Mathematical Model and Tool Path Calculation for Helical Groove Whirling

The universal NC program was inefficient for machining centrifugal pump vanes and a new tool-path generation method along section lines was proposed in this paper. After analyzing curve characteristics of centrifugal pump vanes, the mathematical model for calculating cutting step-lengths and determining the next tool contact parameter ui+1 through step estimating method was put forward. Furthermore, a new iterative algorithm was implemented, along with its terminal condition simplified. The proposed algorithm provided a new idea for developing special NC program of impellers.

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HSM-ADAPTED TOOL PATH CALCULATION FOR POCKETING

Machining Science and Technology ◽

10.1080/10910340600710063 ◽

2006 ◽

Vol 10 (2) ◽

pp. 181-196 ◽

Cited By ~ 3

Author(s):

Vincent Pateloup ◽

Hélène Chanal ◽

Emmanuel Duc ◽

Pascal Ray

Keyword(s):

Tool Path ◽

Path Calculation

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Research on Optimization Method of Tool Path in Five-Axis Process Singular Region

Machine Learning and Artificial Intelligence - Frontiers in Artificial Intelligence and Applications ◽

10.3233/faia200767 ◽

2020 ◽

Author(s):

Yujie Wang ◽

Xin Shen ◽

Yu Peng ◽

Lixin Zhao

Keyword(s):

Mathematical Model ◽

Tool Path ◽

Optimization Method ◽

Rotating Shaft ◽

Processing Efficiency ◽

Machined Surface ◽

Rapid Rotation ◽

Singular Region ◽

Axis Of Rotation ◽

Five Axis

For the five-axis machine into the singular region in the process of parts processing, resulting in a discontinuous and rapid rotation of the axis of rotation of large angles. Based on the analysis of the cause of the obvious ripple on the machined surface and the influence on the machining precision, a mathematical model of the singular region is established, and an optimization method of the tool path in the singular region is proposed. The simulation and practical machining results show that the method can effectively overcome the problem of excessive movement of the rotating shaft in the Song singular region of 5-axis machine tool, and solve the surface corrugated defects caused by the problem, while improving the processing efficiency.

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Tool profile and tool path calculation for free-form thick-layered fabrication

Computer-Aided Design ◽

10.1016/s0010-4485(98)00068-2 ◽

1998 ◽

Vol 30 (14) ◽

pp. 1097-1110 ◽

Cited By ~ 21

Author(s):

Imre Horváth ◽

Joris SM Vergeest ◽

Johan J Broek ◽

Zoltán Rusák ◽

Bram de Smit

Keyword(s):

Tool Path ◽

Free Form ◽

Tool Profile ◽

Path Calculation

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Tool-Path Calculation for NC Machining the Helical Surface of Screw Shaft Based on the End Section

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.569.410 ◽

2012 ◽

Vol 569 ◽

pp. 410-414

Author(s):

Quan Quan Han ◽

Ri Liang Liu

Keyword(s):

Theoretical Approach ◽

Tool Path ◽

Nc Machining ◽

Milling Process ◽

Metal Working ◽

Helical Surface ◽

Standard Cutter ◽

Path Calculation

With the increasingly wide use of screw components in industry, technologies for efficiently fabricating the complex helical surfaces on these components play an important role in modern metal-working. In this paper, the helical surface of a screw shaft is mathematically modeled based on the profile of its end section, and the whirlwind milling process and its requirements for machining the screw using standard cutter blades are overviewed. Then a theoretical approach to calculating the tool path and the corresponding movements of the machine axes for producing such a helical surface are presented. Finally a case study is provided with an example screw whose end section is described using sampled points.

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Research on the Mathematical Model of Helical Groove of the End Mill Based on the Grinding Wheel Attitude

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.589-590.416 ◽

2013 ◽

Vol 589-590 ◽

pp. 416-420 ◽

Cited By ~ 2

Author(s):

Xian Feng Zhao ◽

Lin He ◽

Hong Yan Shi

Keyword(s):

Mathematical Model ◽

Differential Geometry ◽

Relative Motion ◽

3D Model ◽

Rake Angle ◽

Grinding Wheel ◽

End Mill ◽

Helical Groove ◽

The Mathematical Model ◽

Main Factor

This paper presents the mathematical model of helical groove of the end mill according to the differential geometry and meshing principle based on the grinding wheel attitude. The profile of the helical groove can be precisely calculated using a given wheel attitude and the relative motion between the workpiece and the grinding wheel.The relation between the grinding wheel attitude and the rake angle can be obtained through adjusting the grinding wheel attitude angle.And the accurate 3D model of helical groove was generated in the SolidWorks.The research shows that the grinding wheel attitude is the main factor that affects the rake angle of end mill.There is a linear relationship between the rake angle and the grinding wheel attitude. The smooth and accurate 3D model of helical groove lay the foundation for studying the cutting performance and dynamic characteristics of end mill.

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RESEARCH OF THE FORMS OF MOTION TRAJECTORIES OF THE WORKING TOOL OF TOROIDAL PLANETARY EXECUTIVE UNITS OF MINING MACHINES

JOURNAL of Donetsk mining institute ◽

10.31474/1999-981x-2021-1-19-24 ◽

2021 ◽

pp. 19-24

Author(s):

Denys Dovhal ◽

Keyword(s):

Mathematical Model ◽

Rock Mass ◽

Geometric Modeling ◽

Tool Path ◽

Geometric Analysis ◽

Practical Significance ◽

Operating Parameters ◽

Motion Trajectories ◽

Characteristic Features ◽

Executive Body

Purpose. The purpose of this work is to determine and geometric analysis of possible forms of trajectories of the working tool, depending on the design and operating parameters of the torus planetary executive bodies of mining machines in the destruction of rock mass or minerals. Methods. Studies are based on the provisions of analytical and differential geometry, geometric modeling of objects, processes and phenomena, the theory of destruction of rocks and coal, as well as the theory of planetary executive bodies of mining machines. Results. On the basis of the mathematical model of the working process of the torus planetary executive body, the main forms of the trajectory of the spatial motion of a single working tool are considered, their geometric analysis is carried out. The characteristic features of the change in the shape of the trajectories are revealed when the values of the design and operating parameters of the executive body are varied, and their frequency is determined. Scientific novelty. For the first time, in the general case, a mathematical model of the process of movement of a single tool of a torus planetary executive body was analyzed in order to identify all possible characteristic forms of trajectories and, as a result, face surfaces, which constitute the basis for further research and optimization of the kinematic and dynamic characteristics of the process of destruction of a rock mass by executive bodies of mining machines. of the specified type. Practical significance. Scientifically substantiated data on the influence of the values of the design and operating parameters on the parameters of the tool path, the degree of surface treatment of the face and the conditions for the transition of the torus executive body to other design cases of the planetary executive body have been obtained. All this in the future will make it possible to determine rational relationships between the design and operating parameters of the torus executive body, which will provide an effective “grid” of cutting, which will minimize the energy indicators of the destruction process and improve the fractional composition of the separated rock mass.

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Non Destructive Diagnosis for Minimum Invasive Access Preparation in Endodontic Treatment

Nondestructive Evaluation ◽

10.1115/imece2002-33484 ◽

2002 ◽

Author(s):

Janet Dong ◽

Shane Y. Hong ◽

Gunnar Hasselgren

Keyword(s):

Mathematical Model ◽

Root Canal ◽

Tool Path ◽

Root Canal Treatment ◽

Tooth Crown ◽

Tool Selection ◽

Root Canals ◽

Dental Instruments ◽

Micro Drilling ◽

Non Destructive

Root canal treatment of infected root canals represents a large percentage of business in general dental practice. It is an expensive process and often prone to failure. During root canal treatment, destructive access preparation by removing parts of tooth crown and dentin is usually needed even before a clinician’s inspection and diagnosis. This paper presents a non-destructive method for accessing the internal tooth geometry by building a 3-D tooth model from 2-D radiograph. The geometry of root canals is then formulated into a mathematical model. Based on this mathematical model, the treatment procedures utilizing the dental tools/instruments are planned by a computer aided prescription system, which yields the tool selection and tool path for the root canal preparation by an intelligent micro drilling machine with on-line monitoring. To minimize the removal of healthy tooth crown and dentin, thus protecting the strength of the patient’s infected tooth, an optimization algorithm is utilized for planning the access preparation in the root canal treatment. Although an opening of a tooth crown is still needed so that dental instruments can reach the root canal, the non-destructive 3-D modeling and the optimization of the access preparation in the new approach makes the root canal treatment minimally invasive compared to present techniques.

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Virtual Manufacture of the Twist Drill Flute in UG

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.156-157.1223 ◽

2010 ◽

Vol 156-157 ◽

pp. 1223-1226

Author(s):

Pu Gao ◽

Xiao Heng Wang

Keyword(s):

Mathematical Model ◽

Tool Path ◽

Cutting Tool ◽

Nc Machining ◽

Twist Drill ◽

Post Processing ◽

Nc Code ◽

The Mathematical Model

The mathematical model of the twist drill flute is discussed in the paper. The cutting tool path to machine the twist drill flute is obtained under the certain parameters in UG. And the NC machining of the twist drill flute is simulated too. After post-processing, the NC code is obtained and it is verified by virtual manufacture.

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