Michal Piersa

The simulation below has been some time coming – ever since Mike Law wrote his post on suspension kinematics about six weeks ago. Besides life getting in the way, the project ran a bit out of hand, as I became determined to combine the newly acquired suspension kinematics tool with my recent experiments on minimum lap time simulation and transmission modelling. The missing link between these components was extending my earlier 3-DOF vehicle model to a 17-DOF version. This new model includes 6 DOFs describing spatial motion of the chassis (including roll, pitch and yaw), 2 DOFs per wheel representing vertical suspension & wheel spin (8 DOFs in total), and 3 DOFs for the rotational displacements of the three main drivetrain components, being the ICE, gearbox and final drive. The drivetrain DOFs are coupled to the chassis DOFs via the rear wheel spin dynamics and the reaction forces at the ICE mounts & gearbox casing. Following Mike’s guidelines, I constructed a 3D kinematics model of a double wishbone suspension with pushrod actuator, including heave spring, anti-roll bar and anti-squat/dive geometry. I then used this model to extract a 1D lumped-parameter approximation compatible with the simplified suspension kinematics of the 17-DOF model. This involves algebraically linking vertical wheel displacements to key suspension parameters like camber angles, which in turn affect tyre forces through Pacejka’s magical formulas. While this approach sacrifices some accuracy, simplifications like these are necessary to keep simulation times low, especially in the context of minimum lap time optimization. As a Belgian who loves the Ardennes, it was about time I simulated the circuit of Spa-Francorchamps (even if last weekend’s race didn’t entirely meet expectations). Discretizing this hilly circuit into 2000 segments amounts to 40,000 variables to optimize – that’s 2000 times 17 DOFs plus 3 control variables: throttle/brake, steering angle, and gear selection. As I’m extending the capabilities of my simulator, I’m increasingly struggling to decide what and especially what nót to include in the limited space available for the animation. One thing that only subtly made the cut is the interaction between drivetrain and vehicle dynamics when shifting gears – can you spot it? Besides maximizing tyre grip, a critical role of the suspension is to keep the aerodynamic surfaces in optimal orientation relative to the airflow. This aspect wasn’t considered in the simulation below, as I used constant downforce and drag coefficients and ignored aerodynamic yaw and roll. My CFD skills have gotten a bit rusty over time, but lately I’ve been looking for a reason to brush them up. Generating aero maps to explore the impact of vehicle attitude on lap times surely sounds like a good excuse to go further down the race car dynamics rabbit hole.

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Can you do thermal analysis with FEA? At first glance, the answer seems obvious: of course you can. Most FEA software includes thermal analysis capabilities. Thermal elements have only one degree of freedom per node (temperature), making the solution fast. FEA works beautifully for pure conduction problems, and—although slower—it can handle radiation well. But convection? That’s where things get tricky. In FEA, convection is treated as a boundary condition defined by just two numbers: the convection coefficient and the ambient temperature. Simple enough to enter… but how do you know those values, or how they vary across the faces in contact with the fluid? In many cases, you don’t—and your “best guess” might be far from reality. So, can you really do thermal analysis with FEA? Yes, but not on its own. To get realistic results for convection, you need to start with CFD, find accurate convection boundary conditions, and then apply them to your FEA model. #FiniteElementAnalysis #ThermalAnalysis #Convection #HeatTransfer #CFD #EngineeringSimulation #FEA #Simulation #ThermalEngineering #ConjugateHeatTransfer

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In order to improve students' and trainees' understanding of different vibration patterns and how vibrations are generated and analyzed, the following simulation tools have been developed: Available: Free Vibration of a Single Degree of Freedom System Forced Vibration of a Single Degree of Freedom System Free Vibration of a Two Degree of Freedom System Base Excitation of a Single Degree of Freedom System Unbalance of a Single Degree of Freedom System Continuous Systems: Free vibration of Strings Continuous Systems: Free Vibration of a Cantilever Continuous Systems: Forced Vibration of a Cantilever and Resonance Signals: Acceleration, Velocity and Displacement Signals: FFT Processing Signals: FFT Parameters Signals: Harmonics Signals: Modulation Machine Component: Introduction to Vibration Machine Component: Fans Machine Component: Rolling Element Bearings Machine Component: Electrical Motors Advanced Analysis: Orbit and Full Spectrum Advanced Analysis: Phase and Tacho Signals Advanced Analysis: Runup/Coastdown Upcoming: Trainers: Single-plane Balancing Trainers: Two-plane Balancing Trainers: Shaft Alignment

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🧠 𝗗𝗲𝗹𝗮𝘂𝗻𝗮𝘆 𝗧𝗿𝗶𝗮𝗻𝗴𝘂𝗹𝗮𝘁𝗶𝗼𝗻: Still the Backbone of Mesh Generation Delaunay triangulation isn’t just a geometric trick — it’s a fundamental algorithm behind most unstructured meshes in FEM, CFD, and computer graphics. Its core rule is simple: No point lies inside the circumcircle (2D) or circumsphere (3D) of any triangle or tetrahedron. This is enforced using the InCircle test, which checks the sign of a determinant (shown in the picture). If the result is positive, the point lies inside — and violates the Delaunay condition. Why it matters? ✔️ Maximizes the minimum angle in 2D — helps avoid skinny triangles ✔️ Improves tetrahedron quality in 3D — though slivers can still appear 🔄 The Bowyer–Watson Algorithm Start with a super-triangle that encloses all input points Insert one point at a time Delete all triangles whose circumcircle contains the point Connect the new point to the boundary — re-triangulate the "cavity" 👉 Efficient: O(N log N) with spatial indexing (e.g. kd-tree) 👉 Needs robust predicates (like orient2D, inCircle) to avoid errors from floating-point imprecision 🔧 In Practice Constrained Delaunay: keeps input edges (e.g. CAD boundaries) intact Delaunay Refinement: adds extra (Steiner) points to improve quality Sliver removal in 3D uses volume or angle metrics to clean up bad elements Meshers like TetGen, Gmsh, and many hybrid methods rely heavily on Delaunay — even today (after 90 years). 📐 Want quality meshes that adapt to geometry and avoid poor angles? Delaunay is likely under the hood. #meshing #cae #fea #simulation #cad #cfd #tetmesh #femesh #engineering

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