Contact Mechanics in MBD
Contact Mechanics in MBD: Theoretical Foundations
MBD Contact
Professor, how is contact in MBD different from contact in FEM?
FEM contact is surface contact between deformable bodies. MBD contact is contact between rigid bodies (collision, meshing, etc.). The computation is lighter but does not include deformation.
MBD Contact Force Model
The Hertz contact model is fundamental:
$\delta$: penetration depth, $K$: Hertz stiffness, $D$: damping. For sphere-sphere, sphere-plane contact.
Summary
Hertz contact theory originates from a paper submitted by the 24-year-old Hertz in 1882
The classical theory of elastic contact, "Hertz contact," originates from a paper submitted by Heinrich Hertz (then 24 years old) in 1882 to the "Journal für die reine und angewandte Mathematik." Hertz is said to have conceived the mathematical model for contact area while observing interference fringes of light through glass lenses and completed it in two weeks. This theory is directly used in the design of rolling bearings, gears, and railway wheels today, and continues to be active as the fundamental equation for contact models in multibody systems for over 140 years.
Computational Methods for Contact Mechanics in MBD
MBD Contact Implementation
Summary
The choice between penalty method and constraint stabilization method determines accuracy
The main methods for multibody contact analysis are divided into two categories: the penalty method (generates reaction force proportional to penetration) and the Baumgarte constraint stabilization method. If the penalty stiffness is too high, numerical integration becomes unstable; if too low, unrealistic penetration occurs. MSC Adams, since its 2010 version, implemented an algorithm that automatically estimates the default contact stiffness as "material Young's modulus × square root of contact area," significantly reducing user calculation divergence troubles caused by setting failures.
Contact Mechanics in MBD in Practice
MBD Contact in Practice
Power transmission in gear trains, chain motion, ball bearing dynamics.
Practical Checklist
Cam-follower contact is the most frequently analyzed case in MBD
Cam-follower contact in engine valve mechanisms is one of the most typical practical applications of multibody contact analysis. Honda's inline 4-cylinder engine (2.0L) used MBD contact analysis to predict cam-follower bouncing (contact separation) at high RPMs (above 6500 rpm), and the history of optimizing the valve spring design over two generations is documented in the Honda R&D Technical Review (2004).
Contact Mechanics in MBD: Software & Solver Comparison
MBD Contact Tools
RecurDyn holds a top global market share in gear/chain contact analysis
RecurDyn by Korea's FunctionBay specializes in analyzing gear trains, chain drives, and belt mechanisms involving numerous contacting bodies with its fast algorithm (MFBD: Multi-Flexible Body Dynamics), forming a duopoly with MSC Adams in the manufacturing-oriented contact MBD market. The Hyundai Motor Group has adopted RecurDyn for contact analysis of engine accessory belts and automatic transmissions, and has published comparative data showing it is 10 times faster than Adams for chain multi-contact problems.
Advanced Technology
Advanced MBD Contact
Real-time MBD contact is the key to autonomous vehicle simulator development
Real-time multibody dynamics with contact is an essential technology for driving simulators used in autonomous vehicle development. Mechanical Simulation Corporation's CarSim, used by Toyota and GM, achieves real-time calculation of tire-road contact (Pacejka model) and suspension dynamics at 1 kHz. The contact force calculation algorithm is optimized for x86 multi-core CPUs, enabling high-fidelity vehicle dynamics simulation with a time step of 1 ms.
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