[en] The present project belongs to the grinding field and its main objective is the development of an efficient industrial methodology, which allows to calculate, in a fast and simple way, the modulus of elasticity "E" of grinding wheels from their dynamic behavior. In order to fulfill the main objective, first of all, an extensive bibliographic analysis has been carried out, where several methods developed over the years for the calculation of the modulus of elasticity of grinding wheels have been found. However, very few of them have been of great interest from an industrial point of view. Currently, the most widely used methods in the industry and the ones that are the object of study of the present project are the dynamic tests or "Sonic-Tests", where the elastic properties of grinding wheels are related to their dynamic behavior, defined by their fundamental frequency of vibration, which can be calculated by means of experimental modal analysis. These "Sonic-Tests" provide a series of formulas for the calculation of the modulus of elasticity of grinding wheels. However, these formulas involve a parameter called shape factor, the value of which is unknown. In order to solve this problem, another bibliographic analysis has been carried out where two methods for calculating the modulus of elasticity of homogeneous, elastic and isotropic materials from their dynamic behavior have been found, which are, on the one hand, a procedure developed by Gustáv Martincek [18] and, on the other hand, the ASTM standards [17]. However, these methods calculate the modulus of elasticity from the first two natural frequencies, unlike the "Sonic-Tests", which calculate the modulus of elasticity from the fundamental frequency of vibration, which makes them a very good tool from an industrial point of view. In order to develop a methodology that is a good alternative to the Sonic Tests from the industrial point of view for the calculation of the modulus of elasticity of grinding wheels by means of experimental modal analysis, that is to say, that allows the calculation of the modulus of elasticity through a single natural frequency, in the present project a theoretical and experimental study is carried out to relate the form factor of the "Sonic Test" with the characteristic parameters of the grinding wheels. To this end, firstly, the mathematical expression that defines the shape factors as a function of the geometry and the first two natural frequencies of the grinding wheel is calculated for each of the above-mentioned methods of calculating the modulus of elasticity. Secondly, a battery of experimental modal analyses is performed on a series of pre-selected wheels to calculate their first two natural frequencies. Finally, from the results obtained in the experimental modal analysis, both the form factors and the modulus of elasticity of the grinding wheels obtained by the three methods mentioned above will be calculated, in order to obtain representative conclusions about the calculation and variability of the modulus of elasticity of the grinding wheels with their characteristic parameters.

[eu] Proiektu hau artezketaren arlokoa da, eta industria-metodologia eraginkor bat garatzea du helburu nagusi, haren portaera dinamikoan oinarrituta, artezteko gurpilen elastikotasun "E" modulua azkar eta erraz kalkulatu ahal izateko. Helburu nagusia betetzeko, lehenik eta behin, azterketa bibliografiko luze bat egin da. Azterketa horretan, urteetan zehar garatu diren hainbat metodo aurkitu dira, artezteko gurpilen elastikotasunaren modulua kalkulatzeko. Hala ere, oso gutxi izan dira industriaren ikuspegitik interes handikoak. Gaur egun, industrian gehien erabiltzen diren metodoak eta proiektu honetan aztertzen direnak test dinamikoak edo "Sonic-Test"-ak dira, non harri urratzaileen propietate elastikoak beren portaera dinamikoarekin erlazionatzen diren, bibrazioaren funtsezko maiztasunaren arabera zehaztua, analisi modal esperimentalaren bidez kalkula daitekeena. "Sonic-Test" horiek zenbait formula ematen dituzte artezteko gurpilen elastikotasunaren modulua kalkulatzeko. Hala ere, formula horietan forma-faktore izeneko parametro batek esku hartzen du, eta horren balioa ez da ezaguna. Arazo hori konpontzeko, beste azterketa bibliografiko bat egin da. Bertan, material homogeneoen, elastikoen eta isotropoen elastikotasun-moduluak kalkulatzeko bi metodo aurkitu dira, haien portaera dinamikotik abiatuta. Metodo horiek, alde batetik, Gustáv Martincekek garatutako prozedura [18] eta, bestetik, ASTM arauak dira [17]. Hala ere, metodo horiek elastikotasun-moduluak kalkulatzen dituzte lehen bi frekuentzia naturaletatik abiatuta, "Sonic-Test" moduluak ez bezala, horiek elastikotasun-modulua bibrazioaren funtsezko frekuentziatik abiatuta kalkulatzen baitute, eta horrek oso tresna ona bihurtzen ditu industriaren ikuspegitik. Industriaren ikuspegitik Sonic Tests delakoen aurrean alternatiba ona izango den metodologia bat garatzeko, artezteko gurpilen elastikotasun-modulua kalkulatzeko analisi modal esperimentalaren bidez, hau da, elastikotasun-modulua maiztasun natural bakar baten bidez kalkulatu ahal izateko, proiektu honetan azterketa teoriko eta esperimental bat egiten da "Sonic Test" delakoen forma-faktorea artezteko gurpilen parametro bereizgarriekin lotzeko. Horretarako, lehenik eta behin, forma-faktoreak definitzen dituen adierazpen matematikoa kalkulatzen da, artezteko gurpilen geometriaren eta lehen bi frekuentzia naturalen arabera, elastikotasun-modulua kalkulatzeko aipatutako metodo bakoitzerako. Bigarrenik, aurrez hautatutako harri-sorta bati moduzko analisi esperimentalak egiten zaizkio, lehen bi maiztasun naturalak kalkulatzeko. Azkenik, analisi modal esperimentalean lortutako emaitzetatik abiatuta, aipatutako hiru metodoen bidez lortutako forma-faktoreak eta artezteko gurpilen elastikotasun-moduluak kalkulatuko dira, artezteko gurpilen elastikotasun-moduluaren kalkuluari eta aldakortasunari buruzko ondorio adierazgarriak lortzeko, parametro bereizgarriekin.