Mathematical Modeling and Parametric Design of Taper End Mills

2013 ◽  
Vol 797 ◽  
pp. 574-578
Author(s):  
Li Lun He ◽  
Xi Bin Wang ◽  
Zhi Bing Liu ◽  
Ming Chen ◽  
Zong Wei Xu
Keyword(s):  
Mathematical Modeling ◽  
Parametric Design ◽  
Cutting Tools ◽  
Three Dimensional ◽  
Groove Depth ◽  
Design And Manufacturing ◽  
End Mills ◽  
Shape Curve

The mathematical modeling of the cutting tools is an important aspect for the design and manufacturing engineers from the viewpoint of shape realization. Taper mill is composed of side and end edges. In order to make each patch closely combined, the groove section is designed by considering the relation among tapered radius, groove depth and radius of inner land. Through translation and rotation of shape curve, the side flute and end flute model can be established. These models can be rendered in three dimensional software according to parametric design of taper end mills. And this methodology can be easily extended to design, manufacture other tools.

Parametric Design of Tapered End Mills with Variable Pitch for Improving Stability

2014 ◽  
Vol 599-601 ◽  
pp. 381-384
Author(s):  
Li Lun He ◽  
Zhi Bing Liu ◽  
Xi Bin Wang ◽  
Wei Wei Lv
Keyword(s):  
Graphical Representation ◽  
Parametric Design ◽  
Design Method ◽  
Three Dimensional ◽  
Mathematical Expression ◽  
End Mill ◽  
Optimal Angle ◽  
Variable Pitch ◽  
End Mills ◽  
Design And Manufacture

For the problems about design and manufacture of the variable pitch tapered end mills, this study proposes a three-dimensional parametric design method of variable pitch mill. Firstly the equation of calculating the optimal angle between the pitch was presented .Considering existing different patches between two cutting edges, helix edge curve and cross-section groove model of tapered end mill were established .Secondly, mathematical expression of ball end teeth for tapered mill was derived, and all points data of tapered mill surface can be determined by established model. Through the graphical representation, the points set are translated into a solid model.

Geometric Modeling of Fluted Cutters

2008 ◽  
Vol 8 (2) ◽  
Author(s):  
Puneet Tandon ◽  
Phalguni Gupta ◽  
Sanjay G. Dhande
Keyword(s):  
Computer Aided Design ◽  
Geometric Modeling ◽  
Cutting Tools ◽  
Three Dimensional ◽  
New Paradigm ◽  
Inverse Mapping ◽  
Surface Patches ◽  
End Mills ◽  
Detailed Computer ◽  
Aided Design

Geometries of cutting tools are usually represented by two-dimensional models. This paper outlines the construction of detailed computer aided design models for a variety of fluted cutters that includes slab mills, end mills, and drills; and establishes a new three-dimensional definition for the geometry of fluted cutters in terms of biparametric surface patches. This work presents unified models of both plain and helical slab mills, end mills (with different end geometries), and drills (with a variety of point styles). The surfaces meant for cutting operations, known as flutes, are modeled as helicoidal surfaces. To model the flutes, sectional geometry of tip-to-tip profile is developed and then it is swept according to a sweeping rule, determined by the type of the cutter under consideration. The slab mill consists of flutes and two planar end surfaces, while the end mills and drills have shanks and end geometries also (in addition to the flutes). The geometric models of shank and end geometries are separately developed. The transitional surfaces of these cutters are modeled as bicubic Bézier surfaces or biparametric sweep surfaces. The proposed models employ a novel nomenclature that defines the form of cutting tools in terms of three-dimensional rotational angles. The relations required to map the proposed three-dimensional angles to conventional angles (forward mapping) and their reverse relations (inverse mapping) are also developed for all three types of fluted cutters. The new paradigm offers immense technological advantages in terms of numerous downstream applications.

Development of program-driven plug-in for conical counter-rotating twin screw based on SolidWorks

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Liqun Dong ◽  
Junwei Zhang ◽  
Liang Qin ◽  
Ping Xue ◽  
Yun Ma ◽  
...  
Keyword(s):  
Parametric Design ◽  
Cone Angle ◽  
Three Dimensional ◽  
Visual Basic ◽  
Automatic Generation ◽  
Three Dimensional Model ◽  
Modeling Process ◽  
Basic Language ◽  
Twin Screw ◽  
Visual Basic Language

Abstract Owing to the existence of the cone angle, the size of a conical counter-rotating twin screw continuously changes along the axis, so it is not easy to model using SolidWorks. In this study, the parametric design of the modeling process is completed based on the Visual Basic language and a program-driven method. Finally, the SolidWorks program plug-in and user interface are developed to complete the automatic generation of the three-dimensional model of a conical counter-rotating twin screw.

scholarly journals Microstructure and Properties of the AlCrSi(O)N Tool Coatings by Arc Ion Plating

Coatings ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 841
Author(s):  
Yanmei Liu ◽  
Tie-Gang Wang ◽  
Wei Lin ◽  
Qiang Zhu ◽  
Bing Yan ◽  
...  
Keyword(s):  
Cutting Tools ◽  
Medium Carbon Steel ◽  
Arc Ion Plating ◽  
Ion Plating ◽  
Mechanical And Tribological Properties ◽  
Hardness Tester ◽  
Coated Tool ◽  
Solid Carbide ◽  
End Mills ◽  
Coating Design

Aluminum rich nitride coatings are often used to protect cutting tools and prolong their service life. In this work, a preoxidation technique and duplex coating design were combined to further improve the bearing capacity and heat resistance of cutting tools. The Al-Cr-Si-N, Al-Cr-Si-O-N, and Al-Cr-Si-N/Al-Cr-Si-O-N duplex coatings were developed by arc ion plating, respectively. The morphology, phase constituents, mechanical and tribological properties of the coatings were characterized and tested by SEM, XRD, a micro-hardness tester, scratch tester, and tribometer. The results showed the coating became more compact and smoother after oxygen doping. However, the Al-Cr-Si-N coating presented the best mechanical properties and tribological behaviors. Its hardness and critical load showed the highest values, which were about 4000 HV and 81 N, respectively. A friction coefficient of 0.67 and wear rate of 1.4 × 10−3 μm3/N·mm were also the lowest values in the study. The three coatings were deposited on the same solid carbide end mills and performed the cutting tests under same conditions. By comparison, the Al-Cr-Si-N coated tool presented the longest tool life and minimum cutting force when cutting C1045 medium-carbon steel. After 90 min of dry milling, the width of the flank wear band (VB) of the AlCrSiN coated tool reached 135 μm, which was much lower than that of the other two coated tools.

scholarly journals Three-dimensional mathematical modeling of local scour

2005 ◽  
Vol 8 ◽  
pp. 803-812 ◽  
Author(s):  
Hao ZHANG ◽  
Hajime NAKAGAWA ◽  
Taisuke ISHIGAKI ◽  
Yasunori MUTO ◽  
Yasuyuki BABA
Keyword(s):  
Mathematical Modeling ◽  
Three Dimensional ◽  
Local Scour

A Stochastic Hierarchical Population System: Excitement, Extinction and Transition to Chaos

2021 ◽  
Vol 31 (14) ◽  
Author(s):  
Irina Bashkirtseva ◽  
Tatyana Perevalova ◽  
Lev Ryashko
Keyword(s):  
Mathematical Modeling ◽  
Food Chain ◽  
Analytical Method ◽  
Three Dimensional ◽  
Biological Parameters ◽  
Top Predator ◽  
Population System ◽  
Modeling And Analysis ◽  
Transition To Chaos ◽  
Random Fluctuations

A problem of the mathematical modeling and analysis of noise-induced transformations of complex oscillatory regimes in hierarchical population systems is considered. As a key example, we use a three-dimensional food chain dynamical model of the interacting prey, predator, and top predator. We perform a comparative study of the impacts of random fluctuations on three key biological parameters of prey growth, predator mortality, and the top predator growth. A detailed investigation of the stochastic excitement, noise-induced transition from order to chaos, and various scenarios of extinction is carried out. Constructive abilities of the semi-analytical method of confidence domains in the analysis of the noise-induced extinction are demonstrated.

Precision Coating of ta-C Films on Quartz Surfaces

2020 ◽  
Author(s):  
Kotaro Kawai ◽  
Yuki Hirata ◽  
Hiroki Akasaka ◽  
Naoto Ohtake
Keyword(s):  
Cutting Tools ◽  
Three Dimensional ◽  
High Hardness ◽  
Carbon Films ◽  
Vacuum Arc ◽  
High Wear Resistance ◽  
Chemical Inertness ◽  
Filtered Cathodic Vacuum Arc ◽  
Surface Morphologies

Abstract Diamond-like carbon (DLC) films have excellent properties such as high hardness, low friction coefficient, high wear resistance, chemical inertness and so on. Because DLC film is considered as an effective coating material to improve their surface properties, this films are used in various applications such as parts for automobiles engines, hard disk surfaces, cutting tools and dies, and so on. DLC films consist of a mixture of sp2 bonded carbon atoms and sp3 bonded carbon atoms. Among them, ta-C film is known as the hardest and strongest film since it mainly consists of sp3 bonded carbon atoms. One of deposition methods to form ta-C is Filtered Cathodic Vacuum Arc (FCVA). The characteristic of this method is that it is possible to remove the droplets and form a high-quality film.. However, even though lots of mechanical components which require ta-C coating have three-dimensionally shapes, it is difficult to coat ta-C film three dimensionally by using FCVA process. At present, researches on 3D deposition of amorphous carbon films on three dimensional components is still insufficient, and investigation reports on the deposition mechanism and characterization of the deposited films are even more limited. In this study, we tried to deposit films on 3D components by the FCVA method and evaluated the microstructure and surface morphologies of films. Although films were coated successfully in the entire surfaces, different properties were showed depending on the location of components. These properties were investigated by Raman spectroscopy and laser microscope.

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