scholarly journals Thermal Sources of Errors in Surface Texture Imaging

Materials ◽  
2020 ◽  
Vol 13 (10) ◽  
pp. 2337 ◽  
Author(s):  
Karol Grochalski ◽  
Michał Wieczorowski ◽  
Paweł Pawlus ◽  
Jihad H’Roura

This paper presents the influence of thermal phenomena on areal measurements of surface topography using contact profilometers. The research concerned measurements under controlled and variable environmental conditions. The influence of internal heat sources from profilometer drives and their electronic components was analyzed. For this purpose, a thermal chamber was designed and built. Its task was to maintain and control environmental conditions and, at the same time, separate the profilometer from external disturbances. Heat sources and temperature values for elements and systems were determined. It further enabled for the calculation of the displacements in axes as a function of temperature. The largest displacement in the probe due to internal heat sources for the considered cases occurred in the X-axis direction. Its value reached 16.2 μm. However, the displacement in the probe in the Z-axis direction had the greatest impact on the measured surface topography. These displacements for a thermally unstable profilometer reached 7.9 μm in Z, causing results even 90% greater than in the case of a device without such problems. The time after which a proper topography measurement can be started was also determined basing on obtained data. This time for tested profilometers was between 6 and 12 h. It was found that performing thermal stabilization of the profilometer significantly reduced surface irregularity errors. The stabilization time should be determined individually for a specific type of device.

A mathematical model of thermal process in an electrical machine was built as an example, presented as a three-layer cylinder where internal heat sources operate in one of the layers and heat is submitted to the other two by means of heat conduction. A method of solving the boundary-value problems for heat conduction equation in a complex area – a multi-layered cylinder with internal heat sources operating in one part of the layers and external ones in another part, is proposed. A method of problem solution in conditions of uncertainty of one of the boundary condition at the layers interface with conductive heat exchange between the layers is reviewed. The principle of method lies in the averaging of temperature distributions radially in the internal layers. As a result of transformations at the layers interface a boundary condition of the impedance-type conjugation appears. The analytical and numeric-analytical solutions of simplified problems were obtained.


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