Study on Establishment of Helix Flute Mathematic Model of Solid Carbide End Mills

2011 ◽  
Vol 121-126 ◽  
pp. 4753-4757
Author(s):  
Guo Chao Li ◽  
Jie Sun ◽  
Yong He
Keyword(s):  
Mathematical Model ◽  
Main Idea ◽  
Surface Group ◽  
Mathematic Model ◽  
End Mill ◽  
Cross Sectional ◽  
New Approach ◽  
Solid Carbide ◽  
End Mills ◽  
The Mathematical Model

This paper describes a new approach to establish the helix flute model of solid carbide end mills. Based on the theory of differential geometry and coordinate transformation, a mathematical model of the end mill helix flute will be established.The main idea of the study is to envelop the helix flute by a one-parameter surface group which consists of the cross-sectional profiles of the wheel.Then, the mathematical model will be quickly verified by MATLAB.Thus the end mill design time will be saved and the new mathematical model will be checked effectively.

A New and Accurate Mathematical Model for Computer Numerically Controlled Programming of 4Y1 Wheels in 2½-Axis Flute Grinding of Cylindrical End-Mills

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Silai Xiao ◽  
Liming Wang ◽  
Zezhong C. Chen ◽  
Shequan Wang ◽  
Aiming Tan
Keyword(s):  
Mathematical Model ◽  
Research Result ◽  
Rake Angle ◽  
Diamond Wheel ◽  
End Mill ◽  
Helical Angle ◽  
Computer Numerically Controlled ◽  
Solid Carbide ◽  
End Mills ◽  
Set Up

Solid carbide cylindrical end-mills are widely used in machining, and their helical flutes are crucial to their cutting performance. In industry, the flute is simply defined with four key parameters: the helical angle, the radial rake angle, the fluting angle, and the core radius, which are specified in an end-mill design. The flute shape is not fully defined, while it is often generated by a 1A1 or 1V1 diamond wheel in 2½-axis computer numerically controlled (CNC) grinding. Unfortunately, the two simple wheels cannot make largely different flute shapes, preventing further improvement of the end-mills. Although no research result on how the flute geometry affects the end-mill cutting attribute has come into public yet, it is now necessary to employ more complicated wheels to grind flutes with the specified parameter values but much different flute shapes. For this purpose, the 4Y1 diamond wheel is employed in this work. However, the commercial tool grinding software cannot determine the dimensions and the set-up angle for the 4Y1 wheel. To address this problem, a new mathematical model of the flute parameters in terms of the dimensions and the set-up angle of the 4Y1 wheel is formulated, thus, the 4Y1 wheel can be used in flute grinding. This work lays a foundation of using complex wheels to grind flutes with more shapes in order to improve the end-mill's cutting ability.

scholarly journals METHODS OF FORMULATING AND SOLVING OPTIMIZATION PROBLEMS OF CUTTING LOGS OF LARGE SIZE BY BAR-SAWING METHOD WITH CUTTING OUT ONE BAR AND FIVE PAIRS OF SIDE EDGING BOARDS WITH SUBSEQUENT SAWING LUMBER FOR EDGED BOARDS

2017 ◽  
Vol 7 (1) ◽  
pp. 137-150
Author(s):  
Агапов ◽  
Aleksandr Agapov
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Target Function ◽  
Cross Sectional ◽  
Optimization Task ◽  
Cutting Out ◽  
The Mathematical Model ◽  
The Relationship

For the first time the mathematical model of task optimization for this scheme of cutting logs, including the objective function and six equations of connection. The article discusses Pythagorean area of the logs. Therefore, the target function is represented as the sum of the cross-sectional areas of edging boards. Equation of the relationship represents the relationship of the diameter of the logs in the vertex end with the size of the resulting edging boards. This relationship is described through the use of the Pythagorean Theorem. Such a representation of the mathematical model of optimization task is considered a classic one. However, the solution of this mathematical model by the classic method is proved to be problematic. For the solution of the mathematical model we used the method of Lagrange multipliers. Solution algorithm to determine the optimal dimensions of the beams and side edging boards taking into account the width of cut is suggested. Using a numerical method, optimal dimensions of the beams and planks are determined, in which the objective function takes the maximum value. It turned out that with the increase of the width of the cut, thickness of the beam increases and the dimensions of the side edging boards reduce. Dimensions of the extreme side planks to increase the width of cut is reduced to a greater extent than the side boards, which are located closer to the center of the log. The algorithm for solving the optimization problem is recommended to use for calculation and preparation of sawing schedule in the design and operation of sawmill lines for timber production. When using the proposed algorithm for solving the optimization problem the output of lumber can be increased to 3-5 %.

The New Approach to Optimization of Production – Technological Base of a Public Transport Enterprises Network on an Example of City Hanoi

2016 ◽  
Vol 838 ◽  
pp. 39-46
Author(s):  
Andrey Nikolaevich Rementsov ◽  
Victor Akimovich Egorov ◽  
Nguen Huang Manh
Keyword(s):  
Mathematical Model ◽  
Public Transport ◽  
Queuing Systems ◽  
Economic Criterion ◽  
New Approach ◽  
Systems Model ◽  
Maintenance Service ◽  
Technological Base ◽  
The Mathematical Model ◽  
To Receive

In the article application of queuing systems model in the field of operation of motor transport is presented. The system of maintenance service (MS) and operating repair (OR) of the cars on technological base is considered as multichannel multiphase queuing system. The mathematical model allows to receive necessary parameters of system MS and OR and to optimize them on technical-economic criterion.

A Generalized and Efficient Approach for Accurate Five-Axis Flute Grinding of Cylindrical End-Mills

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Lei Ren ◽  
Shilong Wang ◽  
Lili Yi
Keyword(s):  
Singular Points ◽  
Grinding Process ◽  
Core Radius ◽  
End Mill ◽  
New Approach ◽  
Original Algorithm ◽  
Efficient Approach ◽  
Computer Aided ◽  
End Mills ◽  
Five Axis

Wheel position (including wheel location and orientation) in the flute grinding process of an end-mill determines the ground flute's geometric parameters, i.e., rake angle, core radius, and flute width. Current technologies for calculating the wheel position to guarantee the three parameters' accuracy are either time-consuming or only applicable to the grinding wheels with singular points. In order to cope with this problem, this paper presents a generalized and efficient approach for determining the wheel position accurately in five-axis flute grinding of cylindrical end-mills. A new analytic expression of the wheel location is derived and an original algorithm is developed to search for the required wheel position. This approach can apply not only to the wheels with fillets but also to the wheels with singular points. Simulation examples are provided to validate the new approach and compared with the results from other literature. Besides the ability to determine the wheel position, the new approach can evaluate extrema of the core radius and flute width that a specified wheel can generate. Owing to the evaluated extrema, automatic 1V1 wheel customization according to the designed flute is realized in this paper. This work can improve the efficiency and automation degree of the flute grinding process and lay a good foundation for the development of a comprehensive computer-aided design and computer-aided manufacturing system for end-mill manufacturing.

scholarly journals Evaluating the loads on bulldozer undercarriage under longitudinal trim

2020 ◽  
Vol 26 (3) ◽  
pp. 57-60
Author(s):  
Igor Kirichenko
Keyword(s):  
Mathematical Model ◽  
Mathematic Model ◽  
Operating Modes ◽  
The Mathematical Model

Based on the air-wheel type machines simulation, a bulldozer mathematic model for all its operating modes has been worked out. Evaluation of loads on the bulldozer undercarriage under longitudinal trim has been considered as an example of possible implementing the potential of the mathematical model proposed.

scholarly journals Spatial behaviour of thermoelasticity with microtemperatures and microconcentrations

2020 ◽  
Vol 34 ◽  
pp. 02001
Author(s):  
Adina Chirilă ◽  
Marin Marin
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Integrated Circuits ◽  
Boundary Conditions ◽  
Chemical Potential ◽  
Lateral Boundary ◽  
Spatial Behaviour ◽  
Cross Sectional ◽  
Lateral Boundary Conditions ◽  
The Mathematical Model

We consider a thermoelastic material with microtemperatures and microconcentrations. The mathematical model is represented by a system of partial differential equations with the coupling of the displacement, temperature, chemical potential, microconcentrations and microtemperatures fields. The processes of heat and mass diffusion play an important role in many engineering applications, such as satellite problems, manufacturing of integrated circuits or oil extractions. We study the spatial behaviour in a prismatic cylinder occupied by an anisotropic and inhomogeneous material. We impose final prescribed data that are proportional, but not identical, to their initial values. Moreover, we have zero body forces and zero lateral boundary conditions. The spatial behaviour is analysed in terms of some cross-sectional integrals of the solution that depend on the axial variable.

Research on Dynamic Temperature Field Modeling of the Solid Carbide End Mill in High-Speed Milling

2015 ◽  
Vol 1089 ◽  
pp. 350-353
Author(s):  
Wei Bo ◽  
Guang Yu Tan ◽  
Lin Lin Guo ◽  
Guang Hui Li
Keyword(s):  
Temperature Field ◽  
Heat Source ◽  
High Speed ◽  
Cutting Temperature ◽  
Helical Coil ◽  
End Mill ◽  
Dynamic Temperature ◽  
Solid Carbide ◽  
End Mills ◽  
Coil Heat

Cutting temperature is a key factor in impacting the solid carbide end mill’s life, the rule of solid carbide end mill temperature field is the research focus. In this paper, the solid carbide end mill helical side edge is regarded as a helical coil heat source, the tool chip friction surface is considered as a surface heat source which consists of countless helical coil heat source. Based on heat source method, the model of continuous dynamic temperature field simulation of a solid carbide end mills cutting process is established.

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

2013 ◽  
Vol 589-590 ◽  
pp. 416-420 ◽  
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.

Mathematic Model of Displacement Control Unit for Screw Distributor of Asphalt Paver

2013 ◽  
Vol 774-776 ◽  
pp. 295-298
Author(s):  
Zhi Nan Mi ◽  
Long An Chen ◽  
Jia Tao Tang
Keyword(s):  
Mathematical Model ◽  
Hydraulic System ◽  
Control Unit ◽  
Mathematic Model ◽  
Displacement Control ◽  
Rotating Speed ◽  
Dynamical Characteristics ◽  
Inertial Element ◽  
The Mathematical Model

Displacement control unit is an important part of hydraulic system for screw distributor. By adjusting the angle of swashplate, it can change the flow rate of pump and rotating speed of screw distributor. The rotating speed of screw distributor has influence on quality of road. The mathematical model of displacement control unit is presented. Its dynamical characteristics are analyzed. The mathematical model includes a reset spring gradient. The reset spring gradient is much smaller than the hydraulic spring rate, the effect of the reset spring gradient can be neglected. So an inertial element can be substituted by an integration element.

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