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Simulation of Processing of a Helical Surface with the Aid of a Frontal-Cylindrical Milling Tool
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Procedia Manufacturing 32 (2019) 36–41 Procedia Manufacturing 00 (2017) 000–000 www.elsevier.com/locate/procedia
The 12th International Conference Interdisciplinarity in Engineering The 12th International Conference Interdisciplinarity in Engineering
Simulation of Processing of a Helical Surface with the Aid of a Simulation of Processing of a Helical Surface with the Aid of a Frontal-Cylindrical Milling Tool Manufacturing Engineering Society International Conference 2017, Frontal-Cylindrical Milling ToolMESIC 2017, 28-30 June 2017, Vigo (Pontevedra),a,Spain Sorin Cristian Albu * Sorin University Cristian Albua,Pharmacy, * Department of Mechanical Engineering and Management, of Medicine, Sciences and Technology of Targu Mures, 0F
Costing models for capacity Industry 4.0: Trade-off Nicolae Iorga st. optimization No. 1, 540088 Targu Mureş,in Romania Department of Mechanical Engineering and Management, University of Medicine, Pharmacy, Sciences and Technology of Targu Mures, Nicolae Iorga st. No. 1, 540088 Mureş, Romania efficiency between used capacity and Targu operational a
0F
a
Abstract
A. Santanaa, P. Afonsoa,*, A. Zaninb, R. Wernkeb
Abstract a In this paper is studying a method of simulating theofcutting machining of the helical surface of a conveyor worm. Simulation is University Minho, 4800-058 Guimarães, Portugal b Unochapecó, 89809-000 Chapecó, SC, Brazil important in order to provide the data necessary for the processing. In the present paper, it is desired to process a cylindrical bar In this paper is studying a method of simulating the cutting machining of the helical surface of a conveyor worm. Simulation is with a cylindrical-frontal cutter, of a worm with two starts. The worm will have the flanks machined by tapered propellers with a important in order to provide the data necessary for the processing. In the present paper, it is desired to process a cylindrical bar different pitch so that the resulting gap is variable along the axis of symmetry of the worm. The conveyor worm will be used at with a cylindrical-frontal cutter, of a worm with two starts. The worm will have the flanks machined by tapered propellers with a the extruder of 3D FDM technology printers that will use pellets of various materials as raw material. The conveyor auger is different pitch so that the resulting gap is variable along the axis of symmetry of the worm. The conveyor worm will be used at Abstract small in size to in order not to increase the weight of the extruder who is running movements in a plane in two directions. In the extruder of 3D FDM technology printers that will use pellets of various materials as raw material. The conveyor auger is order to process the transport worm at the lowest possible cost, the machining and finishing process is carried out with a single small inthe sizeconcept to in order to increase the production weight of the extruder who is running movements in a plane in two directions. In Under of not "Industry will pushed increasingly interconnected, cylindrical-frontal milling tool through4.0", several passes. So processes simulation is verybeimportant totobebeable to see and study the resulting order to process the transport worm at the lowest possible cost, the machining and finishing process is carried out with a single information on a real Ittime basis and, efficient. In this context, capacity optimization surface beforebased it is processed. is important to necessarily, value the areamuch of themore hollow in the axial section and the thickness of the flank cylindrical-frontal milling tool through several passes. So simulation is very important to be able to see and study the resulting goes the traditional aimsimulation of capacity maximization, contributing also for the organization’s value. walls.beyond The program designed for is executed in AutoLISP. It will calculate points neededprofitability to place the and tool system surface before it is processed. It is important to value the area of the hollow in the axial section and the thickness of the flank and provide them in AutoCad where will be made. In the programsuggest defines the half-finished material, the tool size, Indeed, lean management and representations continuous improvement approaches capacity optimization instead of walls. The program designed for simulation is executed in AutoLISP. It will calculate the points needed to place the tool system and then it is possible to simulate how many crossingsand are costing needed until the ispiece is completely processed. Itthat is possible to maximization. The study of capacity optimization models an important research topic deserves and provide them in AutoCad where representations will be made. In the program defines the half-finished material, the tool size, evaluate the state of the blank after each pass and if the surface does not correspond bypresents point of and viewdiscusses to the shape it can stop the contributions from both the practical and theoretical perspectives. This paper a mathematical and then it is possible to simulate how many crossings are needed until the piece is completely processed. It is possible to process for and a new simulation with other parameters will becosting made. models (ABC and TDABC). A generic model has been model management based onand different evaluate thecapacity state of the blank after each pass if the surface does not correspond by point of view to the shape it can stop the In the conceived program is requires the parametric equations of a conical propeller and vectorial elements for positioning the developed it was used towith analyze capacity to design strategies towards the maximization of organization’s process andand a new simulation other idle parameters willand be made. tool system relative to the reference system of the blank. value. The trade-off capacity maximization vs operational is highlighted and elements it is shown that capacity In the conceived program is requires the parametric equations of aefficiency conical propeller and vectorial for positioning the tool system relative tohide the reference system of the blank. optimization might operational inefficiency. © 2018The Authors. Published by Elsevier Ltd. © 2017 The Authors. by Elsevier B.V. This is an open accessPublished article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) © 2018The 2019 The Authors. Published byElsevier Elsevier Ltd. © Authors. Published by Ltd. Peer-review under responsibility of the scientific of the Manufacturing Engineering Society in International Conference Selection under responsibility ofcommittee the 12th International Conference Interdisciplinarity Engineering. This is anand openpeer-review access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) 2017. Selection and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering. Selection and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering. Keywords: Cost Models; ABC; TDABC; Capacity Management; Idle Capacity; Operational Efficiency
1. Introduction
* Corresponding author. Tel.: +4-0265-233-112; fax: +4-0265-233-212. E-mail address: [email protected] * The Corresponding author. Tel.: +4-0265-233-112; fax: +4-0265-233-212. cost of idle capacity is a fundamental information for companies and their management of extreme importance E-mail address: [email protected] in modern production systems. In general, it Ltd. is defined as unused capacity or production potential and can be measured 2351-9789© 2018The Authors. Published by Elsevier Thisseveral is an open accesstons articleofunder the CC BY-NC-ND license(https://creativecommons.org/licenses/by-nc-nd/4.0/) in ways: production, available hours of manufacturing, etc. The management of the idle capacity 2351-9789© Authors. Published by Elsevier Ltd.International Conference Interdisciplinarity in Engineering. Selection and2018The peer-review under responsibility of the 253 12th * Paulo Afonso. Tel.: +351 253 510 761; fax: +351 604 741 This is an open access article under the CC BY-NC-ND license(https://creativecommons.org/licenses/by-nc-nd/4.0/) E-mail address: [email protected] Selection and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering. 2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under of the scientificbycommittee the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2019responsibility The Authors. Published Elsevier of Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering. 10.1016/j.promfg.2019.02.180
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Sorin Cristian Albu / Procedia Manufacturing 32 (2019) 36–41 Albu Sorin Cristian / Procedia Manufacturing 00 (2018) 000–000
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Keywords: extruder; conveyor worm; helical surfaces; conical propeller; simulation.
1. Introduction In the past few years, the 3D printing industry has witnessed significant growth, especially due to the ability to process prototypes in a short time and at low cost compared to classical processing technologies. As such, there is a high interest in lowering printing costs. Print costs for FDM technology can be significantly reduced by replacing PLA or ABS thread with pellets whose costs are much lower. In order to transport the pellets in the extruder and bring them into the melting zone, as with the injection of plastic materials, a conical conveyor worm is used. In order to execute the spindle worm, it is necessary to use a CNC machining center with a minimum of 5 axes, which equipment is not in the majority of companies. The processing of the conveyor worm is pretentious, thus justifying the simulation of the milling process with several passes after conical helical curves with a constant but different pitch at each pass, to result in a variable void along the axis of symmetry of the worm. According to STAS 915/5-81 the worm is a toothed wheel with inclined teeth, usually with a small number of teeth (with one or more teeth)[1]. The worms, from the point of view of the helical surfaces forming the flanks of the teeth, can be: • ruled worms - are worms having tooth flanks constituted by sections of ruled surfaces (can be generated by the movement of straight generating lines along guiding curves whose shape is determined) STAS 915/5-81 • non-ruled worms - are worms with tooth flanks constituted by non-ruled surfaces (can only be generated by moving curved generating lines along the guiding curves)[2] According to STAS 6845-82 [3] of the ruled worm category are the profile worms: Involute – symbol ZE, Archimedean – ZA, straight in the normal section on the tooth ZN1, straight line in the normal section on the gap of the tooth ZN2, and in the non-ruled worm category are worms: generated with disk-driven double-cone ZK1, generated with conical finger milling tool ZK2. From the point of view of the pitch of the helical surface, worms can be classified as such: Worms with constant pitch, worms with differentiated step (for the left and the right flank). Ruled worms [5], [6] are executed by turning on the lathe, the knife used for roughing is with one or two edges, the finishing being done with a knife with a cut for each side flank. The execution time of a worm by turning is usually high. Due to the precision and low surface quality of the surface resulting from the knife-cutting process, the lifetime of the so-worked worms is reduced. In view of these aspects, it has become necessary to search for new technologies for the manufacture of the worm so as to obtain: • The improved precision, • the higher surface quality, • High productivity. The direction of the winding of the worms may be to the right Fig.1.( a) or to the left Fig.1.(b). Taking into consideration the above mentioned issues, the conveyor worm of the conceived extruder will be a
a.
Fig.1.(a) The direction of the winding to the right
b. (b)The direction of the winding to the left[4]
non-ruler conical worm with a different pitch, the winding direction of the turns is on the right. Processing will be done using a cylindrical-frontal milling tools. The 3D model of the conveyor worm is obtained starting from a 20 mm diameter cylinder. Cylindro-frontal milling process will be simulated with a cylinder that will move radial on a conical propeller with constant pitch for each pass. The next pass is on another helical curve with a constant pitch but different from the previous one. The
Sorin Cristian Albu / Procedia Manufacturing 32 (2019) 36–41 Albu Sorin Cristian / Procedia Manufacturing00 (2018) 000–000
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3
representations are made in different colors so that the tool contact can easily be identified with the flanks of the transport worm. If unwanted contact with one of the flanks is identified, the simulation is stopped and the crossings are resumed by changing the passage parameters where problems have been identified. Thus, the pre-processing simulation avoids the possible non-compliant products resulting from the design errors. Nomenclature r p φ β
the radius of the small base of the cone trunk on which the propeller is wound; the step of the propeller; propeller parameter; the angle of inclination the generator of cone trunk with the OZ axis.
2. Simulation of helical channel processing with cylindrical-frontal milling tool Simulation of the machining is represented in AutoCad, calculations and commands are given with AutoLisp. The principle underlying the representation is the following: • Are introduced the parameters required for the cylinder representation of the extruder; • It is specified the number starts of conveyor worm; • It is defined the dimensions of the cylindrical-frontal cutter; • Until the simulation of processing of the conveyor auger is completed, it enters into a loop that represents the successive passes (at one pass all the beginnings of the worm are processed), consisting of the following instructions: a. It is defined the conical propeller parameters on which the tool moves. b. Are given values to the parameter φ of the system of equations of the conical propeller within a set range. Are calculated points on the conical propeller in which the tool is radially positioned. c. With the help of the subtract command, the successive positions of the tool are extracted from the blank, resulting the gap of the conveyor screw, respectively the flanks obtained after a pass. d. After finishing processing with these parameters of all beginnings, the resulting flanks are visualized, if there is no interference, it goes on to the next pass. The steps from point a, b, c, d are resumed until the piece is completely processed. 2.1. Parametric equations of a conical propeller To simulate processing of the conveyor worm [7], it starts from the parametric equations of a conical propeller [8,9], Fig. 2. relation (1), obtained using coordinate transformations like in [10].
Fig. 2. Conical propeller [11].
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Sorin Cristian Albu / Procedia Manufacturing 32 (2019) 36–41 Albu Sorin Cristian / Procedia Manufacturing 00 (2018) 000–000
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p (r + φ × sin β ) cos φ x(φ ) = 2π p φ × sin β ) sin φ y (φ ) =±(r + π 2 p z (φ ) = 2π φ cos β
(1)
The conic propeller is defined by the following geometric elements: p - step of the propeller, which represents the distance between two consecutive turns, r- the radius of the cone trunk, β - the angle of inclination of the cone with the axis of symmetry, φ- the conical propeller parameter, the winding direction of the coils left or right. 2.2. Logical scheme of the program The logic scheme of the conceived program is presented in Fig.3. and the data used for simulation of the processing are presented in Table 1. START It is defined the lenght and the radius of the worm, number of beginnings, the winding direction of the coils then it is represented in AutoCad the blank It is defined the dimensions of the tool, the angle of inclination in the axial plane, the parameters of the conical propeller
Are calculated the successive points from the conical propeller and the tool is radially positioned and with the help of the subtract command the tool positions are subtracted
Yes
Beginning ≤ Number of beginnings
Yes
No
Simulation of processing
No
Processing View STOP
Fig. 3. Logical scheme of the program
2.3. Result obtained with the program In order to be able to run the written program in AutoLisp, the first step is to load it in AutoCad with the help of the command Load Application from the menu Manage.
Sorin Cristian Albu / Procedia Manufacturing 32 (2019) 36–41 Albu Sorin Cristian / Procedia Manufacturing00 (2018) 000–000
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Table 1. Data required for processing Parameters required simulation
Pass 1
Pass 2
Radius of the worm
10mm
Length of the worm
120 mm
Number of beginning
2
Pass 3
Min radius of the helical goal
4mm
4mm
4 mm
Maximum radius of helical goal
7,5mm
7,5mm
7,5 mm
Step of the propeller
27mm
27,3 mm
26,7 mm
Sense of wrapping
Right
Diameter of the tool
6 mm
6 mm
6 mm
Milling inclination angle
0
15˚
-15˚
To the Command prompt from AutoCad the name of the conceived program is typed, after which are introduced the parameters of the conveyor screw, the cutter and the parameters of the conical propeller for each pass. In the chosen example, the first pass is done with the cylindro-frontal cutter positioned perpendicular to the symmetry axis of the bla nk, at the second pass the left flank of the conveyor worm is processed, and at the third pass the right flank is processed. In Fig. 4. it can see the stages during the simulation with the cylindrical-frontal cutter this hawing associated the coordinate system XOYZ.
a
b
c
Fig. 4. (a) firs t pass; (b) second pass; (c) third pass.
At the end of the simulation, the 3D representation can be saved in a file with the ".stp" extension that can be viewed in Inventor. In the axial section the shape of the hollow and the flanks can be analyzed, and if it meets the expectations, the conveyor worm can be processed with the parameters entered for each pass. 3. Conclusions As a result of the simulations and analyzes made, we can state, using a program that allows simulation of the processing of complex surfaces such as helicoidal ones, the following:
6
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the execution costs are reduced due to the removal of the non-compliant parts resulting from the design mistakes; • the process parameters required for each pass can be provided without the risk of interference; • it is possible to obtain a transport worm with a variable gap along the symmetry axis of the blank without wasting time for tests on machine tools CNC. The main disadvantage of using a 3D simulation program is the long time it takes to run it on a regular computer without special hardware resources. •
Acknowledgements This work was supported by a grant of the Romanian Ministry of Research and Innovation, CCCDI – UEFISCDI, project number PN-III-P2-2.1-CI-2017-0430, within PNCDI III, with support of the company 3DCREATIVITY and Research Center TAPFAAC. References [1] [2] [3] [4] [5] [6] [7]
***, Organe de Masini. Vol. I d. Angrenaje. Reductoare (Colectie STAS). Editura Tehnica. Bucuresti, 1984. C. Elekes, Scule pentru angrenaje melcate, Editura Tehnica Bucuresti, 1985,. STANDARD DE STAT "Angrenaje Melcate Cilindrice. Melcul de referinta." STAS 6845-82 ANSI/AGMA 6022-C93 American National Standard Design Manual for Cylindrical Wormgearing. S. N. Krivoshapko S.N., V. N. Ivanov, Encyclopedia of Analytical Surfaces, Springer, 752 p. (2015). S. N. Krivoshapko, Geometry of linear surfaces with the return rib and linear theory for torso-helicoid calculation, RUDN, p.357 (2009). S. N. Krivoshapko, Marina Rynkovskayaology , Five Types of Ruled Helical Surfaces for Helical Conveyers, Support Anchors and Screws, MATEC Web Conf. ,Volume 95, 2017, 2016 the 3rd International Conference on Mechatronics and Mechanical Engineering (ICMME 2016) [8] S. Albu, Roughing helical flanks of the worms with frontal-cylindrical milling tools on NC lathes, Procedia Technology, Volume 12, 2014, ISSN: 2212-0173, Pag.448–454 [9] S. Albu, V. Bolos, Determining the optimal position of the frontal-cylindrical milling tool in finishing in the new technology for processing worms, Procedia Technology, Volume 12, 2014, ISSN: 2212-0173, Pag.455–461 [10] S. Berbinschi & V. Teodor & N. Oancea, . A study on helical surface generated by the primary peripheral surfaces of ring tool The International Journal of Advanced Manufacturing Technology, July 2012, Volume 61, Issue 1–4, pp 15–24 [11] S. Albu, V. Bolos, Regarding on generation helical cylindrical and cone surfaces with the help of a curve, Procedia Technology , ISSN 2285-0945, pag.136-139, 2012.
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Procedia Manufacturing 32 (2019) 36–41 Procedia Manufacturing 00 (2017) 000–000 www.elsevier.com/locate/procedia
The 12th International Conference Interdisciplinarity in Engineering The 12th International Conference Interdisciplinarity in Engineering
Simulation of Processing of a Helical Surface with the Aid of a Simulation of Processing of a Helical Surface with the Aid of a Frontal-Cylindrical Milling Tool Manufacturing Engineering Society International Conference 2017, Frontal-Cylindrical Milling ToolMESIC 2017, 28-30 June 2017, Vigo (Pontevedra),a,Spain Sorin Cristian Albu * Sorin University Cristian Albua,Pharmacy, * Department of Mechanical Engineering and Management, of Medicine, Sciences and Technology of Targu Mures, 0F
Costing models for capacity Industry 4.0: Trade-off Nicolae Iorga st. optimization No. 1, 540088 Targu Mureş,in Romania Department of Mechanical Engineering and Management, University of Medicine, Pharmacy, Sciences and Technology of Targu Mures, Nicolae Iorga st. No. 1, 540088 Mureş, Romania efficiency between used capacity and Targu operational a
0F
a
Abstract
A. Santanaa, P. Afonsoa,*, A. Zaninb, R. Wernkeb
Abstract a In this paper is studying a method of simulating theofcutting machining of the helical surface of a conveyor worm. Simulation is University Minho, 4800-058 Guimarães, Portugal b Unochapecó, 89809-000 Chapecó, SC, Brazil important in order to provide the data necessary for the processing. In the present paper, it is desired to process a cylindrical bar In this paper is studying a method of simulating the cutting machining of the helical surface of a conveyor worm. Simulation is with a cylindrical-frontal cutter, of a worm with two starts. The worm will have the flanks machined by tapered propellers with a important in order to provide the data necessary for the processing. In the present paper, it is desired to process a cylindrical bar different pitch so that the resulting gap is variable along the axis of symmetry of the worm. The conveyor worm will be used at with a cylindrical-frontal cutter, of a worm with two starts. The worm will have the flanks machined by tapered propellers with a the extruder of 3D FDM technology printers that will use pellets of various materials as raw material. The conveyor auger is different pitch so that the resulting gap is variable along the axis of symmetry of the worm. The conveyor worm will be used at Abstract small in size to in order not to increase the weight of the extruder who is running movements in a plane in two directions. In the extruder of 3D FDM technology printers that will use pellets of various materials as raw material. The conveyor auger is order to process the transport worm at the lowest possible cost, the machining and finishing process is carried out with a single small inthe sizeconcept to in order to increase the production weight of the extruder who is running movements in a plane in two directions. In Under of not "Industry will pushed increasingly interconnected, cylindrical-frontal milling tool through4.0", several passes. So processes simulation is verybeimportant totobebeable to see and study the resulting order to process the transport worm at the lowest possible cost, the machining and finishing process is carried out with a single information on a real Ittime basis and, efficient. In this context, capacity optimization surface beforebased it is processed. is important to necessarily, value the areamuch of themore hollow in the axial section and the thickness of the flank cylindrical-frontal milling tool through several passes. So simulation is very important to be able to see and study the resulting goes the traditional aimsimulation of capacity maximization, contributing also for the organization’s value. walls.beyond The program designed for is executed in AutoLISP. It will calculate points neededprofitability to place the and tool system surface before it is processed. It is important to value the area of the hollow in the axial section and the thickness of the flank and provide them in AutoCad where will be made. In the programsuggest defines the half-finished material, the tool size, Indeed, lean management and representations continuous improvement approaches capacity optimization instead of walls. The program designed for simulation is executed in AutoLISP. It will calculate the points needed to place the tool system and then it is possible to simulate how many crossingsand are costing needed until the ispiece is completely processed. Itthat is possible to maximization. The study of capacity optimization models an important research topic deserves and provide them in AutoCad where representations will be made. In the program defines the half-finished material, the tool size, evaluate the state of the blank after each pass and if the surface does not correspond bypresents point of and viewdiscusses to the shape it can stop the contributions from both the practical and theoretical perspectives. This paper a mathematical and then it is possible to simulate how many crossings are needed until the piece is completely processed. It is possible to process for and a new simulation with other parameters will becosting made. models (ABC and TDABC). A generic model has been model management based onand different evaluate thecapacity state of the blank after each pass if the surface does not correspond by point of view to the shape it can stop the In the conceived program is requires the parametric equations of a conical propeller and vectorial elements for positioning the developed it was used towith analyze capacity to design strategies towards the maximization of organization’s process andand a new simulation other idle parameters willand be made. tool system relative to the reference system of the blank. value. The trade-off capacity maximization vs operational is highlighted and elements it is shown that capacity In the conceived program is requires the parametric equations of aefficiency conical propeller and vectorial for positioning the tool system relative tohide the reference system of the blank. optimization might operational inefficiency. © 2018The Authors. Published by Elsevier Ltd. © 2017 The Authors. by Elsevier B.V. This is an open accessPublished article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) © 2018The 2019 The Authors. Published byElsevier Elsevier Ltd. © Authors. Published by Ltd. Peer-review under responsibility of the scientific of the Manufacturing Engineering Society in International Conference Selection under responsibility ofcommittee the 12th International Conference Interdisciplinarity Engineering. This is anand openpeer-review access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) 2017. Selection and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering. Selection and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering. Keywords: Cost Models; ABC; TDABC; Capacity Management; Idle Capacity; Operational Efficiency
1. Introduction
* Corresponding author. Tel.: +4-0265-233-112; fax: +4-0265-233-212. E-mail address: [email protected] * The Corresponding author. Tel.: +4-0265-233-112; fax: +4-0265-233-212. cost of idle capacity is a fundamental information for companies and their management of extreme importance E-mail address: [email protected] in modern production systems. In general, it Ltd. is defined as unused capacity or production potential and can be measured 2351-9789© 2018The Authors. Published by Elsevier Thisseveral is an open accesstons articleofunder the CC BY-NC-ND license(https://creativecommons.org/licenses/by-nc-nd/4.0/) in ways: production, available hours of manufacturing, etc. The management of the idle capacity 2351-9789© Authors. Published by Elsevier Ltd.International Conference Interdisciplinarity in Engineering. Selection and2018The peer-review under responsibility of the 253 12th * Paulo Afonso. Tel.: +351 253 510 761; fax: +351 604 741 This is an open access article under the CC BY-NC-ND license(https://creativecommons.org/licenses/by-nc-nd/4.0/) E-mail address: [email protected] Selection and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering. 2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under of the scientificbycommittee the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2019responsibility The Authors. Published Elsevier of Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering. 10.1016/j.promfg.2019.02.180
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Sorin Cristian Albu / Procedia Manufacturing 32 (2019) 36–41 Albu Sorin Cristian / Procedia Manufacturing 00 (2018) 000–000
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Keywords: extruder; conveyor worm; helical surfaces; conical propeller; simulation.
1. Introduction In the past few years, the 3D printing industry has witnessed significant growth, especially due to the ability to process prototypes in a short time and at low cost compared to classical processing technologies. As such, there is a high interest in lowering printing costs. Print costs for FDM technology can be significantly reduced by replacing PLA or ABS thread with pellets whose costs are much lower. In order to transport the pellets in the extruder and bring them into the melting zone, as with the injection of plastic materials, a conical conveyor worm is used. In order to execute the spindle worm, it is necessary to use a CNC machining center with a minimum of 5 axes, which equipment is not in the majority of companies. The processing of the conveyor worm is pretentious, thus justifying the simulation of the milling process with several passes after conical helical curves with a constant but different pitch at each pass, to result in a variable void along the axis of symmetry of the worm. According to STAS 915/5-81 the worm is a toothed wheel with inclined teeth, usually with a small number of teeth (with one or more teeth)[1]. The worms, from the point of view of the helical surfaces forming the flanks of the teeth, can be: • ruled worms - are worms having tooth flanks constituted by sections of ruled surfaces (can be generated by the movement of straight generating lines along guiding curves whose shape is determined) STAS 915/5-81 • non-ruled worms - are worms with tooth flanks constituted by non-ruled surfaces (can only be generated by moving curved generating lines along the guiding curves)[2] According to STAS 6845-82 [3] of the ruled worm category are the profile worms: Involute – symbol ZE, Archimedean – ZA, straight in the normal section on the tooth ZN1, straight line in the normal section on the gap of the tooth ZN2, and in the non-ruled worm category are worms: generated with disk-driven double-cone ZK1, generated with conical finger milling tool ZK2. From the point of view of the pitch of the helical surface, worms can be classified as such: Worms with constant pitch, worms with differentiated step (for the left and the right flank). Ruled worms [5], [6] are executed by turning on the lathe, the knife used for roughing is with one or two edges, the finishing being done with a knife with a cut for each side flank. The execution time of a worm by turning is usually high. Due to the precision and low surface quality of the surface resulting from the knife-cutting process, the lifetime of the so-worked worms is reduced. In view of these aspects, it has become necessary to search for new technologies for the manufacture of the worm so as to obtain: • The improved precision, • the higher surface quality, • High productivity. The direction of the winding of the worms may be to the right Fig.1.( a) or to the left Fig.1.(b). Taking into consideration the above mentioned issues, the conveyor worm of the conceived extruder will be a
a.
Fig.1.(a) The direction of the winding to the right
b. (b)The direction of the winding to the left[4]
non-ruler conical worm with a different pitch, the winding direction of the turns is on the right. Processing will be done using a cylindrical-frontal milling tools. The 3D model of the conveyor worm is obtained starting from a 20 mm diameter cylinder. Cylindro-frontal milling process will be simulated with a cylinder that will move radial on a conical propeller with constant pitch for each pass. The next pass is on another helical curve with a constant pitch but different from the previous one. The
Sorin Cristian Albu / Procedia Manufacturing 32 (2019) 36–41 Albu Sorin Cristian / Procedia Manufacturing00 (2018) 000–000
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3
representations are made in different colors so that the tool contact can easily be identified with the flanks of the transport worm. If unwanted contact with one of the flanks is identified, the simulation is stopped and the crossings are resumed by changing the passage parameters where problems have been identified. Thus, the pre-processing simulation avoids the possible non-compliant products resulting from the design errors. Nomenclature r p φ β
the radius of the small base of the cone trunk on which the propeller is wound; the step of the propeller; propeller parameter; the angle of inclination the generator of cone trunk with the OZ axis.
2. Simulation of helical channel processing with cylindrical-frontal milling tool Simulation of the machining is represented in AutoCad, calculations and commands are given with AutoLisp. The principle underlying the representation is the following: • Are introduced the parameters required for the cylinder representation of the extruder; • It is specified the number starts of conveyor worm; • It is defined the dimensions of the cylindrical-frontal cutter; • Until the simulation of processing of the conveyor auger is completed, it enters into a loop that represents the successive passes (at one pass all the beginnings of the worm are processed), consisting of the following instructions: a. It is defined the conical propeller parameters on which the tool moves. b. Are given values to the parameter φ of the system of equations of the conical propeller within a set range. Are calculated points on the conical propeller in which the tool is radially positioned. c. With the help of the subtract command, the successive positions of the tool are extracted from the blank, resulting the gap of the conveyor screw, respectively the flanks obtained after a pass. d. After finishing processing with these parameters of all beginnings, the resulting flanks are visualized, if there is no interference, it goes on to the next pass. The steps from point a, b, c, d are resumed until the piece is completely processed. 2.1. Parametric equations of a conical propeller To simulate processing of the conveyor worm [7], it starts from the parametric equations of a conical propeller [8,9], Fig. 2. relation (1), obtained using coordinate transformations like in [10].
Fig. 2. Conical propeller [11].
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Sorin Cristian Albu / Procedia Manufacturing 32 (2019) 36–41 Albu Sorin Cristian / Procedia Manufacturing 00 (2018) 000–000
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p (r + φ × sin β ) cos φ x(φ ) = 2π p φ × sin β ) sin φ y (φ ) =±(r + π 2 p z (φ ) = 2π φ cos β
(1)
The conic propeller is defined by the following geometric elements: p - step of the propeller, which represents the distance between two consecutive turns, r- the radius of the cone trunk, β - the angle of inclination of the cone with the axis of symmetry, φ- the conical propeller parameter, the winding direction of the coils left or right. 2.2. Logical scheme of the program The logic scheme of the conceived program is presented in Fig.3. and the data used for simulation of the processing are presented in Table 1. START It is defined the lenght and the radius of the worm, number of beginnings, the winding direction of the coils then it is represented in AutoCad the blank It is defined the dimensions of the tool, the angle of inclination in the axial plane, the parameters of the conical propeller
Are calculated the successive points from the conical propeller and the tool is radially positioned and with the help of the subtract command the tool positions are subtracted
Yes
Beginning ≤ Number of beginnings
Yes
No
Simulation of processing
No
Processing View STOP
Fig. 3. Logical scheme of the program
2.3. Result obtained with the program In order to be able to run the written program in AutoLisp, the first step is to load it in AutoCad with the help of the command Load Application from the menu Manage.
Sorin Cristian Albu / Procedia Manufacturing 32 (2019) 36–41 Albu Sorin Cristian / Procedia Manufacturing00 (2018) 000–000
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Table 1. Data required for processing Parameters required simulation
Pass 1
Pass 2
Radius of the worm
10mm
Length of the worm
120 mm
Number of beginning
2
Pass 3
Min radius of the helical goal
4mm
4mm
4 mm
Maximum radius of helical goal
7,5mm
7,5mm
7,5 mm
Step of the propeller
27mm
27,3 mm
26,7 mm
Sense of wrapping
Right
Diameter of the tool
6 mm
6 mm
6 mm
Milling inclination angle
0
15˚
-15˚
To the Command prompt from AutoCad the name of the conceived program is typed, after which are introduced the parameters of the conveyor screw, the cutter and the parameters of the conical propeller for each pass. In the chosen example, the first pass is done with the cylindro-frontal cutter positioned perpendicular to the symmetry axis of the bla nk, at the second pass the left flank of the conveyor worm is processed, and at the third pass the right flank is processed. In Fig. 4. it can see the stages during the simulation with the cylindrical-frontal cutter this hawing associated the coordinate system XOYZ.
a
b
c
Fig. 4. (a) firs t pass; (b) second pass; (c) third pass.
At the end of the simulation, the 3D representation can be saved in a file with the ".stp" extension that can be viewed in Inventor. In the axial section the shape of the hollow and the flanks can be analyzed, and if it meets the expectations, the conveyor worm can be processed with the parameters entered for each pass. 3. Conclusions As a result of the simulations and analyzes made, we can state, using a program that allows simulation of the processing of complex surfaces such as helicoidal ones, the following:
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Sorin Cristian Albu / Procedia Manufacturing 32 (2019) 36–41 Albu Sorin Cristian / Procedia Manufacturing 00 (2018) 000–000
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the execution costs are reduced due to the removal of the non-compliant parts resulting from the design mistakes; • the process parameters required for each pass can be provided without the risk of interference; • it is possible to obtain a transport worm with a variable gap along the symmetry axis of the blank without wasting time for tests on machine tools CNC. The main disadvantage of using a 3D simulation program is the long time it takes to run it on a regular computer without special hardware resources. •
Acknowledgements This work was supported by a grant of the Romanian Ministry of Research and Innovation, CCCDI – UEFISCDI, project number PN-III-P2-2.1-CI-2017-0430, within PNCDI III, with support of the company 3DCREATIVITY and Research Center TAPFAAC. References [1] [2] [3] [4] [5] [6] [7]
***, Organe de Masini. Vol. I d. Angrenaje. Reductoare (Colectie STAS). Editura Tehnica. Bucuresti, 1984. C. Elekes, Scule pentru angrenaje melcate, Editura Tehnica Bucuresti, 1985,. STANDARD DE STAT "Angrenaje Melcate Cilindrice. Melcul de referinta." STAS 6845-82 ANSI/AGMA 6022-C93 American National Standard Design Manual for Cylindrical Wormgearing. S. N. Krivoshapko S.N., V. N. Ivanov, Encyclopedia of Analytical Surfaces, Springer, 752 p. (2015). S. N. Krivoshapko, Geometry of linear surfaces with the return rib and linear theory for torso-helicoid calculation, RUDN, p.357 (2009). S. N. Krivoshapko, Marina Rynkovskayaology , Five Types of Ruled Helical Surfaces for Helical Conveyers, Support Anchors and Screws, MATEC Web Conf. ,Volume 95, 2017, 2016 the 3rd International Conference on Mechatronics and Mechanical Engineering (ICMME 2016) [8] S. Albu, Roughing helical flanks of the worms with frontal-cylindrical milling tools on NC lathes, Procedia Technology, Volume 12, 2014, ISSN: 2212-0173, Pag.448–454 [9] S. Albu, V. Bolos, Determining the optimal position of the frontal-cylindrical milling tool in finishing in the new technology for processing worms, Procedia Technology, Volume 12, 2014, ISSN: 2212-0173, Pag.455–461 [10] S. Berbinschi & V. Teodor & N. Oancea, . A study on helical surface generated by the primary peripheral surfaces of ring tool The International Journal of Advanced Manufacturing Technology, July 2012, Volume 61, Issue 1–4, pp 15–24 [11] S. Albu, V. Bolos, Regarding on generation helical cylindrical and cone surfaces with the help of a curve, Procedia Technology , ISSN 2285-0945, pag.136-139, 2012.