Statistical Error Analysis for Dimensional Control in Automotive Body Assembly Process

The dimensional integrity of an automobile is one of the key quality characteristics, since poor fit can impact not only the downstream production processes, but also the customer's perception of quality. Principal component analysis (PCA) has been widely used to identify patterns of dimensional variation in the automotive body assembly process. It enables engineers to find measurement points that have large variances but fails to identify the measurement points that have large deviation from the mean with small variances. Correspondence analysis (CA) was applied to identify the deviation from the mean and bimodal distribution of measurement points in the automotive body assembly process. Two case studies are presented. By applying both CA and PCA, we have a better understanding for the deformation patterns in automotive body assembly process.

CAD/Tolerancing integration: Mechanical assembly with form defects

The fault diagnosis of dimensional variation plays an essential role in the production of an automotive body. However, it is difficult to identify faults based on small labeled sample data using traditional supervised learning methods. The present study proposed a novel feature extraction method named, semi-supervised complete kernel Fisher discriminant (SS-CKFDA), and a new fault diagnosis flow for automotive assembly was introduced based on this method. SS-CKFDA is a combination of traditional complete kernel Fisher discriminant (CKFDA) and semi-supervised learning. It adjusts the Fisher criterion with the data global structure extracted from large unlabeled samples. When the number of labeled samples is small, the global structure that exists in the measured data can effectively improve the extraction effects of the projected vector. The experimental results on Tennessee Eastman Process (TEP) data demonstrated that the proposed method can improve diagnostic performance, when compared to other Fisher discriminant algorithms. Finally, the experimental results on the optical coordinate data proves that the method can be applied in the automotive assembly process, and achieve a better performance.

<div class="htmlview paragraph">Coordinate measurement gages dominate in the area of dimensional control and variation reduction of automotive body assembly processes. However, coordinate measurement gages do not have the capability to track certain measured features. This incapability introduces inherent measurement error created by part (feature) mislocation in constrained non-measured directions. This inherent measurement error weakens the methods used for process control and variation reduction. In this paper, a principle of measurement uncertainty is developed in order to estimate the measurement error caused by this deficiency. The developed principle describes measurement error, which is independent of any other error related to the mechanical or optical coordinate measurement machines (CMMs, OCMMs). Additionally, an error map determined by the measurement <i>uncertainty principle</i> is created for error compensation. Simulations and two case studies in the area of automotive body assembly process control and variation reduction illustrate the proposed method.</div>

The simultaneous measurement and identification of position-independent geometric errors (PIGEs) and position-dependent geometric errors (PDGEs) of dual rotary axes in five-axis machine tools remain a significant challenge in precision machining. To address this issue, this study develops a geometric error measurement system for the dual rotary axes of a five-axis machine tool by integrating a scanning probe, a block, and a calibration sphere. Unlike conventional touch-trigger probes, the scanning probe acquires continuous measurement signals along the surfaces of the block and the calibration sphere, enabling the extraction of richer geometric features and providing sufficient data for the simultaneous analysis of multiple geometric error components. The proposed measurement system is implemented on a five-axis machine tool, Uni5X-400, manufactured by FALCON Machine Tools Co., Ltd., to measure the geometric information of the calibration sphere and the block and thereby identify 20 PIGEs and PDGEs associated with the dual rotary axes. A kinematic model of the measurement system is established using homogeneous coordinate transformation matrices. By applying forward and inverse kinematics, the spatial positions of the calibration sphere and block are derived, forming an explicit relationship between volumetric errors and geometric errors. The resulting error identification equations are solved using the least squares method. Experimental results demonstrate that the proposed approach can efficiently and accurately identify the geometric errors of the dual rotary axes and maintain robust reliability under real-world operating conditions, making it suitable for practical calibration and accuracy improvement of five-axis machine tools.

This paper proposes a modified volumetric error model that includes spindle error motions as well as geometric errors. The model is constructed using rigid-body kinematics and homogeneous transformation matrices and an additional error matrix describing spindle error motions is included. The suggested model predicts the positioning errors at a given axis position as a function of both the axis position and the engaged spindle rotation angle. Two circular interpolation tests (inner and outer circle of the same radius) are simulated and the machined part profiles are predicted. To verify the simulation results, machining tests are performed according to the ISO 10791-7 standard. The error model with spindle errors shows a better agreement, between the simulated and measured roundness errors, than the simple geometric model. It can be seen that the geometric errors determine the basic part profiles and the spindle errors change the basic profiles according to the magnitude of the errors and the spindle rotation angle.

Musculoskeletal disorder risk during automotive assembly: current vs. seated

X-ray computed tomography (CT) is considered as one of the most common techniques in non-destructive testing and is also an essential and important method in the field of dimensional measurement. For high-precision measurement task scenarios, geometric errors due to the instability of the CT motion equipment cannot be ignored and need to be accurately measured and corrected. In-situ testing of large objects such as geotechnical materials, mechanical assemblies, metal weldments and concrete specimens also requires high-precision CT imaging of their interiors to obtain information of interest. The rotation of the scanning parts for these large in-situ tests and sparse-view scanning mode also makes it difficult to measure geometric errors. This paper therefore proposes a method for simultaneous measurement of geometric errors based on a priori information for in-situ testing characteristics. This method is capable of measuring geometric errors in sparse view projections with a length accuracy of 0.1 mm and an angular accuracy of 6×10−5 radians in 0.5 seconds per angle, as the simulation results show. The reconstruction results show that this level of geometric error measurement accuracy provides a dimensional measurement accuracy of 0.01 mm for the internal structure. The data for the simulation experiments in this paper are generated from real concrete data by noisy simulation.

Recently, the modelling of variation propagation in multistage machining processes has drawn significant attention. In most of the recently developed variation propagation models, the dimensional variation is determined through kinematic analysis of the relationships among error sources and dimensional quality of the product, represented by homogeneous transformations of the actual location of a product's features from their nominal locations. In design and manufacturing, however, the dimensional quality is often evaluated using Geometric Dimensioning and Tolerancing (GD&T) standards. The method developed in this paper translates the GD&T characteristic of the features into a homogeneous transformation representation that can be integrated in existing variation propagation models for machining processes. A mathematical representation using homogeneous transformation matrices is developed for position, orientation and form characteristics as defined in ANSI Y14.5; further, a numerical case study is conducted to validate the developed methods.

A neural network based compensation strategy for five-axis machine tool error correction has been developed. It is capable of significantly reducing geometric, kinematic and thermal errors between the tool tip and the workpiece. The error prediction ability of the neural network is demonstrated using a simulation of the compensation strategy. A two-stage training procedure for learning the weights of the neural network is proposed. The first stage uses a simulation model to train the dominant relationships between the errors and the sensors. The second stage of training would use actual measurements made on a five-axis machine tool to learn the remaining subtle relationships between the errors and the sensors. The simulation of the machine is based on Homogeneous Transformation Matrices (HTM). They model the position and orientation errors in each structural component. These error matrices are multiplied together to find the error between the tool and the workpiece. The coefficients required by the HTM model were selected so that the simulation model closely matched the measured performance of the five-axis machine tool. Thermocouples were used to measure temperature, and a laser interferometer, with the appropriate optics, was used for position and orientation error measurement. Preliminary simulation results based on an analysis of the spindle support arm and the Z column are available for the first stage of training. They indicate that a reduction in error from 100μm to 5μm is possible using a neural network model.

Customized mechanical products based on orders have characteristics such as small batch sizes and multi-variety in production, which results in less availability of sample data related to assembly. Therefore, a problem of prediction of assembly precision exists due to the small number of samples. This paper studies the prediction method of mechanical product assembly precision based on the fusion of measured samples and feature fidelity samples. First, an assembly-feature fidelity sample (AFFS) generation method based on measured data is proposed, which expands the amount of mechanical product assembly feature samples through the meta-model concept. Then, a fusion method of measured samples and AFFS of mechanical products based on a double-layer learning network is proposed, which improves the under-fitting of a few samples and enhances the generalization ability of the model. Finally, case studies of gear-shaft assembly structure that are common in mechanical products, such as engines, gearboxes, and traction machines, were examined to verify the method we proposed and compare them with a tolerance analysis method and a machine learning method. The average errors of the assembly precision predicted by the method in this paper are 1.2% and 5.0%, respectively, which are better than the outcomes of SVR and NNs. The average errors of SVR and NNs are 3.2% and 2.8% in case 1 and 19% and 17% in case 2, respectively. The results show that the method in this paper has advantages of smaller error fluctuations and the best accuracy stability.

Functionality-based Part Orientation for Additive Manufacturing

A statistical analysis of errors is performed by consideration of fringe number and geometrical errors. The results of the analysis are applied to an optimized interferometer for the fringe-counting method, and simple relations for the calculation of the condition number and standard deviation are discussed, taking into account overdetermined equation systems.

Fixtures are an essential component of manufacturing and production. They are used to accurately position a component or workpiece within a machine-tool coordinate system. During material removal, the function of the fixture is to ensure the stability of the workpiece which is constrained to meet the design requirements. The fixture performs this function by providing accurate and repeatable location of the component with respect to the machine tool, and by resisting motions, deflections, and distortions of the workpiece under the influence of the cutting forces. Therefore, the focus of this paper is to develop a methodology that analyses and optimises the fixture parameter configurations using a genetic algorithm (GA) with an ANSYS parametric design language (APDL) of a finite element analysis that minimises the geometric dimensional tolerance errors of the final component dimensions. Here, the workpiece is located and constrained in a fixture, as it undergoes material removal owing to the insertion of a drill bit. The deformations and distortions of the workpiece are modelled at discrete intervals throughout the drilling process. Three case studies were used to illustrate the application of the proposed approach. The first explains the methodology used in this research. The second and third explain the control of deformation and geometric error of the hole in sequential and simultaneous drilling operations by optimising the fixture parameters using GA. This work minimises the deformation of the workpiece using a GA–ANSYS integrated tool. Then, the same layouts given by the integrated tool are used in the experimental setup, and it is found that the errors found in the perpendicularity and circularity of the drilled holes are minimal when the above geometric dimensional tolerances were checked using a coordinate measuring machine.

A new method compensating geometric error components of a four-axis horizontal machine tool is presented in this paper. Homogeneous transformation matrices (HTMS) and error conversion are integrated in the compensation strategy. A mathematical model which contains 29 geometric error components is established based on HTMS and the errors in X, Y and Z directions are obtained through calculation. The errors in three directions are compensated by shifting the corresponding axis. But the configuration of this machine tool is X-axis, Z-axis, B-axis, C-axis without Y-axis, so the errors in X, Y and Z directions need to be converted into X, Z and C directions which is different from the traditional machine tools. The errors after conversion are used to compensation directly. This approach is significant for the error modeling and compensation which is an easy and efficient way to improve the precision of the four-axis machine tools.