In order to prevent global warming, there is a need to reduce emissions of carbon dioxide, a greenhouse gas, and compressors for refrigeration and air-conditioning are required to improve both efficiency and reliability. In this paper, we focus on scroll compressors and examine weld deformation, which affects both efficiency and reliability. A scroll compressor consists of a cylindrical casing with lid caps and bottom caps circumferentially welded to each end of the casing, in which the compression element and electric motor are installed in a sealed container. The frame and bottom frame, which constitute the bearings, are fixed to the casing by plug welding, but deterioration of the coaxiality of these two parts has issues that directly affect the performance and reliability of the compressor. Experimental and analytical investigations of weld deformation in scroll compressors have revealed that the circumferential welding that attaches the lid cap and bottom cap to the casing causes the frame and bottom frame to tilt, which deteriorates the coaxiality of the main bearing and secondary bearing.

The stress intensity factor (SIF) of a semi-elliptical surface crack has been often used for evaluating the fatigue strength of structures. Previously accurate stress intensity factor distributions were analyzed along the crack front of a semi-elliptical surface crack by solving the hypersingular integral equation of the body force method. In this paper, to use the results conveniently, the accurate calculation formulas are provided by considering the solution of an elliptical cracks F_IIE, F_IIIE and the corner point singularity the semi-elliptical surface crack F_IISE, F_IIISE. Regarding mode II SIF F_IISE, by applying the least squares method to the whole range of F_IISE/F_IIE, accurate formulas are proposed. Regarding mode III SIF F_IIISE, accurate formulas are proposed by applying the least squares method to F_IIISE/F_IIIE in the range β ≥ 15° but directly to F_IIISE in the range β ≤ 15°. The formulas proposed in this paper provides the stress intensity factors with better than 1.0% accuracy.