DINAMICA DEI SISTEMI MULTIBODY E DELL'AUTOVEICOLO

The first part of the course intends to provide the basic concepts for formulating the dynamic equations of motion of rigid and deformable bodies. All computational aspects for the computer-aided analysis of general multibody systems will be provided. Starting from the kinematic analysis of constrained systems, the computational methods in kinematics will be discussed using different formulations. The numerical implementation of several dynamic formulations, with emphasis on the Differential-Algebraic Equations, will be described. The main numerical integration schemes will also be investigated and applied to general multibody systems.

The second part of the course aims to provide the students with the main concepts of vehicle dynamics through a deep analysis of forces that govern their motion and determine handling performance (i.e., acceleration, braking, and cornering) and ride comfort. Theory and applications of suspension kinematics and compliance are provided to identify the main parameters related to both handling and ride comfort. Basic knowledge and numerical methods for tire modeling are provided, too. Principles of Multibody dynamics are used to create specific models to simulate K&C analysis of suspension systems and full vehicle dynamic maneuvers.

The skills acquired align with objectives 4, 8, and 9 of the United Nations' 2030 Agenda for Sustainable Development.

DUBLIN DESCRIPTORS:

Students will expand on their first-cycle knowledge, developing a strong inclination toward advanced professional development and the formulation of original ideas in engineering design, with a specific focus on sustainability. They will be able to source and manage computational codes to solve complex problems, as well as propose and compare alternative technical solutions within industrial and interdisciplinary contexts. Students will possess a solid autonomy of judgment, enabling them to critically evaluate sector-specific projects and integrate ethical and environmental considerations into their decision-making. They will demonstrate strong communication skills, effectively collaborating within teams and conveying the results of their work—through reports or technical notes—to specialists, technical staff, and less-qualified interlocutors. Finally, they will develop learning skills that will allow them to independently update their knowledge and readily adapt to the technological evolution of the mechanical sector.

Lectures: 28 hours

Exercises: 65 hours

Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.

Calculus II (Foundational)(Important), 

Linear Algebra (Foundational)(Essential),

 Rational Mechanics (Cultural) (Useful), 

Applied Mechanics (Cultural) (Useful).

1. – Introduction to multibody systems

2. – Fundamentals of planar and spatial kinematics

• Rotation matrices, invariants, and parametrization
• Angular velocity and instant screw
• Type of Coordinates
• Rigid Body kinematics

3. - Kinematic analysis

• Joints and constraints equations
• The Newton-Raphson algorithm

4. - Fundamentals of planar and spatial dynamics

• Review of rigid body dynamics
• Constrained equations of motion and DAE
• Reaction forces and Lagrange multipliers
• Inverse dynamics and examples

5. - Direct dynamics

• The Baumgarte stabilization method
• Penalty and Augmented Lagrangian formulations
• Basic concepts on the numerical integration of the equations of motion
• The Runge-Kutta algorithm and applications
• The Newmark algorithm

6. - Introduction to vehicle dynamics.

• Road vehicle’s performance: handling, ride-comfort, safety
• Forces applied to the vehicle
• Tyre performance

7. - Longitudinal dynamics

• Driveline layouts
• Longitudinal motion at a constant speed, calculation of max speed
• Acceleration performance: basic equations, maximum acceleration and slip limit
• Braking performance: basic equations, maximum longitudinal deceleration

8. – Suspension and steering systems

• Main suspension parameters, kinematics, roll stiffness
• Kinematics and Compliance analysis (K&C)
• Multibody simulation of K&C tests

9. – Cornering and handling

• Single track model: basic equations, steady-state cornering, understeer/oversteer, static margin, force derivatives and vehicle stability, transient dynamics
• Vertical load transfer, suspension effects on cornering, roll motion and roll stiffness distribution
• Multibody simulation of vehicle handling

Genta G., Morello L. (2007). The automotive chassis Vol. 1 – Components design; Vol. 2 – System design. Springer. (Dinamica autoveicolo)

Lecture notes. (Multibody)

Learning assessment may also be carried out online, should the conditions require it.

To ensure equal opportunities and in compliance with current legislation, interested students may request a personal interview to arrange any potential compensatory and/or dispensatory measures, based on the educational objectives and their specific needs. Students may also contact the CInAP faculty liaison (Center for Active and Participatory Integration — Services for Disabilities and/or Specific Learning Disorders - SLD) of their Department (https://www.cinap.unict.it/content/referenti).

MULTIBODY SIMULATION

• rotation matrices
• Kinematics of constrained systems
• Constrained equations of motion and AED
• Reaction forces and Lagrange multipliers
• The stabilization of Baumgarte

VEHICLES DYNAMICS

• Tire forces at contact patch and examples 
• maximum acceleration and deceleration on flat roads 
• understeer plot and gradient
• suspension characteristic angles and lengths, numerical examples