https://hemerotecadigital.uanl.mx/files/original/408/19942/Celerinet_2019_Ano_7_No_1_Enero-Junio.ocr.pdf 5c9204bc694642c1032a6656bed8845d PDF Text Text O) ~ ' IO O) CX) C') C\J z (/) (/) MATHEMATICS, PHYSICS, COMPUTER SCIENCE, ASTROPHYSICS ' UANL FCFM f,-\f'l lLTAD DF C1f.NC7AS FiSICO MATfMAllCAS �PhD. Rogelio Guillermo Garza Rivera Rector PhD. Santos Guzman Lopez Secretario General M.A. Emilia Edith Vasquez Farias Academic Secretary PhD. Celso Jose Garza Acuña Secretary of Cultural Affairs Antonio Ramos Revillas Publications Director PhD. Rogelio Juvenal Sepulveda Guerrero Director of Facultad de Ciencias Físico Matemáticas PhD. Romeo de Jesus Selvas Aguilar Editor in Chief M.A. Alma Patricia Calderon Martinez Editor Dahlia Nayelli Espinoza Segovia lvan Dario Ponce Castillo PhD. Alejandro Martinez Rios PhD. Daniel Toral Acosta PhD. Romeo de Jesus Selvas Aguilar PhD. Manuel PhD. Carlos lzaguirre PhD. Angel E. Sanchez Colin PhD. Pedro Valdes-Sada PhD. Enrique J. Perez PhD. Carlos E. Chávez PhD. Eduardo Perez-Tijerina Authors M.A. Patricia Martinez Moreno PhD. Jose Apolinar Loyola Rodriguez PhD. Romeo de Jesus Selvas Aguilar M.C. Azucena Yoloxochitl Rios Mercado M.A. Alma Patricia Calderon Martinez PhD. Alvaro Reyes Martinez PhD. Maria de Jesus Antonia Ochoa Oliva Editorial Committee Victor Manuel Barrera Herrera Editorial Design Celerinet, Year 7, No. 1, January - June. Published on: July 4th, 2019 Celerinet is a semestral publication edited by the Universidad Autónoma de Nuevo León, through the Facultad de Ciencias Físico Matemáticas. Address: Ave. Universidad S/N. Cd. Universitaria. San Nicolás de los Garza, Nuevo León, México, C.P. 66451. Telephone + 52 81 83294030. Fax: + 52 81 83522954. celerinet.uan l.mx Editor in Chie!: Dr. Romeo de Jesús Selvas Aguilar. Exclusive Rights Number 04-2014-102111595700-203 licenced by the Instituto Nacional de Derechos de Autor. ISSN 2395-8359. Responsible for last update: Unidad Informática, M.A. Reyna Guadalupe Castro Medellín, Ave. Universidad S/N. Cd. Universitaria. San Nicolás de los Garza, Nuevo León, México, C.P. 66451. Last update: July 4th, 2019. The views expressed in th is publication do not necessarily reflect the Editors' views. The partial or total reproduction of the contents and images in th is number is forbidden. AII rights reserved © Copyright 2019 celerinet@uanl.mx �1 10 OPTICAL FIBER LASERS : AOV ANCEO MANUF ACTURING TOOL, ITS IMPACT ON ENERGY SAVING, ANO ITS STATE OF THE ART IN MEXICO QUAOROTORS OAE CONSTRAINEO MOOEL ANO FORCE CONTROL 18 25 OPTICAL CHARACTERIZATION OF A PRI NTED CIRCUIT (ANTENNA) �RESEARCH PAPERS , ARTICULOS DE, INVESTIGACION �RESEARCH/ PHYSICS 1 Alejandro Mar tinez Rios, 2 Daniel Tor al Acosta, 3 Romeo Selvas Aguilar; CIO - UANLº - CICFIMº - FCFMº in San Nicolas de los Garza, Nuevo Leon, Mexico. ABSTRACT Fiber lasers are a mature technology widely used in advanced manufacturing. In this review paper, we describe the principie of operation of fiber lasers, and the extraordinary characteristics that make these devices so convenient when compared to others available laser technologies. Additionally, it will give the current status of the research on these devices in Mexico, besides the potential impact it may have in the industry. Keywords: Opticalfiber laser, laser manufacturing, fiber laser components. RESUMEN Los láseres de fibra son tecnología avanzada utilizada ampliamente en la manufactura avanzada. En este artículo describimos el principio de operación de los láseres de fibra y las características extraordinarias que hacen de estos dispositivos tan convenientes al compararlos con otras tecnologías laser Además, se presentará el estatus actual de investigación sobre estos dispositivos en México, así como el ünpacto potencial que tendría en la industria. Keywords : Láseres de fibra óptica, manufactura de láseres, componentes de láseres de fibracomponents. INTRODUCTION High power fiber lasers are an established technology which plays a central role in advanced manufacturing, mainly as occurs in the automotive and aerospace industries [1 , 2]. There are two principal characteristics promoted of this technological disruption, the first one is the inherent high brightness given by the process of the laser beam generation at the rare-earth doping core of an optical fiber, which results in high-beam qualities and tightly focused spots [3]. The second one is the high wavelength absorption that metals, other ceramic and sorne organic materials exhibit at sorne fiber lasers wavelengths, in particular, with ytterbium-doped high power fiber lasers (the most used fiber lasers in the industry). Martinez, A. Toral, D. & R. Selvas. (2019). Optical fiber lasers: AAdvanced manufacturing tool, its impact on energy saving and its state of the art in Mexico. Celerinet. 7 (1), 1-9. 1 �CELERINET JANUARY - JUNE 2019 Fiber lasers are excellent energy-efficient efforts and the obtained results is a result of the devices with low maintenance/operating financia! problems in Mexico's Govenunent, costs, being comparatively more attractive which over the last few decades has adversely than other laser technologies. Consequently, affected the financia] support to the Research fiber lasers are the preferred choice in the activity in this country. Thus, insufficient automotive/aerospace industries, which widely financia! resources make difficult access to high use cutting/soldering processes of aluminum power fiber laser components, which usually and steel,being its low weight and mechanical are costly and also reduce the possibility to strength useful to comply with safety standards produce relevance/impact in this particular and energy-efficiency requirements. field. In present days, one can find in Mexico's industrial-clusters, diverse manufacturing The above stated brings forward the relevance companies having in operation fiber lasers with of fi ber lasers in the manufacturing industries, output powers ranging from a few hundred watts particularly its impact on the production costs, to several kW. Therefore, it could be relevant where energy efficiency and other important to develop our fiber laser technology, by fiber laser's characteristics play a central role in taking advantage of the existing infrastructure/ the metal cutting processes. background of our research centers to find In recent years, Mexico has been the the way to get a role in the potential industry destination of many intemational automotive demands on these technologies. and aerospace manufacturers, making this country the one with the largest concentration As far as we know, apart from our group at of high power fiber lasers in Latin-America Centro de Investigaciones en Optica (CIO), [4]. Therefore, it is discussed in the next there is no other research group which is also section, the potential impact that Research and developing high power fiber lasers in Mexico. Development of fiber lasers may have in the In relation to our project, it is worth mentioning local industry. that it initiated in the summer of 2015, and today's current status consists of a Laser OVERVIEW OF THE RESEARCH ON Cutting Prototype with a continuous-wave FIBER LASERS IN MEXICO operating power of 200W. Additionally, it is underway the assembly of a ~ lkW fiber laser Along the past few decades in Mexico, cavity ( discussed in section 6). basic research on fi bers lasers have been made at different CONACYT Research Centers OVERVIEW OF THE RESEARCH ON and Universities located across the country, FIBER LASERS IN MEXICO so that every year the number of PhDs and If fiber laser technology is fully developed, MSc 's specialized in optics increases rapidly. Moreover, on sight that over the last 30 years, a and further progress in this field pushed by considerable part of these new experts become dominant Fiber Laser Manufacturers, would it part of the Academic staff, it might be inevitable be worth trying to continue our research on this no notice that there have been no results related field? Our answer is affirmative, and to sustain to impact technological development, which is our opinion, we revise these research activities evidenced for the very few research papers in from the approach of its potential impact in the local manufacturing industry and the intrinsic the particular issue of high power fi ber lasers. The disagreement between the educational relevance that energy efficiency 2 �RESEARCH/ PHYSICS has in production costs as well. The continued growth of the Manufacturing Industry in Mexico has boosted the demand for metal cutting systems. For these companies, the selected cutting technology is an important decision due to parameters like energy consumption, speed/precision characteristics, and maintenance costs impact on the final production costs. So, we mention the most common types of these systems and its performance characteristics, sorted incrementally by cost level. With the lowest purchase cost, plasma cutting systems are a versatile technology which offers the highest cut speeds, and capability to process the thickest layers of metals; although certainly with a form factor that produces the largest kerfs (size of the slit left by the ren1oved material), which are usually in the order offew millimeters [5]. On the other hand, their operating cost is the highest, given the required electrical operation currents are in the l0 's-l00 's Amperes. In a higher cost leve!, appear CO:: laser cutting systems. With optical output powers from a few hundred to severa! thousands of watts, these systems are suitable for a vast variety of material cutting processes. lts good beam quality and focusing spot diameters typically of ~500µm make these devices attractive for precision cutting, offering a 3-fold reduction in kerf sizes when compared with plasma cutting systems. Nevertheless, due to the complex output optics required for beam delivery, as well as the size of its diverse components and low wall-plug efficiencies (~ 15%), maintenance, and operating costs becaome an important constraint in CO:: laser systems. Finally, with the highest cost leve), we find high power fi ber lasers. These systems offer wall-plug efficiencies as high as ~50% [6, 7], with conveniently long life-spans typically in >50000 hours, and em1ss1on wavelengths range in the nearby of the absorption peaks of the most commonly used metals in industry. These characteristics are possible because of pump power is provided by large life-span laser-diodes, operating at such wavelengths that the quantum defect corresponding to the fiber core doping is remarkably low. Additionally, as a result of being monolithic assemblies, the maintenance cost is relatively low due to the only components that deteriorate with use are the output heads, which usually require very short off-times for its replacement. Finally, the outstanding brightness and beam parameter product offered by fiber lasers, make them possible to deliver beam spot diameters as low as <50 µm with deepness of focus [8] , which allows higher precision and cutting speeds. Therefore, fiber lasers not only comparatively cut down the electricity bilis, but also reduce the requirements of electrical installations and in tum the overall size of metal cutting systems. In summary, fiber laser systems, have the best performance but the highest price, on the other hand, CO2 laser and plasma cutting systems are the less expensive altematives but exhibit the lowest performance. Therefore, not only cost/benefits but also the available budget will determine the purchase choice. Under budget limitations, users may prefer CO2 laser or plasma systems due to their lower prices, even if in the long-term this results in higher operational/maintenance costs. Besides that, there are sorne manufacturing companies (rather large-sized ones) which can afford the higher purchase cost of fiber lasers and massively use these systems in metal cutting processes. ln this case, the long-term convenience of fiber lasers becomes evident, first beca use of the energy savings immediately cuts down the electricity costs, and second, due to its higher speed/precision and durability 3 �CELERINET JANUARY - JUNE 2019 reduce the operation/maintenance costs. Nevertheless, due to all these high tech devices are acquired from abroad, the user becomes dependent on the fiber laser manufacturer, which has total control on the adaptation/installation process, spare parts, and maintenance/ training and other technically advanced issues required for specific processes. Thus, it is not a surprise that fiber laser manufacturers are large companies with vast economic resources, diverse technological assets, patent portfolios, and advanced research and development labs. Therefore, without these " unl imited" resources, we could not contend in the same manner with the same technological objectives. In this way, to get a role in this field, we must develop our fiber laser technology to i) decrease the technological gap, and ii) this way we can identify potential opportunity areas in the local industry. With this in mind, we need to study the issues encountered in the supply chain of services and prepare research strategies that allow link projects. Additionally, we believe that this effort must be focused to the development of fiber laser components, particularly, pump combiners [9], cladding power strippers, hightemperature fiber Bragg gratings, and efficient fiber cooling schemes as well as the search of other potential appl ications of this type of lasers. In this respect, we have been working in these activities since 2015, developing sorne fiber laser components mentioned above. power fiber lasers Yb-doped cores are widely used. The principie of operation of a fiber laser can be depicted as a general laser system, in which the active optical fiber simultaneously provides the active laser medium as well as the laser cavity. Fiber lasers convert the multimode optical power coupled into the inner cladding to a laser signal generated in the core, in the particular case of Yb-doped high power fiber lasers, conversion efficiencies of 70-90% are typically obtained [3,8]. This can be technically considered as the brightness enhancement of the incoming pump power, conceming the power departing from the core. The brightness conversion becomes evident if we co1npare the power density of the incoming pump related to the outgoing laser signal. Because of the laser effect, a net optical power is transferred from the cladding towards the core, and given that the core's cross-sectional area is (typically) ~ 100-times smaller than that of the cladding, the power density increases with the same proportion. This outstanding brightness conversion allows the use offiber lasers in high precision metal cutting processes, where high power density is a key parameter. As shown in Fig. 1, the double ciad structure in active fibers can be seen as a three concentric cylindrical waveguides each one with distinct refractive index (Rl). Sorted from higher R1 to lower R1 values, we have in the first place the central doped-core with R1 = n 1, then, ABRIEFOVERVIEWOFHIGHPOWER the second !ayer (inner-cladding) with R1 to FIBER LASERS TECHNOLOGY lower R1 values, we have in the first place the central doped-core with R1 = n 1, then, the An essential characteristic of a high power second !ayer (inner-cladding) with R1 = n2, fiber laser is the active laser medium, which and finally, the externa! !ayer of the waveguide is a double ciad fiber with a central doped (low index polymer) with R1 = n3. ln this way, core. Along this core is where the process of the co1npared R1 values of the core/cladding/ stimulated emission that leads to laser generation low_ index_polymer correspond as nl>n2>n3, occurs, indeed. The core doping used usually respectively. includes one or two rare-earth elements (Yb, Er, Tm, Hm, etc.), although in the case of high 4 �RESEARCH/ PHYSICS Pumping, population inversion and stimulated absorption/emission processes. High power fiber lasers are pumped by multimode optical power, being this power coupled into the inner cladding of the fiber. From the ray tracing approach, pump power can be considered • as being carried by many ray trajectories which also represent the cladding modes supported by the highly multimode fiber cladding. As shown in figure 1, the blue arrow incoming to the fi ber represents one of many pump rays coupled to the inner cladding, so that each ray trajectory will have a chance to cross the doped core and get absorbed by the rare-earth dopant ions. In consequence, these ions will go to an excited meta-stable state, producing an inversion population of excited states which by stimulated absorption/emission processes, will release this stored energy and allowing the coherent amplification of optical signals at the emission wavelength between laser levels. The multimode pump power is provided by multimode fiberpigtailed high power laser diodes, being the pump combiner, the optical component used for this purpose. Figure 2 shows a typical scheme of a fi ber laser, in which pump combiners are located on each side Of an optical fiber cavity. Additionally, in order to have a proper absorption ofthe pump power, the pump wavelength must be within the absorption range wavelength of the rare-earth doping ofthe core. Laser oscillation. As shown in Fig 1. by adding a couple of partially/totally reflective mirrors to the laser cavity allows the bi-directional amplification of the signa! wavelength such that is produced an oscillating wave. This wave bounces back and forth between these mirrors, then, a rapid buildup of a coherent wave occurs by the release of the stored energy of the excited atoms. When a steady stated is reached, the pumping process maintains this energy storage at a certain effective leve!, while the laser oscillation is continuously releasing it at a given rate. This released energy is partially transmitted by the partial mirror so that a laser signal is departing from the core of the optical fiber and producing the single mode, high brightness output laser signal. At the present time, is common to find high power single-mode fiber lasers with operating powers ranging from few l00's - 20000 Watts of optical power [6-8]. cor• (The eore dopants LATERAL VIEW ·a E L.- - ' í!' .. ...... <J•ddirc . core ..... /' ~ - "' '.>,.---- =E 5t Q. 'tl5 ~ fow inde:,. pdvmae:r .- "°2 ~bsorbthepump t-Mr,V) ./ :>- ~ daddin1 (the nof't<'clr-cular ~ t r v help$ to lmpto\lt the claddircfc«e owrlap) z o t; ~ ~ o 5 Fig 1. The geometry of an active double ciad optical fiber, the blue arrow represents any pump ray bounded to the inner-cladding waveguide. Toe non-circular innercladding helps to scramble the pump rays trajectories in order to increase its overlap with the doped core and the attainable absorption as well. FlBER LASER COMPONENTS The sketch in figure 2 shows the key components of an optical fiber laser. The corresponding function of each component is listed below: (a) Active Fiber: lnside this component is where stimulated absorption/e1nission processes give rise to laser generation. In general, the fi ber 's core is doped with rare-earth elements like Ytterbium, Erbium, Neodymium, Thulium, etc. in the case of high power fiber fiber lasers double ciad optical fibers are used. 5 �CELERINET JANUARY - JUNE 2019 (b) Pump modules: These are multimodal laser_diodes/laser_ diode_ bars which provide the optical pump power required to produce the excitation of rare-earth dopants in the core. (c) Pump combiner: This component allows to couple the multimode pump power from laser diodes. In high power fiber lasers, these are usually made by multimode pump fibers laterally fused to a central passive double clad fiber, which can be directly spliced to the active fiber. (d) Cavity mirrors: In fiber lasers, these optical fiber components are denominated fiber Bragg Gratings. These are often fabricated by inscribing a nwnber of periodic refractive index perturbations along the core of double clad optical fibers, in this way an effective degree of reflectivity is achieved if the period length satisfies the Bragg condition. ln order to allow laser oscillation, the selection of the reflected wavelength must be such that it coincides with the signa! wavelength to be amplified. PUMP MODULES g¡\5 :E u \5 a: a: :E a: :,: ■ PUMP COMBINER o RE OPTICAL FIBER ■ .... Laser sicnal PUMP COMBINER Fig 2. Sketch of an optical fiber laser and its components. The HR and OC terms stand for the totally/ partially reflectivity of the cavity mirrors respectively. The term RE stands for the Rare-Earth doping in the active fiber. DEVELOPMENT OF A HIGH POWER FIBER LASER PROTOTYPE AT CIO: LESSONS LEARNED In 20 15, it was started a project in which it was proposed the development of a ~ lkW @ 1060nm high power fiber laser. The goal with this project was to explore the feasibility to create a laser system applications and 6 development laboratory and this way to approach to things concerning this technology. We believe this project is relevant given the increasing demand for metal cutting systems by manufacturing companies in Mexico. This project was also considered feasible in view of the optical fiber 's research background at CIO, taking advantage of sorne essential facilities and special equipment like high-end glass processing systems, optical spectrum analyzers, and additional equipment and materials useful to work with diverse aspects of the fiber lasers assembly process. As it would happen with any development project involving the assembly of high power lasers, it was possible to have to deal with sorne technical problems. In this respect, the first lesson learned from this project is related to the care and detail leve! needed to carry out the assembly process, being noteworthy that even with a fiber laser operating at 200W of output power (as demonstrated in the spring of 2018) the laser cavity must withstand ali this signa! power propagating through a 25 microns diameter's core, so that if any splice loss would be present (as we experienced severa! times before the first successful demonstration), it would have produced the melting of the fiber inner cladding. Both the splice loss and exposed bare fiber sections that need to be packaged and cooled, are always potential problems at the moment to assemble a high power fiber laser and brings forward the type of technical issues to study [10]. For instance, we can mention the research carried out to determine the source of splice losses and its respective solution. To figure out how it occurred this problem, we studied the thermal diffusion of dopants in fibers which yields an increment of the modal field diameter and a modal mismatch in fi ber of splice losses and its respective solution. To figure out how it occurred this problem, we studied the thermal diffusion of dopants in �RESEARCH/ PHYSICS fibers which yields an increment of the modal fiber by July 2019 (depending on the purchase field diameter and a moda] mismatch in fiber and arrival of the high power fiber Bragg splices. With this purpose, and in a similar refl ectors). way as we studied in [ 11 ], we designed a set of experiments involving heating of fibers and In addition to the project goals mentioned the use of an etching solution that reacted more befo re, a ~ l kW fi ber laser cavity is not only rapidly with the core's Rare-Earth dopants, desirable but either we want to add ali the so that the etched fibers were revised by a required engineering to carry the developed Scanning Electron Microscope to obtain the fiber laser cavities, out to the status of a TRLcorresponding surface relief images. On the 4 and 5 [12] fiber laser cutting prototype. This view that the size of the fiber 's surface relief it type of readiness capability will allow getting is correlated to the dopant's diffusion produced the cutting system out of the laboratory for by the heat deposited to the fi bers, these images its use under relevant conditions, in this way helped to indirectly determine the heat <lose and we could comply an important aspect of the other parameters which yielded better splice main objective, which was to have a relevant processes and lower splice losses as well. approaching with these technologies. For this purpose, an additional engineering work was Besides the expected technical issues, it also carried out to the already demonstrated 200W emerged another problem, which was derived fi ber laser cavity, this impl icated not only the refrom the insufficient and slow flow of resources, assembly of the fiber laser cavity on a portable and affecting our agenda in such way, that cabinet but also the packaging and cooling of even with the support of the administration, the bare fiber sections, as well as the design and it was difficult to boost the project progress. (in-house) manufacturing of the laser cut head. Often happened that materia]s or equipment In respect to this laser head, it was designed in financing was stuck in the waiting line among such a way, that it can be mounted overa CNC other researchers needs. At the present date ( computer numerical control) mechanism to of this paper, it is underway the ~ 1kW fi ber permit the transport of the laser power to the laser cavity, in particular, the integration of the metal pieces to process. chillerequipment required to enable the 1.2 kW We expect to use ali the acquired knowledge @ 915nm pump modules. It is worth mentioning up to this point, and apply these same attributes that the theoretical conversion efficiency is to the ~ 1kW fi ber laser once demonstrated. ln given by the ratio between pump_ wavelength/ respect to the ~ I kW fi ber laser cavity, additional emission_wavelength (~86%) as well as the work must be carried out, like a new cabinet to interna! cavity losses determine the final output assemble the fiber laser, active cooling of the power of this fi ber laser. Thus, we expect to Fiber laser, active cooling of the fiber, chiller/ achieve a laser output power in the range of800- pump enabling and cladding power stripping 900W corresponding to a conversion efficiency sections, and a new fi ber laser cutting head with of around 75%. The reason to use a 915nm process gas to avoid swarf have contact with pump wavelength was to add sorne tolerance the laser head's optical components. to thermally-induced wavelength instabilities, CONCLUSIONS which may increase the pump wavelength and cause a detriment in the pump absorption as Ali things considered in this paper put into well as reduced laser conversion efficiency. We context the type of challenges that must be expect to demonstrate this high power laser taken up to achieve relevance on the field of 7 �CELERINET JANUARY - JUNE 2019 high power fiber lasers technologies, and be able to produce a positive impact with respect to the Manufacturing l ndustry's demands in Mexico. In particular, our current fiber laser development's project, reveals that the research/ engineering work needed to sol ve technical problems as well as any quantifiable outcome progress of the project has been engaged to suitable financia] support to make things happen. Ultimately, although the technological gap in the field of fiber lasers is evident, we believe that the research practice in Mexico still can aspire to achieve sorne positive impact in this Country. In our particular case, the ability to provide relevant know-how and tools in the ambit of fiber lasers has been the motivation to work in the development of high power fiber lasers. ACKNOWLEDGMENTS The authors want to acknowledge the support provided by Catedras-CONACYT project l 77 and the SEP-CONACYT project number 432 17 for the realization of this paper. Intemational Inc. [4] Magna Intemational Inc. https://www.magna.com/company/company-information/magna-groups/cosma [5] ESAB Knowledge Center, " What is cutting kerf?" http://www.esabna.com/us/en/education/blog/what-is-cutting-kerf.cfin [6] IPG Ytterbium CW Laser Systems https:// www.ipgphotonics.com/en/products/lasers/high-power-cw-fi ber-lasers/ l -micron-3/y ls-eco1-10-kw [7] lPG High Power CW fiber Lasers https:// www.ipgphotonics.com/en/products/lasers/high-power-cw-fi ber-1 asers [8] . N. Zervas and C. A. Codemard, «High Power Fiber Lasers: A Review," IEEE Joumal of Selected Topics in Quantum Electronics", 20, 0904123-23 pages (2014) [9] K. Madrazo de la Rosa, A. Marti.nez-Rios, T. Porraz-Culebro, D. Toral-Acosta, L.F EnriREFERENCES quez-Gomez, and J .A. Guerrero-Viramontes, " Effect of the surrounding refractive index and [ l] Wijeyasinghe, N. (2018). Fiber lasers: uní- fusion-depth on side-pump combiners", Opque tools for automotive & aerospace manu- tics and Laser Technology, Vol. 107, 468-477 facturing. https://www. idtechex.com/research/ (2018). Doi: https://doi.org/10.1016/j.optlasarticles/fi ber-lasers-unique-tools-for-automoti- tec.2018.06.002 ve-and-aerospace-manufacturing-0014992.asp [ 1O] Z. Huang, X. tang, P. Zhao, C. Li, Q. Li, C. [2] Belforte, D. (2018). Laser joining in the Guo, Z. Li, H. Lin and J. Wang, ''Power scaling spotlight. Industrial laser solutions. https:// analysis of high power fiber laser employing www.industrial-lasers.com/articles/print/vol u- online three-section recoating method of splice me-33/issue-3/departments/my-v iew/laser-j oi- point," Laser Physics, 26, 125103 pp (2016). ning-in-the-spotl ight. html [ 11] Teresa Elena Porraz-Culebro, Alejandro [3] D. J. Richardson, J. Nilsson, and W. A. Clar- Martinez-Rios, Daniel Toral-Acosta, Kenia kson, "High power fiber lasers: current status Madrazo-de-la-Rosa, Luis F. Enriquez-Gomez, and future perspectives [Invited]," J. Opt. Soc. Juan Manuel Sierra-Hernandez, and Guillermo Am. B 27, B63-B92 (20 10) Magna Salceda-Delgado, "Characteristics of LPFGs 8 �RESEARCH/ PHYSICS Written by a CO2-Laser Glass Processing System," J. Lightwave Technol. 37, 1301-1309 (2019) [ 12] NASA, Technology Readiness Leve] https ://www.nasa.gov/ directorates/heo/scan/engineering/technology/txt_accordion l .html NOMBRE COMPLETO DEL AUTOR O DE LOS AUTORES DIRECCIÓN DEL AUTOR O DE LOS AUTORES: Centro de lnvestigacion en Ciencias Fisico Matematicas, Facultad de Ciencias Fisico Matematicas, UANL, Av. Universidad SIN, Cd. Universitaria, C.P. 66455, San Nicolas de los Garza, NL, México. Email: toralacostadaniel@gmail.com PhD. Daniel Toral Acosta received his Bachelor 's Degree in Electronical Engineering in 1999, working as a telecommunications Engineer for 11 years. ln 2015 he recei ved his Ph.D. Degree in Industrial Physical Engineering from the Universidad Autonoma de Nuevo Leon, Nuevo Leon, Mexico. Fro1n 2015-2018 he worked as a Postdoctoral researcher at the Centro de Investigaciones en Optica focused to the development of high power fiber lasers and optical fiber components as well as the required engineering f or optical fi ber processing/packaging and integration/development of diverse co1nponents oriented to high power fiber laser prototypes assembly. He is a holder of l patent, and with another 2 in procedure. S ince 20 l 8 PhD. Toral is at the Universidad Autonoma de Nuevo Leon, as a CONACYT-researcher. PhD. Toral is the coauthor of 11 articles published in lnternational Scientific Journals, and 2 patents his research work has been focused on the development of optical fiber devices and fiber lasers for diverse industrial applications. 9 �CELERINET JANUARY - JUNE 201 9 'Carlos lzaguirre Espinosa, 2 Anand Eleazar Sánchez Orta, 2 Vicente Parra Vega ' Manuel Jiménez Lizárraga; 0 UANL-FCFM San Nicolás de los Garza, Nuevo León, México,° CINVESTAV Campus Saltillo, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Campus Saltillo Ramos Arizpe, Coahuila, México. ABSTRACT The flexibility and performance of the quadrotor as a research platform have been used in recent years applications that reach even the fields of interaction and grasping. In this work, a force/ position control is presented using the orthogonalization principie between the subspaces of force and velocity in constrained flight. A position/force sliding mode is presented to guarantee the tracking of force in the constrained directions and the tracking of position in the non-constrained ones. A stability proof is presented as well as a numerical analysis of the algorithm and sorne insights on what the experimental flight tests might be. Keywords: /orce control, quadrotors, sliding mode.e. RESUMEN The flexibility and performance ofthe quadrotor as a research platform have been used in recent years applications that reach even the fields of interaction and grasping. In this work, a force/ position control is presented using the orthogonalization principie between the subspaces of force and velocity in constrained flight. A position/force sliding mode is presented to guarantee the tracking of force in the constrained directions and the tracking of position in the non-constrained ones. A stability proof is presented as well as a numerical analysis of the algorithm and sorne insights on what the experimental flight tests might be. Keywords: /orce control, quadrotors, sliding mode.e. INTRODUCTION The quadrotor is a ti ight platform that has been used in a big range of applications which can even include interaction applications such as: construction purposes [1, 2], aerial transport and towing [3, 4], inspection of structures [5] and even in art applications [6]. With the advances in Pérez, A.S. & ].P. Salinas. (2018). Size variation ofFe2Q3 embedded in a kaolinitic clay of recent geological age. Celerinet. 6 (2), 1-5. 10 �RESEARCH/ PHYSICS electronics and microcomputers the capabilities of quadrotors for interaction and manipulation of objects raises, as well as the needs for algorithms to handle force control and interaction. The problem of quadrotor interaction and force control starts when the flight regirnen changes from free flight to constrained since switching between control algorithms has to occur during flight and it has to be a smooth transition to manage the contact force disturbances. lt is clear that the force control problem is complicated because of the nonlinear dependences and couplings among force, position and orientation coordinates, [7]. The quadrotor 's force interaction problem has been addressed using a robotic end-effector to establish a contact point [8], though such solution proved to be versatile, the coupled dynamics have been neglected. Another approach, based on end-effectors, neglects the relation among attitude, thrust and exerted force assuming hovering and no aerodynamic effects, and poses wherein no force can be applied [9]. Lastly, we have the approach seen in [10], in which a robust fractional control is used in contact regimen to follow a reference attitude signal compliant with the desired contact force. Despite successfully tracking a desired force, once the quadrotor enters the constrained regimen, its position gets locked and the only degree offreedom (DoF) to manipulate is the angle directly related with the force application. the orthogonalization of force and velocity subspaces bom when the force applied into an object is normal to the constrained translational velocities, allowing to control the force in the constrained directions of the quadrotor while at the same time controlling the position in the non-constrained directions. FORCE CONTROL OF A DIFFERENTIAL ALGEBRAIC CONSTRAINED QUADROTOR In the following, we elaborate on the development of the differential algebraic equations (DAE) to model the constrained flight regimen of a quadrotor the implications and advantages of using this approach. If conditions of the orthogonalization principie persist at ali time, then the dual space of force/velocity of the quadrotor constrained flight can be divided in two orthogonal complementary spaces, one of force and one of velocity, taking that that into account we can then define the quadrotor system in contact as follows: •. T m~ =-T Re=+Jf'. (~)J + mge=+d P R=Raf ➔ JdJ=-a/ J(J) + r + rcx Rr J r. (~ )2 + d 0 f' (fJ(~.,, 1) = Ü ➔ Where ,~ is the vector from the center of mass to the contact point and r, its magnitude, J r. e IR"x"' is the constrained normalized jacobian" of the kinematic constraint (fJ(~f',1) =O , in this sense These studies show that extensi ve research of force quadrotor's dynamics is yet needed we can define =[J r.(c;)l, J r.(c;)l xr, )e !R6" "' stands " " without introducing a restrictive assumption. for the contact wrench where J r. (~)A contains The approach presented in this work is based the contact forces and "' on the force controller develop for robotic manipulators in [ 11], and the map position control seen in [12]. This methodology uses ➔ 11 �CELERINET JANUARY - JUNE 2019 ORTHOGONALIZATION PRINCIPLE Since q,(,;) = 0\:/t, then its time derivative yields This means that J.,(,;) is orthogonal to ,; . That is,; , belongs to the ortogonal projection matrix of [13]. Figure. 1. Schematic description of the quadrotor under a DAE model effects presented on the position dynamics. where Q spans the tangent plane at the contact .-1. e lR"' is a vector of Lagrange multipliers or contact forces, for a single contact point point, thus Qt = ¿ and QJ; = o.Therefore J.,, Q and are orthogonal complements since IR" is m = 1, and q,(,;.,,1) is the kinematic constraint, a rigid and frictionless surface, where generated by the direct sum of two orthogonal subspaces, and rank(im(Q)) = m = n -r as well as ip = f(,;,,,,r): lR" ➔ IR"' is a given scalar function, rank(im(J.,)) =r , such as m +r=n [14]. ,; = [x.,,y,,,,= ,,, f denoting the position of a Q 9 POSITION/FORCE CONTROL fixed coordinated system and r = [lfl.,,0 ,,~,,, f 9 their associated Euler angles. The position aerodynamic disturbances stand for dp while the attitude aerodynamic disturbances stand for d. The goal is to track force signals in the force subspace which is mapped by J ,¡,r. (,;) while tracking position signa Is in thevelocity subspace mapped by Q. For the purpose of simplicity, the physical constraint will be modeled as a wall in the x axis of the quadrotor which is placed at 1 m. of the quadrotors origin. In Figure 1, the contact regimen is represented, and the aim of this scope can be depreciated, the tracking of both force and position of the quadrotor while in constraint flight. 12 We must first define sorne structural properties which will be helpful at the time of presenting the stability proof. BOUNDEDNESS OF DYNAMICS: There exist positive scalars '$;, for i =o,... ,11 , such that IIQIJsP. l td - a,;, 11 5 P2+ /J1IJ,;, 11 llro-11 s P4llo-11 llé>lls fi6 IWd - a!,II5 P, + PsI !, 11 (7) (8) (9) (10) (11) llr sign(Sq, >11s ✓ 3J..,,= (r) (12) 11/Jj;. ¡¡ s"/]9 (13) llr;LIIs Y; lf sign(Sq1 >IJ ll.-1. -2d11s /Jio (14) (15) �RESEARCH/ PHYSICS Then from equation (1) and using the properties related with previously listed: can be bound as llmge=+dp -Y,011 S ,tmax (m )/31 (A llt,11+ .fj;.•= (V)) +,ima,<m)P6(P1ll~.II+ fi4 lall) Where S, = reference as t, =t, +t¡ Where (21) +/JJ;. (~)[~1+sd1 - r):] (22) 9 <:1 = sign( Sq) ( llmge=+dp - r,e¡¡ sx(t) (17) P.. = /3,/31 +P6P2 +Ps/Jrn +Ps"f; + g Amax (m) , Is a state-dependent function. Notice that, X(t) not only includes ali the externa! forces affecting the aircraft (buoyancy forces, aerodynamic forces and gravity) but also a general statedependence of d p . Consider the nominal t .. =Q[td - a~, +sd, - Y<T] +lma, (m )P (ll~JII+ Y; IIJ sign (Sqf )11) +J.max/311 +lldpll t -t,. 23 ) t = sign(S1 ) ( 24) where the tracking position error is defined as ~. = ~ - with reference trajectory ~d (i) e c 2 ; feedback gains a,r,/3 are diagonal positive ~d, definite matrices and is a scalar gain. J . (~) = J is the constrained normalized Jacobian of.tfié kinematic constraint0. Errors are then defined as OPEN LOOP ERROR EQUATION: Notice that the orthogonalization principie is established at velocity leve!, we need to introduce an orthogonalized reference signa! t, = t, +!1 at the velocity leve!, where t:!1= o The main idea is to prove the boundedness of the constrained DAE dynamics (1) and (2). Once accomplished this, we design a controller by using the virtual control u=-TRe, as a full vectorial term. In this way equation ( 1) can be rewritten as m! =-u+J; (~)J +mge=+dP ( l &-9 Following a similar procedure to [15], the parametrization can be expressed in terms of a S, = QS - /3J;.s1 (25) s. = sq + ru (26) s1 = sq, + r/f. (27) Sq =S - Sd (28) sq, =D./ -sd, (29) S = t, + a~, (30) sd, =S(to)e-k(t-to) (31) ~¡ =f A- Ad (32) sd¡ = ~¡ (to)e-k(t-to) (33) For k, k >- O. In this way S, can be stated as nominal reference ~' as mt,. = Y,e 09) Introducing (19) into equation (18) yields 13 �CELERINET JANUARY - JUNE 2019 CONTROL DESIGN A control law that assures semiglobal exponential tracking of force-position reference signals, in closed loop with system ( l ), is given by u = KdSr + J; [Ad +sd, - Y; tanh (µ¡Sq, )] +J; [- r111J +r1Sd, - r1r;'f-] (35) where Kd is a diagonal positive definite matrix, and are positive scalar values. Then substituting equation (35) into (20) yields bounded, we have that (tr,tr) EL~ . The right hand side of open loop (18) shows that exists such that This result shows only local stability of Sr and Sr . Now we prove that the sliding mode arises, taking Sr in (34). Since Sr e L , and Q are q,(;",1) pJ;. (; )S1 ➔ o bounded, then QS, is bounded and, since is sn,ooth and S1 ➔ o then . Now taking into account that Sr is bounded, mSr =- KdSr - J; [112+sd, - Y; tanh(tt¡Sq, )- Y¡D./] - J: [rfsd, - r¡Y;L. ]+mge=+dp - f,e (36) Let the following function v =.!_[s;mS, + ps; s1 ] 2 then :,QS, and ;pJ;.s1 are bounded (this is j;. possible because is bounded and so is Q ). Ali these chains of conclusions prove that there exist constants c2 >- o and c3 >- o such that (37) be a candidate Lyapunov function for equation (36). The total derivative ofLyapunov function (37) along its solution (36) gives rise to t7 = s;msr + p;s1 ( 38) Now we have to prove that for a Q_roper selection of feedback gains r and Y; the trajectories of position and force converge to zero. This is possible if we can prove that sliding modes are established in the position subspace and in the subspace Q of force Considering that the operator Q spans the vector as the direct surn of its image Sr , J; (;). If Kd ,r1 and p are large enough and the initial errors are small, we conclude the seminegative definiteness of equation (39) outside of hyperball c0 = S, 1f7 ~ o centered at the origin, such as the following properties of the state of closed loop system arise. this implies that and implies that im(JJJ;. (;)Sr =s7) , this Sim Sr = Os - s - /J J ¡,'T $f =sim s f ( 42) where S;"' and Sr belongs to orthogonal complements, that meaos (s;m ,S¡') = O . That is, we are able to analyze the s:"' dynamics Then, ( sq,,a) e L~, and since desired trajectories are c 2 and feedback gains are �RESEARCH/ PHYSICS st, st independently of because belongs to the kernel of Q. This is verified if we multiply equation (43) by Q r where lf F: 1 >-0 , then a sq, = o is guaranteed v,. 0.5 50 a j,/J,,¡t 70 8 k Yx.y,= 0.1, 0.15, 0.15 45,200,200 K Y;,o,,,, Kd# /J~ QTSr = S, (44) Since is Q idempotent. It is important to notice that if Ax= Ay for any square nonsingular matrix A and any couple of vectors x, y then d:t .J',: within the span of Q. Now if we multiply Sr by J 'P we obtain J,,,S, = J,,,QS, - /3J,,,1;.s 1 J,,,Sr =- /3S1 (4 5) Now according Q 1 Sr = S, to ín the posítíon subspace of Q if we take derívatíve of equation s;, produces k Y¡ 5 8 0.1 Y; 0.1 ax.y,: Thus, eq uation ( 44) means that Sr = QS, (44), and multíply ít by =r;-~[ts,]. sliding mode at QTSr =QTQS, - PQT1;.sf x=y . F:1 NUMERICALANALYSIS The simulator is developed using 6 main programming blocks identified as the position and force control, position and force dynamics, lambda estimator, attitude reference mapping, attitude dynamics and attitude control. Simulations use the ode 23tb (stiffffR-BDF2) numeric solver with variable step. The desired reference in force is stated as Id = 2 + sin (t) N , while position reference signals are designed = r- F:1 • Thus, we obtain the sliding mode condition if r >- F:1 , such as F:, >- o of Where F:, as [xd, yd,=dr =[J,0.5sin(t),- 05 - 0.5cos(t)]r m Initial conditions for the simulation r =[1,0, -If [x0 ,y0 ,=0 which means that the quadrotor is already in contact Feedback gains are shown in Table 1, as seen sq, = o at ,, ;?: ~•:'.'"'I. However, notice that for in Figures 5, 6 and 7 the tracking of the circle any initial condition sq, (10 ) = o then t, =o , is successful and the contact with the wall is which implies that the sliding 1node at sq, (1) = o maintained at ali time during the si.tnulation. is guaranteed for ali tüne. The tracking of a sine function in force is Siinilarly, if we take the derivative of (45) accomplished as presented in Figure 2. In Figure 4, The virtual control containing the and we multiply it by we have inputs from the position and force controllers is presented, which is then mapped and followed by the attitude controller, resulting in the tracking of the quatemion shown in Figure 3. equation (46) guarantees the sliding mode at s; 15 �CELERINET JANUARY - JUNE 201 9 . t t J • 1; .,. (,) , • ' • Figure. 2. Force tracking of a sine function Í 1 , 1 • Tim, (•) Figure. 3. Attitude behavior according to force application This approach needs to be further developed for experimental tests, important considerations should be made regarding the contact too! to be used, it wi11 require a precise and fast positioning system such as Optitrack or Vicon in order to feedback the position of the center of 1nass of the quadrotor as well as the contact tool tip. Computational cost and latencies for this algorithrn are relatively big, a problen1 which will decide whether this scheme could be running on board the quadrotor or if it will need a ground station to run the controller. In addition to the previous challenges, the typical vibrations of the quadrotor, once in contact, will compromise the capabilities of the quadrotor to keep the orthogonalization principie. in constrained flight. CONCLUSIONS AND DISCUSSIONS 1 1 1 1 f I f f 1' Tu"' (>) Figure. 4. Virtual control input to the attitude reference map. ¡j !., . . -.-::::~. ... ' ' . .. 'liiuo (t) .' . . .. Figure. 5 .Regulation at contact point in the x axis. 1 ' • 'Twi:i(,) 0 0 ' • Figure. 6.Tracking of a sine function in the y axis. ' ' .t ,1 ti "" l l~ii •' ~ I J ! ♦ Tltuu (,;) 1 1 • Figure. 7.Tracking of a cosine function in the z axis. .16 [position/force sliding mode is a precise too! for tracking references in both subspaces of position and force. For experimental analysis one thing to keep in mind is that there has to be changed in control schemes to change from free flight regimento a constrained one for the quadrotor and therefore a switching algorithm in addition to maintain the orthogonalization principie between force and velocities will be very complicated due to the vibrations of the quadrotor. Also, the latencies demanded by this approach would be a problem when trying to have ali programs running on-board the quadrotor. Even considering the challenges previously mentioned about experimental flight test. The position/force sliding mode presents is a powerful tool that can extend the methodology proposed in [7], achieving in this way a real way of handling regular objects in the air by using a set of cooperative quadrotors that can apply a desired force while changing position according to the grip requirements proposed in [7]. �RESEARCH/ PHYSICS REFERENCIAS [9] Jimenez-Cano, A. E., Martín, J., Heredia, G., Ollero, A. , & Cano, R . (2013, May). [l] Lindsey, Q., Mellinger, D., & Kumar, Control of an aerial robot with multi-link arm V. (2012). Construction with quadrotor teams. for assembly tasks. In 2013 IEEE Intemational Autonomous Robots, 33(3), 323-336. Conference on Robotics and Automation (pp. [2] Augugliaro, F., Mirjan, A., Gramazio, 4916-4921). IEEE. F. , Kohler, M., & D ' Andrea, R. (2013, Novem[ 1O] Izaguirre-Espinosa, C., Muñoz-Vázber). Building tensile structures with flying ma- quez, A. J ., Sanchez-Orta, A., Parra-Vega, V., chines. In 20 13 IEEE/RSJ lnternational Confe- & Castillo, P. (2018). Contact force tracking rence on Intelligent Robots and Systems (pp. of quadrotors based on robust attitude control. 3487-3492). IEEE. Control Engineering Practice, 78, 89-96. [3] Sreenath, K., Michael, N., & Kumar, V [ 11] Parra-Vega, V., Rodríguez-Angeles, A., (2013, May). Trajectory generation and control & Hirzinger, G. (2001 ). Perfect position/force of a quadrotor with a cable-suspended load-a tracking of robots with dynamical terminal slidifferentially-flat hybrid system. In 2013 IEEE ding ,node control. Journal of Robotic Systems, l ntemational Conference on Robotics and Au- 18(9), 517-532. tomation (pp. 4888-4895). IEEE. [ 12] Sanchez-Orta, A., Parra-Vega, V, Iza[4] Mellinger, D., Shomin, M ., Michael, guirre-Espinosa, C., & García, O. (2015). PoN., & Kumar, V. (2013). Cooperative grasping sition- yaw tracking of quadrotors. Joumal of and transport using multiple quadrotors. In Dis- Dynrunic Systems, Measurement, and Control, tributed autonomous robotic systems (pp. 545- 137(6), 061011. 558). Springer, Berlín, Heidelberg. [ 13] Parra-Vega, V., & Arimoto, S. ( 1996). [5] Ortiz, A., Bonnin-Pascual, F., & Gar- A passivity-based adaptive sliding mode posicía-Fidalgo, E.(20 14). Vessel inspection: A mi- tion-force control for robot manipulators. Intercro-aerial vehicle-based approach. Journal of national Journal of Adaptive Control and Sigl ntelligent & Robotic Systems, 76(1), 151- 167. na! Processing, 10(4-5), 365-377. [14] García-Rodríguez, R., Dean-Leon, E., [6] Augugliaro, F., Schoellig, A. P., & Parra-Vega, V., & Ruiz-Sanchez, F. (2005, D ' Andrea, R. (2013). Dance of the flying ma- June). An adaptive neura] network controller chines: Methods for designing and executing for visual tracking of constrained robot manian aerial dance choreography. IEEE Robotics pulators. In Proceedings ofthe 2005, American & Auto1nation Magazine, 20( 4), 96- 104. Control Conference, 2005. (pp. 3694-3700). [7] Parra-Vega, V., Sanchez, A., Izagui- IEEE. rre, C., García, O., & Ruiz-Sanchez, F. (2013). [ 15] Parra-Vega, V., Arimoto, S., Liu, Y. H., Toward aerial grasping and manipulation with Hirzinger, G., & Akella, P. (2003). Dynamic multiple U AVs. Journal of Intelligent & Robo- sliding PID control for tracking of robot manitic Systems, 70(1-4), 575-593. pulators: Theory and experiments. IEEE Tran[8] Keemink, A. Q., Fumagalli, M., Strami- sactions on Robotics and Automation, 19(6), gioli, S., & Carloni, R . (20 12, May). Mechani- 967-976. cal design of a n1anipulation system for unmanned aerial vehicles. In 2012 IEEE international conference on robotics and automation (pp. 3147-3152). IEEE. 17 �CELERINET JANUARY - JUNE 2019 1 Carlos Mauricio Santacruz Elizondo; CIO - UANLº - CICFIMº - FCFMº in San Nicolás de los Garza, Nuevo León, México. RESUMEN Presentamos parte del trabajo realizado por el autor referente a la teoría llamada "Theory of Empty Universe" [l ], en este artículo se definirá lo que para la teoría es la naturaleza de la gravedad, así como su relación con la física de las partículas. La relación antes mencionada sigue siendo uno de los grandes problemas de unificación según las teorías actuales. Para esto se presentará un breve resumen de la conjetura de la naturaleza del inicio del universo y cómo su constante expansión define la naturaleza de la fisica del espacio-tiempo, esto coincide con las observaciones en el universo por los experimentos realizados. Explicaremos las fuerzas fundamentales que rigen la gravedad y la forma de las partículas, así como ejemplos y resultados. La teoría contempla de una manera general las fuerzas fundamentales como el electromagnetismo, pero no se abordarán en este artículo. Palabras claves: Gravedad; Física; Partículas; Universo; Naturaleza; Deformación; Espacio; Tiempo. ABSTRACT We present part of the work done by the author about the theory called ''Theory of Empty Universe" [ l], in this article we will define what for the theory is the nature of gravity, as well as its relationship with the physics of particles. The last relationship continues to be one of the great problems of unification according to current theories. F or this a brief summary of the conjecture of the nature of the beginning of the uni verse and how its constant expansion defines the nature of space-time physics will be presented, this coincides with the observations in the universe by the experirnents carried out. We will explain the fundamental forces that govern the gravity and shape of the particles. As well as examples and results. The theory considers in a general way the fundamental forces such as electromagnetism, but they will not be part in this article. Pérez, A.S. & J.P. Salinas. (2018). Size variation of Fe2Ü3 embedded in a kaolinitic clay of recent geological age. Celerinet. 6 (2), 1-5. �ACADEMIC PAPER/ PHYSICS Keywords: Gravity; Physical; Particles; Universe; Nature; Deformation; Space; Tinte. INTRODUCTION According to the theory called "Theory of Empty Universe" (which in the following we will abbreviate as "TEU") the universe was created from a singularity that derives in the convergence of the space dimension with a vector dimension, this last dimension we call it "time". In such convergence the time dimension deformed the space dimension, creating a dynamic multi-dimensional space, what we call "space-time". The space-time suffer a constant deformation derived from the "time" dimension, this deformation occurs in ali directions, the previous data has been confirmed on the Law of Hubble. [3] THETHEORY TEU Type oftheory The General Theory of Relativity defines the curvature of space-titne as a gravitational fiel d. ln the presence of matter, the geometry of space-time is not flat, is curved, a particle in free inertial move1nent inside a gravitational field follows a geodetic trajectory. As well as the Quantum Electrodynamics defines the physics of particles as the phenomena implied by electrically charged particles that interact with each other by means of the electromagnetic force, being the first quantum theory of the field in which the difficulties to construct a complete description of fields and of creation and annihilation of quantum particles, were resolved satisfactorily. [2] However, TEU is at the midpoint of both theories, establishing its arguments in geometric terms, energy fields and at a classical theory level. Due to this defines a connection between the gravity and the particles. TEU Type of theory Toe deformation of space-time derived from the convergence of dimensions creates a spherical space-time that continues to deform in all directions at the speed of light. At the limit of this deformation which is the area of the space-time sphere is what creates the energy. This energy has a wave nature and forms fields. As well have opposite polarities. Toe theory says that hypothetically this energy can be formed by a type of fibers or one-dimensional strings structured in other dimensions due to the expansion of space-time invades those dimensions. This is speculative due the impossibility of observing those dimensions. The fundamental physics of the particle According to TEU at the limit of the deformation of space-time where energy is created, this energy converges in itself in the form of spheres forming fundamental particles such as the electron. When they converge in themselves, they endose a space-time inside them which has a space-time deformation pressure specific to the place where the particle converged and was created. Toe particles once created are formed by the energy of fields in the outer area and the deformation pressure inside them. These are called fundamental particles. The deformation of space-time Before the beginning of the universe, the dimension of space existed in a point infinitely small and unaltered. In its interior TEU says that there was a specific interna! pressure. At the moment of the singularity and creating the dynamic space-time this began to deform in all directions generating a larger volume inside, so the pressure inside it was decreasing, creating what TEU called space-time deformation pressure lower to the space specific befare the singularity. 19 �CELERINET JANUARY - JUNE 201 9 The fundamental physics of the particle According to TEU at the limit of the deformation of space-time where energy is created, this energy converges in itself in the form of spheres forming fundamental particles such as the electron. When they converge in themselves, they enclose a space-time inside them which has a space-time deformation pressure specific to the place where the particle converged and was created. The particles once created are formed by the energy offields in the outer area and the deformation pressure inside them. These are called fundamental particles. The nature ofthe atom According to TEU, the union of many fundamental particles creates larger fields, due to the polarized nature of energy fields are formed on other energy fields due to their attraction, thus creating groups of concentric fields that we call atoms. TEU believes that neutrinos and neutrons are layers of energy fields in pairs that neutralize each other, these fields in pairs forrn the inner layers of the atom. The Beta Decay theory gives clues to these theoretical properties. [4] The force of gravity Previously, we defined particles as spherical energy fields that store inside them a specific space-time deformation at the time of their creation, which is the space-time deformation that the universe had at that moment. The energy field of the particle prevents the spacetime deformation inside it be modify, which keeps it constant. The Law of Hubble tells us that the spacetime ofthe universe has a continuous expansion from the beginning of its existence. Space-time deformation differential Derived from the continuous expansion of the universe, a deformation of the space-time of the variable universe is created with the pass oftime. As the space-time deformation of the interior of the particles is constant and the space-time deformation of the universe is variable, this creates an inequality generating a space-time deformation differential. De-t(particle) < De-t(universe) (1) According to TEU this differential of spacetime deformation between the particles and the outer space, creates a differentiaJ pressure force in ali directions and gives the particles the spherical shape. This we call gravity. ! O_e•t(unlver,e) -·----·•·• - -· - ..... Fig. 1. Atom diagram according to TEU The polarity of the different fields creates a force of attraction that attempt to join them, justas the deformation of space-time that exists inside the same fields creates an opposite force that prevents the fields from joining. This gives the stable form to the fields and the atoms. 20 j Fig. 2. Diagram of the forces of deformation space-time in particles. Interaction of the space-time deformation between two particles. When two particles find each other in the �ACADEMIC PAPER/ PHYSICS empty space, the vectors of deformation forces interferes between the empty space and the particles themselves creating a differential effect. (01 ), that area (Al) is shown on Fig 4. Fig. 4. lnterference diagram of vectors from one particle to another. Fig. 3. Diagram of vector interference between two particles. The closer the particles are to each other, the interference of the vectors will increase, increasing the differential force between them, this creates an acceleration in the displacement. We call this gravitational acceleration. Due this we need to obtain the area ( A 1), this is obtained geometrically from the law of sines: Lawofsines: (r2)/d =(al)/(rl) (3) 0-1 ..:-----r2 ANA LYSIS Mathematical fonnulation of the gravity according to TEU lf we consider that the deformation of the outer space " presses" against the center of the objects in ali its spherical surface radially dueto its deformation differential and the deformation energy inside the objects "press" to outside, then we have a pressure differential over the entire surface of the object that is obtained by dividing the force between the area of the surface considered spherical. This deformation force is the differential a of the deformation force inside the object less the deformation force of the outer space. Interna! pressure = Pressure of deformation / área of the particle's sphere (2) Fig. 5. Vector interference diagram according to its geometry. 0 -1 ~ ~o r1 B1 --:::::: 1 y 11 r1ey+c ---- / Fig. 6. Vector interference diagram according to its geometry. We will omit the mathematical formulation for obtaining (c), [8] which is: e = (rl) * ( 1- ((1- ((rlld)2))1/2) ) (4) If we consider that space is infinite, the space between the objects is negligible, so that the area (Al) of the object (01) that is affected by the other object (02) is the "shadow" that produces the objects vectors of the first object 21 �CELERINET JANUARY - JUNE 201 9 To have the val ue of (c), we can calculate the area of the spherical cap affected. Al = 2 *pi* (rl) * c (5) Al = 2 *pi* (r1)2 * (l-((I-((rl/d)2))1/2)) (6) The pressure in that area 1s equaJ to the pressure in the whole sphere. From equation (11) a differential force is obtained on the object (O l) of attraction of the object (02) to the object (01), at the same time it happens in the other object (02) shown in the Figure 3. Objects in space are attracted to each other, then the force attraction ofthe object will be the sum of them. We ' II call it resultant force. Fr = Fl + F2 A(sphere) = 4 *pi* (rl)2 (7) Pressure(sphere) =Deformation / A(sphere) (8) Therefore we can consider that the pressure in the area (Al) is equal to: Pressure(A 1)=(Deformation/2 )*( 1-(( 1((r 1/d)2)) l/2)) (9) From the previous formula we can see the part " (Deformation / 2)" indicates that only half of the deformation stored in the particles interacts with the other particle. Equivalence with mass. TEU defines the space-time deformation inside the particles as the stored deformation force that interacts with that of other particles, thus defining gravity. Current theories define the force caJled " mass" as the interaction with gravity between the particles. So TEU says that the mass is equivaJent to the deformation force stored in the particles. Mass = De-t( particle) (10) CalcuJation of the deformation force between particles. With the deformation pressure in the area (Al) of equation (9) we can define the strength ofthe area (Al) Fl = Pressure(Al) * (Al) 22 (11) ( 12) Effective force between particles. The resulting forces formulated previously do not consider the space-time deformation of the empty space between the particles, for which a correction must be made as a function of the space-time deformation constant. GravitationaJ constant. TEU understand the gravitational constant as a physical representation of the deformation of the empty space of the universe and its acceleration (Ac). [5] G=6.674E-1 1 (m3)/(kg*s2) G= (m/(s2)) * (m2/kg) G = Ac * ( r / Fr) ( 15) (13) ( 14) GravitationaJ acceleration. TEU derives from the Newtonian equation of gravity, its own equation. Based on the following conjectures. a) The gravitational constant physical representation of the defonnation of the empty space of the universe and its acceleration. b) The larger (massive) object compared to the other, does not move. c) To obtain the resultant force, the space between the objects is considered despised, whereby:. d) The maximum area of the minor object that influences the displacement deformation is haJf the area of minor object, (Ao2) /2 �ACADEMIC PAPER/ PHYSICS e) Due to the previously and to that the space between the objects is despised as if they were joined; it is considered that the effective distance is the radius of a hypothetical sphere with the same perimeter of the affected area. The effective radio will be ( ro2) / 2. Object: Mo = Mass ofthe Object = 523.60 kg ro= Radius of the Object = 0.5 m = 0.0005 km Height of the object on the ground of the earth s = l 00 m = O. 1 km Doing the calculations with the previous equations [(3) to (12)] we obtain a resultant force of: Fr = 9,177,403,644.99 kgf 0-1 Fig. 7. Diagram of effective radio between objects despised their separation in space. In figure 7 we observe that " s" is the projection of the effective area of the object 0-2 in the massive object 0-1 , as well as the perimeter of the effective area "p 1" of the object 0-2 is half of the perimeter of the object 0-2, whereby the effective area "p l" is equal to that of a hypothetical sphere with radius r / 2 (17) Remind that this resultant force does not consider the space-time deformation of the empty space between the particles, for which a correction must be made depending on the deformation constant of the universe. Therefore we will use the equation (13) that uses the gravitational constant to make the correction of the space-time deformation mentioned over in function of the acceleration. Doing the caJcuJations we get the following: From the above TEU gets its own equation for gravitational acceleration. g = ( G * Fr) / ( (r/2)2) (16) where: g= Gravitational acceleration (m/s2) G = Gravitational constant (m3)/( kg*s2) Fr = Resulting force between particles (kg) r = Radius of the object attracted (m) Examples: Case 1) Consider a spherical object at a distance over the ground of our planet Earth with the following characteristics: Earth: Mt = Mass of the Earth = 5.9736 E +24 kg rt = Radius of the Earth = 6,378.10 km g=(G*Fr) / ((r/2)2) ( 13) G = 6.674 E-11 (m3)/( kg * s2) (14) Fr = 9,177,403,644.99 kgf ( 17) r =ro= 0.5 ,n We obtain this result: g = 9.799998708 m / s2 ( l 8) The gravity that exists on the Earth's surface is of 9.8065 m / s2 , with which we obtain a variation of0.06629%.[6] Case 2) Analyzing the previous case, but with the variant of the elevation of the object on the ground of the earth at 412 kms which is the altitude of the orbit of the intemational space station, we obtain : 23 �CELERINET JANUARY - JUNE 2019 g(412km) = 8.647 m / s2 (19) The gravity that exists in the intemational space station is of 8.629 m / s2, with which we obtain a variation of 0.2086%.[7] RESULTS Developing similar anaJysis to the above examples in other celestial bodies in our solar system we obtain the following results. Table: Table 1: Accele ration of gravity according to TEU and its comparison with the cu rrent observations of the ce lestial bodies of the solar system. Celestial Bodies G G Variation (TEU) (Newton) (%) Sun Mercury Venus Earth Mars Jupi ter Saturn Uranus Neptune 274.04 3.7022 8.8724 9.80 3.711 24.79 10.45 8.87 11.1242 274.0 3.70 8.87 9.8065 3.711 24.78 10.44 8.69 11.15 0.01459 0.05945 0.02706 0.06629 0.00 0.04035 0.10536 2.0713 0.2314 Note: The values of mass, diameter and gravity we re obtained from Wi kipedia. [2] . The values are expressed rounded, but were calculated by software with 50 decimals. an additional asymmetric differential effect that alters the previous symmetric, this generates the movement of particles that we name gravity. REFERENCES [1] "Theory of Empty Universe" https:// www. re searchgate. net/ proj ect/Theory-ofEmpty-U niverse [2] Wikipedia https://es.wikipedia.org [3] NASA Wilkinson Microwave Anisotropy Probe https ://wmap.gsfc.nasa.gov/ universe/ uni_ expansion .html [4] Konya, J.; Nagy, N. M. (2012). Nuclear and Radiochemistry. Elsevier. pp. 74-75. ISBN 978-0-12-391487-3. [5] Physical Measurement Laboratory of Nl ST https://physics.nist.gov/cgi-bin/cuu/Value?bg [6] Taylor, Barry N. ; Thompson, Ambler, eds. (March 2008). The intemational system of units (SI) (pdt) (Report). National Institute of Standards and Technology. p. 52. NIST special publication 330, 2008 edition. CON CLUSIONS Experimentation [7] "Euro pean Users Guide to Low With the above discussion we can say that the Gravity Platforms". European Space Agency. 6 resuJts of gravity TEUs are very close to those December 2005. Archived from the original on obtained experimentally. Therefore it could be 2 April 2013 . Retrieved 22 March 2013. considered as correct TEU theory. [8] "Theory of Empty Universe - Gravity" Symmetry and Asym111etry https://www.academia.edu/34961060/Theory_ The space-time deformation of the particles of_ Empty_ Universe_ Gravity_ ?auto=download and their differential with respect to the empty space of the universe create a sy111metrical differential effect in ali directions which gives the spherical shape to the particles. This symmetrical differential effect is aJtered when two or more particles are found, creating 24 �1 Angel Colin, 2 Pedro Valdés-Sada, 'Enrique J. Pérez, 3 Carlos E. Chávez, 'Eduardo Pérez-Tijerina; UANL - FCFMº - FIMEº - UMº in San Nicolás de los Garza, Nuevo León, México. ABSTRACT: We present the optical properties in the visible spectrum for a gold plated printed circuit (antenna) fabricated on a glass substrate of 5x5 cm2. The circuit was designed for an exploratory study of antenna arrays of 2x2 elements, thus covering the surface area of one face of a standardized 1-Unit cubesat. The measurements were conducted at room temperature; the reflectance, absorbance and transmittance spectra were obtained as a function of wavelength in the range 250-2500 nm. Key Words: Printed circuit; Antenna; Optical absorption; Optical re.fl.ection; Optical transmission; Cubesat. RESUMEN: Presentamos las propiedades ópticas en el espectro visible para un circuito impreso (antena) chapeado en oro, fabricado en un substrato de vidrio de 5x5 cm2. El circuito fue diseñado para un estudio exploratorio de matrices de antenas de 2x2 elementos que cubren e1 área superficial de 1a cara de un cubesat estandarizado de 1-Unidad. Las medidas fueron hechas a temperatura ambiente; los espectros de reflectancia, absorbancia y transmitancia, fueron obtenidos como una función de la longitud de onda en el rango de 250-2500 nm. Palabras clave: Circuito impreso; Antena; Absorción óptica; Reflexión óptica; Transmisión óptica; Cubesat. Colin, A., et al. (2018). Emerging planetary astrophysics and related technologies research in Northeastern Mexico. Celerinet. 6 (2), 6-21. 25 �RESEARCH/ ASTROPHYSICS INTRODUCTION EXPERIMENTAL TECHNIQUE Nowadays, printed ciurcuits that include antennas play an important role in wide brand of applications such as astronomical detectors, satellites, the current and the next generation of wireless communications systems, and so forth [1 -3]. With the advent of the new cubesat's generation, this kind of circuits are very demanded, especially because they can be fabricated on the solar panels of small satellites withoutsacrificingsignificantitsperformance [4, 5]. A 1-U nit cubesat, is the minimal standardized satellite platform of 10 x 10 x 10 cm3 with a mass of 1.33 kg [6]. New investigations in this miniaturized satellites emerge every year with a variety of novel circuit designs to maximize its communication systems used for downlink data at different frequencies. Most of them use the ultra-high frequency (UHF) band dueto at this frequencies digital data can be well transmitted in a modulated form [7]. In the literature, it is very common to find electrical and radiation parameters of antenna circuits, but not their optical characteristics, nor the behaviour when multilayer of different materials are used in their electrical wires. In this paper we present the optical characterization of a gold plated printed circuit (antenna), fabricated on a glass substrate of 5x5 cm2 whose ground plane covered with chromium acts as light absorber. This circuit pretends to be a re-scaled model of the design previously reported in [8] in order to study the optical characteristics of the materials used in the multilayer zone. This exploratory study will be the first step towards designs for applications in the communication sub-system of the engineering model of the Refractor Telescope SATellite (RTSAT), which is currently under construction [9, 10]. Three thin film depositions were performed by means the DC sputtering method on a glass substrate of 5x5 cm2 and 2 mm thickness. The substrate was previously cleaned with acetone, immersed in an ultrasound machine for arow1d 4 minutes. To build the gold plated electrical circuit, we used high purity Au (99.99%) at 300 rnA and 4 14 V during a period of 30 s. The bilayer element in the circuit, was made using high purity niobium (Nb 99.99%) at 400 rnA and 350 V during 60 s. Each deposition was made over its corresponding slot printed circuit in a sticker mask, which was removed after each process. The ground plane in the opposite side of the substrate, was built by depositing high purity chrome (Cr 99.99%) at 400 mAand 350 V during 60 s. Toe whole printed circuit after its fabrication is depicted in Fig. 1. Here, ali dimensions are re-scaled around 2500 times from those of the proposed model in [8]. Fig. 1. Gold plated printed circuit fabricated on a glass substrate of SxS cm 2. RESULTS AND DISCUSSION Ali measurements were made at room temperature in the visible spectrwn, using a spectrophotometer UV-VIS (TMTHERMO SCIENTIFIC, Mod. EV600 PC). 26 �CELERINET JANUARY - JUNE 2019 For our purposes, in this experiment we investigated the effects ofNb on metallic layers such as Au. The optical transmittance and reflectance spectra, for the Nb thin film, were recorded in the wavelength range 250-2500 nm, as is depicted in Fig. 2. We observed that there is minimal transmission in the ultraviolet band, whereas it presents a soft increment of around 1% up to the infrared band, giving in consequence that only a small quantity of the ultraviolet light is reflected, as expected. The absorbance and transmittance spectra for the Cr thin film , are show in Fig. 3. We found that around 99% of ali incident light is absorbed homogenously. We observe that the values of transmittance for both Cr and Nb are quite similar. That may be due to the incident beam was directed in the center ofthe substrate, where part ofthe layer of Nb is directly deposited on the glass substrate, which in turn is practically transparent, hence the refracted beam now inside to the Cr film , therefore the transmittance spectra should be interpreted as the addition of those material s. 8:) ;'--- I !' :í) ;g~ fl 16 .E 3) ~ 1- I ! !' ~ 16 ,I .,, 40 '' / i' Transmittanc:e -·- -·- Reflectance 40 ;g- 3) 16 e.l 3) 3) 10 10 o 500 1000 1500 ~ i a: o 2500 A(nm) Fig. 2. Reflectance and transmittance as a function A of far the bilayer zone that includes Au and Nb. 14 14 ----- Absorbance - 12 10 ~ i ~ Transmittance 12 10 ;g~ 8 8 e.l ai E 6 6 ' ' •' '' • •• E ~ ro ~ 4 On the other hand, the high values of 4 reflectance for the zone covered with Nb may 2 be due to the !ayer of Au which was previously ---·----·--------------------deposited for the electrical lines of the circuít. o...,___,__~ ~'-~-'-~ --'-~__,Jo 1000 1500 2000 2500 lt should be taken into account that the A(nm) device presented in this paper was made for Fig. 3. Absorbance and Transmittance as a function A an exploratory study only in order to know the of for the ground plane made of Cr. optical properties in the bilayer zone adding Future experiments will consist in fabricate a third metal !ayer in the opposite side of the and characterize ali the electrical and radiation substrate. parameters of an aptimal antenna array of The radiation parameters ofthe antenna were 2x2 elements connected in parallel, since not considered here; they wili be considered in this combination will provide an antennaa next experiment with a multilayer zone in a module for one face of 1-U Cubesat but with silicon substrate of around 500 µm thickness, 1nuch higher directivity and a de resistance which will include a thin !ayer of SiO2 as approximately the same as for a single antenna. Our preliminary design is shown in Fig. 4. electrical insulating between the Nb and Au. 27 �RESEARCH/ ASTROPHYSICS REFEREN CES [ 1] A. Colín, D. Ortiz, E. Villa, E. Arta!, and E. Martínez-González. An array of lens-coupled antennas for cosmic microwave background measurements in the 30 GHz band. Experünental Astronomy (2012); 33: 27-37 .. Fig. 2. Schematic arrangement (not to scale) of four antennas connected in parallel. Dashed lines limitan area of [2] A. Krauss, H. Bayer, R. Stephan, M.A. Hein. A low-profile user terminal antenna for movile bi-directional Ka-band satellite comrnunications. ESA's ARTES 2012; Available from: https://artes.esa. int/sites/defauJt/files/06_ 1450_ krauss. pdf. [3] K. R. Jha and G. Singh. Terahertz planar antennas for future wireless communication: A technical review. Infrared Physics and TechnoThe novel low-profile printed circuits that logy (2013); 60: 71-80. include antennas, are very promising devices to improve communication systems in small [4] X. Liu, D. R. Jackson, J. Chen, et al. Transsatellites; since the use of this kind of circuits parent and nontransparent microstrip antennas fabricated on the surface of the solar pane Is may on a cubesat. IEEE Antennas & Propagation reduce the weight and cost in the miniaturized Magazine 2017; 59-68. spaces of the small satellites. The study of optical properties of such [5] R. Montaña, N. Neveu, S. Palacio, et al. Decircuits allows confinn that the efficiency of the velopment of low-profile antennas for cubesats. solar cell may not be considerable affected, if 28th Annual AIAA/USU Conference on small printed circuits that cover a small area compared satellites 2014, SSC14-IX-7, 6 pages. with the effective area of the solar panels, are fabricated on them. [6] M. D. D. Staff. Small Spacecraft Techno10x10 cm2. ACKNOWLEDGEMENTS e authors acknowledge to funding from Agencia Espacial Mexicana, through grant number: AEM-2014-01-248438, and to Dr. Manuel García Méndez for his assistance during the experitnental runs in the facilities of his laboratory.obsesionporelcielo.net/) and Facebook (https://www.facebook.com/ obsesionporelcielo/) page to better serve the needs of its audience. logy State Art. National and Space Administration California (2014), Technical Report TP2014-216648. [7] J. Bouwmeester and J. Guo. Survey of worldwide pico-and nanosatellite missions, distributions and subsystem technology. Acta Astronautica 2010; 67: 854-862. [8] Colin A., Pérez-Tijerina E. and Salís-Pomar F. Design and simulation of an antenna coupled microbolometer at 30THz. Intemational Joumal of Antennas and Propagation 28 �CELERINET JANUARY - JUNE 2019 (2017); Vol. 2017: 6 pages. [9] Colin, A. , P. Valdés-Sada, L . Olguín, et al. Implementation ofan 80 mm refractor telescope in a 2U-cubesat. 67th International Astronautical Congress 2016; lAC-1 6, B4,2,3x33235: 6 pages.Vol. 2017: 6 pages. 29 � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Celerinet Description An account of the resource La revista Celerinet, inició en el 2012, sólo en formato digital, es semestral y se mantiene activa; ofrece información de las últimas investigaciones realizadas por docentes, estudiantes y egresados de la Facultad de Ciencias Físico Matemáticas, también se encarga de difundir las actividades institucionales más relevantes. La publicación incluye artículos de  investigación relacionados con las siguientes áreas: matemáticas, matemáticas aplicadas, física, ciencias computacionales, actuaría, multimedia y animación digital, y seguridad en tecnologías de información. Text A resource consisting primarily of words for reading. Examples include books, letters, dissertations, poems, newspapers, articles, archives of mailing lists. Note that facsimiles or images of texts are still of the genre Text. Título Uniforme Celerinet Año de publicación El año cuando se publico 2019 Año Año de la revista (Año 1, Año 2) No es es año de publicación. 7 Número Número de la revista 1 Mes de publicación Mes cuando se publicó Enero-Junio Día Día del mes de la publicación 1 Periodicidad La periodicidad de la publicación (diaria, semanal, mensual, anual) Semestral Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. 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Access Rights may include information regarding access or restrictions based on privacy, security, or other policies. Universidad Autónoma de Nuevo León Rights Holder A person or organization owning or managing rights over the resource. El diseño y los contenidos de La hemeroteca Digital UANL están protegidos por la Ley de derechos de autor, Cap. III. De dominio público. Art. 152. Las obras del dominio público pueden ser libremente utilizadas por cualquier persona, con la sola restricción de respetar los derechos morales de los respectivos autores. Gravity Optical Fiber Lasers Printed circuit Quadrotors