Journal articles: 'Trochoids'

1

Ziaei, Masoud. "Bending Stresses and Deformations in Prismatic Profiled Shafts with Noncircular Contours Based on Higher Hybrid Trochoids." Applied Mechanics 3, no. 3 (August 23, 2022): 1063–79. http://dx.doi.org/10.3390/applmech3030060.

Full text

Abstract:

This paper presents an analytical method for determining the bending stresses and deformations in prismatic, noncircular profile shafts with trochoidal cross sections. The so-called higher trochoids can be used as form-fit shaft-hub connections. Hybrid (mixed) higher trochoids (M-profiles) were developed for the special application as a profile contour for the form-fit shaft and hub connections in an earlier work by the author. M-profiles combine the advantages of the two standardised polygonal and spline contours, which are used as shaft-hub connections for the transmission of high torques. In this study, the geometric and mechanical properties of the higher hybrid trochoids were investigated using complex functions to simplify the calculations. The pure bending stress and shaft deflection were determined for M-profiles using bending theory based on the theory of mathematical elasticity. The loading cases consisted of static and rotating bends. Analytical, numerical, and experimental results agreed well. The calculation formulas developed in this work enable reliable and low-cost dimensioning with regard to the stresses and elastic deformations of profile shafts subjected to bending loads.

APA, Harvard, Vancouver, ISO, and other styles

2

Abele, E., M. Weber, and C. Daume. "Spindelwälzlagerbelastung beim trochoiden Fräsen*/Spindle bearing load during trochoidal milling." wt Werkstattstechnik online 108, no. 10 (2018): 730–35. http://dx.doi.org/10.37544/1436-4980-2018-10-94.

Full text

Abstract:

In den vergangenen 15 Jahren wurde die Prozessvariante des trochoiden Fräsens weiterentwickelt und wird gegenwärtig in der Schruppbearbeitung eingesetzt. Höhere Zeitspanvolumina bei gleichzeitig geringerem Werkzeugverschleiß sind gegenüber dem konventionellen Fräsen erzielbar. Das trochoide Fräsen besitzt eine verfahrenstypische Dynamik, deren Auswirkung auf die Lagerbelastung der Motorspindel mithilfe von Zerspanversuchen und einer Mehrkörpersimulation untersucht wird.   In the past 15 years the trochoidal milling process has been developed. Currently it is used for roughing operations. Higher metal removal rates including lower tool wear compared to the conventional linear milling can be achieved. The trochoidal milling has a distinctive process dynamic whose impact on the bearing load of the motor spindle is investigated. Therefore, trochoidal und linear cutting tests are performed as well as a multi-body simulation including the motor spindle.

APA, Harvard, Vancouver, ISO, and other styles

3

Hall, Leon M. "Trochoids, Roses, and Thorns-Beyond the Spirograph." College Mathematics Journal 23, no. 1 (January 1992): 20. http://dx.doi.org/10.2307/2686194.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Pasali Atmaca, Sibel. "The geometry of map equations for Trochoids." New Trends in Mathematical Science 2, no. 6 (March 20, 2018): 6–18. http://dx.doi.org/10.20852/ntmsci.2018.265.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Hall, Leon M. "Trochoids, Roses, and Thorns—Beyond the Spirograph." College Mathematics Journal 23, no. 1 (January 1992): 20–35. http://dx.doi.org/10.1080/07468342.1992.11973429.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

Farrington, Eleanor. "Parametric Equations at the Circus: Trochoids and Poi Flowers." College Mathematics Journal 46, no. 3 (May 2015): 173–77. http://dx.doi.org/10.4169/college.math.j.46.3.173.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Wagner, Peter J. "Phylogenetics of the Early Paleozoic Archaeogastropoda." Paleontological Society Special Publications 6 (1992): 300. http://dx.doi.org/10.1017/s2475262200008601.

Full text

Abstract:

The Archaeogastropoda are one of the most abundant orders of the Paleozoic, but they have received surprizingly little systematic analysis. I have conducted a cladistic analysis of archaeogastropod species appearing during the initial radiation of the clade during the latest Cambrian through the Ordovician. The analysis included over 100 species. Most specimens were from North America, but some European and Asian material was included. The hypothesized phylogeny also includes an additional 40 Ordovician species from a previous cladistic work on a single family (the Lophospiridae), and only the stem members of this clade were included here.The analysis used 54 meristic and 12 morphometric traits encompassing 154 character states. This seemingly large number of character states for a group considered character-poor can be attributed to: 1) the breadth of morphologic diversity produced during the initial phases of the clade's radiation, resulting in nearly all conceivable morphologies being included here; and 2) the high number of character states for “types” of selenizones and sinuses, morphologies absent on most extant gastropods.The results of the analysis suggest the following:1. There were two large clades present by the Early Ordovician that most closely correspond to present definitions of the Murchisonoidea and Euomphaloidea. The clades shared an anisostrophically coiled common ancestor and thus were not derived separately from bellerophonts. However, the Macluritidae appear to have been derived separately from bellerophonts, corroborating a widely held hypothesis.2. Early Paleozoic species presently considered “pleurotomaroids” comprise a polyphyletic assemblage, with the major families independently derived from either the murchisonoid clade (the Eotomaridae, Lophospiridae and Phanerotrematidae) or from the euomphaloid clade (the Liospiridae, Luciellidae and post-Middle Ordovician members of the Raphistomatidae). It had been assumed previously that pleurotomaroids represent the least-derived anisostrophically coiled gastropods, as well-developed selenizones and sinuses were considered primitive traits. However, those features actually represent derived conditions of the Ordovician that appear to have been secondarily lost in later lineages; thus seemingly “modern” appearing early Paleozoic species often simply retained non-derived conditions. As the Mesozoic Pleurotomaria can not be linked with any Early Paleozoic clades, there is no basis for classifying early Paleozoic gastropods in the Pleurotomaroidea.3. The Subulitoidea and Loxonematoidea (which may be ancestral to the Caenogastropoda) evolved separately from murchisonoids. The origins of the Trochoidea are not clear. If the Holopeidae represent the stem members of the Trochoidea, then trochoids evolved from euomphaloids. However, the Platyceratidae also have been linked with trochoids. The earliest known members of that group possess many unique homologies and no obvious synapomorphies with any other archaeogastropods. The taxon can not be linked reliably with holopeids or any other taxon included in this study, and I do not discount the possibility that platyceratids were evolved separately from bellerophonts.4. Gross shell convergences abound, as turritelliform and planispiral-to-hyperstrophic shells both evolved at least four times. However, the combinations of character states used to achieve these gross morphologies differ among clades, allowing “homoplasies” of character complexes to be recognized.

APA, Harvard, Vancouver, ISO, and other styles

8

Salleh, Noor Deenina Haji Mohamed, and Somnuk Phon Amnuaisuk. "Quantifying aesthetic beauty through its dimensions: a case study on trochoids." International Journal of Knowledge Engineering and Soft Data Paradigms 5, no. 1 (2015): 51. http://dx.doi.org/10.1504/ijkesdp.2015.073479.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Su, Xiaogen, and Donald R. Houser. "Characteristics of trochoids and their application to determining gear teeth fillet shapes." Mechanism and Machine Theory 35, no. 2 (February 2000): 291–304. http://dx.doi.org/10.1016/s0094-114x(99)00004-x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Omirou, Sotiris L., and Marios M. Fyrillas. "A CNC Manufacturing Method for Parts with Trochoidal Profile." Journal for Manufacturing Science and Production 14, no. 2 (August 29, 2014): 103–13. http://dx.doi.org/10.1515/jmsp-2013-0024.

Full text

Abstract:

AbstractThis paper presents a manufacturing method for parts with trochoidal profile on CNC milling machines. The method is based on a new real-time interpolation algorithm capable to drive the cutter along the offset of trochoid curves with precision equal to the resolution of the machine. The structure of the presented algorithm may be adapted accordingly so as to be used either for parts with an epitrochoidal or a hypotrochoidal profile. Both types of curves, known as trochoid curves, have important industrial applications such as gears with trochoidal tooth-profile, cams, trochoidal-shaped housings for rotary internal combustion engines and rotary piston pumps etc. The effectiveness and accuracy of the proposed method is verified by simulation tests of the generated tool path for the machining of two representative mechanical parts, an inner rotor of a hypogerotor pump and an epitrochoidal-shaped housing.

APA, Harvard, Vancouver, ISO, and other styles

11

Maeda, Taro, and Hideyuki Ando. "Omnidirectional Mobility Following Through Trochoidal Trajectory." Journal of Robotics and Mechatronics 31, no. 4 (August 20, 2019): 567–82. http://dx.doi.org/10.20965/jrm.2019.p0567.

Full text

Abstract:

The trochoid is a geometrically complete solution for realizing omnidirectional mobility with a rotating mechanism. The proposed mechanism is implemented as a novel omnidirectional vehicle with following a geometrically complete trochoidal trajectory. Because the mechanism has a large camber angle, it has an improved ability to travel past rough terrain as compared to a regular vehicle with regular wheels. In this paper, a complete mechanical control using link mechanism to generate not only the steering angle and camber angle for an ideal trochoidal wave but also the angular velocity of the wheel axis is proposed.

APA, Harvard, Vancouver, ISO, and other styles

12

Bonandrini, G., G. Mimmi, and C. Rottenbacher. "Theoretical analysis of internal epitrochoidal and hypotrochoidal machines." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 223, no. 6 (February 4, 2009): 1469–80. http://dx.doi.org/10.1243/09544062jmes1163.

Full text

Abstract:

In this article, a complete and original method to analyse both the epitrochoidal and the hypotrochoidal rotary machines is presented. The internal trochoidal machines consist of two rotors: the first rotor is an envelope of a trochoid, the second rotor is its conjugate. In particular, in this article, the profiles of the trochoidal rotor and its conjugate are expressed by original and particularly synthetic equations using a method based on the theory of gearing. Then the geometry of these machines is completely defined by the choice of four non-dimensional parameters. Once these parameters are selected, the geometric and kinematic characteristics of the rotor profiles are obtained in an original analytic form; hence, the main theoretical performance indexes are computed by a proper method. The results of the analysis allow us to choose the best geometric configuration for a specific application.

APA, Harvard, Vancouver, ISO, and other styles

13

Healy, J. M. "Euspermatozoa and paraspermatozoa in the trochoid gastropodZalipais laseroni (Trochoidea: Skeneidae)." Marine Biology 105, no. 3 (October 1990): 497–507. http://dx.doi.org/10.1007/bf01316321.

Full text

APA, Harvard, Vancouver, ISO, and other styles

14

Hsieh, Chiu-Fan, and Yii-Wen Hwang. "Study on the High-Sealing of Roots Rotor With Variable Trochoid Ratio." Journal of Mechanical Design 129, no. 12 (December 10, 2006): 1278–84. http://dx.doi.org/10.1115/1.2779897.

Full text

Abstract:

Vacuum pump plays an important role in the vacuum system. In this paper, a new method is proposed to design the Roots rotor that was the trochoidal curve with variable trochoid ratio. The fifth-order polynomial and cubic spline functions are used to generate smoothly trochoid ratio functions and thus a regular addendum curve for Roots rotor will be generated. Based on the addendum curve, the tooth profile for the complete Roots rotor is derived by the gearing theory. In order to improve the sealing between the rotor tip and the chamber, a design procedure is also developed for roots rotor with high sealing and high area efficiency. In addition, the undercutting equation is used to study the constraints of design parameters and the center of curvature is used to check the occurrence of the carryover on the tooth profile. Finally, some design examples are presented to show the feasibility of the proposed method.

APA, Harvard, Vancouver, ISO, and other styles

15

Šajgalík, Michal, Milena Kušnerová, Marta Harničárová, Jan Valíček, Andrej Czán, Tatiana Czánová, Mário Drbúl, Marian Borzan, and Ján Kmec. "Analysis and Prediction of the Machining Force Depending on the Parameters of Trochoidal Milling of Hardened Steel." Applied Sciences 10, no. 5 (March 5, 2020): 1788. http://dx.doi.org/10.3390/app10051788.

Full text

Abstract:

Current demands on quality are the engine of searching for new progressive materials which should ensure enough durability in real conditions. Due to their mechanical properties, however, they cannot be applied to conventional machining methods. In respect to productivity, one of the methods is the finding of such machining technologies which allow achieving an acceptable lifetime of cutting tools with an acceptable quality of a machined surface. One of the mentioned technologies is trochoidal milling. Based on our previous research, where the effect of changing cutting conditions (cutting speed, feed per tooth, depth of cut) on tool lifetime was analysed, next, we continued with research on the influences of trochoid parameters on total machining force (step and engagement angle) as parameters adjustable in the CAM (computer-aided machining) system. The main contribution of this research was to create a mathematical-statistical model for the prediction of cutting force. This model allows setting up the trochoid parameters to optimize force load and potentially extend the lifetime of the cutting tool.

APA, Harvard, Vancouver, ISO, and other styles

16

Zhang, Jin Feng, Ya Dong Dong, Yong Zhen Zhang, and Jun Cheng. "The Mechanism of Surface Trajectories and Milling Forces in Micro-Milling Processing." Advanced Materials Research 472-475 (February 2012): 2422–25. http://dx.doi.org/10.4028/www.scientific.net/amr.472-475.2422.

Full text

Abstract:

In practical industrial processing, in order to make the tiny functional devices assembly accuracy as high as possible, which raises an very high requirement for surface quality of micro workpiece. Some of the important factors in controlling the surface quality with the level of the trajectories and forces of the blade across on the workpiece have a great relationship. This paper presents generalized mathematical models of the trochoid and forces combined with the helix cutter geometry used in the industry. And then from both of these aspects analytical laws in-depth of the trochoidal curves and micro-cutting forces variation. It will be of great reference value for the study of micro-milling mechanism.

APA, Harvard, Vancouver, ISO, and other styles

17

Haszprunar, Gerhard, Martin Brückner, and Bernhard Ruthensteiner. "Skeneimorph but not skeneid: systematics and anatomy of Lodderena Iredale, 1924 (Vetigastropoda: Trochoidea)." Journal of Molluscan Studies 86, no. 3 (July 7, 2020): 157–72. http://dx.doi.org/10.1093/mollus/eyaa011.

Full text

Abstract:

ABSTRACT The genus Lodderena Iredale, 1924 has been classified in the Skeneidae by most recent authors. However, this family, originally characterized by their minute size, lack of nacre in the teleoconch and a rhipidoglossate radula, is currently considered to be polyphyletic assemblage, and preliminary molecular systematic data suggest exclusion of Lodderena from Skeneidae. In order to shed light on the systematic position of this genus, we provide a detailed description of the anatomy and histology of the type species, Lodderena minima (Tenison-Woods, 1878), and of L. ornata (Olsson & McGinty, 1958). The anatomical data confirm the vetigastropod-trochoid nature of Lodderena but exclude the genus from Skeneidae. Skeneidae are mainly characterized by a propodial penis, a hermaphroditic condition with separated testis and ovary, and a large receptaculum in the mantle roof. In contrast, Lodderena species lack both a copulatory organ and receptaculum, and have a true ovotestis. We also provide a critical review of nominal species in the genus. Based on molecular and morphological evidence, we exclude Lodderena from Skeneidae, instead treating it as a genus incertae sedis within Trochoidea. We discuss the implications of small size for functional morphology and reproduction.

APA, Harvard, Vancouver, ISO, and other styles

18

Kasko, A. A., A. A. Zelentsov, and V. P. Minin. "End window profiling of a trochoid machine." Proceedings of Higher Educational Institutions. Маchine Building, no. 11 (752) (November 2022): 47–57. http://dx.doi.org/10.18698/0536-1044-2022-11-47-57.

Full text

Abstract:

There is a proposal of a method for the profiling the end windows of trochoid rotary machines according to the given geometric parameters for constructing the trochoid and the degree of gas pressure increase. Its area of application is rotary piston engines and trochoid compressors and pumps. Verification of the mathematical model was carried out on the basis of gas flow simulation data in a three-dimensional setting in the AVL Fire software package. The model of the working process of a trochoid machine is based on the fundamental equations of momentum, energy, diffusion and continuity, written in the Reynolds form and supplemented by the k–?–f turbulence model. The developed method makes it possible to estimate quickly the throughput of the windows of a trochoid rotary machine with less computing resources than in a three-dimensional calculation.

APA, Harvard, Vancouver, ISO, and other styles

19

Zhou, Ke, Changming Zhang, and Siyuan Du. "Cutting Force Prediction for Trochoid Milling of 300M Ultra-High Strength Steel." Processes 10, no. 12 (December 6, 2022): 2617. http://dx.doi.org/10.3390/pr10122617.

Full text

Abstract:

Trochoid milling can improve the quality of machining of difficult materials as well as the efficiency of machining. However, its complex tool trajectory makes it difficult to predict the instantaneous cutting forces during cutting. Therefore, in this paper, the transient cutting thickness model in the cycloidal milling process was established using numerical combined with analytical methods, and the semi-mechanical cutting force model was established. Experiments were designed to compare the differences between the cutting force coefficients extracted from the slot milling experiments and those extracted from the trochoid milling. Finally, experiments were designed to validate the established cutting force model. The results showed that there was an error of 5–23% between the tangential cutting force coefficients extracted from slot milling and the tangential cutting force coefficients extracted from trochoid milling, while there was an error of 21–35% in the radial cutting force coefficients, indicating that the cutting force coefficients extracted from slot milling cannot be used to predict the cutting force in the trochoid milling process. It was verified that the error of the established cutting force model in predicting the cutting force of trochoid milling was 12%, indicating that the established model has a high accuracy, which provides a theoretical basis for the selection of cutting parameters and parameter optimization in the future.

APA, Harvard, Vancouver, ISO, and other styles

20

Li, Kai Zhu, and Shi Xiong Wu. "Tool Path Optimization Based on the Constrain of Radial Cutting Depth in High Speed Milling." Advanced Materials Research 314-316 (August 2011): 1734–39. http://dx.doi.org/10.4028/www.scientific.net/amr.314-316.1734.

Full text

Abstract:

In order to decrease the radial amout of cutting depth in high speed milling,optimized arc transition has been proposed in corner milling and the circular trochoid model has been used to remove the residual. Mathematical relationship based on radial depth of cutting constrain among tool radius, trochoid radius and tool step length in circular trochoid model have been analyzed .Based on the goal to limiting the radial cutting depth, appropriate parameters have been computed for higher machining quality. To verify the effectiveness of the proposed method, a compared test has been conducted. Experiment shows that optimized tool paths cause a slight increase in machining time but obtain weaker processing vibration and superior machining precision.

APA, Harvard, Vancouver, ISO, and other styles

21

Uhlmann, Eckart, Sascha Reinkober, Martin Hoffmann, and Peer Käpernick. "Trochoide Fräsbearbeitung mit Industrierobotern." ZWF Zeitschrift für wirtschaftlichen Fabrikbetrieb 113, no. 7-8 (August 20, 2018): 458–61. http://dx.doi.org/10.3139/104.111955.

Full text

APA, Harvard, Vancouver, ISO, and other styles

22

Ross, David S. "The inverse trochoid problem." Journal of the Franklin Institute 347, no. 7 (September 2010): 1281–308. http://dx.doi.org/10.1016/j.jfranklin.2010.06.003.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

Karkalos, Nikolaos E., Panagiotis Karmiris-Obratański, Szymon Kurpiel, Krzysztof Zagórski, and Angelos P. Markopoulos. "Investigation on the Surface Quality Obtained during Trochoidal Milling of 6082 Aluminum Alloy." Machines 9, no. 4 (March 30, 2021): 75. http://dx.doi.org/10.3390/machines9040075.

Full text

Abstract:

Surface quality has always been an important goal in the manufacturing industry, as it is not only related to the achievement of appropriate geometrical tolerances but also plays an important role in the tribological behavior of the surface as well as its resistance to fatigue and corrosion. Usually, in order to achieve sufficiently high surface quality, process parameters, such as cutting speed and feed, are regulated or special types of cutting tools are used. In the present work, an alternative strategy for slot milling is adopted, namely, trochoidal milling, which employs a more complex trajectory for the cutting tool. Two series of experiments were initially conducted with traditional and trochoidal milling under various feed and cutting speed values in order to evaluate the capabilities of trochoidal milling. The findings showed a clear difference between the two milling strategies, and it was shown that the trochoidal milling strategy is able to provide superior surface quality when the appropriate process parameters are also chosen. Finally, the effect of the depth of cut, coolant and trochoidal stepover on surface roughness during trochoidal milling was also investigated, and it was found that lower depths of cut, the use of coolant and low values of trochoidal stepover can lead to a considerable decrease in surface roughness.

APA, Harvard, Vancouver, ISO, and other styles

24

McCarthy, Lauren A., Kyle W. Smith, Xiang Lan, Seyyed Ali Hosseini Jebeli, Luca Bursi, Alessandro Alabastri, Wei-Shun Chang, Peter Nordlander, and Stephan Link. "Polarized evanescent waves reveal trochoidal dichroism." Proceedings of the National Academy of Sciences 117, no. 28 (June 29, 2020): 16143–48. http://dx.doi.org/10.1073/pnas.2004169117.

Full text

Abstract:

Matter’s sensitivity to light polarization is characterized by linear and circular polarization effects, corresponding to the system’s anisotropy and handedness, respectively. Recent investigations into the near-field properties of evanescent waves have revealed polarization states with out-of-phase transverse and longitudinal oscillations, resulting in trochoidal, or cartwheeling, field motion. Here, we demonstrate matter’s inherent sensitivity to the direction of the trochoidal field and name this property trochoidal dichroism. We observe trochoidal dichroism in the differential excitation of bonding and antibonding plasmon modes for a system composed of two coupled dipole scatterers. Trochoidal dichroism constitutes the observation of a geometric basis for polarization sensitivity that fundamentally differs from linear and circular dichroism. It could also be used to characterize molecular systems, such as certain light-harvesting antennas, with cartwheeling charge motion upon excitation.

APA, Harvard, Vancouver, ISO, and other styles

25

Otkur, M., and I. Lazoglu. "Trochoidal milling." International Journal of Machine Tools and Manufacture 47, no. 9 (July 2007): 1324–32. http://dx.doi.org/10.1016/j.ijmachtools.2006.08.002.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Deng, Qi, Rong Mo, Zezhong C. Chen, and Zhiyong Chang. "An Analytical Approach to Cutter Edge Temperature Prediction in Milling and Its Application to Trochoidal Milling." Applied Sciences 10, no. 5 (March 4, 2020): 1746. http://dx.doi.org/10.3390/app10051746.

Full text

Abstract:

Cutter edge temperature in milling is an important factor to cutter life. With high cutting speed and feedrate, the cutting efficiency is high; however, the cutter edge temperature is high, shortening the cutter life. Therefore, it is necessary to know the cutter edge temperature in milling. Unfortunately, the cutter edge temperature is difficult to measure and predict in milling. To address the technical challenge, an analytical approach was proposed to predict cutter edge temperature in milling. First, the heat flux into the cutter edge was calculated. Second, by using the Green function, the cutter edge temperature was figured out, and the results obtained from this approach agreed well with that of a recognized test. Then, based on the engagement between the cutter and workpiece in trochoidal milling, the cutter edge temperature was obtained in trochoidal milling. Finally, a temperature comparison was made between trochoidal and side milling based on this analytical approach, and the reasons that trochoidal machining could extend the cutter life were found. This approach is first proposed to calculate the cutter edge temperature in trochoidal milling and can be applied to machining parameters optimization in trochoidal milling and cutter design optimization.

APA, Harvard, Vancouver, ISO, and other styles

27

Wu, Bao Hai, Cheng Yu Zheng, Ming Luo, and Xiao Dong He. "Investigation of Trochoidal Milling Nickel-Based Superalloy." Materials Science Forum 723 (June 2012): 332–36. http://dx.doi.org/10.4028/www.scientific.net/msf.723.332.

Full text

Abstract:

Nickel-based superalloy is a relatively new class of materials that exhibit high mechanical strength, ductility, creep resistance at high operating temperatures and stress levels. It is widely used in aero engine parts such as blade and blisk. Due to its high hardness and high strength at high temperature, it’s difficult to machine nickel-based alloy. In order to reduce tool wear, trochoidal milling strategy is studied in this paper. With trochoidal tool path strategy, tool load can be reduced and the tool has enough time to be cooled under high cutting temperature. Tool immersion angle in trochoidal milling is smaller than slot milling, thus the tool load can be reduced. Experiment results show that tool flank wear with normal slot milling is about four times larger than that with trochoidal milling. Trochoidal tool path strategy can be further developed for rough milling of compressor blades or rough milling hub of blisks.

APA, Harvard, Vancouver, ISO, and other styles

28

Uhlmann, E., S. Reinkober, M. Hoffmann, and P. Käpernick. "Trochoid milling with industrial robots." Procedia Manufacturing 43 (2020): 447–54. http://dx.doi.org/10.1016/j.promfg.2020.02.189.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Shi, Congcong, Xiaojian Zhang, and Xu Zhang. "Five-axis toolpath planning for aero-integral blisk cavities." Journal of Physics: Conference Series 2355, no. 1 (October 1, 2022): 012051. http://dx.doi.org/10.1088/1742-6596/2355/1/012051.

Full text

Abstract:

Abstract Integral blisks generally made of high-temperature alloys (such as titanium alloys) are important components in aero-engines. During machining, the tool load is large and the tool wear is serious. Because trochoidal milling can maintain a small contact angle between the tool and the workpiece during the cutting process, it is widely used in the processing of complex aviation blisks. However, when the traditional U-shaped trochoidal toolpath or the maximum inscribed trochoidal toolpath is applied, there are high cutting vibration and low efficiency. Therefore, this paper proposes a new five-axis trochoidal side milling strategy, which is suitable for machining more complex three-dimensional cavities by adjusting the shape of the inscribed arc. Different from the traditional trochoidal pattern, the proposed method can generate a spatial UV parameter line-based tool path from a given complex 3D cavity and map it to the machining surface. In addition, a scheme to optimize the tool orientation of the boundary tool is proposed, so that the machine tool motion axis can run smoothly, thus the blisk can be roughened efficiently. Finally, the proposed schemes are verified by computer simulation and physical cutting experiments, and results show the validity and effectiveness.

APA, Harvard, Vancouver, ISO, and other styles

30

Roesler, Bernard T., Malia L. Kawamura, Eric Miller, Matthew Wilson, Jonathon Brink-Roby, Eric Clemmenson, Matthew Keller, and Brenden P. Epps. "Experimental Performance of a Novel Trochoidal Propeller." Journal of Ship Research 60, no. 01 (March 1, 2016): 48–60. http://dx.doi.org/10.5957/jsr.2016.60.1.48.

Full text

Abstract:

In the quest for higher energy efficiency in marine transportation, a promising alternative marine propulsor concept is the trochoidal propeller. The authors have 1) designed and tested a novel trochoidal propeller using a sinusoidal blade pitch function and 2) created a theoretical model to describe the principal physics governing the operation of such propellers. The main results presented herein are measurements of thrust and torque, as well as the calculated hydrodynamic efficiency, for a range of absolute advance coefficients. The performance of the present sinusoidal-pitch trochoidal propeller is compared with prior cross-flow propellers, as well as a representative screw propeller. Although the efficiency of the present sinusoidal-pitch propeller exceeds that of prior cycloidal-pitch trochoidal propellers, it is slightly lower than the efficiencies of the other propellers considered. Model predictions show excellent agreement with the experimental data, which opens possibilities for future investigation and optimization of novel blade pitch motions.

APA, Harvard, Vancouver, ISO, and other styles

31

Grechishnikov, V. A., Yu E. Petukhov, P. M. Pivkin, V. B. Romanov, E. A. Ryabov, S. Yu Yurasov, and O. I. Yurasova. "Trochoidal slot milling." Russian Engineering Research 37, no. 9 (September 2017): 821–23. http://dx.doi.org/10.3103/s1068798x17090106.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Bong, Ha Yoon, and Moon Ki Kim. "Optimal Cutting Condition of Rough Cutting Using Trochoidal Motion." Journal of The Korean Society of Manufacturing Technology Engineers 26, no. 1 (February 15, 2017): 13–19. http://dx.doi.org/10.7735/ksmte.2017.26.1.13.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

Wang, Haiwei, Lulu Li, and Geng Liu. "Research on Meshing Characteristics of Trochoidal Roller Pinion Rack Transmission." Applied Sciences 12, no. 11 (June 1, 2022): 5620. http://dx.doi.org/10.3390/app12115620.

Full text

Abstract:

As a precision transmission mechanism, the trochoidal roller pinion rack has been paid more and more attention in recent years, but its meshing characteristics have not been deeply explored. In order to investigate the meshing characteristics of the trochoidal roller pinion rack transmission, it is particularly important to research its line of action and meshing stiffness. The equation of the line of action of the trochoidal roller pinion rack is deduced by using its tooth profile formation principle. The motion simulation of the trochoidal roller pinion rack transmission is carried out to verify the correctness of the theoretical derivation of the equation of the line of action, and the influence of the basic parameters on the line of action is summarized. The meshing stiffness of the trochoidal roller pinion rack is calculated based on the energy method used for gear meshing stiffness, and the meshing stiffness is defined considering the time-varying characteristics of its pressure angle, and the influence of each basic parameter on the meshing stiffness is studied. The results shows that the meshing stiffness increases first and then decreases in the double tooth meshing area, while the meshing stiffness gradually decreases in the single tooth meshing area. The basic parameters including number of roller pins, the module, the rack tooth profile offset coefficient, the diameter coefficient of roller pin, and the addendum coefficient of rack have different effects on the line of action and meshing stiffness. The research conclusion can provide reference for the parameter design of the trochoidal roller pinion rack, and provide the meshing stiffness calculation method for the dynamic analysis of the transmission.

APA, Harvard, Vancouver, ISO, and other styles

34

Hwang, Y.-W., and C.-F. Hsieh. "Study on high volumetric efficiency of the Roots rotor profile with variable trochoid ratio." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 220, no. 9 (September 1, 2006): 1375–84. http://dx.doi.org/10.1243/09544062jmes176.

Full text

Abstract:

Vacuum pumps play an important role in vacuum systems. The method proposed in this article, which uses the extended cycloid curve with a variable trochoid ratio, can be utilized to improve pump performance. The third-order and the fifth-order polynomials are used, and their boundary conditions are designed to generate a smooth trochoid ratio function. Hence, a regular addendum curve for the Roots rotor is generated. The tooth profile for the complete Roots rotor is derived from the addendum curve. Undercutting and carryover analyses are used to verify the feasibility of the designed method. Finally, a design flow on how to achieve high volumetric efficiency for a vacuum system is presented.

APA, Harvard, Vancouver, ISO, and other styles

35

Liu, Xiaofang, Yang Liu, Md Abu Noman, Satheeswaran Thangaraj, and Jun Sun. "Physiological Changes and Elemental Ratio of Scrippsiella trochoidea and Heterosigma akashiwo in Different Growth Phase." Water 13, no. 2 (January 8, 2021): 132. http://dx.doi.org/10.3390/w13020132.

Full text

Abstract:

The elemental ratios in phytoplankton are important for predicting biogeochemical cycles in the ocean. However, understanding how these elements vary among different phytoplankton taxa with physiological changes remains limited. In this paper, we determine the combined physiological–elemental ratio changes of two phytoplankton species, Scrippsiella trochoidea (Dinophyceae) and Heterosigma akashiwo (Raphidophyceae). Our results show that the cell growth period of S. trochoidea (26 days) was significantly shorter than that of H. akashiwo (32 days), with an average cell abundance of 1.21 × 104 cells·mL−1 in S. trochoidea and 1.53 × 105 cells·mL−1 in H. akashiwo. The average biovolume of S. trochoidea (9.71 × 103 μm3) was higher than that of H. akashiwo (0.64 × 103 μm3). The physiological states of the microalgae were assessed based on elemental ratios. The average ratios of particulate organic nitrogen (PON) to chlorophyll-a (Chl-a) and particulate organic carbon (POC) to Chl-a in S. trochoidea (57.32 and 168.16) were higher than those of H. akashiwo (9.46 and 68.86); however, the ratio of POC/PON of the two microalgae was nearly equal (6.33 and 6.17), indicating that POC/Chl-a may be lower when the cell is actively growing. The physiological variation, based on the POC/Chl-a ratio, in different phytoplankton taxa can be used to develop physiological models for phytoplankton, with implications for the marine biogeochemical cycle.

APA, Harvard, Vancouver, ISO, and other styles

36

Liu, Xiaofang, Yang Liu, Md Abu Noman, Satheeswaran Thangaraj, and Jun Sun. "Physiological Changes and Elemental Ratio of Scrippsiella trochoidea and Heterosigma akashiwo in Different Growth Phase." Water 13, no. 2 (January 8, 2021): 132. http://dx.doi.org/10.3390/w13020132.

Full text

Abstract:

The elemental ratios in phytoplankton are important for predicting biogeochemical cycles in the ocean. However, understanding how these elements vary among different phytoplankton taxa with physiological changes remains limited. In this paper, we determine the combined physiological–elemental ratio changes of two phytoplankton species, Scrippsiella trochoidea (Dinophyceae) and Heterosigma akashiwo (Raphidophyceae). Our results show that the cell growth period of S. trochoidea (26 days) was significantly shorter than that of H. akashiwo (32 days), with an average cell abundance of 1.21 × 104 cells·mL−1 in S. trochoidea and 1.53 × 105 cells·mL−1 in H. akashiwo. The average biovolume of S. trochoidea (9.71 × 103 μm3) was higher than that of H. akashiwo (0.64 × 103 μm3). The physiological states of the microalgae were assessed based on elemental ratios. The average ratios of particulate organic nitrogen (PON) to chlorophyll-a (Chl-a) and particulate organic carbon (POC) to Chl-a in S. trochoidea (57.32 and 168.16) were higher than those of H. akashiwo (9.46 and 68.86); however, the ratio of POC/PON of the two microalgae was nearly equal (6.33 and 6.17), indicating that POC/Chl-a may be lower when the cell is actively growing. The physiological variation, based on the POC/Chl-a ratio, in different phytoplankton taxa can be used to develop physiological models for phytoplankton, with implications for the marine biogeochemical cycle.

APA, Harvard, Vancouver, ISO, and other styles

37

Dong, Yongheng, Shujuan Li, Qian Zhang, Pengyang Li, Zhen Jia, and Yan Li. "Modeling and Analysis of Micro Surface Topography from Ball-End Milling in a Trochoidal Milling Mode." Micromachines 12, no. 10 (September 30, 2021): 1203. http://dx.doi.org/10.3390/mi12101203.

Full text

Abstract:

The trochoidal milling mode is widely used in high-speed machining, and due to good adaptability and flexible posture adjustment, ball-end milling cutters are conducive to complex surface machining with this mode. However, the processes of material removal and formation of machined micro surfaces are very difficult to describe as the profile of cutter teeth is complex and the trajectory direction changes continuously during the trochoidal milling process. A modeling method for the generation of micro surface topography of ball-end milling in the trochoidal milling mode is put forward. In this method, the locus equation of each cutter tooth is established based on the principle of homogeneous coordinate transformation, after which a Z-MAP algorithm is designed to simulate the micro surface topography. The Z-MAP algorithm can quickly obtain the part grid nodes potentially swept by the cutter tooth within a unit time step through the establishment of servo rectangular encirclement and instantaneous sweeping quadrilateral of the element of cutter teeth; the part grid nodes actually swept are further determined through an angle summation method, and the height coordinate is calculated with the method of linear interpolation according to Taylor’s formula of multivariate functions. Experiments showed that the micro surface topography resulting from ball-end milling in the trochoidal milling mode had high consistency with the simulation, which indicates that the proposed method can predict micro surface topography in practical manufacturing. In addition, a comparison of micro surface topography between trochoidal milling and ordinary straight-linear milling was conducted, and the results showed that the former was overall superior to the latter in resulting characteristics. Based on this conclusion, the influences of cutting parameters of ball-end trochoidal milling on surface characteristics, particularly amplitude and function, were analyzed according to the simulated micro surface topography data.

APA, Harvard, Vancouver, ISO, and other styles

38

Kim, Myung Sik, Won Jee Chung, Seung Won Jeong, and Ju Yeal Jeon. "Methodology for Simulation of Trochoid Pump." Journal of manufacturing engineering & technology 22, no. 3 (June 15, 2013): 465–71. http://dx.doi.org/10.7735/ksmte.2013.22.3.465.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

Armon, Uzi. "Representing trochoid curves by DUOPOLY procedure." International Journal of Mathematical Education in Science and Technology 27, no. 2 (March 1996): 177–87. http://dx.doi.org/10.1080/0020739960270202.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Yuan, Ping, and Hui Yue Dong. "Analysis of Milling Forces in Slot Milling of Aluminum Alloy with Three Flutes Cutter." Applied Mechanics and Materials 84-85 (August 2011): 396–401. http://dx.doi.org/10.4028/www.scientific.net/amm.84-85.396.

Full text

Abstract:

A new finite element simulation model based on two trochoidal tool-paths was constructed, and was used to simulate a full immersed milling with three flutes cutter. In this FEM model, the special method used here is to construct two trochoidal curves at the beginning with an offset value which is just equal to the feed value per tooth. These two linked trochoidal curves represent tool paths generated by two flutes respectively so as to construct the workpiece model. Cutting forces in the feed direction and in the normal direction were analyzed in detail. A verifying experiment shows this simulation is credible in general. This method can also be applied into situations of milling with more flutes such as face milling.

APA, Harvard, Vancouver, ISO, and other styles

41

Zhang, Zhi Jun, Shi Wei Zhang, and Cheng Hai Xu. "The Profile and Structure Design on Trochoidal Vacuum Pump." Advanced Materials Research 129-131 (August 2010): 453–57. http://dx.doi.org/10.4028/www.scientific.net/amr.129-131.453.

Full text

Abstract:

Vacuum pump plays an important role in vacuum applications. The rotor and stator profile is one of the key factors for improving pump performance. In this paper, the traditional trochoidal vacuum pump that the rotor and stator profile both are trochoidal equation was introduced. The profile of trochoidal vacuum pump with two angle rotor was studied. In order to simply the design and manufacture, the rotor profile was substituted by the arc curve. The design parameter and performance was deducted on slenderness ratio. The slenderness ratio should larger than 4, otherwise the down part of the stator profile would be dent to upper. When slenderness ratio is 4, the utilization ratio of volume would be getting the maximum value, 0.5851942. The utilization ratio of volume was decreased with the slenderness ratio increased.

APA, Harvard, Vancouver, ISO, and other styles

42

Li, Shuangqing, and J. B. Shung. "Geometry and Pressure in a Trochoidal-Type Machine Without Apex Seal." Journal of Mechanical Design 118, no. 2 (June 1, 1996): 209–13. http://dx.doi.org/10.1115/1.2826871.

Full text

Abstract:

In a trochoidal-type machine, the friction and wear due to the apex seal is a major problem. In order to increase the efficiency and reliability of this type of machine, we propose to replace the apex seals by tight running clearances. A peritrochoid with its special conjugate envelope is a good candidate for a trochoidal-type machine without apex seal. This paper presents its geometry attributes and pressure processes inside the pockets. First, the coordinates of contact point and pocket volumes at any shaft angle are derived. Then, the pressure processes inside the pockets are simulated with simplified valves. Finally, the effect of clearance on pocket pressure at different speeds is studied. The results indicate that a trochoidal-type machine without apex seal is worthy of further research and development.

APA, Harvard, Vancouver, ISO, and other styles

43

Liu, Dongsheng, Ying Zhang, Ming Luo, and Dinghua Zhang. "Investigation of Tool Wear and Chip Morphology in Dry Trochoidal Milling of Titanium Alloy Ti–6Al–4V." Materials 12, no. 12 (June 16, 2019): 1937. http://dx.doi.org/10.3390/ma12121937.

Full text

Abstract:

Titanium alloys are widely used in the manufacture of aircraft and aeroengine components. However, tool wear is a serious concern in milling titanium alloys, which are known as hard-to-cut materials. Trochoidal milling is a promising technology for the high-efficiency machining of hard-to-cut materials. Aiming to realize green machining titanium alloy, this paper investigates the effects of undeformed chip thickness on tool wear and chip morphology in the dry trochoidal milling of titanium alloy Ti–6Al–4V. A tool wear model related to the radial depth of cut based on the volume of material removed (VMR) is established for trochoidal milling, and optimized cutting parameters in terms of cutting speed and axial depth of cut are selected to improve machining efficiency through reduced tool wear. The investigation enables the environmentally clean rough machining of Ti–6Al–4V.

APA, Harvard, Vancouver, ISO, and other styles

44

Simoson, Andrew J. "Albrecht Dürer's Trochoidal Woodcuts." PRIMUS 18, no. 6 (November 12, 2008): 489–99. http://dx.doi.org/10.1080/10511970701625068.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

Skorulski, Grzegorz. "Determination of cutting resistance in the process conventional and trochoidal milling." Mechanik 91, no. 10 (October 8, 2018): 874–76. http://dx.doi.org/10.17814/mechanik.2018.10.149.

Full text

Abstract:

Cutting forces in the process of conventional and trochoidal milling of aluminum 2017 alloy were determined and analyzed. A machining strategy, testing guidelines and the possibility of using a measuring platform based on resistance tensometry elements were developed. The paper also presents an analysis of the results concerning the distribution of the cutting forces in the processes of conventional and trochoidal milling, carried out with the same cutting parameters and tools. An attempt was made to interpret the results.

APA, Harvard, Vancouver, ISO, and other styles

46

Wiegel, R. L., and J. W. Johnson. "ELEMENTS OF WAVE THEORY." Coastal Engineering Proceedings 1, no. 1 (May 12, 2010): 2. http://dx.doi.org/10.9753/icce.v1.2.

Full text

Abstract:

The first known mathematical solution for finite height, periodic waves of stable form was developed by Gerstner (1802). From equations that were developed, Gerstner (1802) arrived at the conclusion that the surface curve was trochoidal in form. Froude (1862) and Rankine (1863) developed the theory but in the opposite manner, i.e., they started with the assumption of a trochoidal form and then developed their equations from this curve. The theory was developed for waves in water of infinite depth with the orbits of the water particles being circular, decreasing in geometrical progression as the distance below the water surface increased in arithmetical progression. Recent experiments (Wiegel, 1950) have shown that the surface profile, represented by the trochoidal equations (as well as the first few terms of Stokes' theory), closely approximates the actual profiles for waves traveling over a horizontal bottom. However the theory necessitates molecular rotation of the particles, while the manner in which waves are formed by conservative forces necessitates irrotational motion.

APA, Harvard, Vancouver, ISO, and other styles

47

UENO, Hisanori, Yoshio MATSUI, Masato HASEGAWA, and Yousuke IMAMURA. "Study on Cavitation Characteristic of Trochoid Pump." Proceedings of Conference of Hokuriku-Shinetsu Branch 2004.41 (2004): 47–48. http://dx.doi.org/10.1299/jsmehs.2004.41.47.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

UENO, Hisanori, Akito NAKAMURA, and Masashi KUMITA. "K-1428 Cavitation in a Trochoid Pump." Proceedings of the JSME annual meeting II.01.1 (2001): 259–60. http://dx.doi.org/10.1299/jsmemecjo.ii.01.1.0_259.

Full text

APA, Harvard, Vancouver, ISO, and other styles

49

Gómez, G., P. Fernández De Lucio, A. Del Olmo, G. Martínez De Pissón, A. Jimeno, H. González, and L. N. López De Lacalle. "Comparison between milling roughing operations in full slotting manufacturing: trochoidal, plunge and conventional milling." IOP Conference Series: Materials Science and Engineering 1193, no. 1 (October 1, 2021): 012003. http://dx.doi.org/10.1088/1757-899x/1193/1/012003.

Full text

Abstract:

Abstract Manufacturing improvements in terms of manufacturing-chain costs and times reduction are becoming a real need in the industry, especially for roughing operations. To satisfy these industrial requirements, more efficient machining processes have been developed, such as High Efficiency Milling (HEM). According to the above mentioned direction, trochoidal milling appears as an efficient method for roughing operations of full slots. This work presents an analysis in terms of production time between conventional, plunge and trochoidal milling to determine which process configuration is more productive.

APA, Harvard, Vancouver, ISO, and other styles

50

Zhang, Xing Hong, Fang Yu Peng, Feng Qiu, Rong Yan, and Bin Li. "Prediction of Cutting Force in Trochoidal Milling Based on Radial Depth of Cut." Advanced Materials Research 852 (January 2014): 457–62. http://dx.doi.org/10.4028/www.scientific.net/amr.852.457.

Full text

Abstract:

This paper proposes an approach to predict cutting force of trochoidal milling based on radial depth of cut in order to study the mechanics of trochoidal milling. The tool entry angle and exit angle can be easily achieved to get the cutting force infinitesimals via the radial depth of cut. Through coordinate transformation, a time domain analytical model of cutting force is introduced. Subsequently, a corresponding experiment was done to measure the actual cutting force. Compared with the actual measurement data, the theoretical model is verified to be valid.

APA, Harvard, Vancouver, ISO, and other styles

Journal articles on the topic 'Trochoids'

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles