目的 超音速火焰喷涂（High-Velocity Oxygen-Fuel, HVOF）广泛用于复杂曲面构件涂层制备,但传统基于几何投影的厚度预测模型未充分考虑动态喷涂中距离与角度的耦合变化,导致精度不足。本文旨在建立融合喷涂距离与角度动态响应的多变量沉积模型,以提升复杂曲面上的涂层厚度预测精度。方法 通过设计喷涂距离与角度的梯度实验,系统获取涂层轮廓数据;基于此构建以双高斯分布为核心、能同时响应距离与角度变化的多变量参数化沉积模型。进一步以不同尺寸球阀为对象,在实际喷涂场景中对比传统投影模型与本模型的预测精度。结果 静态喷涂条件下,所建多变量模型对涂层厚度的拟合决定系数（R²）超过0.98。动态喷涂验证表明,该模型预测的平均相对误差低于15%,相较于传统模型误差降低约60%,显著提高了复杂曲面上的预测准确性。结论 通过融合多组沉积实验数据,所提出的多变量沉积模型实现了喷涂距离与角度的动态耦合建模,有效提升了超音速火焰喷涂在复杂曲面上的厚度预测精度。该模型不仅适用于球阀类构件,也可为航空发动机叶片、涡轮盘等复杂型面部件的喷涂厚度控制提供理论指导。

This study presents a high-fidelity dynamic model developed to accurately predict coating thickness distribution in high-velocity oxygen-fuel (HVOF) thermal spraying, a process critically important for applying protective coatings onto complex components such as turbine blades and industrial valves. A significant limitation in current process planning is the inaccuracy of traditional geometric models, which typically rely on projecting a static, axisymmetric deposition pattern onto the workpiece surface. These models fail to account for the dynamic and interdependent variations of two paramount process parameters: the instantaneous spray distance and the gun-to-surface incidence angle. This oversight introduces substantial prediction inaccuracies on curved surfaces, ultimately hindering the achievement of uniform coating thickness and the transition towards robust digital manufacturing protocols. The primary contribution of this work is a novel multivariable parametric deposition model that dynamically integrates the coupled effects of spray distance and angle, thereby enabling a fundamental shift from simplistic projection-based methods towards a physics-informed simulation of the actual deposition process. The foundation of this model is a meticulously designed experimental campaign aimed at decoupling the intertwined effects of spray distance and angle. Single-track deposition experiments are conducted on flat substrates using a commercial WC-12Co powder feedstock. A Praxair JP-8000 HVOF system is employed, with fuel flow rates and powder feed rate maintain at constant and optimized levels. The experimental matrix constitutes a full factorial design, with spray distances systematically varying from 150 millimeters to 350 millimeters in increments of 50 millimeters, and gun incidence angles varying from 0 degrees to 60 degrees in 15-degree increments. The three-dimensional topography of each resultant coating bead is captured with high precision using a white-light optical profilometer, generating a comprehensive dataset of deposition profiles under varied geometrical conditions. Analysis of this dataset yields a critical insight: the fundamental deposition footprint is not a fixed entity but a shape-changing function. Key profile characteristics, including the peak deposition rate, the longitudinal and transverse distribution widths, and the degree of profile asymmetry, are all determined to be complex, non-linear functions of both spray distance and angle simultaneously. This finding invalidates modeling approaches that treat these parameters' effects as separable or additive. In light of this, a new multivariable deposition model is formulated. The model architecture centers on a dual Gaussian function, which provides a flexible basis for representing asymmetric deposition patterns. Its core innovation lies in parameterizing this Gaussian footprint: the four defining parameters are not constants but are instead expressed as distinct second-order response surfaces, where each parameter is a function of the instantaneous spray distance and angle. The coefficients for these response surface equations are uniquely determined through multivariate regression analysis of the complete experimental dataset. Consequently, the model's deposition footprint dynamically adapts its shape at every point along a robotic toolpath based on the real-time local geometry. For final thickness prediction on a complex part, the total coating buildup at any surface point is computed by spatially integrating the contributions from this continuously adapting footprint along the entire spray trajectory. Model validation is performed at two levels. Under static and single-track conditions, the model demonstrated exceptional fidelity, achieving a coefficient of determination exceeding 0.98 when fitting the measured bead profiles across the entire range of tested distances and angles. The most significant evaluation involves dynamic spraying trials on rotating spherical test specimens designed to mimic industrial ball valves of varying diameters. Compared with thickness maps obtained via coordinate measurement machining, the predictions from the proposed model show a mean relative error of less than fifteen percent. In a direct comparative assessment, a conventional normal projection model utilizing a fixed Gaussian distribution yields a mean relative error of approximately thirty-seven percent for the same components. This represents a sixty percent reduction in prediction error attributed to the new model. The detailed spatial analysis of the error distribution further confirms that the conventional model produces consistent and systematic biases, over-predicting thickness on surfaces oriented away from the gun and under-predicting on surfaces facing it. The proposed model successfully mitigates this systematic bias by accurately capturing the coupled distance-angle effect. In conclusion, this research delivers a significant advancement in the simulation and prediction of thermal spray processes. The developed model moves beyond the limitations of static projection by introducing a dynamic and coupled-response framework that accurately reflects the physical deposition behavior on complex geometries. It provides a powerful and practical tool for offline robot path programming and process optimization, enabling "first-time-right" coating applications on critical components. Furthermore, the generalizable response surface methodology establishes a foundation for future model extensions, such as the inclusion of additional process variables like traverse speed, or its adaptation to other thermal spray or directed energy deposition techniques, paving the way for more integrated and intelligent digital manufacturing solutions.