Analytical-Numerical Stress Analysis and Redesign of Perforated Backing Plates in Industrial Diaphragm Pumps: Degradation of Boundary Conditions and Optimal Ligament Configuration

Abstract

Abstract

The perforated backup plate of KARL KROYER MP 2C120 diaphragm pumps, used in the starch processing food industry, exhibits recurrent in-service fractures whose quantitative explanation and redesign solution have not been previously addressed in the literature. To solve this problem, an integrated analytical model is developed that combines, in a calibrable expression, small-magnitude spherical curvature, regular square-pattern perforation, and stepped peripheral clamping, calibrated against finite element numerical simulation and applied to the screening of eighteen geometrically feasible configurations. The chemical composition of the installed material was verified by portable optical emission spectrometry (PMI), identifying it as austenitic stainless steel AISI 301/1.4310 X10CrNi18-8, with nominal annealed yield strength σy=195 MPa according to EN 10088-2. The calibration quantifies an overestimation of 22.6% for the simply supported edge model and an underestimation of 51.7% for the clamped edge model; the dimensionless parameter ηBC=0.695 describes the effective degradation of clamping due to the reduced stiffness of the perforated belt adjacent to the edge and supports the use of the simply supported model as a conservative screening bound. The currently installed configuration operates with a safety factor FSop=0.89 with respect to yield strength, quantitatively explaining the observed fractures. Within the standard manufacturable space, the configuration d=5 mm, p=7.5 mm (η=0.333) minimizes the maximum equivalent stress predicted by the conservative screening model; this selection corresponds to the configuration with the maximal ligament efficiency and is preserved under the single-point calibration, which acts as a single global positive scale factor. The screening is verified by a direct finite element campaign performed on the complete d=5 mm family (configurations 1, 2 and 3) with the experimentally verified material properties. The verification confirms the predicted ranking and the peripheral location of the critical region, but shows that the smooth cross-center field is essentially invariant across configurations (187.3, 195.0 and 186.0 MPa), so the linear-scaling estimate previously used to anchor absolute margins is not supported; the benefit of the redesign accrues at the governing hole-edge concentration, which decreases from 338.2 to 261.5 MPa (22.7% reduction) yet remains above the yield strength of the annealed material. Geometric modification alone is therefore insufficient, and industrial adoption requires combining configuration 3 with material substitution to a cold-worked hardened state (C700: FS=1.91 on the governing peak) or a duplex alloy (FS=1.76), together with periodic non-destructive inspection. The central contribution of this work is the parameter ηBC as a quantitative descriptor of effective clamping degradation and the proposal of an industrially feasible redesign, integrated with complementary mitigation strategies, for KARL KROYER MP 2C120 pumps and geometrically equivalent equipment.