In recent years, renovation of hydropower facilities has become an important issue in Quebec, as in most developed countries. Turbine runners, subject to fatigue cracking and cavitation, are among the most critical components needing repair. Repairs are done by welding. On martensitic stainless steel turbine wheels, a post welding heat treatment is required to reduce residual stresses, to restore the microstructure, and thereby maximize the lifespan of the repairs. This is the case of the Francis turbine wheels made of CA6NM. However, it is currently impossible to perform such a heat treatment on site.
To perform in-situ post-welding heat treatment, the Hydro-Québec Research Institute is currently developing a new robotic induction heat-treatment system. The system involved a flat spiral coil moved by a robot arm over the area to treat. One critical aspect is the accurate control of the temperature distribution in the area to be treated. For instance, the required temperature range on CA6NM is 620±10 °C. To this end, the objective of this research project is twofold: on one hand, it aims to develop a numerical model of the induction heating system to predict the temperature generated in the workpiece; on the other hand, the objective is to develop a method to optimize the heating path and parameters to generate the required temperature distribution. In both cases, the numerical methods must be as easily compute as possible, so it can be used on a laptop computer in the field.
As a first approach, the heat flux generated by the inductor is represented by an empirical heat source, implemented in a thermal finite element model. The heat flux density generated by the moving inductor is considered proportional to the time the inductor spends over a point. The average temperature distribution is then computed at each time step of a transient thermal simulation, reducing significantly the simulation time. A conjugate gradient algorithm is added to the finite element model to optimize the parameters of this average heat input source. Thus, the electrical power, the inductor path and geometry, as well as the inductor-workpiece distance are optimized to make the temperature distribution as uniform and as close as possible to the target temperature, in a given workpiece volume. The temperature distribution and the optimal parameters calculated with this approach are used to successfully perform a post-welding heat treatment on a CA6NM test plate.
Although these results demonstrate the validity of the average heat flux density approach for the moving coil, the empirical model is only valid for a limited range of electrical power, inductor position, and workpiece geometry. In order to accurately represent the physics of induction heating, a thermal-electromagnetic model is developed. The main challenge is to take into account the effect of the high-frequency of the induction system on the current distribution in inductors. The strong skin and proximity effects make the current distribution highly non-uniform: the uniform current distribution assumption used to model similar electromagnetic applications generates a significant error in power losses calculation; this results in a poor evaluation of the system efficiency.
To minimize the computation time, the actual current distribution is evaluated based on the integral formulation of the Maxwell equations. Compared to the widespread finite element method, the main advantage is that only the conductive regions are considered, reducing the number of unknowns. To simplify the model, the 3D geometries of the inductor and conductors are respectively represented by axisymmetric and straight 2D geometries. Conductors are discretized into circular or straight elements, for which the current density is assumed constant. Each element is represented by a resistor, with a self- and a mutual inductance. Kirchhoff's law is used to form a linear system of complex equations. The current flowing in each element is computed by solving a linear matrix system.
The self-inductance and mutual inductance of each element are calculated from the mutual inductance equation for filaments, separated by the geometric mean distance of their crosssection. New mutual inductance formulas between circular filaments are developed to take into account the effect of a ferromagnetic workpiece. New expressions are also developed to calculate the magnetic flux density generated by the inductor in presence of the ferromagnetic workpiece. These new formulas are expressed in terms of elliptic integrals, which are very efficient to compute. The results of the multifilament electromagnetic model agree with those obtained with a commercial finite element analysis software.
The electromagnetic multifilament model is coupled to a finite difference thermal model to compute the temperature in conductors and to the thermal finite element model to compute the workpiece temperature. The model is also coupled to a lumped element circuit that represents the induction system. The hysteresis losses in ferromagnetic materials are taken into account based on the concept of complex magnetic permeability. The coupled thermoelectromagnetic model is validated comparing the calculated losses in the induction system to experimental measurements. In addition, the measured temperature distributions in an UNS S31600 austenitic stainless steel plate and an AISI 1045 carbon steel plate are compared with the model predictions. Results confirm the accuracy and the efficiency of the model.
| Date | 15 Jan 2018 |
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| Original language | French |
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| Awarding Institution | - École de technologie supérieure
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| Supervisor | Henri Champliaud (Supervisor) & Tan Pham (Co-supervisor) |
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Gendron, M. (Author),
Champliaud (Supervisor) &
Pham (Co-supervisor),
15 Jan 2018Student thesis: Doctoral thesis › Doctorate in Engineering: Engineering