Digital Twin Series · Level 2 · Physics
Physics-Based Digital Twins
What will this machine actually do under load, heat and vibration, and can we trust the prediction?
A physics-based digital twin uses engineering physics (finite element analysis, thermal, fluid flow, multibody dynamics and more) together with real geometry, material properties and boundary conditions to predict how a real asset behaves in operation. It captures things a simple model cannot: stress, temperature, deformation, natural frequencies, contact and friction. It is validated with real-world data and then forms the physics engine of a high-fidelity digital twin. The tools below use simple hand-calculation physics, so you can see the cause and effect that a full FEA or CFD run would show.
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A beam on supports with a load at the middle (or at the tip for the cantilever) gives deflection and stress by closed-form equations, which is what FEA also solves for far more complex shapes. The colour shows how much of the allowable bending stress is used along the beam: blue is low, red is the peak. The deflection is drawn exaggerated. The optimiser looks for the lightest hollow section, keeping your width, that meets your deflection limit and safety factor. Use values from your own drawings and materials; mild steel is taken as 235 MPa yield and aluminium 6061-T6 as about 240 MPa.
This is a lumped model: the motor is one thermal mass that heats from its losses and loses heat through a thermal resistance to the ambient air. The steady temperature is ambient plus losses times resistance, and the time constant is resistance times heat capacity. A fan lowers the resistance. A full thermal FEA gives the temperature distribution inside the motor, but the same energy balance sits behind it. Insulation class limits: B 130 C, F 155 C and H 180 C maximum winding temperature, for motors designed for a 40 C ambient.
A machine on its support structure behaves like a mass on a spring. Its natural frequency is the square root of stiffness over mass, divided by 2 pi. If a running speed (or a multiple of it, such as a gear mesh) is near the natural frequency, vibration is amplified. Damping limits the peak but does not remove it. Modal analysis in FEA finds the natural frequencies and mode shapes of the real structure.
A linear model assumes force is always proportional to displacement. Real machines break that rule when the material yields, when a gap closes, or when friction sticks and slips. Nonlinear analysis follows the load in steps, which takes more time but predicts permanent deformation, contact forces and stick-slip, which a linear model misses.
Thermal-structural coupling is the simplest multi-physics case: heat from a motor or the process warms a part, it grows by the expansion coefficient times length times temperature rise, and if it is held back it carries stress instead. Other common couplings are electrical losses to heat, airflow (CFD) to temperature, and fluid pressure to structural deformation.
The test data come from a made-up test with a little measurement noise. The model has a stiffness error, which is what a missing joint flexibility or a wrong boundary condition looks like. Calibrate fits the stiffness to the test data by least squares. Validation then checks the model against data it was not tuned on, over the range where it will be used. A model is accepted when it predicts the measured data across the required operating conditions. For vibration, natural frequencies and mode shapes are compared with a modal test.
Mesh convergence: refine the mesh until the result stops changing. The curves are an illustrative pattern, not a measurement: displacement converges quickly, stress converges slowly, and the cost grows steeply. Always run your own study.
Figures are indicative and the examples are simplified hand-calculation versions of what FEA, thermal and dynamic solvers do. Verify any design with your own analysis and measurements.