Simulation analysis of cathodic ablation under the arcing action of vacuum rotary contacts

During the breaking process of the switchgear, a rotational movement of 1-10 degrees per millisecond is added to the contacts. Allowing for more even distribution of arc energy affects the cathodic ablation process. The cathode ablation process under the action of a vacuum rotary contact arc and the effect of rotary motion on the cathode surface are studied during arc ignition in a vacuum metal vapour arc in the paper. A three-dimensional (3D) cathodic ablation transient model with contact rotation characteristics is developed by considering the effects of arc pressure and the Marangoni effect, combined with the hydrodynamic equations and heat transfer equations. Based on a 3D transient model, the action of the arc on the cathode surface is compared and analyzed for different modes of contact movement. The results show that there is a lower cathode surface temperature, a smaller melt zone and a smaller ablation volume by the contact rotation method.


Introduction
Generally speaking, cathode ablation is much more severe than anode ablation when the anode is not active under low current conditions.When an arc is applied to a point on the contact, the pressure of the arc column and the energy of the arc injected into the cathode surface causes the contact material to melt and create a crater, resulting in a loss of mass and damage to the contact.A rotary motion is added to the linear motion of the contact, so that the arc energy spreads on the surface of the contact in a wider range, thereby affecting the ablation of the contact.
A modified 2D axisymmetric model was developed to consider the effects of plasma clouds, evaporation, hot-field emission and back-diffusion electrons to simulate the detailed physical processes of the development and formation of vacuum arc cathode sites [1] .The generation and development of a cathode pit at the cathode point in a vacuum arc are modelled using hydrodynamic and heat transfer equations [2] .A 2D axisymmetric transient model of the three-phase phase transition is developed, which takes into account the Marangoni effect and the role of surface tension in the formation of cathodic etch pits [3] .A semi-empirical hydrodynamic model based on the structure of the vacuum arc cathode point was developed to describe the formation of micro-pits on the cathode surface and the initial stages of liquid metal jet formation [4] .A 2D axisymmetric fluid dynamics model has been developed to describe the formation of craters and liquid metal jets on vacuum arc cathodes using the Navier-Stokes equation for incompressible viscous fluids with free surfaces and the heat transfer equation that takes convective heat transfer into account [5] .
Most domestic and international researchers have studied the process of vacuum arc action on the cathode surface in the traditional straight pull-open manner.In this paper, on the basis of the group's previous research, a 3D transient cathodic ablation model is established with the results of a steady-state vacuum arc simulation as the boundary conditions.This paper analyses variations of parameters such as temperature, melt pool extent and ablation of the cathode surface by the vacuum arc in the presence of rotating contacts.This is an innovative exploration of the vacuum arc opening mechanism, which clarifies the action on the cathode surface under the rotating action of the vacuum arc contact under low current conditions.

Physical model
Since the melting and evaporation of the cathode material is a time-varying process, the simulation uses a transient model.In our simulation we set the arc ignition time to 10 ms, due to the short simulation time and the relatively slow heat transfer rate, so the 3D modelling was only carried out for the contact piece.The simulation is set up as follows: the whole contact piece material is pure copper with a radius of 27.5 m and thickness of 5 mm.The cathode ablation model is shown in Figure 1.The physical model is based on the following assumptions: (1) When the anode is localized in a solid-liquid or liquid phase, the gravitational effect of the molten zone is considered.
(2) The loss of cathode material mass is considered due to evaporation and the deformation of the surface.
(3) The energy loss is considered due to the evaporation of metal vapour.
(4) The effect of the latent heat of melting during the phase change is considered.

Mathematical models
The mathematical model includes the mass conservation equation, the momentum conservation equation and the heat transfer equation.
where ρ is the density of copper; u is the liquid flow rate vector; t is the simulation time. ( where P is the static pressure; τ is the stress tensor.
where T is the temperature; k is the thermal conductivity of the material; H is the enthalpy of the material; σ is the electrical conductivity of the material; j is the current density and the peak jm is taken as 2.3×10 7 A/m 2 .The data are from [6-7] and are presented as Gaussian pulses in the simulation as the current density varies in the radial direction.

Initial and boundary conditions 2.3.1. Initial conditions.
It is assumed the initial temperature T 0 = 295 K in the calculation domain at the start of the calculation.

Momentum boundary conditions.
P max is the peak pressure generated by the arc column during the arc ignition process [6, 7].r represents the role of the arc in the cathode surface center position and the distance between the center of the contact.The arc is not unique or fixed on the location, and can be generated in any position in the contact, in order to better study the contact rotation under the vacuum arc on the anode surface.In the simulation, we take x 0 = 12.5 mm, y 0 = 0 mm as the arc action position, and the arc action radius d l = 1.5 mm. m is the pressure distribution parameter.The momentum boundary condition u = 0 is set on the side.

Thermal boundary conditions.
We set the contact side and bottom thermal boundary conditions to 0. The energy on the cathode surface is divided into the energy injected directly into the contact by the arc q m , the energy lost by electron emission q e , and the energy loss caused by evaporation during the arc burning process q out , so the energy flow density injected into the cathode surface is expressed as:

Physical parameters of copper.
The physical parameters such as density, constant pressure heat capacity and thermal conductivity of the contact material in different states are related to temperature.The physical parameters of copper are described in [8-10].

Analysis of simulation results
The simulation is based on the MHD model [6-7] which simulates an energy flow density of approximately 1.5×10 7 W/m 2 at a peak of 50A and a peak current density of 2.3×10 7 A/m 2 .The contact is rotated by 0 deg, 30 deg, 45 deg, 60 deg and 90 deg in different opening modes to simulate the temperature, surface condition and ablation of the cathode surface during arc ignition in melting and evaporation, and to investigate the effect of vacuum arc on the ablation of the cathode under different rotation angles.

Contact surface temperature distribution curve
The contact surface temperature variation curves at different rotation angles are shown in Figure 2.With the injection of arc energy, the cathode surface temperature begins to rise.Because the arc energy is distributed along the radial direction, the temperature at the center of the arc is higher than the periphery.
As the energy continues to be injected into the cathode surface temperature rises to its peak, the curve is roughly consistent with the energy distribution trend, and its temperature peak is delayed by 1~2 ms, compared to the energy peak.As the contact imposes a rotating action, the arc cannot stay at a certain point.With the increase in the rotation angle, the temperature peak tends to reduce.In a given range of rotation, the larger the angle the contact turns, the more pronounced the trend will be.The figure shows that with the addition of rotation, the rate of the cathode surface temperature reaching the melting point decreases, and the time to reach the melting point at different rotation angles is 3.5 ms, 3.8 ms, 4.7 ms, 4.9 ms, and 4.9 ms, respectively.

Contact surface melt zone width distribution curve
Starting from the arc generation, the temperature of the cathode surface starts to increase under the action of an electric field and heat conduction.When the surface temperature reaches the contact material melting point of 1355 K, the contact point between the arc and the cathode surface begins to melt.As the temperature continues to rise, the melt pool range begins to expand.After the temperature reaches its peak and starts to drop, because the contact temperature is still above the material melting point at this time, the range of the melt pool will continue to increase.When the temperature drops for a certain period of time, the melt pool range reaches its peak.Since the temperature of the surrounding area of the arc action is lower than the central area, even though the central part of the arc action range is still above the melting point of the material, the peripheral melting area will begin to solidify, making the melt pool range rapidly become smaller.After that when the temperature continues to drop below the melting point of the material, the melt pool range becomes 0. The contact surface melt pool width curves at different rotation angles are shown in Figure 3.The peak melt pool width sizes at different rotation angles of the contact are 3.68 mm, 3.68 mm, 2.45 mm, and 2.45 mm, respectively.

Contact surface melt zone depth distribution curve
As energy is injected into the cathode for a period of time, the contact material begins to melt.Under the effect of heat conduction, the temperature transfer to the inside of the contact starts as the surface temperature continues to rise, the internal contact also begins to melt, and the depth of the melt pool increases.As with the melt pool range, the depth of the melt pool does not peak when the cathode surface temperature peaks.After a period of decline following the peak surface temperature, the melt pool depth peaks and then decreases.The inward transfer of temperature decreases in layers, and when the surface temperature drops to a certain level, the depth of inward transfer will be below the melting point of the material, causing the depth of the melt pool to begin to decrease.When the temperature of the action center region is below the melting point of the material, the molten pool region on the cathode surface returns from the liquid state to the solid state and the depth of the pool drops to 0. The cathode pool depth versus time curve for different rotation angles is shown in Figure 4.It can be seen that the variation law under different opening and breaking methods is similar to the width of the fusion pool.The peak melt pool depths at different rotation angles of the contact were 0.38 mm,0.35mm,0.19 mm,0.1 mm, and 0.08 mm, respectively.

Contact ablation volume distribution curve
When the cathode surface melt pool appears, under the action of the arc pressure and arc energy, the cathode surface begins to appear molten crater, and the quality of the contact is changed.With the continuous input of arc energy, the molten pool increases in extent and depth, and the volume of the molten pit changes continuously.Since the rate of depression is related to temperature, when the temperature increases, the rate of change of the crater also accelerates.When the surface temperature reaches its peak, the rate of change also reaches its peak and then the rate of change gradually decreases.When the temperature is below the melting point of the material, the rate becomes 0, after which the volume of ablation does not change.The contact ablation volume variation curves for different rotation angles are shown in

Vacuum arc opening and closing test
A detachable vacuum interrupter was used to perform a 50 A straight pull opening and a 90 deg rotating opening, and a video camera was used to record the cathode surface changes during the experiment.The experimental comparison diagram is shown in Figure 6, from which it can be seen that the spread of the arc in the rotating opening is greater than that in the straight pulling opening under the same circumstances, allowing the arc energy to be evenly dispersed over the contact surface, which is mutually verified with the simulation.
(a) (b) Figure 6.Comparative diagram of opening and closing experiments

Conclusions
Through the simulation of the cathode action in the arc burning stage, the paper compares the effect of the vacuum arc on the contact action under different rotation angles of the contact rotating opening method and the traditional opening method.From the above analysis and discussion of the simulation results, the following conclusions are drawn.
(1) Contact rotation causes the energy injected into the contact not to be concentrated at one point.Thus, the energy is evenly distributed over an area of the contact surface.Compared to the traditional direct pull opening method, contact rotation tends to reduce the peak temperature of the negative surface.The trend becomes more obvious as the rotation angle increases.
(2) Contact rotation makes the vacuum arc at a point in the contact time shorter.Compared to the traditional straight pull open to increase the range of the melt pool, it reduces the longitudinal temperature transfer gradient.Therefore, the melt pool depth has a tendency to reduce, with the rotation angle increasing and the trend more obvious.
(3) Compared to the conventional straight pull movement, it reduces arc ablation of the cathode material during vacuum arc ignition.The greater the angle of contact rotation turns over a given range of rotation angles, the more pronounced the trend will be.

Figure 1 .
Figure 1.Schematic diagram of the cathodic ablation model.

Figure 3 .
Figure 3. Contact surface melt zone width distribution curve.