Systematic modeling of workpiece-fixture geometric default and compliance for the prediction of workpiece machining error

Control of workpiece machining error (WME) is a key concern in the design of a fixture system. In this paper, source errors, which are categorized into workpiece-fixture geometric default and workpiece-fixture compliance, are systematically investigated to reveal their effects upon the WME. The underlying mechanism is that source errors lead to the workpiece position error (WPE), the workpiece elastic deformations (WED), and the inconsistent datum error (IDE), and all of them will contribute together to the WME. Here, the IDE refers to the dimension deviation of the processing datum from the locating datum once two references do not coincide. An overall quantitative formulation is proposed for the computing of WME in terms of WPE, WED, and IDE for the first time. In detail, the WPE raised in the workpiece-locating and clamping process is evaluated based on the geometric defaults and local deformations of workpiece-fixture in the contact region. The WED relative to the workpiece-clamping process is determined by solving a nonlinear mathematical programming problem of minimizing the total complementary energy of the frictional workpiece-fixture system. Some numerical tests are finally demonstrated to validate the proposed approach on the basis of both theoretical and experimental data given in the references.