Research Papers

Analysis of an Approach for Detecting Arc Positions During Vacuum Arc Remelting Based on Magnetic Flux Density Measurements

[+] Author and Article Information
Miguel F. Soler

School of Mechanical, Industrial,
and Manufacturing Engineering,
Oregon State University,
Corvallis, OR 97331-6001
e-mail: solerm@oregonstate.edu

Kyle E. Niemeyer

School of Mechanical, Industrial,
and Manufacturing Engineering,
Oregon State University,
Corvallis, OR 97331-6001
e-mail: kyle.niemeyer@oregonstate.edu

1Present address: Sierra Olympic Technologies, Hood Rover, OR 97031.

2Corresponding author.

Manuscript received May 19, 2017; final manuscript received February 12, 2018; published online April 6, 2018. Assoc. Editor: Satish Bukkapatnam.

J. Manuf. Sci. Eng 140(7), 071004 (Apr 06, 2018) (9 pages) Paper No: MANU-17-1330; doi: 10.1115/1.4039439 History: Received May 19, 2017; Revised February 12, 2018

Vacuum arc remelting (VAR) is a melting process for the production of homogeneous ingots, achieved by applying a direct current to create electrical arcs between the input electrode and the resultant ingot. Arc behavior drives quality of the end product, but no methodology is currently used in VAR furnaces at large scale to track arcs in real time. An arc position sensing (APS) technology was recently developed as a methodology to predict arc locations using magnetic field values measured by sensors. This system couples finite element analysis of VAR furnace magnetostatics with direct magnetic field measurements to predict arc locations. However, the published APS approach did not consider the effect of various practical issues that could affect the magnetic field distribution and thus arc location predictions. In this paper, we studied how altering assumptions made in the finite element model affect arc location predictions. These include the vertical position of the sensor relative to the electrode–ingot gap, a varying electrode–ingot gap size, ingot shrinkage, and the use of multiple sensors rather than a single sensor. Among the parameters studied, only vertical distance between arc and sensor locations causes large sources of error and should be considered further when applying an APS system. However, averaging the predicted locations from four evenly spaced sensors helps reduce this error to no more than 16% for a sensor position varying from 0.508 m below and above the electrode–ingot gap height.

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Fig. 1

Cross section of VAR furnace. Image taken from Woodside et al., Reprinted by permission from Springer Nature © 2013 [2].

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Fig. 2

Diagram of the geometry employed in the model (not to scale)

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Fig. 3

Norm (i.e., vector magnitude) of the magnetic flux density with respect to arc location in Cartesian coordinates

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Fig. 4

Overhead cross-sectional diagram of a VAR furnace, shown with four two-axis magnetic field sensors and the geometry of the variables for one sensor

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Fig. 5

Predicted arc locations compared to exact locations (calculated using furnace coefficients mr = 8.15 × 10−8 N/A2, mt = 4.98 × 10−8 N/A2)

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Fig. 6

Statistical error distribution of predicted arc locations with respect to vertical sensor position using constant furnace coefficients

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Fig. 7

Error distribution of predicted arc locations with respect to vertical sensor position using adaptive furnace coefficients

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Fig. 8

Arc location prediction trends for varying, single sensor position in the positive z direction using constant furnace coefficients; the sensor is located at (0 and −0.64 m): (a) arc location prediction with a sensor at the electrode–ingot gap (0 m above the electrode–ingot gap), (b) arc location prediction with a sensor 0.0762 m above the electrode–ingot gap, (c) arc location prediction with a sensor 0.254 m above the electrode–ingot gap, and (d) arc location prediction with a sensor 0.508 m above the electrode–ingot gap

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Fig. 9

Arc location predictions with varying gap height for a single sensor location

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Fig. 10

Error in predicted arc locations with varying contact zone height, mimicking ingot shrinkage

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Fig. 11

Arc location predictions for two sensors positioned on opposite sides of the furnace: (0 m and −0.64 m) and (0 m and 0.64 m)

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Fig. 12

Arc location predictions using four sensors around the furnace; these locations are the average of the locations predicted by each of the four sensors

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Fig. 13

Comparison of error distribution and magnitude from using one sensor versus four sensor averages; error is based on the difference between predicted and exact values: (a) percent error of arc location predictions using one sensor from the exact locations and (b) percent error of arc location predictions using four sensor averaging from the exact locations

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Fig. 14

Percent error statistical distribution for 1, 2, 4, 8, and 16 sensors

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Fig. 15

Error distribution of predicted arc locations with respect to vertical sensor position using the average results from four sensors



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