剛?cè)狁詈舷到y(tǒng)的動(dòng)力學(xué)建模與響應(yīng)分析
發(fā)布時(shí)間：2018-08-13 13:42
【摘要】：在航空航天、旋轉(zhuǎn)機(jī)械、車輛工程、軍工器械、機(jī)器人以及微機(jī)電系統(tǒng)(MEMS)領(lǐng)域中,這類工程中系統(tǒng)的各個(gè)柔性部件存在大范圍的剛體運(yùn)動(dòng),同時(shí)其自身發(fā)生彈性變形,這就涉及結(jié)構(gòu)部件的剛體運(yùn)動(dòng)與彈性變形相互耦合的問題。運(yùn)動(dòng)與變形耦合動(dòng)力學(xué)系統(tǒng)涉及到剛體動(dòng)力學(xué)與變形體力學(xué)之間的統(tǒng)一,柔性體在作大范圍運(yùn)動(dòng)時(shí)呈現(xiàn)出的動(dòng)力過程非常復(fù)雜。隨著剛?cè)狁詈舷到y(tǒng)規(guī)模越來越龐大,結(jié)構(gòu)越來越復(fù)雜,及其運(yùn)行速度要求不斷加快,對(duì)系統(tǒng)在不同的約束、不同的受力與控制環(huán)節(jié)等工況下的運(yùn)行過程的精確掌握,這些都成為工程預(yù)研與設(shè)計(jì)的重大難題。目前對(duì)剛?cè)狁詈舷到y(tǒng)動(dòng)力學(xué)的研究主要集中在力學(xué)建模、計(jì)算求解、柔性多體系統(tǒng)的接觸與碰撞問題和多物理場下的運(yùn)動(dòng)與變形耦合效應(yīng)等方面,然而對(duì)剛?cè)狁詈舷到y(tǒng)的動(dòng)力學(xué)建模尤為關(guān)鍵,要求所建模型既能反映系統(tǒng)的耦合效應(yīng),同時(shí)能夠在無剛體運(yùn)動(dòng)時(shí)退化為經(jīng)典彈性力學(xué),而在不考慮彈性體變形時(shí)能夠退化成剛體動(dòng)力學(xué)。對(duì)于剛?cè)狁詈舷到y(tǒng)動(dòng)力學(xué)中存在動(dòng)力剛化效應(yīng)的機(jī)理,目前存在較大爭議,其中涉及到幾何非線性、運(yùn)動(dòng)非線性以及材料非線性等大變形理論,這些問題的探討仍是研究的重點(diǎn)。隨著含偶應(yīng)力線彈性理論的不斷完善,將物質(zhì)點(diǎn)的旋轉(zhuǎn)變形考慮于彈性體的變形,并計(jì)及其產(chǎn)生的偶應(yīng)力對(duì)彈性體的影響,以含偶應(yīng)力線彈性理論為基礎(chǔ),研究彈性體的剛?cè)狁詈蟿?dòng)力學(xué)過程,對(duì)于這方面的研究受到越來越多的關(guān)注,為微觀尺寸下柔性體的動(dòng)力學(xué)研究帶來較大突破。首先,本文對(duì)質(zhì)量彈簧離心振動(dòng)系統(tǒng)的剛?cè)狁詈蟿?dòng)力學(xué)建模、數(shù)值求解及其動(dòng)力學(xué)響應(yīng)分析等作了重點(diǎn)闡述,解析了耦合系統(tǒng)的動(dòng)力學(xué)本質(zhì)、慣性效應(yīng)及其動(dòng)力學(xué)特性,并研制出離心振動(dòng)復(fù)合實(shí)驗(yàn)裝置來驗(yàn)證該理論模型;其次,考慮彈性體的平動(dòng)變形和旋轉(zhuǎn)變形,將偶應(yīng)力理論應(yīng)用于剛?cè)狁詈蟿?dòng)力學(xué)模型中,建立了廣義彈性體作定軸剛體轉(zhuǎn)動(dòng)的剛?cè)狁詈蟿?dòng)力學(xué)模型,并開發(fā)了相應(yīng)的有限元計(jì)算程序;最后,基于廣義彈性體的剛?cè)狁詈蟿?dòng)力學(xué)模型,對(duì)旋轉(zhuǎn)懸臂梁、中心剛體-柔性梁系統(tǒng)、風(fēng)輪葉片以及超大噸位起重機(jī)臂架系統(tǒng)的動(dòng)力學(xué)過程作了深入研究。論文的主要工作和結(jié)論如下:(1)針對(duì)單質(zhì)點(diǎn)雙自由度的質(zhì)量彈簧離心振動(dòng)系統(tǒng)的剛?cè)狁詈蟿?dòng)力學(xué)過程進(jìn)行重點(diǎn)研究,建立了已知?jiǎng)傮w轉(zhuǎn)動(dòng)情況時(shí)質(zhì)量彈簧系統(tǒng)的動(dòng)力學(xué)方程,對(duì)其進(jìn)行計(jì)算求解,并對(duì)其解析解進(jìn)行詳細(xì)、系統(tǒng)地研究和分析,尤其針對(duì)其動(dòng)力學(xué)特性和動(dòng)力學(xué)響應(yīng)作了專門研究,為探究剛?cè)狁詈舷到y(tǒng)動(dòng)力學(xué)耦合的本質(zhì),對(duì)各種慣性力隨時(shí)間的變化過程進(jìn)行了相關(guān)研究。為驗(yàn)證剛?cè)狁詈舷到y(tǒng)中質(zhì)點(diǎn)出現(xiàn)花瓣形狀的運(yùn)動(dòng)軌跡,設(shè)計(jì)并研制出離心振動(dòng)復(fù)合實(shí)驗(yàn)裝置,通過對(duì)比分析得到剛?cè)狁詈舷到y(tǒng)模型的合理性。(2)以Mindlin線彈性偶應(yīng)力理論為基礎(chǔ),創(chuàng)建了含三個(gè)材料參數(shù)的廣義彈性理論,并結(jié)合質(zhì)量彈簧系統(tǒng)的動(dòng)力學(xué)建模方法,通過哈密爾頓原理推導(dǎo)出作定軸剛體轉(zhuǎn)動(dòng)的廣義彈性體的剛?cè)狁詈蟿?dòng)力學(xué)模型,該模型計(jì)及了相對(duì)慣性力、離心力、科氏力和切向慣性力。考慮以彈性體的位移和變形轉(zhuǎn)角為獨(dú)立變量,利用約束變分原理建立了廣義彈性體作定軸剛體轉(zhuǎn)動(dòng)的有限元控制方程,其中單元離散采用8個(gè)節(jié)點(diǎn)48個(gè)自由度的三維六面體實(shí)體等參元或4個(gè)節(jié)點(diǎn)24個(gè)自由度的三維四面體單元。對(duì)廣義彈性體的有限元分析可以考慮各種慣性力因素對(duì)其內(nèi)力分布造成的影響,也能夠給出其動(dòng)力特性的變化規(guī)律,還可以考慮結(jié)構(gòu)的尺寸效應(yīng)。(3)數(shù)值分析旋轉(zhuǎn)懸臂梁的動(dòng)力學(xué)特性和動(dòng)力學(xué)響應(yīng),得到旋轉(zhuǎn)懸臂梁在不同恒定轉(zhuǎn)速下動(dòng)頻的變化規(guī)律,對(duì)比分析不同旋轉(zhuǎn)姿態(tài)、不同恒定轉(zhuǎn)速等工況時(shí)懸臂梁的等效應(yīng)力、等效偶應(yīng)力及其位移等動(dòng)力學(xué)響應(yīng)。特別指出了花瓣形狀的質(zhì)點(diǎn)運(yùn)動(dòng)軌跡和旋轉(zhuǎn)系統(tǒng)最大轉(zhuǎn)速概念等新的結(jié)論。進(jìn)一步對(duì)旋轉(zhuǎn)微梁進(jìn)行動(dòng)力學(xué)特性和動(dòng)力學(xué)響應(yīng)分析,突出旋轉(zhuǎn)變形對(duì)整個(gè)計(jì)算結(jié)果的影響,體現(xiàn)出廣義彈性理論的剛?cè)狁詈蟿?dòng)力學(xué)模型對(duì)微觀結(jié)構(gòu)部件進(jìn)行動(dòng)力分析時(shí)的合理性和精確性。(4)計(jì)算選取中心剛體-柔性梁的剛?cè)狁詈舷到y(tǒng),對(duì)系統(tǒng)最大轉(zhuǎn)速問題展開深入研究,從而為結(jié)構(gòu)的控制提供新的途徑�？紤]剛?cè)狁詈舷到y(tǒng)中柔性梁受到不同外力載荷作用時(shí),柔性梁在整個(gè)旋轉(zhuǎn)過程中的動(dòng)力學(xué)響應(yīng),更加準(zhǔn)確和合理地模擬出柔性梁的動(dòng)力學(xué)過程,精確解析了系統(tǒng)結(jié)構(gòu)部件在離心場中的剛?cè)狁詈蠙C(jī)理,為更好地?cái)?shù)值仿真工程實(shí)際結(jié)構(gòu)的運(yùn)轉(zhuǎn)過程及控制旋轉(zhuǎn)系統(tǒng)結(jié)構(gòu)部件的位移值和應(yīng)力值提供理論依據(jù)和技術(shù)指導(dǎo)。(5)建立風(fēng)輪葉片的力學(xué)模型,采用廣義彈性體作定軸剛體轉(zhuǎn)動(dòng)的剛?cè)狁詈蟿?dòng)力學(xué)模型,數(shù)值模擬了風(fēng)輪葉片從啟動(dòng)加速階段至額定轉(zhuǎn)速工作階段的動(dòng)力學(xué)過程。計(jì)算還考慮了不同載荷作用時(shí)風(fēng)輪葉片的動(dòng)力學(xué)響應(yīng)存在的差異,為更精確和合理地仿真風(fēng)輪葉片的動(dòng)力學(xué)過程提供重要的參考價(jià)值。(6)用經(jīng)典彈性理論以及傳統(tǒng)梁,桿單元去仿真求解剛體-柔性多體系統(tǒng)的動(dòng)力學(xué)過程,以超大噸位輪式起重機(jī)臂架作大范圍回轉(zhuǎn)運(yùn)動(dòng)的剛?cè)狁詈蟿?dòng)力學(xué)過程作為依托,建立其柔性多體動(dòng)力學(xué)模型,并編寫相關(guān)程序?qū)ζ溥M(jìn)行計(jì)算求解,仿真了輪式起重機(jī)通過鋼絲繩提起吊物,然后回轉(zhuǎn)吊臂使得吊物在空中擺動(dòng)的整個(gè)過程,計(jì)算得出吊物的偏擺角和吊臂不同位置的等效應(yīng)力值隨時(shí)間的變化曲線,并將仿真結(jié)果與試驗(yàn)測量結(jié)果進(jìn)行對(duì)比分析,進(jìn)一步驗(yàn)證了本文模型在建模思想和方法上的合理性。
[Abstract]:In the fields of aerospace, rotating machinery, vehicle engineering, military equipment, robots and micro-electro-mechanical systems (MEMS), the flexible components of such engineering systems have a large range of rigid body motion, while their own elastic deformation occurs, which involves the coupling of rigid body motion and elastic deformation of structural components. Coupled dynamics system involves the unification between rigid body dynamics and deformable body mechanics. The dynamic process of flexible body in large-scale motion is very complex. With the increasing size of rigid-flexible coupling system, the structure is becoming more and more complex, and its speed requirements are accelerating, the system under different constraints, different forces. At present, the study on dynamics of rigid-flexible coupling systems mainly focuses on mechanical modeling, calculation and solution, contact and collision problems of flexible multi-body systems and coupling effects of motion and deformation in multi-physical fields. For the rigid-flexible coupling system, the dynamic modeling is especially important. It requires that the model can reflect the coupling effect of the system and degenerate into classical elasticity when the rigid body is moving, but degenerate into rigid body dynamics when the deformation of the elastic body is not considered. With the development of linear elasticity theory with couple stresses, the rotational deformation of a material point is considered as the deformation of an elastic body and the couple stresses produced by it are taken into account. Based on the theory of linear elasticity with couple stresses, the rigid-flexible coupling dynamics of elastic body is studied. More and more attention has been paid to this field, which brings about a breakthrough in the dynamics of flexible body in micro-size. Firstly, the rigid-flexible coupling dynamics model of mass-spring centrifugal vibration system is established. Value solution and its dynamic response analysis are emphatically expounded. The dynamic essence, inertia effect and dynamic characteristics of the coupled system are analyzed. A centrifugal vibration compound experimental device is developed to verify the theoretical model. Secondly, considering the translational and rotational deformation of elastic body, the couple stress theory is applied to the rigid-flexible coupling dynamics. In the model, the rigid-flexible coupling dynamic model of the generalized elastic body rotating as a fixed-axis rigid body is established, and the corresponding finite element calculation program is developed. Finally, based on the rigid-flexible coupling dynamic model of the generalized elastic body, the dynamic forces of the rotating cantilever beam, the central rigid-flexible beam system, the wind turbine blade and the boom system of the super-tonnage crane are analyzed. The main work and conclusions of this paper are as follows: (1) The rigid-flexible coupling dynamic process of mass spring centrifugal vibration system with single particle and two degrees of freedom is studied emphatically, and the dynamic equation of mass spring system with known rigid body rotation is established, and its analytical solution is obtained. In order to explore the essence of dynamic coupling of rigid-flexible coupling system, the variation process of inertial force with time is studied. In order to verify the motion track of petal shape of particle in rigid-flexible coupling system, the design and research are carried out. (2) Based on Mindlin's linear elastic couple stress theory, a generalized elastic theory with three material parameters is established. Combining with the dynamic modeling method of mass spring system, a rigid body with fixed axis is deduced by Hamilton principle. A rigid-flexible coupling dynamic model of a rotating generalized elastic body is developed, which takes into account the relative inertia force, centrifugal force, Coriolis force and tangential inertia force. Considering the displacement and deformation angle of the elastic body as independent variables, the governing equations of a rotating rigid body with the generalized elastic body as a fixed axis are established by using the constrained variational principle. A 3-D hexahedral solid isoparametric element with 8 nodes and 48 degrees of freedom or a 3-D tetrahedral element with 4 nodes and 24 degrees of freedom are used in the finite element analysis of a generalized elastic body. (3) The dynamic characteristics and dynamic responses of the rotating cantilever beam are analyzed numerically, and the dynamic frequencies of the rotating cantilever beam at different constant rotational speeds are obtained. The equivalent forces, equivalent couple stresses and displacements of the cantilever beam under different rotational postures and rotational speeds are compared and analyzed. Further more, the dynamic characteristics and dynamic response of the rotating micro-beam are analyzed, and the influence of the rotating deformation on the whole calculation result is highlighted. It shows that the rigid-flexible coupling dynamic model of the generalized elastic theory is reasonable for the dynamic analysis of micro-components. (4) Computing and selecting the rigid-flexible coupling system of the center rigid-flexible beam, the maximum speed of the system is studied in depth, which provides a new way to control the structure. The dynamic process of the flexible beam is simulated reasonably, and the rigid-flexible coupling mechanism of the structural components in the centrifugal field is analyzed accurately. The theoretical basis and technical guidance are provided for the better numerical simulation of the actual structure operation process and the control of the displacement and stress values of the structural components of the rotating system. (5) The mechanics of the wind turbine blade is established. A rigid-flexible coupling dynamic model with generalized elastomer as fixed-axis rigid-body rotation was used to simulate the dynamic process of wind turbine blades from start-up acceleration stage to rated speed operation stage. (6) Using classical elastic theory and traditional beam and bar element to simulate the dynamic process of rigid-flexible multi-body system, the flexible multi-body dynamic model is established based on the rigid-flexible coupling dynamic process of large-tonnage wheeled crane boom in large-scale rotation. The whole process of lifting the lifting object through wire rope and swinging the lifting object in the air by swinging the boom is simulated. The swing angle of the lifting object and the curve of the equivalent stress at different positions of the boom with time are calculated, and the simulation results are compared with the experimental results. Comparative analysis further validates the rationality of this model in modeling thought and method.
【學(xué)位授予單位】：重慶大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O313.3
，
本文編號(hào)：2181163
[Abstract]:In the fields of aerospace, rotating machinery, vehicle engineering, military equipment, robots and micro-electro-mechanical systems (MEMS), the flexible components of such engineering systems have a large range of rigid body motion, while their own elastic deformation occurs, which involves the coupling of rigid body motion and elastic deformation of structural components. Coupled dynamics system involves the unification between rigid body dynamics and deformable body mechanics. The dynamic process of flexible body in large-scale motion is very complex. With the increasing size of rigid-flexible coupling system, the structure is becoming more and more complex, and its speed requirements are accelerating, the system under different constraints, different forces. At present, the study on dynamics of rigid-flexible coupling systems mainly focuses on mechanical modeling, calculation and solution, contact and collision problems of flexible multi-body systems and coupling effects of motion and deformation in multi-physical fields. For the rigid-flexible coupling system, the dynamic modeling is especially important. It requires that the model can reflect the coupling effect of the system and degenerate into classical elasticity when the rigid body is moving, but degenerate into rigid body dynamics when the deformation of the elastic body is not considered. With the development of linear elasticity theory with couple stresses, the rotational deformation of a material point is considered as the deformation of an elastic body and the couple stresses produced by it are taken into account. Based on the theory of linear elasticity with couple stresses, the rigid-flexible coupling dynamics of elastic body is studied. More and more attention has been paid to this field, which brings about a breakthrough in the dynamics of flexible body in micro-size. Firstly, the rigid-flexible coupling dynamics model of mass-spring centrifugal vibration system is established. Value solution and its dynamic response analysis are emphatically expounded. The dynamic essence, inertia effect and dynamic characteristics of the coupled system are analyzed. A centrifugal vibration compound experimental device is developed to verify the theoretical model. Secondly, considering the translational and rotational deformation of elastic body, the couple stress theory is applied to the rigid-flexible coupling dynamics. In the model, the rigid-flexible coupling dynamic model of the generalized elastic body rotating as a fixed-axis rigid body is established, and the corresponding finite element calculation program is developed. Finally, based on the rigid-flexible coupling dynamic model of the generalized elastic body, the dynamic forces of the rotating cantilever beam, the central rigid-flexible beam system, the wind turbine blade and the boom system of the super-tonnage crane are analyzed. The main work and conclusions of this paper are as follows: (1) The rigid-flexible coupling dynamic process of mass spring centrifugal vibration system with single particle and two degrees of freedom is studied emphatically, and the dynamic equation of mass spring system with known rigid body rotation is established, and its analytical solution is obtained. In order to explore the essence of dynamic coupling of rigid-flexible coupling system, the variation process of inertial force with time is studied. In order to verify the motion track of petal shape of particle in rigid-flexible coupling system, the design and research are carried out. (2) Based on Mindlin's linear elastic couple stress theory, a generalized elastic theory with three material parameters is established. Combining with the dynamic modeling method of mass spring system, a rigid body with fixed axis is deduced by Hamilton principle. A rigid-flexible coupling dynamic model of a rotating generalized elastic body is developed, which takes into account the relative inertia force, centrifugal force, Coriolis force and tangential inertia force. Considering the displacement and deformation angle of the elastic body as independent variables, the governing equations of a rotating rigid body with the generalized elastic body as a fixed axis are established by using the constrained variational principle. A 3-D hexahedral solid isoparametric element with 8 nodes and 48 degrees of freedom or a 3-D tetrahedral element with 4 nodes and 24 degrees of freedom are used in the finite element analysis of a generalized elastic body. (3) The dynamic characteristics and dynamic responses of the rotating cantilever beam are analyzed numerically, and the dynamic frequencies of the rotating cantilever beam at different constant rotational speeds are obtained. The equivalent forces, equivalent couple stresses and displacements of the cantilever beam under different rotational postures and rotational speeds are compared and analyzed. Further more, the dynamic characteristics and dynamic response of the rotating micro-beam are analyzed, and the influence of the rotating deformation on the whole calculation result is highlighted. It shows that the rigid-flexible coupling dynamic model of the generalized elastic theory is reasonable for the dynamic analysis of micro-components. (4) Computing and selecting the rigid-flexible coupling system of the center rigid-flexible beam, the maximum speed of the system is studied in depth, which provides a new way to control the structure. The dynamic process of the flexible beam is simulated reasonably, and the rigid-flexible coupling mechanism of the structural components in the centrifugal field is analyzed accurately. The theoretical basis and technical guidance are provided for the better numerical simulation of the actual structure operation process and the control of the displacement and stress values of the structural components of the rotating system. (5) The mechanics of the wind turbine blade is established. A rigid-flexible coupling dynamic model with generalized elastomer as fixed-axis rigid-body rotation was used to simulate the dynamic process of wind turbine blades from start-up acceleration stage to rated speed operation stage. (6) Using classical elastic theory and traditional beam and bar element to simulate the dynamic process of rigid-flexible multi-body system, the flexible multi-body dynamic model is established based on the rigid-flexible coupling dynamic process of large-tonnage wheeled crane boom in large-scale rotation. The whole process of lifting the lifting object through wire rope and swinging the lifting object in the air by swinging the boom is simulated. The swing angle of the lifting object and the curve of the equivalent stress at different positions of the boom with time are calculated, and the simulation results are compared with the experimental results. Comparative analysis further validates the rationality of this model in modeling thought and method.
【學(xué)位授予單位】：重慶大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O313.3
，
本文編號(hào)：2181163
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