Análise das vibrações no processo de fresamento de topo esférico de superfícies planas inclinadas de aço ferramenta endurecido AISI D6

Detalhes bibliográficos
Ano de defesa: 2026
Autor(a) principal: Silva, Fábio Fernandes da
Orientador(a): Não Informado pela instituição
Banca de defesa: Não Informado pela instituição
Tipo de documento: Tese
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Universidade Tecnológica Federal do Paraná
Curitiba
Brasil
Programa de Pós-Graduação em Engenharia Mecânica e de Materiais
UTFPR
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Link de acesso: http://repositorio.utfpr.edu.br/jspui/handle/1/40603
Resumo: Ball-end milling is widely employed in the finishing of molds and dies, a process characterized by intermittent cutting and by the complex dynamics between the hemispherical tool geometry and the machined surface. Tools with high length-to-diameter ratios, often required for deep cavities, intensify vibratory phenomena that compromise surface integrity and tool life. Although several studies have investigated the effect of cutting path orientation on surface quality, few have simultaneously integrated vibration measurements, cutting forces, and topography in ball-end milling. Addressing this gap, the present work investigated the influence of cutting path orientations (OTCs) and tooth passing frequency on the surface quality of inclined flat surfaces of hardened AISI D6 steel (55-56 HRC), machined with a 10 mm diameter TiSiN-coated solid carbide (WC-10 % Co) ball-end mill and 110 mm overhang (L/D = 11). The dynamic behavior of the tool-holder system was characterized through Frequency Response Function, identifying the dominant mode at 663.8 Hz. In the first stage, eight OTCs were applied at three surface inclination angles (15°, 45°, and 75°) at 3840 rpm, with three repetitions per condition, totaling 72 tests. In the second stage, spindle speed was varied from 1225 to 10,000 rpm across 40 levels, to map the influence of tooth passing frequency on dynamic response and surface finish. In the third stage, the OTCs were reassessed under a more stable condition (7075 rpm). The instrumentation simultaneously integrated inductive displacement sensors, a piezoelectric dynamometer, and an open-field microphone. 3D surface roughness was characterized by optical interferometric profilometry, with Sa and Sz parameters analyzed with and without a roughness filter. Signals were analyzed in the time domain, through frequency spectra via Fast Fourier Transform, and using the Symmetric Dot Pattern (SDP) technique as a complementary tool for instability identification. The results revealed a strong dependence of surface topography on the proximity between tooth passing frequency and the system’s natural modes, confirming the predominance of forced vibrations. The excitation of non-harmonic components proved to be the most relevant indicator of process instability, with a direct impact on surface integrity. RMS displacement values showed no direct relationship with roughness, while spectral content proved decisive for topographic quality. At the 15° inclination, the HDC orientation (horizontal downward concordant) yielded the best surface finish, demonstrating that the down milling cutting mechanism was the determining factor under this condition. At 45°, the horizontal downward orientations (HDC and HDD) achieved the lowest roughness values, whereas at 75° this trend reversed, with horizontal upward orientations (HAC and HAD) delivering the best performance. Among vertical orientations, VDD consistently produced the best finish at 45° and 75°. Under the higher stability condition (7075 rpm), a marked roughness reduction was observed for most OTCs, with the most pronounced effect at 75°, where horizontal upward orientations achieved equivalent finishes regardless of down milling or discordant cutting. Inverse OTC pairs with similar dynamic responses were identified at 45° and 75°, enabling a conceptual reclassification based on tilt (tool inclination perpendicular to the feed direction) and lead (inclination along the feed direction) angles that extends the geometric interpretation of three-axis milling strategies to the multi-axis machining context.
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spelling Análise das vibrações no processo de fresamento de topo esférico de superfícies planas inclinadas de aço ferramenta endurecido AISI D6Vibration analysis in the ball-end milling process of inclined flat surfaces of hardened AISI D6 tool steelFresagem (Trabalhos em metal)VibraçãoAspereza de superfícieFerramentas para cortar metaisAço para ferramentasProcessamento de sinais - Técnicas digitaisUsinagem em alta velocidadeMilling (Metal-work)VibrationSurface roughnessMetal-cutting toolsTool-steelSignal processing - Digital techniquesHigh-speed machiningCNPQ::ENGENHARIAS::ENGENHARIA MECANICA::PROCESSOS DE FABRICACAOEngenharia MecânicaBall-end milling is widely employed in the finishing of molds and dies, a process characterized by intermittent cutting and by the complex dynamics between the hemispherical tool geometry and the machined surface. Tools with high length-to-diameter ratios, often required for deep cavities, intensify vibratory phenomena that compromise surface integrity and tool life. Although several studies have investigated the effect of cutting path orientation on surface quality, few have simultaneously integrated vibration measurements, cutting forces, and topography in ball-end milling. Addressing this gap, the present work investigated the influence of cutting path orientations (OTCs) and tooth passing frequency on the surface quality of inclined flat surfaces of hardened AISI D6 steel (55-56 HRC), machined with a 10 mm diameter TiSiN-coated solid carbide (WC-10 % Co) ball-end mill and 110 mm overhang (L/D = 11). The dynamic behavior of the tool-holder system was characterized through Frequency Response Function, identifying the dominant mode at 663.8 Hz. In the first stage, eight OTCs were applied at three surface inclination angles (15°, 45°, and 75°) at 3840 rpm, with three repetitions per condition, totaling 72 tests. In the second stage, spindle speed was varied from 1225 to 10,000 rpm across 40 levels, to map the influence of tooth passing frequency on dynamic response and surface finish. In the third stage, the OTCs were reassessed under a more stable condition (7075 rpm). The instrumentation simultaneously integrated inductive displacement sensors, a piezoelectric dynamometer, and an open-field microphone. 3D surface roughness was characterized by optical interferometric profilometry, with Sa and Sz parameters analyzed with and without a roughness filter. Signals were analyzed in the time domain, through frequency spectra via Fast Fourier Transform, and using the Symmetric Dot Pattern (SDP) technique as a complementary tool for instability identification. The results revealed a strong dependence of surface topography on the proximity between tooth passing frequency and the system’s natural modes, confirming the predominance of forced vibrations. The excitation of non-harmonic components proved to be the most relevant indicator of process instability, with a direct impact on surface integrity. RMS displacement values showed no direct relationship with roughness, while spectral content proved decisive for topographic quality. At the 15° inclination, the HDC orientation (horizontal downward concordant) yielded the best surface finish, demonstrating that the down milling cutting mechanism was the determining factor under this condition. At 45°, the horizontal downward orientations (HDC and HDD) achieved the lowest roughness values, whereas at 75° this trend reversed, with horizontal upward orientations (HAC and HAD) delivering the best performance. Among vertical orientations, VDD consistently produced the best finish at 45° and 75°. Under the higher stability condition (7075 rpm), a marked roughness reduction was observed for most OTCs, with the most pronounced effect at 75°, where horizontal upward orientations achieved equivalent finishes regardless of down milling or discordant cutting. Inverse OTC pairs with similar dynamic responses were identified at 45° and 75°, enabling a conceptual reclassification based on tilt (tool inclination perpendicular to the feed direction) and lead (inclination along the feed direction) angles that extends the geometric interpretation of three-axis milling strategies to the multi-axis machining context.O fresamento de acabamento com fresa de topo esférico é amplamente empregado na fabricação de moldes e matrizes, processo caracterizado pelo corte intermitente e pela dinâmica complexa entre a geometria semiesférica da ferramenta e a superfície usinada. Ferramentas com elevada relação comprimento/diâmetro, frequentemente exigidas por cavidades profundas, intensificam fenômenos vibratórios que comprometem a integridade superficial e a vida útil do elemento cortante. Embora diversos estudos tenham investigado o efeito da orientação da trajetória de corte na qualidade superficial, poucos integraram simultaneamente medições de vibração, forças de corte e topografia no fresamento com fresa de topo esférico. Diante dessa lacuna, o presente trabalho investigou a influência de orientações de trajetória de corte (OTCs) e da frequência de passagem dos dentes na qualidade superficial de planos inclinados de aço AISI D6 temperado (55-56 HRC), fresados com fresa de topo esférico de metal duro microgrão (WC- 10% Co) revestida com TiSiN, de 10 mm de diâmetro e balanço de 110 mm (L/D = 11). O comportamento dinâmico do sistema foi caracterizado por Função de Resposta em Frequência, identificando-se o modo dominante em 663,8 Hz. Na primeira etapa, oito OTCs foram aplicadas em três inclinações de superfície (15°, 45° e 75°) a 3840 rpm, com três repetições por condição, totalizando 72 ensaios. Na segunda etapa, variou-se a rotação de 1225 a 10000 rpm em 40 níveis, para mapear a influência da frequência de passagem dos dentes na resposta dinâmica e no acabamento. Na terceira etapa, as OTCs foram reavaliadas em condição de maior estabilidade (7075 rpm). A instrumentação integrou simultaneamente sensores indutivos de deslocamento, dinamômetro piezoelétrico e microfone de campo aberto. A rugosidade 3D foi caracterizada por perfilometria óptica interferométrica, com análise dos parâmetros Sa e Sz com e sem filtro de rugosidade. Os sinais foram analisados no domínio do tempo, por espectros de frequência via Transformada Rápida de Fourier e pela técnica de dispersão pontual simétrica (SDP), como ferramenta complementar para identificação de instabilidade. Os resultados evidenciaram forte dependência da topografia em relação à proximidade entre a frequência de passagem dos dentes e os modos naturais do sistema, confirmando o predomínio de vibrações forçadas. A excitação de componentes não harmônicas mostrou-se o indicador mais relevante de instabilidade, com reflexo direto na integridade superficial. Os valores de deslocamento RMS não apresentaram relação direta com a rugosidade, enquanto o conteúdo espectral mostrou-se determinante para a qualidade topográfica. Na inclinação de 15°, a OTC HDC (horizontal descendente concordante) apresentou o melhor acabamento, evidenciando que o mecanismo de remoção concordante foi o fator determinante nessa condição. A 45°, as OTCs horizontais descendentes (HDC e HDD) obtiveram os menores valores de rugosidade, enquanto a 75° observou-se inversão, com as horizontais ascendentes (HAC e HAD) assumindo o melhor desempenho. Entre as verticais, a VDD consolidou-se como melhor condição a 45° e 75°. Na condição de maior estabilidade (7075 rpm), verificou-se redução expressiva da rugosidade para a maioria das OTCs, sendo o efeito mais pronunciado a 75°, onde as horizontais ascendentes alcançaram acabamentos equivalentes entre concordante e discordante. Identificaram-se pares de OTCs inversas com respostas dinâmicas semelhantes a 45° e 75°, o que permitiu propor reclassificação conceitual com base nos ângulos de tilt (inclinação da ferramenta perpendicular ao avanço) e lead(inclinação na direção do avanço), ampliando a interpretação geométrica das estratégias de fresamento em três eixos para o contexto multieixos.Universidade Tecnológica Federal do ParanáCuritibaBrasilPrograma de Pós-Graduação em Engenharia Mecânica e de MateriaisUTFPRPolli, Milton Luizhttps://orcid.org/0000-0003-2936-6738https://lattes.cnpq.br/3005966147961108Machado, Álisson Rochahttps://orcid.org/0000-0002-5388-2954https://lattes.cnpq.br/0203667980247686Costa, Dalberto Dias dahttps://orcid.org/0000-0002-5665-579Xhttps://lattes.cnpq.br/4341776945732864Gomes, Marcio Henrique de Avelarhttps://orcid.org/0000-0001-7279-9307https://lattes.cnpq.br/6090334823327910Polli, Milton Luizhttps://orcid.org/0000-0003-2936-6738https://lattes.cnpq.br/3005966147961108Volpato, Nerihttps://orcid.org/0000-0003-1523-3977https://lattes.cnpq.br/8414652619232683Silva, Fábio Fernandes da2026-06-19T20:01:17Z2026-06-19T20:01:17Z2026-03-20info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisapplication/pdfSILVA, Fabio Fernandes da. Análise das vibrações no processo de fresamento de topo esférico de superfícies planas inclinadas de aço ferramenta endurecido AISI D6. 2026. Tese (Doutorado em Engenharia Mecânica e de Materiais) - Universidade Tecnológica Federal do Paraná, Curitiba, 2026.http://repositorio.utfpr.edu.br/jspui/handle/1/40603porhttp://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccessreponame:Repositório Institucional da UTFPR (da Universidade Tecnológica Federal do Paraná (RIUT))instname:Universidade Tecnológica Federal do Paraná (UTFPR)instacron:UTFPR2026-06-20T06:10:52Zoai:repositorio.utfpr.edu.br:1/40603Repositório InstitucionalPUBhttp://repositorio.utfpr.edu.br:8080/oai/requestriut@utfpr.edu.br || sibi@utfpr.edu.bropendoar:2026-06-20T06:10:52Repositório Institucional da UTFPR (da Universidade Tecnológica Federal do Paraná (RIUT)) - Universidade Tecnológica Federal do Paraná (UTFPR)false
dc.title.none.fl_str_mv Análise das vibrações no processo de fresamento de topo esférico de superfícies planas inclinadas de aço ferramenta endurecido AISI D6
Vibration analysis in the ball-end milling process of inclined flat surfaces of hardened AISI D6 tool steel
title Análise das vibrações no processo de fresamento de topo esférico de superfícies planas inclinadas de aço ferramenta endurecido AISI D6
spellingShingle Análise das vibrações no processo de fresamento de topo esférico de superfícies planas inclinadas de aço ferramenta endurecido AISI D6
Silva, Fábio Fernandes da
Fresagem (Trabalhos em metal)
Vibração
Aspereza de superfície
Ferramentas para cortar metais
Aço para ferramentas
Processamento de sinais - Técnicas digitais
Usinagem em alta velocidade
Milling (Metal-work)
Vibration
Surface roughness
Metal-cutting tools
Tool-steel
Signal processing - Digital techniques
High-speed machining
CNPQ::ENGENHARIAS::ENGENHARIA MECANICA::PROCESSOS DE FABRICACAO
Engenharia Mecânica
title_short Análise das vibrações no processo de fresamento de topo esférico de superfícies planas inclinadas de aço ferramenta endurecido AISI D6
title_full Análise das vibrações no processo de fresamento de topo esférico de superfícies planas inclinadas de aço ferramenta endurecido AISI D6
title_fullStr Análise das vibrações no processo de fresamento de topo esférico de superfícies planas inclinadas de aço ferramenta endurecido AISI D6
title_full_unstemmed Análise das vibrações no processo de fresamento de topo esférico de superfícies planas inclinadas de aço ferramenta endurecido AISI D6
title_sort Análise das vibrações no processo de fresamento de topo esférico de superfícies planas inclinadas de aço ferramenta endurecido AISI D6
author Silva, Fábio Fernandes da
author_facet Silva, Fábio Fernandes da
author_role author
dc.contributor.none.fl_str_mv Polli, Milton Luiz
https://orcid.org/0000-0003-2936-6738
https://lattes.cnpq.br/3005966147961108
Machado, Álisson Rocha
https://orcid.org/0000-0002-5388-2954
https://lattes.cnpq.br/0203667980247686
Costa, Dalberto Dias da
https://orcid.org/0000-0002-5665-579X
https://lattes.cnpq.br/4341776945732864
Gomes, Marcio Henrique de Avelar
https://orcid.org/0000-0001-7279-9307
https://lattes.cnpq.br/6090334823327910
Polli, Milton Luiz
https://orcid.org/0000-0003-2936-6738
https://lattes.cnpq.br/3005966147961108
Volpato, Neri
https://orcid.org/0000-0003-1523-3977
https://lattes.cnpq.br/8414652619232683
dc.contributor.author.fl_str_mv Silva, Fábio Fernandes da
dc.subject.por.fl_str_mv Fresagem (Trabalhos em metal)
Vibração
Aspereza de superfície
Ferramentas para cortar metais
Aço para ferramentas
Processamento de sinais - Técnicas digitais
Usinagem em alta velocidade
Milling (Metal-work)
Vibration
Surface roughness
Metal-cutting tools
Tool-steel
Signal processing - Digital techniques
High-speed machining
CNPQ::ENGENHARIAS::ENGENHARIA MECANICA::PROCESSOS DE FABRICACAO
Engenharia Mecânica
topic Fresagem (Trabalhos em metal)
Vibração
Aspereza de superfície
Ferramentas para cortar metais
Aço para ferramentas
Processamento de sinais - Técnicas digitais
Usinagem em alta velocidade
Milling (Metal-work)
Vibration
Surface roughness
Metal-cutting tools
Tool-steel
Signal processing - Digital techniques
High-speed machining
CNPQ::ENGENHARIAS::ENGENHARIA MECANICA::PROCESSOS DE FABRICACAO
Engenharia Mecânica
description Ball-end milling is widely employed in the finishing of molds and dies, a process characterized by intermittent cutting and by the complex dynamics between the hemispherical tool geometry and the machined surface. Tools with high length-to-diameter ratios, often required for deep cavities, intensify vibratory phenomena that compromise surface integrity and tool life. Although several studies have investigated the effect of cutting path orientation on surface quality, few have simultaneously integrated vibration measurements, cutting forces, and topography in ball-end milling. Addressing this gap, the present work investigated the influence of cutting path orientations (OTCs) and tooth passing frequency on the surface quality of inclined flat surfaces of hardened AISI D6 steel (55-56 HRC), machined with a 10 mm diameter TiSiN-coated solid carbide (WC-10 % Co) ball-end mill and 110 mm overhang (L/D = 11). The dynamic behavior of the tool-holder system was characterized through Frequency Response Function, identifying the dominant mode at 663.8 Hz. In the first stage, eight OTCs were applied at three surface inclination angles (15°, 45°, and 75°) at 3840 rpm, with three repetitions per condition, totaling 72 tests. In the second stage, spindle speed was varied from 1225 to 10,000 rpm across 40 levels, to map the influence of tooth passing frequency on dynamic response and surface finish. In the third stage, the OTCs were reassessed under a more stable condition (7075 rpm). The instrumentation simultaneously integrated inductive displacement sensors, a piezoelectric dynamometer, and an open-field microphone. 3D surface roughness was characterized by optical interferometric profilometry, with Sa and Sz parameters analyzed with and without a roughness filter. Signals were analyzed in the time domain, through frequency spectra via Fast Fourier Transform, and using the Symmetric Dot Pattern (SDP) technique as a complementary tool for instability identification. The results revealed a strong dependence of surface topography on the proximity between tooth passing frequency and the system’s natural modes, confirming the predominance of forced vibrations. The excitation of non-harmonic components proved to be the most relevant indicator of process instability, with a direct impact on surface integrity. RMS displacement values showed no direct relationship with roughness, while spectral content proved decisive for topographic quality. At the 15° inclination, the HDC orientation (horizontal downward concordant) yielded the best surface finish, demonstrating that the down milling cutting mechanism was the determining factor under this condition. At 45°, the horizontal downward orientations (HDC and HDD) achieved the lowest roughness values, whereas at 75° this trend reversed, with horizontal upward orientations (HAC and HAD) delivering the best performance. Among vertical orientations, VDD consistently produced the best finish at 45° and 75°. Under the higher stability condition (7075 rpm), a marked roughness reduction was observed for most OTCs, with the most pronounced effect at 75°, where horizontal upward orientations achieved equivalent finishes regardless of down milling or discordant cutting. Inverse OTC pairs with similar dynamic responses were identified at 45° and 75°, enabling a conceptual reclassification based on tilt (tool inclination perpendicular to the feed direction) and lead (inclination along the feed direction) angles that extends the geometric interpretation of three-axis milling strategies to the multi-axis machining context.
publishDate 2026
dc.date.none.fl_str_mv 2026-06-19T20:01:17Z
2026-06-19T20:01:17Z
2026-03-20
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/doctoralThesis
format doctoralThesis
status_str publishedVersion
dc.identifier.uri.fl_str_mv SILVA, Fabio Fernandes da. Análise das vibrações no processo de fresamento de topo esférico de superfícies planas inclinadas de aço ferramenta endurecido AISI D6. 2026. Tese (Doutorado em Engenharia Mecânica e de Materiais) - Universidade Tecnológica Federal do Paraná, Curitiba, 2026.
http://repositorio.utfpr.edu.br/jspui/handle/1/40603
identifier_str_mv SILVA, Fabio Fernandes da. Análise das vibrações no processo de fresamento de topo esférico de superfícies planas inclinadas de aço ferramenta endurecido AISI D6. 2026. Tese (Doutorado em Engenharia Mecânica e de Materiais) - Universidade Tecnológica Federal do Paraná, Curitiba, 2026.
url http://repositorio.utfpr.edu.br/jspui/handle/1/40603
dc.language.iso.fl_str_mv por
language por
dc.rights.driver.fl_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidade Tecnológica Federal do Paraná
Curitiba
Brasil
Programa de Pós-Graduação em Engenharia Mecânica e de Materiais
UTFPR
publisher.none.fl_str_mv Universidade Tecnológica Federal do Paraná
Curitiba
Brasil
Programa de Pós-Graduação em Engenharia Mecânica e de Materiais
UTFPR
dc.source.none.fl_str_mv reponame:Repositório Institucional da UTFPR (da Universidade Tecnológica Federal do Paraná (RIUT))
instname:Universidade Tecnológica Federal do Paraná (UTFPR)
instacron:UTFPR
instname_str Universidade Tecnológica Federal do Paraná (UTFPR)
instacron_str UTFPR
institution UTFPR
reponame_str Repositório Institucional da UTFPR (da Universidade Tecnológica Federal do Paraná (RIUT))
collection Repositório Institucional da UTFPR (da Universidade Tecnológica Federal do Paraná (RIUT))
repository.name.fl_str_mv Repositório Institucional da UTFPR (da Universidade Tecnológica Federal do Paraná (RIUT)) - Universidade Tecnológica Federal do Paraná (UTFPR)
repository.mail.fl_str_mv riut@utfpr.edu.br || sibi@utfpr.edu.br
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