Functional Availability Modelling of CNC Machine Tools

2014 ◽  
Vol 915-916 ◽  
pp. 395-399 ◽  
Author(s):  
Xiao Bing Li ◽  
Jun Gao ◽  
Zheng Zhang ◽  
Xiao Cui Zhu
Keyword(s):  
Least Square Method ◽  
Smoothing Method ◽  
Least Square ◽  
Cnc Machine Tools ◽  
Linear Regression Method ◽  
Cnc Machine ◽  
Basis System ◽  
Functional Linear Regression ◽  
Availability Model ◽  
Fitting Parameters

A new method for calculating the instantaneous availability was proposed based on Functional Data Analysis method. It introduced the Quadratic Bernstein Polynomial into the smoothing method firstly for the reliability which estimated by median rank method and estimated the fitting parameters by least square method. Then, under the assumption that the maintenance difficult of the CNCs was decreasing over the work time, chosen the appropriate smoothing basis function based on the trend after the time section adjustment for the estimated maintainability value. The Fourier basis system and the non-linear least squares were selected for the maintainability function smoothing method and the fitting parameters. Finally, the instantaneous availability model of CNCs was built based on the functional linear regression method, and a case example of 15 CNCs was given.

A Practical Algorithm for Compensating the Whole-Error of On-Machine Measurement

2010 ◽  
Vol 431-432 ◽  
pp. 462-465
Author(s):  
Sheng Bao ◽  
Ping Fa Feng
Keyword(s):  
Reference Frame ◽  
Machine Tools ◽  
Least Square Method ◽  
Least Square ◽  
Cnc Machine Tools ◽  
Cnc Machine ◽  
Valid Data ◽  
Practical Algorithm ◽  
Normal Vectors ◽  
Structural Parts

The On-machine measurement is usually based on the data of points. When data come from the CNC machine tools, the information they carry may be invalid. Therefore, it is unsuitable to compensate the errors by rotating and translating all data. In this paper, a practical algorithm is proposed to compensate the errors. Firstly, the valid data are picked out and sorted according to their normal vectors. By using the least square method, an error reference frame is constructed. Then the relation between the compensation values and coordinates of the theoretical points is derived. Finally, an example of aircraft structural parts is presented to validate the design.

scholarly journals Reliability Analysis on Domestic Special CNC Machine Tools Based on Weibull Distribution

2021 ◽  
Vol 2101 (1) ◽  
pp. 012024
Author(s):  
Zhanghu Shi ◽  
Xi Zhao ◽  
Huang Zhang ◽  
Hailong Sun ◽  
Chao Zeng ◽  
...  
Keyword(s):  
Machine Tool ◽  
Model Building ◽  
Hypothesis Test ◽  
Least Square Method ◽  
Least Square ◽  
Test Method ◽  
Cnc Machine Tools ◽  
Model Parameters ◽  
Reliability Model ◽  
Cnc Machine

Abstract Mean time between failures (MTBF), regarded as an important target to evaluate the performance of machine tool, is widely applied in analysis of reliability, especially in reliability model building. Taking Huazhong CNC HNC-848C Complex Machine Tool as research object, this paper conducted censored test to collect MTBF data during a period of 226 days. Based on the data and presupposed Weibull reliability model. Parameters of the model were estimated by least square method. Graph test Method and Kolmogorov-Smirnov Method are implemented to perform the hypothesis test on obtained parameters, which provides evaluation on MTBF of complex machine tool with theoretical basis and data reference.

scholarly journals Determination of the Sediment Carrying Capacity Based on Perturbed Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Zhi-hui Ni ◽  
Qiang Zeng ◽  
Wu Li-chun
Keyword(s):  
Carrying Capacity ◽  
Influencing Factor ◽  
Least Square Method ◽  
Least Square ◽  
New Method ◽  
Linear Regression Method ◽  
Average Flow Velocity ◽  
New Formula ◽  
Sediment Carrying Capacity

According to the previous studies of sediment carrying capacity, a new method of sediment carrying capacity on perturbed theory was proposed. By taking into account the average water depth, average flow velocity, settling velocity, and other influencing factors and introducing the median grain size as one main influencing factor in deriving the new formula, we established a new sediment carrying capacity formula. The coefficients were determined by the principle of dimensional analysis, multiple linear regression method, and the least square method. After that, the new formula was verified through measuring data of natural rivers and flume tests and comparing the verified results calculated by Cao Formula, Zhang Formula, Li Formula, Engelung-Hansen Formula, Ackers-White Formula, and Yang Formula. According to the compared results, it can be seen that the new method is of high accuracy. It could be a useful reference for the determination of sediment carrying capacity.

scholarly journals Geometric Interpretation of Errors in Multi-Parametrical Fitting Methods Based on Non-Euclidean Norms

Stats ◽  
2019 ◽  
Vol 2 (4) ◽  
pp. 426-438 ◽  
Author(s):  
Livadiotis
Keyword(s):  
Optimal Parameter ◽  
Least Square Method ◽  
Geometric Interpretation ◽  
Least Square ◽  
Geometric Representation ◽  
Geometric Meaning ◽  
Normal Equations ◽  
Optimal Values ◽  
Parameter Values ◽  
Fitting Parameters

The paper completes the multi-parametrical fitting methods, which are based on metrics induced by the non-Euclidean Lq-norms, by deriving the errors of the optimal parameter values. This was achieved using the geometric representation of the residuals sum expanded near its minimum, and the geometric interpretation of the errors. Typical fitting methods are mostly developed based on Euclidean norms, leading to the traditional least–square method. On the other hand, the theory of general fitting methods based on non-Euclidean norms is still under development; the normal equations provide implicitly the optimal values of the fitting parameters, while this paper completes the puzzle by improving understanding the derivations and geometric meaning of the optimal errors.

scholarly journals Reliability Modeling and Estimation of the Gear System

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Enjun Bai ◽  
Liyang Xie ◽  
Hongyi Ma ◽  
Jungang Ren ◽  
Shijian Zhang
Keyword(s):  
Order Statistics ◽  
Least Square Method ◽  
Small Sample ◽  
Gear System ◽  
Least Square ◽  
Linear Regression Method ◽  
Reliability Model ◽  
Statistical Parameters ◽  
Reliability Modeling ◽  
Reliability Models

Traditional reliability models of the gear system either simplify the gear system unreasonably or are too complicated to be applicable for some gear systems. Therefore, a reliability model of the gear system considering statistically dependent failure based on the theory of the order statistics is developed in this paper. Firstly, the gear bending fatigue test of small sample is implemented to obtain the P-S-N curves that are fitted by using the least square method and the linear regression method of the statistical parameters under the test stress levels. Then, according to stress-strength interference theory and the theory of the order statistics, the reliability models considering the number of load cycles from a gear to gear system are built, which indicates clear modeling process of the gear system. Finally, the proposed reliability model of gear system is validated by using the Monte Carlo Simulation (MCS) and the system reliability under special load history is analyzed qualitatively.

Researches on Lifetime Modeling of LED Luminaires

2014 ◽  
Vol 1061-1062 ◽  
pp. 662-665
Author(s):  
Hua Jing Li ◽  
Lei Nie ◽  
Fei Huang ◽  
Wen Jing Xiang
Keyword(s):  
Mathematical Reasoning ◽  
Great Influence ◽  
Least Square Method ◽  
Exponential Model ◽  
Least Square ◽  
Linear Regression Method ◽  
Testing Method ◽  
Accelerate Life Testing ◽  
Vibration Stress ◽  
Arrhenius Function

The temperature and vibration have great influence on the properties and materials of LED luminaires. Therefore, the bi-stress accelerate life testing method under temperature and vibration stress was designed and demonstrated. Based on the large amounts of experimentally obtained data and Arrhenius function, life models of LED luminaires were built rapidly by using mathematical reasoning (least square method and unary linear regression method). The results showed that the method we mentioned can sharply reduce the test life test and the life curve of LED luminaires obey to exponential model.

Key Subsystem Identification of the CNC Machine Tools

2013 ◽  
Vol 329 ◽  
pp. 157-162 ◽  
Author(s):  
Xiao Cui Zhu ◽  
Fei Chen ◽  
Xiao Bing Li ◽  
Zhao Jun Yang ◽  
Ying Nan Kan ◽  
...  
Keyword(s):  
Machine Tools ◽  
Probability Function ◽  
Likelihood Estimation ◽  
Least Square ◽  
Cnc Machine Tools ◽  
Cnc Machine ◽  
Least Square Estimation ◽  
Failure Data ◽  
Novel Method

In order to find the key subsystems which affect the reliability of the CNC machine tools is an important and yet harder problem due to the lack of failure data and statistical analysis. A novel method based on posterior probability function for identifying the key subsystems of the CNC machine tools was proposed. Firstly, subsystem reliability of the CNC machine tools was estimated using the John estimator, since the failure data were censored. Secondly, parametric fitting was conduct with Weibull distribution using the maximum likelihood estimation (MLE) or the least square estimation (LSE). Thirdly, the probability function of each subsystems were attained by the reliability modes of the systems and the whole system. Finally, a case study was given, which proved that the proposed method could find out the key subsystems rapidly and accurately.

Research on Diagnosis Method of GIS Insulation Defects Based on Polynomial Fitting

2013 ◽  
Vol 805-806 ◽  
pp. 888-891 ◽  
Author(s):  
Yu Sheng Quan ◽  
Zong Cheng Zhang ◽  
Guang Chen ◽  
Dai Juan Wang
Keyword(s):  
Partial Discharge ◽  
Least Square Method ◽  
Development Stage ◽  
Linear Mapping ◽  
Least Square ◽  
Reference Database ◽  
Initial Stage ◽  
Diagnosis Method ◽  
Three Stages ◽  
Fitting Parameters

GIS is currently widely used in the power system and is the Developing Trends of Electrical appliances manufacturing. At present, a lot of research on GIS PD, but the study of the recognition of the PD severity is less. By analyzing a large number of partial discharge sample data, a new GIS PD severity diagnostic method is proposed in this paper. Partial discharge is divided into three stages (initial stage, development stage and dangerous stage) in the method according to the severity of the partial discharge. These three stages are fitted with non-linear mapping and get the fitting parameters. GIS partial discharge fault reference database can be dynamically generated with these fitting parameters. The similarity between the detected data and the reference data is discriminated with the least square method and Supplier division method, and then the GIS PD severity can be diagnosed. A large number of simulation results initially confirmed the effectiveness and feasibility of the proposed method.

Accuracy Enhancement of Alignment for Five-Axis CNC Machine Tools through Touch Trigger Probes

2011 ◽  
Vol 381 ◽  
pp. 11-15
Author(s):  
Sheng Bao ◽  
Fu Zhang ◽  
Xi Zhang
Keyword(s):  
Reference Frame ◽  
Machine Tools ◽  
Measuring Method ◽  
Least Square ◽  
Cnc Machine Tools ◽  
Random Errors ◽  
Cnc Machine ◽  
Method Of Least Square ◽  
Touch Trigger Probe ◽  
Five Axis

The random errors exist in measuring with touch trigger probe. These errors are directly introduced into workpiece coordinate system with conventional alignment method. An enhanced measuring method is proposed in this paper to improve the accuracy of alignment for five-axis CNC machine tools. By using the method of least square, an error reference frame is constructed, and the relationship between the alignment parameters and the error reference frame is derived. An example of aircraft structural parts is presented to validate the presented method.

Research on Non-Linear Parameters Identification for Servo System of CNC Machine Tools

2012 ◽  
Vol 220-223 ◽  
pp. 344-347
Author(s):  
Guang Sheng Chen ◽  
Hao Lin Li
Keyword(s):  
Machine Tools ◽  
Position Control ◽  
Taylor Series Expansion ◽  
Friction Model ◽  
Least Square ◽  
Numerical Control ◽  
Cnc Machine Tools ◽  
Cnc Machine ◽  
Precise Position ◽  
Non Linear

As phenomena of friction in computer numerical control(CNC) machine tools is inevitable, accurately modeling of friction is need for precise position control and performance evaluation of CNC machine tools. This paper proposed an identification method that non-linear friction model described as Stribeck are linearized by using high order Taylor series expansion and parameters of the model are obtained by least square method (LSM). Signals of servo motor current and rotating rate which are offered in many modern CNC machine tools are needed for the identification and experiments results show that parameters of Stribeck model can be obtained accurately by identification. The method is suited for industrial condition and has its practicality.

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