Diagnosis of Multiple Fixture Faults in Machining Processes Using Designated Component Analysis

Fixture imperfections influence dimensional variation on machining processes. Therefore, a systematic method to isolate fixture faults will allow improving product quality. This paper presents a diagnosis methodology to identify root causes of fixture induce workpiece variation in machining. The proposed methodology is based on designated component analysis which extracts predefined variation patterns from the production data. The proposed methodology integrates on-line measurement data, part geometry, fixture layout and sensor layout to detect multiple fixture faults occurring simultaneously. An application of the proposed method is presented through a computer simulation. INTRODUCTION Fixtures are used to locate and hold workpiece in machining. Fixture elements can be classified into locators and clamps. Locators establish the datum reference frame and provide deterministic locating. Clamps provide total restraint by holding the part in position under the application of external forces during the manufacturing process. In general for a machining process, a 3-2-1 locating scheme is used to uniquely locate rigid bodies. The 3-2-1 scheme constrains the six degrees of freedom of the parts. According to this principle three locators are placed in the primary plane (L1, L2, L3), two in the secondary plane (L4, L5) and one in the tertiary plane (L6). Consequently, variation or failures on each locator will directly affect the workpiece location and dimensional quality in machining. Dimensional quality for machining has been studied for decades, focusing on modeling and controlling variation sources such as kinematic error, static error, thermal error, tool wear and dynamic error. Methods such as Homogeneous Transformation Matrix (HTM) and Trigonometric method have been applied in machine tools to model the kinematic error [Love and Scarr, 1974]. Mechanistic and numerical methods (e.g., Finite Element Methods) have been developed for force induced static error, thermal and dynamic errors [Sutherland and DeVor, 1986]. In addition, several authors have studied dimensional quality for machining processes at the system level. Huang et al. [2002], and Djurdjanovic and Ni [2001] studied modeling and diagnosis of kinematic error using a state space representation. Zhong, et al. [2002] modeled how variation propagates in a machining system, considering multiple sources of variation including the kinematic variation and the force introduced static variation. Based on the new knowledge of product and manufacturing processes, measurement data can be “integrated” to the dimensional variation models to better predict the system behavior. In general, past research in fixture diagnosis is based on three major approaches: correlation clustering [Shiu, 1996], least square regression [Barton and Gonzalez-Barreto, 1996; Apley and Shi, 1998; Rong et al., 2001] and principal component analysis [Hu and Wu, 1992; Ceglarek and Shi, 1996; Ding et al., 2000]. Nevertheless, the aforementioned methods are generally not adequate for pattern recognition in the presence of multiple fixture faults. Since multiple faults are not uncommon in real applications, it is necessary to develop a diagnostic methodology that works for multiple fault cases as well as for single fault cases. Liu and Hu [2003] proposed a new method called designated component analysis (DCA) for process diagnosis. This methodology enables to successfully identify multiple fixture failures occurring simultaneously for sheet metal parts in a 3-2-1 locating scheme. However, they did not consider any interaction between the fixture faults and the manufacturing process. This paper presents a systematic methodology for multiple fixture fault diagnosis in machining processes based on designated component analysis. The proposed methodology enables to detect and isolate simultaneous fixture faults for a 3-2-1 locating scheme. A machining process variation model considering kinematic variation is used to study how fixture faults affect the final product variation. The variation propagation is modeled using the Homogeneous Transformation Matrix (HTM). The methodology integrates on-line measurement data after the machining process, part geometry, fixture layout and sensor layout to detect simultaneous fixture faults. The methodology considers processes of multiple operations at station level. This paper is organized as follows. Section 2 focuses on the variation modeling. Section 3 discusses the concept of designated components analysis. In Section 4, the diagnosis methodology for multiple fixture fault isolation in machining process is presented. A diagnosability analysis is addressed on section 5. In Section 6, a case study is conducted using computer simulation. Finally, conclusions are drawn in Section 7. FIXTURE VARIATION MODELING The diagnosis methodology requires simulating different variation patterns for machining. The calculation of the different modes relies on a machine level model, which is discussed in this section. The model uses a point-based representation of workpieces, fixtures, and machining operations. Fixture variation is modeled using the Homogeneous Transformation Matrix (HTM). According to [Zhong, et al., 2002], workpieces and machining operations can be represented by a set of points generated from a 3-D meshed model. These points include measurement, locating and clamping points. Each point (e.g., point 1 p ) is represented by a 4×1 vector (e.g., 1 1 ] 1 , , , [ T z y x p = ) using its local coordinates with respect to the local workpiece coordinate system (LCS_P). A machining process can be viewed as the interaction of a tool path (formed by a cutting tool) with the machined workpiece. Any point p on the newly machined surface corresponds to a point p′ on the tool path such that the ideal tool path is overlapped with the ideal new surface (Fig. 1). Therefore, a machining process is represented with a new surface using the pointbased model. New Surface Cutting Tool