Efficient Simulation of Nonlinear Heat Transfer during Thermal Spraying of Complex Workpieces

Abstract

The quality of coatings, produced by thermal spraying processes, considerably decreases with the occurrence of higher residual stresses, which are especially pronounced for complex workpiece geometries. To understand the occurring effects and to aid in the planning of coating processes, simulations of the highly transient energy flux of the HVOF spray gun into the substrate are of great value. In this article, a software framework for the simulation of nonlinear heat transfer during (HVOF) thermal spraying is presented. One part of this framework employs an efficient GPU-based simulation algorithm to compute the time-dependent input boundary conditions for a spray gun that moves along a complex workpiece of arbitrary shape. The other part employs a finite-element model for a rigid heat conductor adhering to the computed boundary conditions. The model is derived from the fundamental equations of continuum thermodynamics where nonlinear temperature-depending heat conduction is assumed.

Towards a finite element simulation of coating by means of thermal spraying

“…However, these types of boundary conditions are not employed within the application of the presented framework. The implementation of the Robin boundary conditions follows [4], and the discretisation of equation (1) in space and time within an isoparametric finite element framework is outlined in [1].…”

“…Here, θ 0 is a reference temperature, θ e denotes the temperature of the element before the assembly, whereas θ e * represents the temperature of the element after the assembly. The energy difference, ∆E e * = E e − E e * , is induced as an internal heat source and has to be taken into account as a heat supply contribution to equation (1). This implies a transformation to the respective weak form and a discretisation in analogy to the procedure in [1].…”

“…The energy difference, ∆E e * = E e − E e * , is induced as an internal heat source and has to be taken into account as a heat supply contribution to equation (1). This implies a transformation to the respective weak form and a discretisation in analogy to the procedure in [1]. In the special case θ e = θ e * , the energy difference ∆E e * vanishes identically.…”

“…All other outer surfaces are assumed to be exposed to quasi non-moving air. The material parameters are chosen as documented in [1]. In time steps of ∆t = 100 ms, a total of 36 WC-Co splats are deposited step-wise to the plate so that, after 3700 ms, the whole plate is coated with 1 mm WC-Co coating and the discretisation comprises 20700 elements.…”

“…A very common coating system with high wear resistance consists of tungsten carbide (WC) and cobalt (Co) and is typically applied during the High Velocity Oxygen Fuel (HVOF) thermal spraying process at which thermal energy is induced into the coating as well as into the substrate. In order to simulate the heat transfer during thermal spraying, a finite-element-based software tool was recently proposed, [1]. In the present work this approach, based on [2,3] and references cited therein, is extended by the deposition of mass on the surface of a workpiece to be coated.…”