DINAMICA DEI SISTEMI MULTIBODY E DELL'AUTOVEICOLO

Course Objectives and Overview

Part 1: Multibody System Dynamics

The first part of the course aims to provide fundamental concepts for formulating dynamic equations of rigid and flexible bodies, as well as computational aspects for computer-aided analysis of Multibody systems. Starting from the kinematic analysis of constrained systems, computational kinematic methods will be discussed using various formulations. The numerical implementation of different dynamic formulations will be presented, with a specific focus on differential-algebraic equations (DAE). Main numerical integration schemes will be analyzed and applied to general Multibody systems.

Part 2: Vehicle Dynamics

The second part of the course aims to provide students with core concepts of vehicle dynamics by analyzing the forces governing vehicle motion and determining handling performance (acceleration, braking, and cornering) as well as vibrational comfort. Theoretical and practical knowledge will be provided to perform elastokinematic analysis of suspension systems and determine characteristic parameters related to handling and ride-comfort performance. Additionally, widely used numerical methods for tire modeling will be analyzed. Concepts acquired regarding Multibody methodology will be used to build simulation models for suspension elastokinematic analysis and full-vehicle dynamic analysis.

Dublin Descriptors

1. Applying Knowledge and Understanding

• Multibody Modeling and Numerical Integration: Ability to formulate and numerically implement dynamic equations for rigid and flexible bodies, applying numerical integration schemes and differential-algebraic equation (DAE) formulations to solve complex kinematic and dynamic systems.
• Elastokinematic Analysis and Vehicle Dynamics: Capability to perform elastokinematic analysis of suspensions and build advanced simulation models (Multibody methods and tire modeling) to evaluate and optimize vehicle handling, braking, acceleration, and ride-comfort performance.

2. Making Judgements / Professional Profile

• Applicability and Sustainability: The acquired skills can be directly applied to quality management within organizations in the civil, industrial, and service sectors, in alignment with Goals 9, 11, and 12 of the United Nations 2030 Agenda for Sustainable Development.

3. Communication Skills and Teamwork

• Teamwork and Project Development: Ability to operate effectively within project teams to produce simulation models and engineering assignments, developing skills in collaboration, task coordination, and workload management in complex operational contexts.
• Presentation and Reporting: Ability to clearly, critically, and concisely present and defend dynamic simulation and analysis results developed in group settings, engaging constructively with team members and external stakeholders.

Lectures: 39 hours

Exercises: 52 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.

Rational Mechanics (Essential)

Applied Mechanics (Important)

Modeling and Simulation of Mechanical Systems (Important)

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, forcederivatives and vehicle stability, transient dynamics
• Vertical load transfer, suspension effects on cornering, roll motion and roll stiffness distribution
• Multibody simulation of vehicle handling

[1] Nikravesh, P. E. (2007). Planar multibody dynamics: formulation, programming and applications. CRC press.

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

[3] Shabana, A. A. (2009). Computational dynamics. John Wiley & Sons.

[4] De Jalon, J. G., & Bayo, E. (2012). Kinematic and dynamic simulation of multibody systems: the real-time challenge. Springer Science & Business Media.

[5] Shabana, A. A. (2013). Dynamics of multibody systems. Cambridge university press.

[6] Pennestrì, E. (2001). Dinamica tecnica e computazionale: sistemi lineari (Vol. 2). Casa Editrice Ambrosiana.

[7] Lecture notes.

[8] Jorge Angeles, Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms-Springer International Publishing (2014).

[9] Paulo Flores, Concepts and Formulations for Spatial Multibody Dynamics-Springer International Publishing(2015)

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

To guarantee equal opportunities and in compliance with current legislation, interested students may request a personal interview to arrange any compensatory and/or dispensatory measures, based on the learning objectives and specific needs. Students may also contact the departmental representative for CInAP (Center for Active and Participatory Integration — Services for Disabilities and/or Specific Learning Disabilities): 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