A particle-system-based simulation method for robot spray coating thickness

Coating thickness uniformity is a key indicator of spray quality, and its improvement depends on process parameter optimization. Therefore, a simulation method combining computational efficiency with physical interpretability is required to predict coating thickness distribution under different process parameters. Existing methods primarily include physics- and model-based simulations. The former offers high physical interpretability but suffers from high computational cost and long solution times, while the latter is efficient but relies heavily on fitted experimental data and often lacks robustness when spray conditions or workpiece geometry change. To address these limitations, this study proposes a particle system-based simulation method for robot spray coating thickness prediction and trajectory optimization.

A particle system-based simulation framework for robot spray coating thickness is established in Unity. By retaining essential particle attributes, such as mass, velocity, and acceleration, and simplifying complex multiphysics processes such as atomization, airflow coupling, droplet breakup, and splash, the spray process is efficiently modeled. The workpiece surface is discretized into grid cells, and coating thickness is obtained by accumulating particle impacts on each grid element. For particle emission modeling, the droplet size is characterized by the volume median diameter, and the particle emission rate is determined based on the paint flow rate. A probability density approximation method for the initial particle emission velocity direction is established based on rejection sampling, enabling the simulation to be theoretically applicable to arbitrary distribution models. Furthermore, an elliptical double-beta distribution is adopted to describe the initial particle emission velocity direction. For spray gun motion modeling, trajectory interpolation is employed, with trapezoidal velocity interpolation used for position and spherical linear interpolation used for orientation to ensure smooth and continuous motion. In addition, a transfer efficiency parameter is introduced to represent the effective deposition ratio after the combined effects of diffusion, evaporation, and splash, such that the dissipative effects in the particle flight and deposition processes can be considered in a simplified manner. Coating thickness is then calculated based on the particle volume and material properties. Furthermore, a joint simulation and optimization framework is constructed by integrating Unity and Python through ML-Agents, enabling interaction between the simulation environment and external optimization algorithms. The performance of the proposed method is evaluated in terms of computational efficiency and prediction accuracy under typical spraying conditions.

The experimental results are as follows: 1) The computational efficiency of the proposed framework is mainly affected by the particle emission rate and grid density. Under appropriate parameter settings, the computation time of a single simulation ranges from several seconds to tens of seconds, which is significantly shorter than the tens of hours required by traditional physics-based simulation methods; 2) In planar specimen validation, the relative error between simulated and measured coating thickness is within 12%, indicating that the proposed method achieves acceptable prediction accuracy for practical applications.

By combining simplified physical modeling with an efficient particle system framework, this study efficiently predicts coating thickness distribution under different process parameters while balancing computational efficiency and physical interpretability. The proposed method maintains an acceptable prediction accuracy and can provide effective support for spray process parameter optimization.