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Article Excerpt
1. Introduction
The calibration of part locating fixtures has significant effects on the dimensional quality of final products in a multi-station assembly process. Here, "multi-station" refers to the multiple stations or operations that are involved in producing a product within a complex assembly system. Examples of multi-station assembly processes include automotive body assembly, aircraft assembly and home appliances assembly.
Earlier research has indicated that 72% of all dimensional faults in automotive body assembly is due to fixture locator errors (Ceglarek and Shi, 1995). These fixture locators refer to the locating pins, or NC blocks, that directly determine the position and orientation of a part. In a 3-2-1 locating mechanism, the six degrees of freedom need to be controlled to position a rigid part. In a typical automobile body assembly process, there are more than 150 sheet metal parts that are assembled by more than 100 assembly stations using more than 1000 locators. During mass production, fixture locators may deviate from their designed positions which can lead to defects and quality loss in the final products. As a result, effective identification and control of those fixture locator errors are important, yet challenging, tasks due to the complexity of variation and propagation in a multi-station assembly process. The existing quality assurance techniques are mainly based on Statistical Quality Control (SQC), which focuses on on-line monitoring of quality measurements during production. In general, SQC techniques are effective in detecting quality changes, but they may not always provide a systematic means for adjusting fixture locators to eliminate the root causes of quality changes, especially for complex multi-station assembly processes. As a result, it is desirable to develop an effective approach to optimally adjust fixture locators based on in-process quality measurement with consideration of the overall cost of quality defects and the cost of adjustments throughout a whole production run. In this paper, the production run is defined as the total number of products produced by the existing production setup.
The proposed fixture locator adjustment strategy is based on the integration of Statistical Process Control (SPC) with Automatic Process Control (APC). SPC is used to monitor process changes while APC utilizes feedback or feedforward control to compensate the process change. Box and Kramer (1992) provided a detail discussion on SPC and APC integration. Grubbs (1983) first studied the adjustment problem by setting machine or process parameters to produce the desired outputs. His rule is to adjust a process by an entire observed deviation after the first item is produced. Then, a half deviation is adjusted after producing the second item and so on. More investigations have been done to extend Grubbs' work (Trietsch, 1998, 2000; Del Castillo et al., 2003). Triethsch (1998, 2000) referred to Grubbs' adjustment rule as the harmonic rule. In contrast to Grubbs, he allowed some adjustments to be skipped (Trietsch, 1998) and also took into consideration measurement and adjustment cost (Trietsch, 2000). Del Castillo et al. (2003) proposed a general formulation for the setup adjustment problems, including the Grubbs harmonic rule. The Bayesian method based on a Kalman filter is used in their formulation.
One major objective of the process adjustment is to reduce manufacturing cost, including the loss due to off-target quality and process adjustment cost. Various efforts (Crowder, 1992; Luceno, 2003; Lian and Del Castillo, 2006) have been made to control a manufacturing process to achieve those objectives with great success. However, most of those research efforts focus on a single variable or a single-station process. Some recent research provided the analysis of the adjustment problem in the case of multiple inputs in the model (Sachs et al., 1995). Del Castillo and Rajagopal (2002) applied the double EWMA control scheme to a multiple-input mutiple-output case. Although there are some studies that discuss multiple inputs and outputs in the process adjustment, the multi-station assembly process has not been fully investigated due to the complexity of the variation propagation and interactions among different stations. As a result, the fixture adjustment based on a single station alone (e.g., current, intermediate station) may not be able to fully ensure the optimal solution in terms of the total manufacturing cost in a multi-station assembly process. In the case of making adjustments in a multiple station process, Wang and Huang (2007) developed an automatic process adjustment method to compensate the mean shift of machining processes by adjusting fixture locators based on the equivalent fixture error (EFE) concept. A minimum-mean-square-error controller is designed based on the dynamic EFE model. However, this method cannot be directly applied to multi-station assembly process control. Therefore, this paper aims to develop an optimal fixture adjustment strategy by considering the variation propagation and interaction among different stations in a multi-station assembly process.
The proposed fixture locator adjustment methodology was inspired by the work by Lian and Del Castillo (2006), in which they proposed an optimal machine setup adjustment strategy for a single machine. However, their method is not directly applicable to the adjustment in multi-station assembly processes due to the inability to model the complex interrelations among stations. The complexity of variation propagation in a multi-station assembly process can be shown in two aspects: (i) fixture errors and adjustments on the upstream stations' effect on the performance of the downstream stations; and (ii) a part being transferred through different fixtures at different stations may generate propagated variations that combine all fixture errors among stations. Therefore, this paper aims to extend the existing adjustment strategy from single station control to multi-station assembly process control by using a dynamic programming approach.
The objective of this research is to develop a systematic methodology to determine the optimal fixture adjustment strategy for a prespecified control interval using the quadratic off-target cost function and the constant adjustment cost in a multi-station assembly process. In this study, it is assumed that the fixture position can be accurately adjusted or the variance of the adjustment errors can be obtained either from the tooling specifications or through off-line tooling calibration tests. The initial fixture errors are random variables that follow an unknown multivariate normal distribution. In order to adjust a multi-station assembly process, a state space model proposed by Jin and Shi (1999) and Shi (2006) is adopted to capture the fixture error propagation through all stations and its effect on product quality. This model describes the complex interrelation of variation propagation among stations and therefore provides an...
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