Investigation of influence of fixture layout on dynamic response of thin-wall multi-framed work-piece in machining

• The objective of this paper predicts dynamic responses of thin-wall multi-framed workpiece (TMW) with fixture constraints during machining.
• This workpiece-fixture system may be equivalent as a thin-multi-span plate (TMSP) with line and point supports.
• Double functions of Euler-Bernoulli beam can be utilized to describe mode shape of a TMSP
• The Lagrangian method is used to build an equation of dynamics of workpiece-fixture system by new mode shape functions.

In the aerospace industry, milling of the thin-wall multi-framed work-piece (TMW) is a critical challenging task due to the mutually coupling dynamics of adjacent frames and side plates. Evaluation of the effect of fixture layout on the dynamic response of thin-walled work-piece is a critical measure to determine whether the designed fixture can meet the requirements for the tightly specified tolerance of the part. A new analytical technique is proposed to determine the effect of fixture layout on the dynamic response of TMW during machining. In this modeling process, a workpiece-fixture system may be equivalent as a thin-multi-span plate (TMSP) with intermediate line and point supports. And then, double functions of Euler-Bernoulli beam can be utilized to describe mode shape of a TMW on basis of a span-by-span approach. Further, a dynamic equation of work-piece-fixture system can be modeled by the Lagrangian method in terms of new mode shape functions. Implementation of this technique is simple, enables avoidance of cumbersome mathematical calculations. Finally, the feasibility of the proposed approach is validated by a machining case.