Comparative Analytical Solutions to the Problem of Profiling the End Mill Cutter to Generate Helical Surfaces

2015 ◽  
Vol 809-810 ◽  
pp. 39-44
Author(s):  
Gabriel Frumuşanu ◽  
Virgil Teodor ◽  
Nicolae Oancea
Keyword(s):  
Minimum Distance ◽  
Symmetry Axis ◽  
The Other ◽  
Numerical Representation ◽  
Classical Theorem ◽  
End Mill ◽  
Helical Surface ◽  
Constant Pitch ◽  
Revolution Surfaces ◽  
Mill Cutter

In this paper, we present, comparatively, two analytical methods for profiling the tools delimited by revolution surfaces, used to generate helical surfaces with constant pitch. The first method lays on a complementary theorem used for tools profiling, namely the Minimum distance theorem. A specific algorithm for applying it has been developed, in order to profile the tools delimited by revolution surfaces, which generates helical surfaces with constant pitch by enwrapping. The methodic is referring, here, to a tool whose symmetry axis is incident and, at the same time, normal to the helical surface axis – the end mill cutter. The other analytical method here applied grounds on Nikolaev classical theorem. We also present an example of application for both methods, in the case of profiling the end mill cutter used to generate a helicoid with circular frontal generatrix. The tool axial sections are determined and compared in a numerical representation.

Graphical Method in CAD Environment for Profiling End Mill Tool

2015 ◽  
Vol 809-810 ◽  
pp. 787-792 ◽  
Author(s):  
Camelia Lǎcrǎmioara Popa
Keyword(s):  
Graphical Method ◽  
Screw Compressor ◽  
End Mill ◽  
Design Environment ◽  
Disk Cutter ◽  
Revolution Surfaces ◽  
Helical Flute ◽  
Mill Cutter ◽  
Graphic Solution

The actives surfaces of screw compressors are helical surfaces, cylindrical and uniform pitch. The generation of helical surfaces can be done using tools bordered by revolution surfaces (as end mill cutter, or disk cutter). The shaping of generating tools is based on fundamentals theorem of the enveloping surfaces. This paper consists to propose a graphic solution, using specific tools of the design environment AUTOCAD, to problem concerning the shaping end mill tool which generates the helical flute of male rotor component of screw compressor. The algorithm has been developed based on a complementary theorem - "The theorem of substituting circles family".

Graphic Method Profiling of the End Mill Cutter Generating the Screw Compressor Rotor

2014 ◽  
Vol 658 ◽  
pp. 123-128 ◽  
Author(s):  
Camelia Lacramioara Popa ◽  
Viorel Popa
Keyword(s):  
Screw Compressor ◽  
Graphic Method ◽  
End Mill ◽  
Helical Channel ◽  
Compressor Rotor ◽  
Mill Cutter ◽  
Front Section

Helical rotors, components of screw compressors have different structural shapes: rotors circular front section, rotors elliptic front section or asymmetric rotors. Manufacturing rotors involves profiling a tool bordered by a revolution surface, enveloping of each helical channel. This paper proposes a method developed in AutoCAD, in order to determine the profile of end mill cutter which generates the helical channel. Graphic method is based on the principle of complementary theorems' "Substitute Circles Family Method" component of envelope surfaces theory.

scholarly journals Mathematical and geometrical modeling of braided ropes bent over a sheave

2020 ◽  
Vol 15 ◽  
pp. 155892502093972
Author(s):  
Guifang He ◽  
Chunfu Sheng ◽  
Hongwei He ◽  
Rong Zhou ◽  
Ding Yuan ◽  
...  
Keyword(s):  
Mathematical Method ◽  
Phase Difference ◽  
Computational Simulation ◽  
The Other ◽  
Force Transmission ◽  
Helical Surface ◽  
Modeling Process ◽  
Mathematical Equations ◽  
The Difference ◽  
Final Equation

As soft elements for force transmission, braided fiber ropes play important roles in many fields where the fiber ropes are used bent over sheaves, while the relevant experiments are time-consuming and expensive. Computational simulation is a promising choice for evaluating the performance of fiber ropes when bent over a sheave. This article presents two methods that could be employed to build a model of braided rope bent over a sheave. One is the mathematical method which deduces the exact mathematical equations of braiding curves based on the Frenet–Serret frame. The spatial equations, considering the phase difference of strands in the same direction and the difference of strands’ projection in different directions, are discussed carefully. The final equation of braided strands is confirmed by modeling the braided rope in Maple® 17. The other method, which is inspired by the analysis of braiding movements, is based on the intersection of surfaces of braiding surface and helical surface which are introduced and defined based on the motion analysis of bobbins and take-up roller. The SolidWorks® 2018 is successfully employed to realize the modeling process.

221Evaluating the ability of different substrate mapping techniques to identify scar-related ventricular tachycardia circuits using computational modelling

EP Europace ◽  
2020 ◽  
Vol 22 (Supplement_1) ◽  
Author(s):  
F Campos ◽  
M Orini ◽  
J Whitaker ◽  
M O"neill ◽  
R Razavi ◽  
...  
Keyword(s):  
Minimum Distance ◽  
Computational Modelling ◽  
Hemodynamic Instability ◽  
Vulnerability Index ◽  
The Other ◽  
Exit Site ◽  
Accurate Identification ◽  
Ablation Therapy ◽  
Arrhythmogenic Substrate ◽  
Reentrant Circuit

Abstract Funding Acknowledgements National Institute for Health Research; British Heart Foundation; and The Wellcome Trust and Engineering and Physical Sciences Research Council. Background Accurate identification of targets for catheter ablation therapy of ventricular tachycardias (VTs) in the postinfarction heart remains a significant challenge. Identification of such targets often requires VT-induction to delineate the entry/exit points of the reentrant circuit sustaining the VT. However, inducibility may not be possible due to hemodynamic instability. In this scenario, substrate ablation strategies can still be performed to uncover the arrhythmogenic substrate during sinus or paced rhythm. However, substrate mapping may fail to accurately delineate the reentrant circuit resulting in VT recurrence after the procedure. Purpose To use computer simulations to compare the ability of different electroanatomical maps constructed following typical substrate ablation strategies to identify the VT exit site. Methods An image-based computational model of the porcine post-infarction left ventricle was constructed to simulate VT and paced rhythm. Electroanatomical maps were constructed based on the following features extracted from electrograms computed on the endocardial surface: activation time (AT), bipolar electrogram amplitude, signal fractionation and the reentry vulnerability index (RVI - a metric combining activation and repolarization timings to identify tissue susceptibility to reentry). Potential ablation targets during substrate mapping were compared for: highest 5% AT gradient; lowest 5% bipolar signal amplitudes; areas with fragmented signals (more than one peak); and lowest 5% RVI. The minimum distance, d, between the manually identified VT exit site and the targets was measured. Results The RVI performed better than the other metrics at detecting the VT exit site (see Figure). The minimum distance between sites of lowest RVI and the exit site was 3.2mm compared to 13.1mm and 15.9mm in traditional AT and voltage maps, respectively. As the scar was not transmural, parameters derived from all electrograms (including those located on dense scar regions) were used to construct the electroanatomical maps. This improved the performance of the RVI significantly, making it more specific than the other metrics as can be seen in the Figure. Conclusions Among all metrics investigated here, the RVI identified the vulnerable region closest to VT exit site. This finding suggests that activation-repolarization metrics may improve the detection of pro-arrhythmic regions without having to induce VT. Moreover, the RVI may be particularly well suited for detecting vulnerable regions within non-transmural scars. Abstract Figure. VT and Substrate Mapping

Side Mill Tool Profiling for Generation of Helical Surfaces Determined by Reverse Engineering

2014 ◽  
Vol 657 ◽  
pp. 28-32
Author(s):  
Camelia Popa ◽  
Virgil Gabriel Teodor ◽  
Nicuşor Baroiu ◽  
Nicolae Oancea
Keyword(s):  
Reverse Engineering ◽  
Cutting Tool ◽  
Special Problem ◽  
Helical Surface ◽  
Surface Type ◽  
Axial Section ◽  
Compressor Rotor ◽  
Constant Pitch ◽  
Measuring Machine

The compressor rotors usually are helical surfaces with constant pitch and are composed crossing profiles. Frequently, for repair operations occurs the reconstruction necessity for one or both of the worms, drive and driven, from the helical compressors gear. The helical composed surface of rotor flank is generated usually with side mill. The knowledge of worm shape can not be made from geometrical conditions. In these conditions it is necessary to determine the flank form by actual measuring the crossing profiles of these parts. So, the theoretical helical surface of the worm is being substituted by an assembly of helical lines which together with crossing profiles forms points cloud resulted from measuring leads to a polyhedral expression of the flank rotor. Numerically, this surface type is expressed by a coordinate array which shows its discrete image. The profiling of cutting tool bounded by a revolution surface reciprocally enveloping with the substitutive surface of the helical one represents a special problem. In this paper is proposed an algorithm for polyhedral expression of the helical surface previously determined by reverse engineering methods and an algorithm for the determination of the specific enveloping condition at contact with a discrete surface.It is presented an example for a compressor rotor measured on a 3D measuring machine, the algorithm for the transformation of the gathered points cloud in a surface with polyhedral expression. Given these conditions there were determined the enveloping condition and the axial section of the side mill.

Self-deployment of mobile robotic networks: an algorithm for decentralized sweep boundary coverage

Robotica ◽  
2016 ◽  
Vol 35 (9) ◽  
pp. 1816-1844 ◽  
Author(s):  
Anna A. Semakova ◽  
Kirill S. Ovchinnikov ◽  
Alexey S. Matveev
Keyword(s):  
Computer Simulations ◽  
Minimum Distance ◽  
A Priori ◽  
Safety Margin ◽  
The Other ◽  
Robotic Networks ◽  
Wheeled Robots ◽  
Visibility Range ◽  
Current Minimum ◽  
Unknown Region

SUMMARYSeveral non-holonomic Dubins-car-like robots travel over paths with bounded curvatures in a plane that contains an a priori unknown region. The robots are anonymous to one another and do not use communication facilities. Any of them has access to the current minimum distance to the region and can determine the relative positions and orientations of the other robots within a finite and given visibility range. We present a distributed navigation and guidance strategy under which every robot autonomously converges to the desired minimum distance to the region with always respecting a given safety margin, the robots do not collide with one another and do not get into clusters, and the entire team ultimately sweeps over the respective equidistant curve at a speed exceeding a given threshold, thus forming a kind of a sweeping barrier at the perimeter of the region. Moreover, this strategy provides effective sub-uniform distribution of the robots over the equidistant curve. Mathematically rigorous justification of the proposed strategy is offered; its effectiveness is confirmed by extensive computer simulations and experiments with real wheeled robots.

scholarly journals Nesting of the Eurasian spoonbill (Platalea leucorodia) on the Utlyukskiy Liman (Zaporozhye region)

2020 ◽  
Vol 2020 (23) ◽  
pp. 139-143
Author(s):  
V. M. Popenko ◽  
Keyword(s):  
Water Level ◽  
Breeding Season ◽  
Minimum Distance ◽  
The Other ◽  
Nesting Behavior ◽  
Great Egret ◽  
The South ◽  
Xxth Century ◽  
Xxist Century

In the 70s of the XXth century, the nesting of the Eurasian spoonbill in Ukraine was known only in the lower reaches of the Danube and Dniester, and at the beginning of the XXIst century, it began to spread to the East and the Eurasian spoonbill began to nest on the Tiligulskiy Liman, Karkinit Bay, Western and Eastern Sivash. Since 2016, the Eurasian spoonbill has been observed during the breeding season in the upper reaches of the Utlyukskiy Liman and the estuarine areas of the Bolshoy and Maly Utlyuk Rivers. According to observations that were held in 2016-2020, first there were: a pair with unproven nesting (2016), then flocks of up to 17-26 individuals (2018-2019). In 2020, both individual pairs with nesting behavior and flocks were found near a mixed colony of the Gray heron and the Great egret. Finally, on 24.05.2020, the Eurasian spoonbill nests were found in this colony. Among the 8 nests, one contained 2 eggs and two chicks, four nests contained 4 eggs and the other three - 3 ones. Nests are located on the periphery of the heron colony on clump of reeds. The height of the nesting platforms is about 4-70 cm above the water level, the minimum distance between the nests is about 4 m. It is possible that the flock of 26 adult and young individuals, that was observed on 2.08.2018, consisted of local nesting birds. Thus, another nesting location was found in the South of Ukraine.

scholarly journals The optimization of binary group sequences generated by the nonlinear code multiplexing

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
O. Y. Berdyshev ◽  
◽  
◽  
Keyword(s):  
Minimum Distance ◽  
The Other ◽  
Entire Group ◽  
Walsh Functions ◽  
Full System ◽  
Binary Group

This paper presents the challenge of optimization of binary group sequences obtained from the nonlinear code multiplexing. It shows that at optimal element wise methodology for group sequences in a full system of orthogonal Walsh functions, a maximum criterion for the minimum distance of group sequences is equal to a maximum criterion for the minimum correlation response for the information orthogonal Walsh functions which contain group sequences. After a nonlinear code multiplexing group sequences are often contained errors, that makes using this method of multiplexing more difficult. To eliminate this source of errors the algorithm of optimization of group sequences was suggested. In this algorithm some elements of group sequences can be replaced with the opposite elements. Additionally, the algorithm of receiving of the entire group sequence among the nearest group sequences was developed. This algorithm provides considerable increasing of immunity while group sequence receiving unlike the other algorithm of element-to-element receiving in a full system of orthogonal Walsh functions.

scholarly journals Lengths for Which Fourth Degree PP Interleavers Lead to Weaker Performances Compared to Quadratic and Cubic PP Interleavers

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 78
Author(s):  
Lucian Trifina ◽  
Daniela Tarniceriu ◽  
Jonghoon Ryu ◽  
Ana-Mirela Rotopanescu
Keyword(s):  
Upper Bound ◽  
Turbo Codes ◽  
Minimum Distance ◽  
Prime Numbers ◽  
Upper Bounds ◽  
The Other ◽  
Small Range ◽  
Generator Matrix ◽  
Fourth Degree ◽  
Minimum Distances

In this paper, we obtain upper bounds on the minimum distance for turbo codes using fourth degree permutation polynomial (4-PP) interleavers of a specific interleaver length and classical turbo codes of nominal 1/3 coding rate, with two recursive systematic convolutional component codes with generator matrix G = [ 1 , 15 / 13 ] . The interleaver lengths are of the form 16 Ψ or 48 Ψ , where Ψ is a product of different prime numbers greater than three. Some coefficient restrictions are applied when for a prime p i ∣ Ψ , condition 3 ∤ ( p i − 1 ) is fulfilled. Two upper bounds are obtained for different classes of 4-PP coefficients. For a 4-PP f 4 x 4 + f 3 x 3 + f 2 x 2 + f 1 x ( mod 16 k L Ψ ) , k L ∈ { 1 , 3 } , the upper bound of 28 is obtained when the coefficient f 3 of the equivalent 4-permutation polynomials (PPs) fulfills f 3 ∈ { 0 , 4 Ψ } or when f 3 ∈ { 2 Ψ , 6 Ψ } and f 2 ∈ { ( 4 k L − 1 ) · Ψ , ( 8 k L − 1 ) · Ψ } , k L ∈ { 1 , 3 } , for any values of the other coefficients. The upper bound of 36 is obtained when the coefficient f 3 of the equivalent 4-PPs fulfills f 3 ∈ { 2 Ψ , 6 Ψ } and f 2 ∈ { ( 2 k L − 1 ) · Ψ , ( 6 k L − 1 ) · Ψ } , k L ∈ { 1 , 3 } , for any values of the other coefficients. Thus, the task of finding out good 4-PP interleavers of the previous mentioned lengths is highly facilitated by this result because of the small range required for coefficients f 4 , f 3 and f 2 . It was also proven, by means of nonlinearity degree, that for the considered inteleaver lengths, cubic PPs and quadratic PPs with optimum minimum distances lead to better error rate performances compared to 4-PPs with optimum minimum distances.

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