Research on identification and quantification method of weak parts of machine tool structure stiffness with uneven distribution of measuring points

Accurately identifying the weak spots of machine tool stiffness is of great significance for enhancing the overall structural stiffness. In practical engineering applications of damage identification, sensor placement on the structure being measured is often obstructed. As a result, it is difficult to achieve equidistant sensor distribution during the actual measurement process. During the identification of weak spots, the identification indicators designed based on equidistant sensor distribution often fail or produce relatively large errors. This paper proposes a novel method of identifying weak spots based on the flexibility curvature matrix, introducing a new indicator ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mrow> <mml:mi>a</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>″</mml:mo> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> ) that eliminates the equidistant sensor distribution constraint and enables the quantification of damage severity. Using a cantilever beam as an example, the study systematically evaluates the effectiveness of this indicator in identifying damage under various damage scenarios and noise interference through simulations. It also explores the impact of various indicators on identification results and enhances the identification accuracy for practical applications. The experimental verification of the proposed weak spot quantification indicator was performed through testing on an equivalent cantilever beam. The results confirmed its applicability even with unequally spaced sensors. This study shows that the developed identification indicator has high accuracy in detecting stiffness degradation in practical testing, even when measurement points are unevenly distributed. Thus, this work offers a solid experimental and theoretical basis for machine tool stiffness weak spot identification.