the stakeholders are and identify the generated documentation.
• Interpret the implementation of production and assembly resources and methods, as well as product inspection and improvement.
• Acquire notions of cost / quality / deadline controls at all levels of the development and manufacturing cycle, with the objective of mastering the geometric quality of a product.
• Know the main technical means used for the dimensional and geometric inspection of mechanical parts.
• Know how to establish an inspection workflow for a specification by zone or gauge, using a surface plate or a CMM (Coordinate Measuring Machine).
• Know the main criteria for surface fitting (Least Squares, Tangent Least Squares, Min-Max).
• Be able to characterize a measuring device (calibration, interpretation of measurement uncertainties, etc.).
• Have some baseline concepts of arithmetic and statistical functional dimensioning.

Heat Treatments

• Special Steels for Mechanical Construction.
• Concepts of Heat Treatment of Steels: Quenching and Tempering.
• Implementation of a selection method for heat treatment conditions: IRSID-OTUA method.
• Implementation of heat treatments.
• Mechanical characterization of treated mechanical parts: Hardness testing - Tensile testing.

Welding

• Concepts in electric arc welding.
• Implementation of SMAW (Stick), MIG, and TIG techniques on Steel.

SIMGEST

• Simulation of 5 years of company operations (decision-making regarding production, finance, and marketing) using the SIMGEST business game.

Description

• Income statement.
• Cash flow.
• Balance sheet.
• Cost elements.
• Break-even point.
• Accounting for inventory in financial statements.
• Loan financing.
• Company profitability.