Research and Realization of the Tool Radius Compensation Algorithm for Material Machining in the CNC System

2010 ◽  
Vol 154-155 ◽  
pp. 1064-1067
Author(s):  
Li Bing Zhang ◽  
Ting Wu
Keyword(s):  
Mathematical Model ◽  
High Speed ◽  
High Accuracy ◽  
Experimental Results ◽  
Numerical Control ◽  
Machining Accuracy ◽  
Nc Code ◽  
Cad Cam ◽  
Radius Compensation ◽  
The Mathematical Model

A numerical control (NC) code program is usually generated by a complex CAD/CAM system, which does not include the value of the tool radius compensation. To increase the material machining accuracy within the permissible machining accuracy range, this paper presented the approach of the tool radius compensation for high-speed and high-accuracy material machining. The principle and method of the tool radius compensation were put forward and analyzed, the mathematical model of the tool radius compensation was deduced according to the correlative factors, and the algorithm of the tool radius compensation was constructed for high-speed and high-accuracy. The simulative and experimental results verified the feasibility and validity of the proposed approach.

Machine Bed Support with Sliding Surface for Improving the Motion Accuracy

2016 ◽  
Vol 10 (3) ◽  
pp. 447-454 ◽  
Author(s):  
Yusaku Shirahama ◽  
◽  
Ryuta Sato ◽  
Yusuke Takasuka ◽  
Hidenori Nakatsuji ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Machine Tool ◽  
Frequency Response ◽  
High Speed ◽  
Numerical Control ◽  
Sliding Surface ◽  
Response Curves ◽  
Support Mechanism ◽  
Speed Tracking ◽  
The Mathematical Model

The purpose of this study is to develop a new machine bed support mechanism for reducing the vibration generated during the high-speed tracking motion of numerical control machine tools. In order to achieve this, the frequency response and motion trajectory of a machine tool with the proposed machine bed, which has a sliding surface, are measured and compared with that of the conventional support. Based on the modal analysis of the machine tool structure, a mathematical model representing the influence of the machine bed characteristics on the vibration is also developed. The model consists of a bed, saddle, table, column, and spindle head. Every component has three degrees of freedom for each of the translational and rotational axes. In order to evaluate the characteristics of the machine bed, the mathematical model determines the stiffness and damping along the X-, Y-, and Z-axis between the bed and the ground. The frequency response curves simulated by using the mathematical model are compared with that of the measured ones. From the results of the experiments and simulations, it is confirmed that the vibration generated during high-speed tracking motions can be reduced by using the proposed machine bed with a sliding surface.

Mathematical Model for the Influence of Machine Tool Parts Deformation on Machining Accuracy

2014 ◽  
Vol 556-562 ◽  
pp. 1354-1357
Author(s):  
Li Gong Cui ◽  
Gui Qiang Liang ◽  
Fang Shao
Keyword(s):  
Mathematical Model ◽  
Mathematical Method ◽  
Machine Tool ◽  
Cutting Tool ◽  
Lower Surface ◽  
Design Stage ◽  
Machining Accuracy ◽  
Cutting Point ◽  
The Mathematical Model

This paper presents a mathematical method to analyze the influence of each machine tool part deformation on the machining accuracy. Taking a 3-axis machine tool as an example, this paper divides the machine tool into the cutting tool sub-system and workpiece sub-system. Taking the deformation of lower surface of the machine bed as the research target, the mathematical model of the deformation on the displacement of the cutting point was established. In order to distribute the stiffness of each part, the contribution degree of each part on the machining accuracy was analyzed. Using this mathematical model, the stiffness of each part can be distributed at the design stage of the machine tool, and the machining accuracy of the machine tool can be improved economically.

Research on the Performance Simulation of the Transmission System of Loader with Secondary Regulating Technique

2010 ◽  
Vol 426-427 ◽  
pp. 299-302
Author(s):  
Fa Ye Zang
Keyword(s):  
Mathematical Model ◽  
Fuzzy Control ◽  
Energy Saving ◽  
High Speed ◽  
Transmission System ◽  
Performance Simulation ◽  
Constant Torque ◽  
Braking Torque ◽  
The Mathematical Model ◽  
Inertial Energy

Based on deeply analyzing the working principles and energy-saving theory of loader secondary regulating transmission system, regenerating the transmission system’s inertial energy by controlling constant torque was put forward. Considering large changes of the parameters of the transmission system and its non-linearity, a fuzzy control was adopted to control the transmission system, and the mathematical model of the system was established, then the simulations of the performance of the transmission system has been conducted. The conclusion was made that the inertial energy can be reclaimed and reused in the system by the application of the secondary regulation technology, and braking by controlling constant torque is stable, it can ensure the security of braking at high speed and also permits changing the efficiency of recovery by changing the braking torque. The system’s power has been reduced and energy saving has been achieved.

Increasing the mobility of a high-speed tracked vehicle based on a controlled skid algorithm

2020 ◽  
pp. 29-33
Author(s):  
S. V. Kondakov ◽  
O.O. Pavlovskaya ◽  
I.D. Ivanov ◽  
A.R. Ishbulatov
Keyword(s):  
Mathematical Model ◽  
Dynamic Stability ◽  
Simulation Modeling ◽  
Automatic System ◽  
High Speed ◽  
Control Algorithm ◽  
Loss Of Stability ◽  
Tracked Vehicle ◽  
Hydrostatic Transmission ◽  
The Mathematical Model

A method for controlling the curvilinear movement of a high-speed tracked vehicle in a skid without loss of stability is proposed. The mathematical model of the vehicle is refined. With the help of simulation modeling, a control algorithm is worked out when driving in a skid. The effectiveness of vehicle steering at high speed outside the skid is shown. Keywords: controlled skid, dynamic stability, steering pole displacement, hydrostatic transmission, automatic system, fuel supply. [email protected]

Multi-Object Multi-Discipline Probabilistic Design of High-Pressure Turbine Blade-Tip Radial Running Clearance

2013 ◽  
Vol 572 ◽  
pp. 551-554
Author(s):  
Wen Zhong Tang ◽  
Cheng Wei Fei ◽  
Guang Chen Bai
Keyword(s):  
Mathematical Model ◽  
High Pressure ◽  
Optimal Design ◽  
Mechanical System ◽  
High Accuracy ◽  
Probabilistic Design ◽  
High Pressure Turbine ◽  
Surface Method ◽  
Blade Tip ◽  
The Mathematical Model

For the probabilistic design of high-pressure turbine (HPT) blade-tip radial running clearance (BTRRC), a distributed collaborative response surface method (DCRSM) was proposed, and the mathematical model of DCRSM was established. From the BTRRC probabilistic design based on DCRSM, the static clearance δ=1.865 mm is demonstrated to be optimal for the BTRRC design considering aeroengine reliability and efficiency. Meanwhile, DCRSM is proved to be of high accuracy and efficiency in the BTRRC probabilistic design. The present study offers an effective way for HPT BTRRC dynamic probabilistic design and provides also a promising method for the further probabilistic optimal design of complex mechanical system.

Study on Mathematical Model of High Speed Milling Force for Plastic Mold Steel 3Cr2Mo

2011 ◽  
Vol 291-294 ◽  
pp. 710-714
Author(s):  
Jun Min Xiao ◽  
Ying Xu
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
High Speed ◽  
High Hardness ◽  
Milling Force ◽  
High Speed Milling ◽  
Engineering Requirement ◽  
Practical Engineering ◽  
Cad Cam ◽  
Plastic Mold

Mold steel 3Cr2Mo has been used widely in manufacturing of plastic mold formed parts, owing to fine mechanical properties. However, it is also very difficult to cut mold formed parts of steel 3Cr2Mo due to high hardness. Ordinary NC cutting method of steel 3Cr2Mo is unable to relate to modern mold manufacturing due to bad cutting property, so it is extremely significant for improving cutting property of steel 3Cr2Mo to study the high speed milling technology. On the basis of improving the traditional cutting force formula, the mathematical model of high speed milling force for steel 3Cr2Mo was derived and solved by using the experimental data and constructing matrix equation based on MATLAB software. Comparing with experimental data, the error of mathematical model of high speed milling force could be controlled within 6 percent. Due to high precision the model of high speed milling force can meet practical engineering requirement and has great value in the fields of CAD/CAM/CAE.

scholarly journals The analysis of flutter characteristics based on generalized parameters of eigen modes of vibrations

2021 ◽  
pp. 95-102
Author(s):  
K. I Barinova ◽  
A. V Dolgopolov ◽  
O. A Orlova ◽  
M. A Pronin
Keyword(s):  
Mathematical Model ◽  
High Speed ◽  
Dynamic Pressure ◽  
Mode Shapes ◽  
Scaled Model ◽  
Design Specifications ◽  
Operation Conditions ◽  
Flutter Analysis ◽  
Generalized Parameters ◽  
The Mathematical Model

Flutter numerical analysis of a dynamically scaled model (DSM) of a high aspect ratio wing was performed using experimentally obtained generalized parameters of eigen modes of vibrations. The DSM is made of polymer composite materials and is designed for aeroelastic studies in a high-speed wind tunnel. As a result of the analysis, safe operation conditions (flutter limits) of the DSM were determined. The input data to develop the flutter mathematical model are DSM modal test results, i.e. eigen frequencies, mode shapes, modal damping coefficients, and generalized masses obtained from the experiment. The known methods to determine generalized masses have experimental errors. In this work some of the most practical methods to get generalized masses are used: mechanical loading, quadrature component addition and the complex power method. Errors of the above methods were analyzed, and the most reliable methods were selected for flutter analysis. Comparison was made between the flutter analysis using generalized parameters and a pure theoretical one based on developing the mathematical model from the DSM design specifications. According to the design specifications, the mathematical model utilizes the beam-like schematization of the wing. The analysis was performed for Mach numbers from 0.2 to 0.8 and relative air densities of 0.5, 1, 1.5. Comparison of the two methods showed the difference in critical flutter dynamic pressure no more than 6%, which indicates good prospects of the flutter analysis based on generalized parameters of eigen modes.

Mathematical Modeling of Electrochemical Deburring

2010 ◽  
Vol 126-128 ◽  
pp. 545-550 ◽  
Author(s):  
Wen Ji Xu ◽  
W. Wang ◽  
Xu Yue Wang ◽  
Gui Bing Pang
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Influencing Factors ◽  
Applied Voltage ◽  
Experimental Results ◽  
Electrode Gap ◽  
Workpiece Material ◽  
Burr Height ◽  
Object A ◽  
The Mathematical Model

The drilling burr is taken as the research object. A mathematical model of electrochemical deburring (ECD) is established and the effects of main influencing factors, such as inter-electrode gap, applied voltage and deburring time, on burr height have been analyzed. The results show that the deburring time increases with the increase of initial burr height, inter-electrode gap, with the decrease of volume of electrochemical equivalent of the workpiece material, conductivity of electrolyte and applied voltage. The deburring time for various burr heights can be predicted by the mathematical model. The calculated results obtained from the mathematical model are approximately consistent with the experimental results. The results show that initial burr height h0=0.722mm is removed, and the fillet radius R=0.211mm is obtained.

Exact Solutions of the Vibration Problem of Beam Structures

2013 ◽  
Vol 390 ◽  
pp. 242-245 ◽  
Author(s):  
Alexander V. Chekanin
Keyword(s):  
Mathematical Model ◽  
Exact Solutions ◽  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Numerical Solutions ◽  
High Accuracy ◽  
Displacement Method ◽  
Actual Problem ◽  
Beam Structures ◽  
The Mathematical Model

The article deals with the actual problem of improving the accuracy of determining the dynamic characteristics of beam structures. To solve such problems the displacement method is used. Defining matrices are calculated with the Godunovs scheme. Numerical solutions in this case can be obtained practically with any accuracy within accepted hypotheses of the mathematical model of the calculated object. This suggests that the resulting solutions are standard. The examples of determining the natural frequencies of vibrations of beam structures that demonstrate an extremely high accuracy of the proposed algorithm are given.

scholarly journals Suppression of Ground Borne Vibration Induced by High-Speed Lines

2018 ◽  
Vol 152 ◽  
pp. 02001
Author(s):  
Ali Mohamed Rathiu ◽  
Mohammad Hosseini Fouladi ◽  
Satesh Narayana Namasivayam ◽  
Hasina Mamtaz
Keyword(s):  
Mathematical Model ◽  
Analytical Model ◽  
High Speed ◽  
Moving Load ◽  
Ground Vibration ◽  
Harmonic Excitation ◽  
Vibration Response ◽  
Vibration Velocity ◽  
Velocity Response ◽  
The Mathematical Model

Vibration of high-speed lines leads to annoyance of public and lowering real estate values near the railway lines. This hinders the development of railway infrastructures in urbanised areas. This paper investigates the vibration response of an isolated rail embankment system and modifies the component to better attenuate ground vibration. Mainly velocity response is used to compare the responses and the applied force is of 20 kN at excitation frequencies of 5.6 Hz and 8.3 Hz. Focus was made on ground-borne vibration and between the frequency range of 0 and 250 Hz. 3D Numerical model was made using SolidWork software and frequency response was produced using Harmonic Analysis module from ANSYS Workbench software. For analytical modelling MATLAB was used along with Simulink to verify the mathematical model. This paper also compares the vibration velocity decibels (VdB) of analytical two-degree of freedom model mathematical model with literature data. Harmonic excitation is used on the track to simulate the moving load of train. The results showed that modified analytical model gives the velocity response of 75 VdB at the maximum peak. Changes brought to the mass and spacing of the sleeper and to the thickness and the corresponding stiffness for the ballast does not result in significant vibration response. Limitations of two-degree analytical model is suspected to be the cause of this inactivity. But resonance vibration can be reduced with the aid of damping coefficient of rail pad. Statistical analysis methods t-test and ANOVA single factor test was used verify the values with 95% confidence.

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