基于维修程度的数控机床可靠性建模与分析
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摘要
数控机床是技术密集的现代制造装备,是组成制造系统的基本单元。近年来,随着数控机床、特别是中高档数控机床功能的不断增强,先进功能的维持能力——可靠性问题越加重要。目前,国产数控机床的功能与国际先进水平的差距不断减小,但可靠性技术落后,差距明显,已经成为行业发展的瓶颈,同时也引起了行业和学术界的高度关注。可靠性建模是数控机床可靠性研究中的一项重要内容,正确建模是实现可靠性设计与可靠性增长的前提和保证。迄今为止,限于数据的积累和建模的方便,该领域多采用指数分布和威布尔分布对故障数据进行建模,是在“修复如新”的完全维修假设下进行研究的。事实上,对于数控机床这种复杂可修系统而言,在对故障进行维修时,大多为“修复如旧”的最小维修或不完全维修。因此,需要对数控机床的建模方法进行改进,考虑维修程度对它的不同影响,并进行相关研究。
本文主要以整机和子系统不同的维修程度为前提基础,分别研究了基于非齐次泊松过程的整机可靠性建模和基于不完全维修的子系统的可靠性建模方法,并对不同维修程度下的故障模式和可用度进行了深入的研究,论文的工作主要涉及以下几个方面:
(1)论文首先分析了数控机床可靠性方法的国内外研究现状,结合数控机床和关键功能部件可靠性设计课题的实际需要,提出了基于不同维修程度的数控机床可靠性建模新方法。
(2)根据维修程度最小,即“最小维修”的假设前提,建立了数控机床整机的数学模型并对该模型进行了数学求解。在对可修系统进行了理论分析的基础上,提出了数控机床非齐次泊松过程的数学模型。同时,针对现场试验故障数据的多样本、随机截尾的特点,使用故障总时间法进行预处理。在此基础上,依据不同的故障趋势,提出基于威布尔过程和两重威布尔过程的可靠性模型,通过最大似然估计的求解算法,确定模型参数。文中对某机床厂的数控车床和加工中心的故障数据进行了可靠性建模,通过相关的检验,结果具有较好的拟合优度,更符合数控机床作为可修系统的工程实际情况。
(3)数控机床子系统各子系统的可靠性是评价数控机床可靠性的关键环节之一。考虑到维修程度对各子系统的影响是介于“修复如新”和“最小修复”之间的情况,提出了基于不完全维修的子系统可靠性建模方法。该模型是建立在Kijima I不完全维修模型基础上的,所建立模型的故障率符合浴盆曲线形式。同时,综合使用最大似然法和遗传算法求出模型的参数估计值。结果表明,该模型不仅能够得出早期故障期和偶然期的临界值,还能评价出在偶然期和损耗期内的维修程度,可以真实的反应各子系统可靠性变化的真实情况。
(4)在建立了数控机床整机和各子系统的可靠性模型的基础上,对数控机床的故障模式进行了研究,分析了FMECA方法未考虑维修程度的缺陷,提出了改进的FMECA方法。该方法综合了故障模式的定性分析和定量分析结果,建立了基于加权欧氏距离和影响因素空间图的求解算法,避免了传统方法中风险优先数的各组成因素相乘所导致的放大效应。同时,维修程度是影响故障模式的重要因素,因此,将其引入危害度定量分析中,有助于更加全面充分的研究故障模式。通过对数控车床主要故障模式的分析,可以找出数控车床的薄弱环节,为可靠性设计和可靠性增长提供关键的参考依据。
(5)研究了计及维修程度的数控机床可用性数学模型,针对修复性维修的数据信息,提出了基于蒙特卡罗的可用度分析方法,对最小维修和不完全维修假设下的整机和子系统进行了研究。结果表明,利用本文所建立的可用度模型可以描绘出瞬时可用度曲线,并能得到数控机床的可用度规律,进一步完善了数控机床可用度分析方法。通过本文的研究,使数控机床整机和子系统的可靠性模型更加合理,丰富了数控机床可用度分析方法,提高了可靠性评价的准确性,为数控机床可靠性建模方法开辟了一种新的解决思路。纵观全文,本论文的创新性工作主要有以下几方面:
(1)将最小维修的建模思想应用于数控机床整机的可靠性建模中,提出了基于非齐次泊松过程的建模方法,建立了“修复如旧”假设下的整机数学模型,该方法具有良好的拟合优度,为数控机床整机建模提供了一种新的解决思路。
(2)建立了数控机床各子系统的不完全维修模型。该方法能够得到各子系统的早期故障期和偶然故障期的临界值和维修程度,计算结果能够反应出各子系统所处的寿命阶段特征。
(3)将维修程度作为FMECA故障分析方法的影响因素之一,并将FMEA的定性分析指标RPN与定量分析的危害度有机结合,提出综合风险评估的数学方法,使数控机床的故障分析结果更符合实际情况。
(4)针对数控机床可用度问题,研究了可用度函数,建立了不同维修程度下的基于蒙特卡罗的可用度数学模型。通过该方法能够得到不同维修程度下的可用度曲线,丰富了数控机床可用度分析方法。
As the basic unit of manufacturing system, CNC machine tools is a technology- integrated manufacturing equipment. With the function diversifies, especially for the high-speed &high-precision, the reliability problem which describes the sustainability of the function arised. Nowadays, the function gap of the domestic and the overseas CNC machine tools is decreased gradually. However, the reliability gap is obvious. The reliability problem has become the bottle-neck for the domestic CNC machine tools industry and attracted the attentions of the researchers and engineers. Reliability modeling is a significant work for the CNC machine tools reliability research, whether the model is accurate or not is the assurance and premise for the reliability design and growth. So far, limited to the convenience of the data accumulation and reliability modeling, the Weibull and Exponential distribution are common used statistical models and the as-good-as-new is the general assumption. However, the repair effect is between as-good-as-new and as-bad-as-old to the complex system such as CNC machine tools, So, the repair effect must be considered for the reliability modeling .
The paper focuses on the repair degree to the CNC machine tools and its’features, and the reliability modeling method was proposed based on NHPP and incomplete repair circumstances. Then, the failure modes and the availability under different repair degree is was studied and the specific work include:
(1) This paper first describes the domestic and international research progress, and presents a new modeling method of CNC machine tools based on various maintenance degrees considering the practical needs of the subject about reliability design of CNC machine tools and key components.
(2) This work sets up the mathematical model of the whole CNC machine tools and solves it according to the assumption of the minimum maintenance, and put forward the mathematical model of the non-homogeneous Poisson process of CNC machine based on the theoretical analysis on repairable system. Aiming at failure data for the field test having traits such as multi-sample and random censoring, total failure time method is used to pre-treat, based on these, depending on the different fault tread, reliability model based on weibull process and twofold weibull process is put forward of which the model parameters are determined by maximum likelihood estimation. The paper establishes reliability modeling of the fault data for CNC lathes and machining centers in a machine tool plant, the result of which has better goodness of fit and is more suitable to engineering condition of the CNC machine tools as repairable system through the relevant inspection
(3) The reliability assessment of the key components is one of the key links of assessing the reliability of CNC machine tools. A new method of modeling the reliability of the key components with incomplete maintenance is proposed considering that the maintenance degrees’impacts on the key components is between the two states“as-good-as-new”and“minimum maintenance”. This model is established based on the Kijima I incomplete maintenance model, of which the hazard rate curve had the“bathtub”form. Meanwhile, the model’s parameters are calculated using the method integrating maximum likelihood method and genetic algorithm. The results shows that: this model can not only get the critical values of early-failures period and random-failures period, but also the maintenance degrees within the random-failures period and wear out-failures period, reflecting the real states of each sub-system’s changes in reliability.
(4) Based on the reliability models of the CNC machine tools and the key components, the failure modes of the CNC machine tools are researched, and the defects of the FMECA not considering maintenance degrees are analyzed, then the improved FMECA is proposed considering maintenance degrees. This method integrated the results of qualitative analysis and quantitative analysis, established the algorithm based on weighted Euclidean Distance and Risk Space Diagram, thus avoiding the amplification effect caused by the multiplication of the components of PRN in the traditional methods. Meanwhile, the maintenance degree is an important factor influencing the failure modes, thus it is helpful to introduce it into the quantitative analysis of criticality in order to fully research the failure modes. Through the failure mode analysis of CNC lathe, the weak link of the machine can be found out, thus providing critical references for reliability-design and reliability growth.
(5) In the end,the availability mathematical model concerned the CNC machine maintenance is researched. According to the data of corrective maintenance, author puts forward the availability analysis method based on Monte Carlo. And the simulations of the whole machine and subsystem are made under the assumption of the minimum maintenance and imperfect maintenance. The results show that the availability model describes the instantaneous availability curve from which author gets the law of CNC machine availability. And it consummates the availability analysis method of CNC machine.
The research rationalizes the reliability model of the CNC machine and subsystem, enriches the availability analysis method of CNC machine and improves the accuracy of the reliability evaluation. And it puts forward a new idea and method of the reliability analysis. The innovations of this thesis are mainly the following aspects:
(1) The minimum maintenance modeling idea is used in the reliability modeling of CNC machine based on Non-Homogeneous Poisson Process. The mathematical model is made under the assumption of repair as-bad-as-old. The method has a good goodness-of-fit and provides a new solution for the whole machine modeling of CNC machine.
(2) Establish the incomplete repair model of the key functional components. It gets the critical value and maintenance degree of the early failure period and occasional failure period. And the results can reflect the life stage characteristic of each key functional component.
(3) In this paper, the maintenance degree is regarded as one of influence factors. Furthermore, the RPN obtained by qualitative analysis and criticality obtained by quantitative analysis are organically combined, and a mathematical method for comprehensive risk assessment is proposed, which could make the fault analysis results for CNC machine tools repairable systems accords with actual situation.
(4) In view of the availability problem for CNC machine tools, the availability function is discussed, and a Monte-Carlo based availability mathematical model in different maintenance degree was built. In this way, we could get the availability curve in different maintenance degree, which make a new extension for available analysis methods of CNC machine tools.
本文主要以整机和子系统不同的维修程度为前提基础,分别研究了基于非齐次泊松过程的整机可靠性建模和基于不完全维修的子系统的可靠性建模方法,并对不同维修程度下的故障模式和可用度进行了深入的研究,论文的工作主要涉及以下几个方面:
(1)论文首先分析了数控机床可靠性方法的国内外研究现状,结合数控机床和关键功能部件可靠性设计课题的实际需要,提出了基于不同维修程度的数控机床可靠性建模新方法。
(2)根据维修程度最小,即“最小维修”的假设前提,建立了数控机床整机的数学模型并对该模型进行了数学求解。在对可修系统进行了理论分析的基础上,提出了数控机床非齐次泊松过程的数学模型。同时,针对现场试验故障数据的多样本、随机截尾的特点,使用故障总时间法进行预处理。在此基础上,依据不同的故障趋势,提出基于威布尔过程和两重威布尔过程的可靠性模型,通过最大似然估计的求解算法,确定模型参数。文中对某机床厂的数控车床和加工中心的故障数据进行了可靠性建模,通过相关的检验,结果具有较好的拟合优度,更符合数控机床作为可修系统的工程实际情况。
(3)数控机床子系统各子系统的可靠性是评价数控机床可靠性的关键环节之一。考虑到维修程度对各子系统的影响是介于“修复如新”和“最小修复”之间的情况,提出了基于不完全维修的子系统可靠性建模方法。该模型是建立在Kijima I不完全维修模型基础上的,所建立模型的故障率符合浴盆曲线形式。同时,综合使用最大似然法和遗传算法求出模型的参数估计值。结果表明,该模型不仅能够得出早期故障期和偶然期的临界值,还能评价出在偶然期和损耗期内的维修程度,可以真实的反应各子系统可靠性变化的真实情况。
(4)在建立了数控机床整机和各子系统的可靠性模型的基础上,对数控机床的故障模式进行了研究,分析了FMECA方法未考虑维修程度的缺陷,提出了改进的FMECA方法。该方法综合了故障模式的定性分析和定量分析结果,建立了基于加权欧氏距离和影响因素空间图的求解算法,避免了传统方法中风险优先数的各组成因素相乘所导致的放大效应。同时,维修程度是影响故障模式的重要因素,因此,将其引入危害度定量分析中,有助于更加全面充分的研究故障模式。通过对数控车床主要故障模式的分析,可以找出数控车床的薄弱环节,为可靠性设计和可靠性增长提供关键的参考依据。
(5)研究了计及维修程度的数控机床可用性数学模型,针对修复性维修的数据信息,提出了基于蒙特卡罗的可用度分析方法,对最小维修和不完全维修假设下的整机和子系统进行了研究。结果表明,利用本文所建立的可用度模型可以描绘出瞬时可用度曲线,并能得到数控机床的可用度规律,进一步完善了数控机床可用度分析方法。通过本文的研究,使数控机床整机和子系统的可靠性模型更加合理,丰富了数控机床可用度分析方法,提高了可靠性评价的准确性,为数控机床可靠性建模方法开辟了一种新的解决思路。纵观全文,本论文的创新性工作主要有以下几方面:
(1)将最小维修的建模思想应用于数控机床整机的可靠性建模中,提出了基于非齐次泊松过程的建模方法,建立了“修复如旧”假设下的整机数学模型,该方法具有良好的拟合优度,为数控机床整机建模提供了一种新的解决思路。
(2)建立了数控机床各子系统的不完全维修模型。该方法能够得到各子系统的早期故障期和偶然故障期的临界值和维修程度,计算结果能够反应出各子系统所处的寿命阶段特征。
(3)将维修程度作为FMECA故障分析方法的影响因素之一,并将FMEA的定性分析指标RPN与定量分析的危害度有机结合,提出综合风险评估的数学方法,使数控机床的故障分析结果更符合实际情况。
(4)针对数控机床可用度问题,研究了可用度函数,建立了不同维修程度下的基于蒙特卡罗的可用度数学模型。通过该方法能够得到不同维修程度下的可用度曲线,丰富了数控机床可用度分析方法。
As the basic unit of manufacturing system, CNC machine tools is a technology- integrated manufacturing equipment. With the function diversifies, especially for the high-speed &high-precision, the reliability problem which describes the sustainability of the function arised. Nowadays, the function gap of the domestic and the overseas CNC machine tools is decreased gradually. However, the reliability gap is obvious. The reliability problem has become the bottle-neck for the domestic CNC machine tools industry and attracted the attentions of the researchers and engineers. Reliability modeling is a significant work for the CNC machine tools reliability research, whether the model is accurate or not is the assurance and premise for the reliability design and growth. So far, limited to the convenience of the data accumulation and reliability modeling, the Weibull and Exponential distribution are common used statistical models and the as-good-as-new is the general assumption. However, the repair effect is between as-good-as-new and as-bad-as-old to the complex system such as CNC machine tools, So, the repair effect must be considered for the reliability modeling .
The paper focuses on the repair degree to the CNC machine tools and its’features, and the reliability modeling method was proposed based on NHPP and incomplete repair circumstances. Then, the failure modes and the availability under different repair degree is was studied and the specific work include:
(1) This paper first describes the domestic and international research progress, and presents a new modeling method of CNC machine tools based on various maintenance degrees considering the practical needs of the subject about reliability design of CNC machine tools and key components.
(2) This work sets up the mathematical model of the whole CNC machine tools and solves it according to the assumption of the minimum maintenance, and put forward the mathematical model of the non-homogeneous Poisson process of CNC machine based on the theoretical analysis on repairable system. Aiming at failure data for the field test having traits such as multi-sample and random censoring, total failure time method is used to pre-treat, based on these, depending on the different fault tread, reliability model based on weibull process and twofold weibull process is put forward of which the model parameters are determined by maximum likelihood estimation. The paper establishes reliability modeling of the fault data for CNC lathes and machining centers in a machine tool plant, the result of which has better goodness of fit and is more suitable to engineering condition of the CNC machine tools as repairable system through the relevant inspection
(3) The reliability assessment of the key components is one of the key links of assessing the reliability of CNC machine tools. A new method of modeling the reliability of the key components with incomplete maintenance is proposed considering that the maintenance degrees’impacts on the key components is between the two states“as-good-as-new”and“minimum maintenance”. This model is established based on the Kijima I incomplete maintenance model, of which the hazard rate curve had the“bathtub”form. Meanwhile, the model’s parameters are calculated using the method integrating maximum likelihood method and genetic algorithm. The results shows that: this model can not only get the critical values of early-failures period and random-failures period, but also the maintenance degrees within the random-failures period and wear out-failures period, reflecting the real states of each sub-system’s changes in reliability.
(4) Based on the reliability models of the CNC machine tools and the key components, the failure modes of the CNC machine tools are researched, and the defects of the FMECA not considering maintenance degrees are analyzed, then the improved FMECA is proposed considering maintenance degrees. This method integrated the results of qualitative analysis and quantitative analysis, established the algorithm based on weighted Euclidean Distance and Risk Space Diagram, thus avoiding the amplification effect caused by the multiplication of the components of PRN in the traditional methods. Meanwhile, the maintenance degree is an important factor influencing the failure modes, thus it is helpful to introduce it into the quantitative analysis of criticality in order to fully research the failure modes. Through the failure mode analysis of CNC lathe, the weak link of the machine can be found out, thus providing critical references for reliability-design and reliability growth.
(5) In the end,the availability mathematical model concerned the CNC machine maintenance is researched. According to the data of corrective maintenance, author puts forward the availability analysis method based on Monte Carlo. And the simulations of the whole machine and subsystem are made under the assumption of the minimum maintenance and imperfect maintenance. The results show that the availability model describes the instantaneous availability curve from which author gets the law of CNC machine availability. And it consummates the availability analysis method of CNC machine.
The research rationalizes the reliability model of the CNC machine and subsystem, enriches the availability analysis method of CNC machine and improves the accuracy of the reliability evaluation. And it puts forward a new idea and method of the reliability analysis. The innovations of this thesis are mainly the following aspects:
(1) The minimum maintenance modeling idea is used in the reliability modeling of CNC machine based on Non-Homogeneous Poisson Process. The mathematical model is made under the assumption of repair as-bad-as-old. The method has a good goodness-of-fit and provides a new solution for the whole machine modeling of CNC machine.
(2) Establish the incomplete repair model of the key functional components. It gets the critical value and maintenance degree of the early failure period and occasional failure period. And the results can reflect the life stage characteristic of each key functional component.
(3) In this paper, the maintenance degree is regarded as one of influence factors. Furthermore, the RPN obtained by qualitative analysis and criticality obtained by quantitative analysis are organically combined, and a mathematical method for comprehensive risk assessment is proposed, which could make the fault analysis results for CNC machine tools repairable systems accords with actual situation.
(4) In view of the availability problem for CNC machine tools, the availability function is discussed, and a Monte-Carlo based availability mathematical model in different maintenance degree was built. In this way, we could get the availability curve in different maintenance degree, which make a new extension for available analysis methods of CNC machine tools.
引文
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