The Parameters Calibration and Error Compensation of Circular Gratings for Parallel Double-Joint Coordinate Measuring Machine (CMM)

2011 ◽  
Vol 105-107 ◽  
pp. 1899-1902 ◽  
Author(s):  
Xiao Wei Zhang ◽  
Xing Hua Li ◽  
Bo Chen
Keyword(s):  
Mathematical Model ◽  
Measurement Error ◽  
Curve Fitting ◽  
Error Compensation ◽  
Coordinate Measuring Machine ◽  
Measuring Machine ◽  
Circular Grating ◽  
The Impact ◽  
The Mathematical Model ◽  
Main Factor

In this paper, the mathematical model with errors for parallel double-joint coordinate measuring machine (CMM) was proposed. The main factor of the impact of circular grating measurement error--radial install eccentric error--was analyzed. The error was measured and the data obtained from measurement was used to curve fitting and form the error compensation formula. Experiments show that the method of error compensation has good usability and accuracy.

Error Model and Calibration Analysis of the Flexible Coordinate Measuring Machine

2011 ◽  
Vol 121-126 ◽  
pp. 3273-3277 ◽  
Author(s):  
Fang Li ◽  
Shu Gui Liu ◽  
Lei Zhao
Keyword(s):  
Mathematical Model ◽  
Coordinate Measuring Machine ◽  
Least Square Method ◽  
Coefficient Matrix ◽  
Error Model ◽  
Least Square ◽  
Parameter Calibration ◽  
Measuring Machine ◽  
Improving Accuracy ◽  
The Mathematical Model

A new 5-DOF flexible coordinate measuring machine (CMM) is introduced in this paper, which uses REVO system produced by Renishaw. According to the D-H method, the mathematical model is built, and then the error model of the flexible CMM is derived. The parameter calibration based on the nonlinear least square method is analyzed theoretically. Due to the disadvantages of Gauss-Newton method, LM method is researched, which improved the singularity of the coefficient matrix. The calibration analysis is a basis for improving accuracy of the flexible CMM.

A study on the key techniques of application of REVO five-axis system in non-orthogonal coordinate measuring machine

2016 ◽  
Vol 231 (4) ◽  
pp. 730-736 ◽  
Author(s):  
Haitao Zhang ◽  
Shugui Liu ◽  
Xinghua Li
Keyword(s):  
Mathematical Model ◽  
Measurement Data ◽  
Coordinate Measuring Machine ◽  
Coordinate Measuring Machines ◽  
Measurement Results ◽  
Measuring Machine ◽  
Key Techniques ◽  
Five Axis ◽  
The Mathematical Model ◽  
Body Theory

REVO five-axis system, designed for the orthogonal coordinate measuring machines, must be reconfigured for the application in the non-orthogonal coordinate measuring machines. First, in this article, error sources of the system and components of measurement data are analyzed; then, scale values of coordinate measuring machine axes, which are essential to derive the coordinates of measured points in non-orthogonal coordinate measuring machine, are separated out. Besides, the mathematical model of REVO is established based on the quasi-rigid body theory, from which the measurement results can be evaluated by data derived instead of that returned by the system. The effectiveness of both separation of scale values and mathematical model of REVO is proved by experiments and practice. The research of this article is of great significance to the application of REVO five-axis system in the non-orthogonal coordinate measuring machine.

Measuring the Flanks of a Bevel Gear Made by Heidenreich-Harbeck Cutting Machine

2012 ◽  
Vol 186 ◽  
pp. 163-168
Author(s):  
Faluvegi Erzsebet ◽  
Mate Csaba Zoltan ◽  
Cristea Luciana
Keyword(s):  
Mathematical Model ◽  
Coordinate Measuring Machine ◽  
Bevel Gear ◽  
Face Gear ◽  
Straight Bevel Gear ◽  
Machine Type ◽  
Cutting Machine ◽  
The Face ◽  
Measuring Machine ◽  
The Mathematical Model

This paper presents the mathematical model of the straight bevel gear flanks with octoid II teething which is measured with a coordinate measuring machine, type DEA Global Performance. The mathematical model is realized by theoretical equations which occur in the face gear. The experimental data, obtained by using the coordinate measuring machine, is analyzed and the compensation of the probe tip is calculated. The differences between the surfaces are determined.

Effects of Wheel Dressing Errors on the Accuracy of CNC Gear Form Grinding

2013 ◽  
Vol 328 ◽  
pp. 400-407 ◽  
Author(s):  
Hu Zhang ◽  
Xiao Diao Huang
Keyword(s):  
Mathematical Model ◽  
Theoretical Foundation ◽  
Coordinate Measuring Machine ◽  
Tooth Surface ◽  
Wheel Surface ◽  
Precision Control ◽  
Form Grinding ◽  
Measuring Machine ◽  
Grinding Machine ◽  
The Mathematical Model

Gear form grinding is a finish machining method for hard tooth surface with a form wheel. Wheel dressing is an important process in gear form grinding, and affects the precision of the ground gear directly. Based on the envelope theory the mathematical model of the dressed wheel surface was built in the case of wheel dressing errors. Then the real profile of the ground tooth in the transverse plan was solved and its deviations from the designed profile were evaluated. Finally the effects of each dressing error on the precision of the ground gear were analyzed using the proposed mathematical model. The results provided theoretical foundation for the precision control during manufacturing a gear form grinding machine. A grinding experiment was implemented using the gear form grinding machine and the ground gear was measured by a three-coordinate measuring machine. The measure result indicated that the accuracy grade of the ground gear achieved 4 (ISO1328-1: 1997).

Study on the Compensation for Mounting Eccentric Errors of Circular Grating Angle Sensors

2011 ◽  
Vol 301-303 ◽  
pp. 1552-1555 ◽  
Author(s):  
Guan Bin Gao ◽  
Wen Wang ◽  
Li Xie ◽  
Dong Bo Wei ◽  
Wen Qin Xu
Keyword(s):  
Error Compensation ◽  
Rotation Angle ◽  
Coordinate Measuring Machine ◽  
Experimental Result ◽  
Measuring Error ◽  
Calibration Data ◽  
Error Sources ◽  
Measuring Machine ◽  
Circular Grating ◽  
After Error

The mounting eccentric error is one of the largest error sources for circular grating angle sensors (CGASs). To improve the measuring accuracy of CGASs, one error compensation method based on mounting eccentricity is proposed in this paper. The mounting eccentricity and measuring error of CGASs was modeled after analysis. Six joints mounted with CGASs were used in the eccentric error compensation experiment. The rotation error of the joints was calibrated with a coordinate measuring machine and a gauge block. Then with the calibration data, the parameters of the eccentric error compensation model were calculated. The experimental result shows that after error compensation the rotation angle errors of the joints are reduced about 58 to 543 times.

scholarly journals The Impact of Elongation on Change in Electrical Resistance of Electrically Conductive Yarns Woven into Fabric

Materials ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3390
Author(s):  
Željko Knezić ◽  
Željko Penava ◽  
Diana Šimić Penava ◽  
Dubravko Rogale
Keyword(s):  
Mathematical Model ◽  
Electrical Resistance ◽  
Electrically Conductive ◽  
Textile Materials ◽  
Measurement Results ◽  
Conductive Yarns ◽  
Yarn Count ◽  
As Relationship ◽  
The Impact ◽  
The Mathematical Model

Electrically conductive yarns (ECYs) are gaining increasing applications in woven textile materials, especially in woven sensors suitable for incorporation into clothing. In this paper, the effect of the yarn count of ECYs woven into fabric on values of electrical resistance is analyzed. We also observe how the direction of action of elongation force, considering the position of the woven ECY, effects the change in the electrical resistance of the electrically conductive fabric. The measurements were performed on nine different samples of fabric in a plain weave, into which were woven ECYs with three different yarn counts and three different directions. Relationship curves between values of elongation forces and elongation to break, as well as relationship curves between values of electrical resistance of fabrics with ECYs and elongation, were experimentally obtained. An analytical mathematical model was also established, and analysis was conducted, which determined the models of function of connection between force and elongation, and between electrical resistance and elongation. The connection between the measurement results and the mathematical model was confirmed. The connection between the mathematical model and the experimental results enables the design of ECY properties in woven materials, especially textile force and elongation sensors.

The Impact Analysis of Revolute Pair Clearance to the End Pose Accuracy of Welding Robot

2015 ◽  
Vol 778 ◽  
pp. 259-263
Author(s):  
Fa Jun Zhang ◽  
Lin Zi Li ◽  
Hui Lin ◽  
Yin Lin Pu ◽  
Zhu Xin
Keyword(s):  
Mathematical Model ◽  
Impact Analysis ◽  
Joint Clearance ◽  
Welding Robot ◽  
Movement Characteristic ◽  
Movement Stability ◽  
Simulation Results ◽  
The Impact ◽  
The Mathematical Model ◽  
Welding Position

Various uncertain factors affect the movement of the welding robot, thus welding gun tend to deviate from the theory of welding position which reduces the welding accuracy, of which the revolute pair clearance have an greater effect on the movement of the welding robot. In order to study the influence of revolute pair clearance to the end pose accuracy of welding robot, the mathematical model of revolute pair clearance was established, and the software SolidWorks was used for establishing the welding robot model, making simulations of the mechanical arm with joint clearance and no joint clearance. At last, the movement characteristic of the hinge shaft is attained. The simulation results showed that the shaft velocity and displacement of mechanical arm with joint clearance has a certain degree of fluctuation, which affecting the end pose accuracy of welding robot , and reducing the movement stability and the welding accuracy of welding robot.

Enhancement the Solar Still Performance Using Chimney Exhaust Gases

2021 ◽  
Author(s):  
Hamdy Hassan
Keyword(s):  
Mathematical Model ◽  
Theoretical Study ◽  
Saline Water ◽  
Kutta Method ◽  
Solar Still ◽  
Climate Conditions ◽  
Exhaust Gases ◽  
Runge Kutta Method ◽  
The Impact ◽  
The Mathematical Model

Abstract In this paper, a theoretical study is presented on enhancement of the solar still performance by using the exhaust gases passing inside a chimney under the still basin. The impact of the exhaust gases temperature on the solar still temperature, productivity, and efficiency are considered. The performance of solar still with chimney is compared with that of conventional solar still. The study is carried out under the hot and climate conditions of Upper Egypt. A complete transient mathematical model of the physical model including the solar still regions temperatures, productivity, and heat transfer between the solar still and the exhaust gases are constructed. The mathematical model is solved numerically by using fourth-order Runge-Kutta method and is programmed by using MATLAB. The mathematical model is validated using an experimental work. The results show that the solar still saline water temperature increases and productivity with using and rising the exhaust gases. Furthermore, the impact of using exhaust gases on the still performance in winter is greater than in summer. using chimney exhaust gases at 75 °C and 125 °C enhances the daily freshwater yield of the conventional still by more than three times and about six times in winter, respectively, and about two and half times and more than three times in summer, respectively.

scholarly journals NECESSITY TO IMPROVE THE MATHEMATICAL MODEL OF FREIGHT CARS TO STUDY CASES OF ITS DERAILMENTS

2020 ◽  
pp. 442-451
Author(s):  
А.V. Batig ◽  
A. Ya. Kuzyshyn
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Computer Experiment ◽  
Rolling Stock ◽  
Software Systems ◽  
Freight Car ◽  
The Stability ◽  
The Many ◽  
The Impact ◽  
The Mathematical Model

One of the most important problems that pose a serious threat to the functioning of railways is the problem of freight cars derailment. However, according to statistics, the number of cases of the derailments of freight cars in trains annually grows. Тo prevent such cases, the necessary preventive measures are developed, and to study the causes of their occurrence, a significant number of mathematical models, programs and software systems created by leading domestic and foreign scientists. Studies of such mathematical models by the authors of this work have led to the conclusion that they are not sufficiently detailed to the extent that it is necessary for analyze the reasons of its derailment. At the same time, an analysis of the causes of the rolling stock derailments on the railways of Ukraine over the past five years showed that in about 20 % of cases they are obvious, and in 7 % of cases they are not obvious and implicitly expressed. The study of such cases of rolling stock derailment during an official investigation by the railway and during forensic railway transport expertises requires the use of an improved mathematical model of a freight car, which would allow a quantitative assessment of the impact of its parameters and rail track on the conditions of railway accidents. Therefore, taking into account the main reasons that caused the occurrence of such railroad accidents over the last five years on the railways of Ukraine, the article selected the main directions for improving the mathematical model of a freight car, allowing to cover all the many factors (explicit and hidden) and identify the most significant ones regarding the circumstances of the derailment rolling stock off the track, established on the basis of a computer experiment. It is proposed in the mathematical model of a freight car to take into account the guiding force, the value of which is one of the main indicators of the stability of the rolling stock. The authors of the article noted that not taking into account the influence of the guiding forces on the dynamics of the freight car can lead to an erroneous determination of the reasons for the rolling stock derailment or even to the impossibility of establishing them.

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