Analise de Fadiga em Mola de Lamina Calculos e Seguranca

FADIGA Prof Me Guilherme Bueno Aquino de Oliveira Agenda Revisão Exemplo 611 Uma mola de lâmina é usada para reter um seguidor oscilante em contato com um came da placa A amplitude de movimento do seguidor é de 2 pol e fixa de modo que o componente alternado de força momento de flexão e tensão também são fixos A mola é précarregada para ajustar a várias velocidades do came A précarga deve ser aumentada para evitar flutuação ou salto do seguidor Para velocidades mais baixas a précarga deve ser diminuída para obter maior vida útil do came e superfícies seguidoras A mola é um cantilever de aço com 32 pol de comprimento 2 pol de largura e 14 pol de espessura como visto na Fig 630a As propriedades da mola são Sut 150 kpsi Sy 127 kpsi e Sn 28 kpsi totalmente corrigidas O movimento total do came é de 2 pol O projetista deseja précarregar a mola defletindoa 2 pol para baixa velocidade e 5 pol para alta velocidade a Trace as linhas de falha de GerberLanger com a linha de carga b Quais são os fatores de segurança correspondentes a 2 pol e 5 pol de précarga Exemplo 611 Table A9 Shear Moment and Deflection of Beams Note Force and moment reactions are positive in the directions shown equations for shear force V and bending moment M follow the sign conventions given in Sec 32 1 Cantilever end load R1 V F M1 Fl M Fx l y F x² 6 EIx 3l ymax Fl³ 3 EI The stress components are thus σa K2δ Kδ 2 K 1099 kpsi σm K2δ Kδ 2 K1δ 10991δ For δ 0 σa σm 1099 11 kpsi Fatigue factor of safety nf 12 Sutσm2 σaSe 1 1 2σmSeSutσa2 σm 0 We begin with preliminaries The second area moment of the cantilever cross section is I bh312 2025312 000260 in4 Since from Table A9 beam 1 force F and deflection y in a cantilever are related by F 3EI yl3 then stress σ and deflection y are related by σ McI 32FcI 323EI ycl3 I 96Ecyl3 Ky where K 96Ecl3 9630106 0125323 1099 103 psiin 1099 kpsiin Now the minimums and maximums of y and σ can be defined by ymin δ σmin Kδ ymax 2 δ σmax K2 δ For δ 2 in σa 11 kpsi σm 109912 33 kpsi For δ 5 in σa 11 kpsi σm 109915 659 kpsi a A plot of the Gerber and Langer criteria is shown in Fig 630b The three preload deflections of 0 2 and 5 in are shown as points A A and A Note that since σa is constant at 11 kpsi the load line is horizontal and does not contain the origin The intersection between the Gerber line and the load line is found from solving Eq 642 for Sm and substituting 11 kpsi for Sa Sm Sut 1 SaSe 150 1 1128 1169 kpsi The intersection of the Langer line and the load line is found from solving Eq 644 for Sm and substituting 11 kpsi for Sa Sm Sy Sa 127 11 116 kpsi The threats from fatigue and firstcycle yielding are approximately equal b For δ 2 in nf Smσm 116933 354 ny 11633 352 and for δ 5 in nf 1169659 177 ny 116659 176 The stress components are thus σa K2δ Kδ2 K 1099 kpsi σm K2δ Kδ2 K1 δ 10991 δ For δ 0 σa σm 1099 11 kpsi GENERAL ADMINISTRATION DEPARTMENT GENERAL SERVICES NOTIFICATION New Delhi the 15th August 1969 In pursuance of subsection 1 of section 2 of the Rajya Sabha Disqualification on ground of defection Act 1969 28 of 1969 the Central Government with the previous approval of the President hereby makes the following rules namely 1 Short title commencement and application 1 These rules may be called the Rajya Sabha Disqualification on ground of defection Rules 1969 2 They shall come into force on the date of their publication in the Official Gazette 3 They shall apply to every State Legislature and every House of Parliament 2 Definitions In these rules unless the context otherwise requiresa Act means the Rajya Sabha Disqualification on ground of defection Act 1969 b House includes the House of the People and the Council of States and the Legislative Assembly and the Legislative Council of a State c Presiding Officer includes the Chairman the Deputy Chairman and any other person performing the duties of the Chairman of the Rajya Sabha the Speaker the Deputy Speaker and any other person performing the duties of the Speaker of the Legislative Assembly of a State d political party means a political party registered with the Election Commission under any law relating to the election to the House or Houses of Parliament or the Legislature or Legislatures of a State or States e recognized political party means a political party recognized as such in accordance with the directions issued by the Election Commission under the Representation of the People Act 1951 43 of 1951 f member means a sitting member of the House and includes a nominated member 3 Submission of notice and statement 1 A notice under subsection 1 of section 3 of the Act shall be in the form set out in the First Schedule and shall be given personally or by registered post to the Presiding Officer together with a statement setting out the grounds which in the opinion of the member justify his change of party or his defection as the case may be 2 The Presiding Officer shall if the notice is received from a member within the time specified in subsection 2 of section 3 of the Act decide the question entailed within the period specified in subsection 3 of that section and also cause a copy of the decision to be sent to the member and the political party or parties concerned 4 Maintenance of Register 1 The Presiding Officer shall maintain a register showing the particulars of the notice received the decision given and other relevant information 2 The register shall be a public document and shall be made available for inspection on any working day during the office hours by any person on payment of a fee of rupees five 5 Notice to political party or political parties concerned The Presiding Officer shall send a copy of the notice under subsection 1 of section 3 of the Act to the political party or parties concerned 6 Constitution of the committee 1 The Presiding Officer shall unless he himself settles the question under subsection 1 of section 3 of the Act within the period specified in subsection 3 of the said section refer the same to a committee consisting of the following persons namely a The Chairperson of the House who shall be the Chairperson of the committee b One member nominated by the Chairperson of the House being a member belonging to the same political party as the member concerned c One member nominated by the Chairperson of the House other than the member referred to in clause b 2 The committee shall report its findings and recommendations to the Presiding Officer who shall thereupon pass the appropriate order Combinação de Carregamentos Tensão equivalente de von Mises para um típico eixo Considerando componentes média e alternada para um eixo com flexão tensão axial deve ser dividida por 085 por antever excentricidades de carregamento e torção Exemplo 614 Um eixo rotativo é feito de um tubo de aço estirado a frio AISI 1018 de 42 4 mm e tem um furo de 6 mm de diâmetro perfurado transversalmente através dele Estime o fator de segurança contra fadiga e falha estática usando os critérios de falha de Gerber e Langer para o seguintes condições de carregamento a O eixo é submetido a um torque completamente reverso de 120 N m em fase com um momento de flexão completamente invertido de 150 Nm b O eixo é submetido a um torque pulsante que varia de 20 a 160 Nm e um momento de flexão constante de 150 N m Exemplo 614 A Eq Marin Superfície tamanho Fator de concentração de tensão Equação de Neuber em polegadas e em kpsi Fator de concentração de tensão torção 𝐾 𝑓𝑠1𝑞 h 𝑐𝑖𝑠𝑎𝑙 𝐾𝑡𝑠1 Rajya Sabha is the Upper House of Parliament and consists of Two Hundred and Forty members Out of these members Twelve members are nominated by the President of India and the rest are elected by the State and Union Territory Legislative Assemblies The higher majority of the members are elected by the members of Legislative Assemblies in their respective states by single transferable vote through proportional representation Duration and eligibility criteria for membership of Rajya Sabha is as follows Duration 6 Years Eligibility Criteria The candidate must be a citizen of India Minimum age of the candidate is 30 years The candidate must possess such other qualifications are prescribed by Parliament The candidate must be registered voter in the concerned State HeShe must be a member of the Legislative Assembly of the concerned State HeShe should not hold any Office of Profit under the Government Procedure for Election of Rajya Sabha Members Rajya Sabha is a permanent house and is not subject to dissolution even after the expiry of its term Onethird of the total members retire every two years and new members are elected through indirectly Members of Rajya Sabha are not directly elected by voters They are elected by indirectly Members of state legislative assemblies The election of members to Rajya Sabha is conducted through a system of proportional representation by means of a single transferable vote through a secret ballot The order of election for Rajya Sabha members from each state is determined by the number of seats vacant in that state at that time The members of the State Legislative Assembly cast their votes proportionally based on the number of vacancies This procedure is followed to ensure the principle of proportional representation for election of the Rajya Sabha members The vacancy of a member in Rajya Sabha due to death resignation disqualification or any other causes will be filled by election as soon as possible The person elected through this election will be a member of Rajya Sabha only till remaining duration of the vacancy Correção do limite de resistência à fadiga Sₙ Equação de Marin Sₙ Ccarga Cconf Csup Ctam Ctemp Cdiv SₙCP Obtido experimentalmente É sempre fornecido no enunciado dos exercícios de fadiga As tabelas servem para converter R R Moore outras condições diferentes Carga Ccarga Flexão 1 Axial 07 Torção 0577 Cisalhamento 0577 Combinadas 1 Confiabilidade Cconf 50 1 90 0897 95 0868 99 0814 999 0753 9999 0702 99999 0659 Tamanho Ctam d mm d8 1 8d250 1189 d0097 d250 06 Ctam 1 carga axial Ctam pode ser usado para ligas não ferrosas Csup A σrb Na fórmula do Csup sempre usar σr Acabamento A b retificado 158 0085 laminado a frio usinado estampado 451 0265 laminado a quente 577 0718 forjado 272 0995 Csup 1 materiais não ferrosos Cdiv experimental Temperatura Ctemp T C T450 1 450T550 1 00058 T 450 Obs as informações desse slide constam no formulário da P1 42 Fatigue factor of safety nf 12 Sut σm2 σa Se 1 sqrt1 2σm Se Sut σa2 σm 0 From Table A20 we find the minimum strengths to be Sut 440 MPa and Sy 370 MPa The endurance limit of the rotatingbeam specimen is 05440 220 MPa The surface factor obtained from Eq 619 and Table 62 p 279 is ka 451 Sut0265 4514400265 0899 From Eq 620 the size factor is kb d7620107 427620107 0833 The remaining Marin factors are all unity so the modified endurance strength Se is Se 08990833220 165 MPa a Theoretical stressconcentration factors are found from Table A16 Using aD 642 0143 and dD 3442 0810 and using linear interpolation we obtain A 0798 and Kt 2366 for bending and A 089 and Kts 175 for torsion Thus for bending Znet πA32D D4 d4 π07983242 424 344 331 106 mm3 and for torsion Jnet πA32 D4 d4 π08932 424 344 155 103 mm4 Next using Figs 620 and 621 pp 287288 with a notch radius of 3 mm we find the notch sensitivities to be 078 for bending and 096 for torsion The two corresponding fatigue stressconcentration factors are obtained from Eq 632 as Kf 1 qKt 1 1 0782366 1 207 Kfs 1 096175 1 172 The alternating bending stress is now found to be σxa Kf M Znet 207 150 331106 938 106 Pa 938 MPa and the alternating torsional stress is τxya Kfs TD 2 Jnet 172 12042103 2155109 280 106 Pa 280 MPa The midrange von Mises component σm is zero The alternating component σa is given by σa σxa2 3τxya212 9382 328212 1056 MPa Since Se Sa the fatigue factor of safety nf is nf Sa σa 165 1056 156 Exemplo 615 Dada uma peça com Sut 151 kpsi e no local crítico da peça Sn 675 kpsi Para o carregamento da Fig 633 estime o número de repetições do bloco stresstempo na Fig 633 que pode ser feito antes da falha Goodman modificado Figure 632 Designers fatigue diagram for Ex 614 From the same table with r σa σm 2821006 0280 the strengths can be shown to be Sae 855 MPa and Sam 305 MPa See the plot in Fig 632 The firstcycle yield factor of safety ny is ny Sy σa σm 370 282 1006 287 There is no notch yielding The likelihood of failure may first come from firstcycle yielding at the notch See the plot in Fig 632 The firstcycle yield factor of safety is ny Sy σa 370 1056 350 There is no localized yielding the threat is from fatigue See Fig 632 b This part asks us to find the factors of safety when the alternating component is due to pulsating torsion and a steady component is due to both torsion and bending We have Ta 160 202 70 Nm and Tm 160 202 90 Nm The corresponding amplitude and steadystress components are τxya Kfs Ta D 2 Jnet 172 7042103 2155109 163 106 Pa 163 MPa τxym Kfs Tm D 2 Jnet 172 9042103 2155109 210 106 Pa 210 MPa The steady bending stress component σxm is σxm Kf Mm Znet 207 150 331106 938 106 Pa 938 MPa The von Mises components σa and σm are σa 3163212 282 MPa σm 9382 321212 1006 MPa From Table 67 p 299 the fatigue factor of safety is nf 12 440 10062 282 165 1 sqrt1 21006 165 4402822 303 Figure 633 Variable stress diagram prepared for assessing cumulative damage Fadiga de superfície Cilindros de laminação rolamentos engrenagens rodas de trem Irregularidades que atuam como concentradores de tensão Rugosidade superficial influência direta no fenômeno Não é completamente compreendida ainda Trincas iniciamse na superfície da peça Tópico 616 Shigley cálculo de resistência à fadiga de superfície Equacionamento com auxílio de dados experimentais Peças com contato superficial Função da dureza superficial Tratamento superficial Melhoria das propriedades superficiais melhoria da resistência à fadiga Fadiga de superfície Surface fatigue cracks observed by SEM Cu15atAl ANFG specimens Download Scientific Diagram researchgatenet Jateamento com esferas O processo de jateamento com granalhas é um tratamento superficial muito utilizado em peças com o intuito de melhorar as propriedades de resistência à fadiga A deformação controlada do impacto das esferas introduz tensões residuais compressivas na camada superficial do material Geralmente este processo é executado na temperatura ambiente Efeito do jateamento a quente na vida em fadiga de um aço mola SAE 5160 httpswwwtesesuspbrtesesdisponiveis8888131tde 20092016111735ptbrphp Bibliografia Os slides de aula são apenas um guia de estudo são parte integrante da aula e foram complementados durante a mesma Os slides não excluem a leitura da bibliografia referida Shigley J E Elementos de Máquinas Vol1 Shigleys Mechanical Engineering Design Eighth Edition 2008 Elementos de Máquinas I YouTube httpswwwyoutubecomplaylistlistPLd10Go8vsVYj cKKBCNS9sDlnVKPWSJ André Ferreira Costa Vieira Slides do Curso de Elementos de Máquinas para Automação PMR 3320 A04 Teorias de Falha USP Politécnica 2020 Statics and Mechanics of Materials by Ferdinand Beer E Johnston John DeWolf and David Mazurek NIEMANN G Elementos de máquinasSão Paulo Blucher 2016 v 1 Ebook Disponivel em httpsplataformabvirtualcombrLeitorPublicacao16916 2pdf NIEMANN G Elementos de máquinas São Paulo Blucher 2016v 2 Ebook Disponivel em httpsplataformabvirtualcombrLeitorPublicacao16915 9pdf NIEMANN G Elementos de máquinas São Paulo Blucher 2015 v 3 Ebook Disponivel em httpsplataformabvirtualcombrLeitorPublicacao16916 0pdf