کنترل کیفیت آماری از طریق تجزیه و تحلیل ارتعاش کلی

The present study introduces the concept of statistical quality control in automotive wheel bearings manufacturing processes. Defects on products under analysis can have a direct influence on passengers’ safety and comfort. At present, the use of vibration analysis on machine tools for quality control purposes is not very extensive in manufacturing facilities. Noise and vibration are common quality problems in bearings. These failure modes likely occur under certain operating conditions and do not require high vibration amplitudes but relate to certain vibration frequencies. The vibration frequencies are affected by the type of surface problems (chattering) of ball races that are generated through grinding processes. The purpose of this paper is to identify grinding process variables that affect the quality of bearings by using statistical principles in the field of machine tools. In addition, an evaluation of the quality results of the finished parts under different combinations of process variables is assessed. This paper intends to establish the foundations to predict the quality of the products through the analysis of self-induced vibrations during the contact between the grinding wheel and the parts. To achieve this goal, the overall self-induced vibration readings under different combinations of process variables are analysed using statistical tools. The analysis of data and design of experiments follows a classical approach, considering all potential interactions between variables. The analysis of data is conducted through analysis of variance (ANOVA) for data sets that meet normality and homoscedasticity criteria. This paper utilizes different statistical tools to support the conclusions such as chi squared, Shapiro–Wilks, symmetry, Kurtosis, Cochran, Hartlett, and Hartley and Krushal–Wallis. The analysis presented is the starting point to extend the use of predictive techniques (vibration analysis) for quality control. This paper demonstrates the existence of predictive variables (high-frequency vibration displacements) that are sensible to the processes setup and the quality of the products obtained. Based on the result of this overall vibration analysis, a second paper will analyse self-induced vibration spectrums in order to define limit vibration bands, controllable every cycle or connected to permanent vibration-monitoring systems able to adjust sensible process variables identified by ANOVA, once the vibration readings exceed established quality limits.

Periodically, the mass media report on the appearance of defective lots not detected during the manufacturing process and that therefore have come to the market. On occasions, the announced quantities are extremely high and the manufacturers face high losses in expenses of review and substitution of elements. This type of problem is usual in the automotive market, where volumes manufactured are high. The appearance of this type of situation persists in spite of the existence of agreements of quality coordinated between manufacturers and suppliers, as well as rigorous statistical systems of internal quality control, which assure the maintenance of processes within the quality levels established. In some cases, the nature of the quality problems makes their control complex, especially when the product specifications are tight. In this paper, condition monitoring-technologies are applied to the study of the mechanical behaviour of high-precision processes and then extend the concept of predictive maintenance to quality control. The aim is to discover the nature of vibrations generated by the process itself to detect early symptoms that indicate a separation from the quality zone objective, as well as to determine which are the variables that induce the vibration most suitable for predicting quality problems. It must be considered that at the moment there are very few companies that apply vibration analysis to machine tools in the periodical control of quality insurance. At present, the study of vibration analysis induced by the process is a subject that is almost unexplored. Specifically, one of the major quality problems in the bearings industry is the occurrence of noises when bearings are in certain functioning conditions. The existence of this fault does not need very big amplitudes but it conditions the frequency of the vibration, which has been determined by the type of chattering obtained in the manufacturing processes of their tracks of tread. Harris [17] defines that the roundness of a part on a certain section is correct when a point exists in this section from which all the points of the periphery are halfway, this point being the center of the circle. When the section is not totally circular, the part is considered to be out of roundness and this is specified as the difference in distance between the outlying points and the center. In Fig. 1, the degree of deviation of the roundness is the value r2−r1, that is, the difference between the maximum and minimum radii.When a part is manufactured by a machine tool, the profile obtained is of an irregular type in the rolling tracks and in the rolling elements (see Fig. 2); this will affect the durability and operation of the bearing.Chattering has a decisive influence on the final vibration of the bearing; its importance depends on the number of existing lobes and their depth. Besides, the problem is greater when taking into account that the final vibration is the result of the combined effect of roundness of rolling tracks, balls, superficial finishes of all surfaces and assembly conditions. This may lead to the manufacturing of noisy bearings if certain natural frequencies are excited, which is especially uncomfortable in automotive wheel bearings. The final consequences of a certain chattering of tracks are difficult to predict by means of theoretical models, due to the fact that in the final response of the mechanical system many variables related with the suspension system, tyres, etc. intervene; As a result what generally occurs is that, the frequencies of noxious chattering are evaluated rather than the final response of the vehicle. The chattering of surfaces is a phenomenon that is impossible to fully eradicate, although it can be controlled. These problems are more serious as requirements of roundness of pieces are more demanding. Therefore, the purposes of this paper are to identify important design variables affecting the quality of the bearings by using statistical tools in the field of machine tools, to evaluate quality results of the parts corresponding to the variation of process parameters, and to evaluate the quality of components by means of a cross-vibration analysis. In a bearing there are different sources of vibration, whose repercussion on its functioning will depend on the amplitude and frequency of occurrence. The condition-monitoring techniques have been applied with success in different systems and machinery; in DC motors [45], helicopters [22], turbine driving a centrifugal compressor [31], rolling element bearings [39] or railway systems [30]. However, their application to the motor vehicle industry is more limited, though some interesting contribution in this sector has been developed (see [25] but more related to warranty claims. In the literature related to the diagnosis of machinery, there are a great number of contributions (generally applied to bearings and gear boxes) that use vibration analysis together with statistical concepts; among them, the following can be outlined: [2], [6], [20], [23], [24], [26], [34], [36], [38], [40], [41], [43] and [47]. The diagnosis specifically applied to machine tools has been extensively analysed in literature too; in [35] a sum of condition-monitoring techniques applied to machine tools can be checked. In [42] autocorrelation analysis is used in conjunction with windowing capability to isolate causes for subsequent remedial actions. In [8] the Taguchi method and analysis of variance (ANOVA) were used to analyse the effect of the process of self-induced vibration. Snoeys [37] and Biera et al. [4] and [5] justify instability in the behaviour of self-induced vibrations of the grinding process. Ref. [11] presents experimental results from the in-process measurement of δ under chatter conditions on a cylindrical grinding machine.Ref. [12] describes the tests conducted to measure the variation in force caused by oscillation in part speed and its significant effect on chatter in grinding. In [46] a non-linear dynamic model is developed so that numerical simulations can provide a view of the stability of this grinding process for the design, analysis and verification of manufacturer roll grinding measurements. In spite of the work of Hahn [16], where different input variables are selected in the grinding process to improve the production grinding performance, the application to the follow-up and control of the quality processes by means of the application of these condition-monitoring techniques is a field that is practically unexplored at present. As explained in [3], less attention is devoted to developments in integrated condition-monitoring systems with data collected from maintenance, quality, production, etc., though the necessity to identify and eliminate quality deviations and causes of failure at early stages, thus assuring high-quality products, is widely recognised [1]. Nevertheless, the few papers and existing research that might be applied to quality control in machine tools are of a very general type. Neither process tolerances nor critical frequencies of vibration are considered, because the quantity of data produced would turn out to be impossible to handle [7] and [27]. This paper applies vibration analysis technology to a high-volume production line, composed of a group of similar high-precision grinding machines. The problem analysed is the sporadic appearance of chattered surfaces. This problem may cause quality defects to the extent of 10−6 m in parts due to the lobes resulting to any machining process. Thus, an effort must be made to control these small deviations that may, however, generate quality problems or otherwise seriously affect the behaviour of the vehicle and passengers’ comfort; the part analysed has significant influence on the safety of the vehicle, and therefore, control of potential failures is critical. During their normal cyclical functioning, the machine tools cross zones of insufficient quality, which suggests the existence of vibrations induced by the process itself. This aspect depends on the natural response of the mechanical system faced with the stimulation caused by the process. These deviations happen even when all the process parameters under control are within tolerance. The object of this paper is to reach conclusions about the relation between the mechanics of the process and the resulting quality, and thereby to establish a generic protocol of analysis. In order to do this, it is first necessary to evaluate the behaviour of global values of the different vibration units during work cycles, as well as analysing the influence of process variables in different mechanical vibration units in order to discover which mechanical variables show greater sensitivity against failure occurrence; this will be the starting point of the spectral analysis that will be developed in later contributions. For the attainment of these aims, an experimental design and variance analysis of the mechanical response of the process (alert variables) has been chosen, expressed as global values of displacements, velocities and accelerations, depending on the variation of entry parameters (cause variables). The number of variables that influence the quality of the part or mechanical behaviour of the process is high. The present protocol establishes criteria for selecting the most influential variables. Preliminary experiments were developed by altering different process variables; these experiences were evaluated along with other considerations to determine the most appropriate experimental design methodology for the analysis. Hereby, the set of variables effect, reason and alert with influence on the problem will be determined and included in the statistical analyses (see Fig. 3 for the process description followed in this paper).In the global experimentation, the quality outcome of parts manufactured (effect variables) during the sequence of experiments is also assessed in order to be able to detect the possible relation of the overall vibration value with the quality obtained. During the tests, the profiles of changes in magnitudes in different work cycles are also assessed, including the load and unload cycles of parts, the grinding wheel to part distance and the machining phases (rough, finishing). The aim of ANOVA of overall vibration values is to distinguish which of them or their interactions must be the basis for a later spectral analysis. The study is applied to interior and exterior rectified machines in a bearings factory of an important company that manufactures automotive components. The experimental phase of the protocol required the placement of vibration sensors in strategic places in machines, near the grinding wheel–part contact, so that vibrations caused during the elimination of material processes could be registered. The analysis carried out in this paper, applied to bearings, controls potential catastrophic failures in the bearings that could risk safety and comfort of the vehicle passengers. The paper layout is as follows. Section 2 explains the characteristics of the behaviour of the machine tools. In Section 3, the measurement system used for data acquisition is explained. In Section 4, the selection process of the variables to be included in the research is described. In Section 5, the hypotheses of the statistical quality control (SQC) model are shown. In Section 6, the overall vibration analysis carried out by means of ANOVA and quality results from the process to the product (automotive bearings) are described. Section 7 gives the conclusions and finally the bibliography.

Observation of the results obtained after the realization of the experiments previously described does not permit us to extract direct conclusions, so we turn to statistical analysis, which rigorously allows us to establish relationships between input and output variables. The multi-factorial ANOVA carried out with controllable variables and their effect on the influential variables provides the following results: 1. High-frequency displacements are related with 95% reliability to the input parameters grinding wheel diameter and grinding wheel speed. The statistical analysis also indicates that the influence of these variables is especially related to the interaction between them. This result coincides with observations on the field in which it is observed that the operator of the machine carries out changes in the grinding wheel speed when a situation where parts appear with chattering. 2. The rest of the vibration magnitudes do not present such a direct dependency as the displacement on the variation of process parameters, and so these must not be chosen from now on as characteristic elements of the process. 3. Output variables Lob A and Lob B are dependent on the grinding wheel diameter. Lob B is also influenced by the grinding wheel speed and high-frequency displacements. The ANOVA also provides other interesting conclusions, although the three previous points are the starting point for the search for a relationship between the quality of the processes and the predictive variables. The analysis presented is the starting point to extend the use of predictive grinding wheels (vibration analysis) to quality control once it demonstrated the sensitivity of predictive variables (high-frequency displacements) to the behaviour of the processes. Future contributions about the previous conclusions will look in more detail at the spectral character of the vibrations, in order to, once the maximum high-frequency vibration displacement values allowed are known, be able to define the limit spectrums, controllable cycle by cycle and even connected to permanent motorization controls of the machines so that they may modify their sensitive parameters, identified by ANOVA and according to the vibration readings. This feedback of the processes focused on quality control constitutes the principle contribution of the current SQC by means of overall vibration analysis and later spectral SQC. In this first stage, the SQC is proposed as a new technique for the determination of mechanical vibration variables for quality control of processes with high quality requirements, through the application of existing predictive tools (vibration analysis) according to experimental design and applying statistical tools to confirm the results. This conclusion validates the method presented and opens the doors for spectral analysis based on high-frequency displacements, which will be developed later. Future investigations consist of a spectral study that will allow us to establish which vibration frequencies are especially harmful for the processes and which are the process variables that can restore the functioning conditions with quality assured. The spectral focus will be made possible by the fact of knowing the different natures of the overall mechanical variables measured, the high-frequency displacements being the variable chosen as a result of the SQC by means of vibration analysis presented in this study.