Generalized definition and application of tolerance

2019 ◽  
Vol 233 (19-20) ◽  
pp. 6807-6814
Author(s):  
Hao Jianjun ◽  
Wang Youli ◽  
Wang Xiaohui
Keyword(s):  
Error Compensation ◽  
Extreme Values ◽  
Probabilistic Method ◽  
Tolerance Analysis ◽  
Machining Process ◽  
Negative Number ◽  
Absolute Value ◽  
Calculation Results ◽  
Relationship Of ◽  
Dimensional Homogeneity

Tolerance with upper deviation less than lower deviation is defined as virtual tolerance; the dimension between two extreme values required with tolerance (virtual tolerance) is expressed by a set. The changed characteristics of the set range when the tolerance value is continuously reduced from positive to negative are explored. The nature of virtual tolerance is that the absolute value of virtual tolerance is the error compensation amount, and the dimension between two extreme values is the error compensation range. On the basis of the concept of positive and negative number, the theory of dimensional homogeneity, the existing conditions of the general formula of the dimensional chain, the accuracy of the calculation results of tolerance, and so on, the concept of virtual tolerance and its relationship of unity of opposites with tolerance are proposed. Based on the concept of virtual tolerance, analysis and calculation processes of various assembly dimensional chains are unified, and general formulation of calculating the range of false waste is established, and the method of determining the range of false waste by using probabilistic method in machining process is deduced.

The Level-Crossing Problem: First-Passage, Escape and Extremes

2014 ◽  
Vol 13 (04) ◽  
pp. 1430001 ◽  
Author(s):  
Jaume Masoliver
Keyword(s):  
Brownian Motion ◽  
Diffusion Processes ◽  
Extreme Values ◽  
Level Crossing ◽  
First Passage ◽  
One Dimensional ◽  
Absolute Value ◽  
Dimensional Diffusion

We review the level-crossing problem which includes the first-passage and escape problems as well as the theory of extreme values (the maximum, the minimum, the maximum absolute value and the range or span). We set the definitions and general results and apply them to one-dimensional diffusion processes with explicit results for the Brownian motion and the Ornstein–Uhlenbeck (OU) process.

CALCULATION OF ADDITIONAL AXIAL FORCE OF ANGULAR-CONTACT BALL BEARINGS IN ROTOR SYSTEM

2016 ◽  
Vol 40 (4) ◽  
pp. 585-596
Author(s):  
Zhenhuan Ye ◽  
Zhansheng Liu ◽  
Liqin Wang
Keyword(s):  
Axial Force ◽  
Dynamic Properties ◽  
Descent Method ◽  
Rotor System ◽  
Ball Bearings ◽  
Rolling Bearings ◽  
System A ◽  
Calculation Results ◽  
Relationship Of ◽  
Raphson Method

Based on a loading-deformation relationship of bearing elements and the coordination of displacement between bearings in the rotor system, a model for calculating the additional axial force of angular-contact ball bearings in a single-rotor system is established. Nonlinear equations of this model are solved through the Rapid Descent method and Newton-Raphson method. The simulation results which are based on Gupta’s example verify that both the model and solving methods in this paper are reliable. A pair of 276927NK1W1(H) angular-contact ball bearings in symmetry in the single-rotor system is used as the example, calculation results of the additional axial force of bearings from the model in this paper and from the ISO method are compared and the influence of bearing geometry parameters and working conditions on the additional axial force is further studied. This model and its conclusions could provide the basic data and reference for analyzing the carrying ability and dynamic properties of rolling bearings.

Interference Fit Design Assessment and Improvement for the Railway Wagon Wheelset with 30 Ton Axle Weigh

2013 ◽  
Vol 658 ◽  
pp. 318-322
Author(s):  
A.S. Xue ◽  
Y.X. Zhao ◽  
B. Yang
Keyword(s):  
Hole Diameter ◽  
Original Design ◽  
Design Assessment ◽  
Interference Fit ◽  
Railway Wagon ◽  
The Press ◽  
Reasonable Range ◽  
Calculation Results ◽  
Stress States ◽  
Relationship Of

Design reliability is analyzed for the interference fits of the railway wagon wheelset with 30 ton axle weigh. Aim focus on eliminating fretting fatigue damage of the wheelset. An extreme wheelset loads set is deduced by which can yields the thermal mechanical loads on the wheel same to the code AAR S 660. Integrated wheelset model of finite element method is applied to calculate the stresses on the fits to consider the physical fit relationship of wheelset, in which the rail pieces, wheels, axle, bearings, and adapters are fitted together by contact phases. It is revealed that the fits are all in the press stress states for the original design. But the stresses seem smaller than the least reasonable value for the reliable fits between wheels-axle. An improvement suggestion is provided to rise the fit scale to 0.23 mm equal to 0.01 percentage of the wheel-hub hole diameter. Calculation results verify that the press stresses have been controlled in the reasonable range.

Development of a Mathematical Model of Plate Rolling on Hot Reversing Mills

2017 ◽  
Vol 746 ◽  
pp. 48-55
Author(s):  
Vasiliy V. Yashin ◽  
Evgenii V. Aryshenskii ◽  
Erkin D. Beglov ◽  
Maksim S. Tepterev ◽  
Anna F. Grechnikova
Keyword(s):  
Rolling Force ◽  
Work Roll ◽  
Calculation Model ◽  
Production Environment ◽  
Plate Rolling ◽  
Process Reliability ◽  
Calculation Results ◽  
Roll Gap ◽  
Relationship Of ◽  
Force Calculation

Objective of the work: develop a model for calculation of plate exit thickness. This model is supposed to improve process reliability in obtaining specified thickness with +/- 0.5 mm tolerance. The work identifies major influences on obtaining specified thickness and relationship of their effects. Based on derived relationships, the work develops rolling force calculation model with the following inputs: alloy grade, feedstock temperature, feedstock entry and exit gage, feedstock width, rotational speed of the rolls. Mill stand characteristics, like mill stiffness, backlash, work roll behavior, were studied in relation to force and temperature. The resulting model allows to predict the value of work roll gap increase during rolling. The model was validated in production environment and demonstrated high confidence level of calculation results.

Positioning Error Compensation for Machining Center Based on Spline Interpolation

2012 ◽  
Vol 472-475 ◽  
pp. 3029-3034
Author(s):  
Peng Li ◽  
Ying Hu ◽  
Zi Ma
Keyword(s):  
Error Compensation ◽  
Laser Interferometer ◽  
Spline Interpolation ◽  
Machining Process ◽  
Accuracy Evaluation ◽  
Positioning Error ◽  
Positioning Errors ◽  
Machining Center ◽  
Compensation Function ◽  
Manual Correction

Related to the machining precision, especially for the middle and low end machining center, the positioning error is often considered as a major factor, which can be traditionally decreased by the pitch compensation function integrated in the CNC system. However, the function is just founded on that all of positioning errors remain constant in the machining process, and it is difficulty to meet the compensation needs in different machining condition. At the same time, it involves a mass of parameters that need professional manual correction. Therefore, the software error compensation method is put forward. Firstly, based on cubic spline interpolation, the error compensation model is designed through the processing of positioning error which is collected by the laser interferometer. Secondly, with the characteristics of G codes, the database is established for error compensation, which can effectively correct different machining G codes with enough error information. Finally, by the experiment and accuracy evaluation, results show that after the positioning error of machining center is compensated by the presented scheme, its precision is improved obviously.

Fitting straight lines to experimental data

1977 ◽  
Vol 233 (3) ◽  
pp. R94-R99 ◽  
Author(s):  
R. A. Brace
Keyword(s):  
Standard Error ◽  
Least Squares Regression ◽  
Simple Method ◽  
Mean Values ◽  
Absolute Value ◽  
Best Value ◽  
The Mean ◽  
Straight Lines ◽  
Relationship Of ◽  
Conventional Regression

The problem associated with use of statistical methods for determining a best linear relationship of the form Y = AX +B have been examined for a condition quite prevalent with experimental research, i.e., when the values of both variables are subject to essentially unknown errors. Under this condition standard least-squares regression analysis underestimates the value of the slope A. A very simple method for determining the best value of the slope and intercept has been introduced which can be used when errors are present in both variables. With this proposed method, the calculated slope is equal to the standard error of Y divided by the standard error of X (with the appropriate sign) and the intercept is found from the mean values of X and Y, i.e., B = Y - AX. The best estimate of the slope is also equal to the slope found with the conventional regression method divided by the absolute value of the correlation coefficient. The line determined with the suggested method can be considered to be a line of symmetry through the data.

A Micro-Fracture Model and its Application in Hardened Cement Paste

2016 ◽  
Vol 25 (2) ◽  
pp. 096369351602500 ◽  
Author(s):  
Kan Jin ◽  
Cao Wei
Keyword(s):  
Porous Media ◽  
Ultimate Strength ◽  
Elastic Properties ◽  
Cement Paste ◽  
Fracture Model ◽  
Hardened Cement ◽  
Average Pore ◽  
Calculation Results ◽  
Strain Relationship ◽  
Relationship Of

A micro-fracture model is presented to investigate mechanics properties of porous media such as cement paste on basis of micromechanics theory and fracture theory. Relationships between mechanics properties of porous media and the parameters of pores such as shape, size, and porosity are analysed by this model. Calculation results show that, to a hypothetic porous media with same porosity, the ultimate strength and elastic properties are reduced with an increase of average pore diameter. Nano-scale pores have little effect on the ultimate strength of this porous media while the micron-scale pores have great effect on it. The stress-strain relationship of this porous media with the micron-scaled pores is nonlinear obviously. The results also show that the ultimate strength and elastic properties of the porous media are reduced with an increase of the porosity and shape parameter. Mechanics properties of a cement paste with water cement ratio of 0.5 are tested. The calculation results from the model are in agreement with the experimental results.

Based on the Nc Machining System Error Aspheric Analysis and Research

2011 ◽  
Vol 383-390 ◽  
pp. 7649-7653
Author(s):  
Hong Ying Wang ◽  
Xue Me Hu
Keyword(s):  
Error Compensation ◽  
Dynamic Error ◽  
Machining Process ◽  
System Error ◽  
Machining Precision ◽  
Processing Error ◽  
Machining Errors ◽  
Machining System ◽  
Forward Process

From the machining errors and static dynamic error influence two aspects are discussed in this paper, the analysis of machining process on the processing precision influence of error, puts forward process design. Long-term since, improving precision machine tool is through the two methods: error and avoid error compensation. Avoid error is a "hard", focusing on design and processing in the error may eliminate all stages. And error compensation in existing machine, can work environment to further improve the machining precision, it is a kind of economic effectively improve the machining precision of the method. For error analysis and calculation, the ultimate goal is to eliminate and reduce processing error, the improvement of the machining errors of classification in many ways. According to the machining process of the factors causing error to occur any regularity, processing error into system error and the random error, According to the nature of the changes with time, and can be divided into static error and dynamic error.

Error Compensation of a NC Machining System Based on a Dynamic Feedback Neural Network

2011 ◽  
Vol 52-54 ◽  
pp. 1890-1894 ◽  
Author(s):  
Huang Lin Zeng ◽  
Yong Sun ◽  
Xiao Hong Ren ◽  
Li Xin Liu
Keyword(s):  
Neural Network ◽  
Error Compensation ◽  
Nc Machining ◽  
Machining Process ◽  
Dynamic Feedback ◽  
Machining System ◽  
Nc Machine ◽  
Feedback Neural Network ◽  
Set Up ◽  
Errors Analysis

Machining error of a NC machining system is a kind of comprehensive error in dynamically machining process; especially it is of errors with non-linear characteristics. In this paper, we will set up a kind of model of comprehensive errors analysis for a NC machining system and present an error compensation for high-precision a NC machining system by a dynamic feedback neural network embedded in a NC machine tool. The results obtained shows that this approach can effectively improve compensation precision and real time of error compensation on machine tools.

scholarly journals HUBUNGAN PARITAS DENGAN DERAJAT LASERASI JALAN LAHIR DI POLINDES JETIS LOR KECAMATAN NAWANGAN KABUPATEN PACITAN

2019 ◽  
Vol 6 (1) ◽  
pp. 48-53
Author(s):  
Etika Desi Yogi
Keyword(s):  
Correlation Analysis ◽  
Pelvic Floor ◽  
Vaginal Wall ◽  
Labor Process ◽  
Birth Process ◽  
Birth Canal ◽  
Calculation Results ◽  
Independent Variable ◽  
Relationship Of ◽  
The Relationship

For women, the perineum is very important stretching and lubricating the perineum during labor can weaken the pelvic floor muscles in the vaginal wall, trauma to the perineum also causes discomfort and pain during sexual intercourse and an estimated 85% of maternal mothers experience birth canal lacerations (Kettle and Tohil 2008). One of the fears that are often felt by pregnant women, especially third timers, is fear of being torn and afraid of sewing. Especially for mothers who have experienced it, this can make their own trauma when facing the birth process later (USU, 2006). The purpose of this study was to determine the relationship of parity to the degree of laceration of the birth pathway in Jetis Lor Polindes, Nawangan District, Pacitan Regency. The design or design in this study is correlation analysis, with the "retrospective" approach. This study analyzed the relationship of parity with the degree of laceration of the birth path in Jetis Lor Polindes, Nawangan District, Pacitan Regency. In this study, the population was all mothers giving birth at Jetis Lor Polindes, Nawangan District, Pacitan Regency. The samples in this study were all mothers giving birth at Jetis Lor Polindes, Nawangan District, Pacitan Regency. In this study by looking at the last 1 year data. In this study the independent variable is parity. In this study the dependent variable is the degree of laceration of the birth canal. Based on the calculation results of SPSS 11.5 for Windows, it was found that there was no relationship between parity and laceration degrees in the Jetis Lor Polindes, Nawangan Subdistrict, Pacitan Regency, from the results of probability (sig. 2-tailed) 0.22 <0.05.The researcher hopes that the mother will seek information and increase knowledge about the labor process, so that with good knowledge will reduce lacerations on the birth canal

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