帶軸向變形的柔順機構多自由度偽剛體模型研究
發(fā)布時間：2019-06-03 01:02
【摘要】：柔順機構是一種可以利用自身柔性構件的彈性變形來轉換運動、力和能量的新型機構。與傳統(tǒng)的剛性機構相比,由于它免去了運動副間的裝配和摩擦磨損,因而表現(xiàn)出許多優(yōu)點,近年來已成為國內外機構學領域的一個研究熱點。柔順機構具有獨特的性能和廣泛的應用前景,但是對于大變形造成的幾何非線性導致柔順機構的分析和設計變得非常困難。由Howell提出的偽剛體模型法將柔順機構的非線性問題轉化為等效剛性機構的線性問題來求解,為柔順機構的研究奠定了基礎。后來學者陸續(xù)提出了2R、PR偽剛體模型,但這些偽剛體模型自由度不足,導致其模擬精度和范圍有限,限制了其進一步應用。針對上述問題,本文在現(xiàn)有模型的基礎上,增加偽剛體模型的自由度,提出一種帶軸向變形的多自由度PRR偽剛體模型,考慮多種復雜載荷情況,建立了相應的偽剛體新模型,并對該模型進行了相關研究。主要內容歸納如下:1、針對末端受力矩載荷時的柔順桿,建立大變形柔順機構的PRR偽剛體模型。將力矩載荷施加到模型的末端,采用參數(shù)近似化法建立模型特征半徑系數(shù)的三維搜索過程,并對偽剛體模型中移動副引起的軸向位移占整個軸向移動的比例做定量分析。研究表明,在力矩載荷作用下,該移動副幾乎不發(fā)生軸向位移,此時PRR模型與2R偽剛體模型基本一致。2、針對末端受力載荷的柔順桿,建立大變形柔順機構的PRR偽剛體模型。通過運動學正解得出模型特征參數(shù)的數(shù)值表達式,運用參數(shù)化近似法建立程序求解框圖,運用線性回歸法擬合模型的剛度系數(shù)。利用數(shù)值分析軟件,通過與現(xiàn)有偽剛體模型以及柔順桿的末端軌跡特征進行分析對比,表明PRR偽剛體模型的模擬精度進一步提高。3、針對末端受復合載荷形式的柔順桿,建立大變形柔順機構的PRR偽剛體模型。將載荷比進行極端化處理,推導出兩種極端載荷形式下偽剛體模型的數(shù)學表達式。通過建立三維搜索程序和線性擬合方法求解出模型的特征參數(shù),通過與其他模型對比分析驗證了受復合載荷時PRR模型的優(yōu)越性。4、將受不同載荷時的PRR偽剛體模型應用到平面柔順機構中,建立柔順四桿機構和柔順曲柄-滑塊機構的PRR偽剛體模型,通過力-變形分析得出滑塊位移和曲柄轉角關系的曲線圖及柔順四桿機構中柔順桿末端的位姿變化圖,通過與有限元分析結果對比,驗證了PRR偽剛體模型在實際柔順機構應用中的有效性。
[Abstract]:Compliance mechanism is a new type of mechanism which can transform motion, force and energy by using the elastic deformation of its own flexible components. Compared with the traditional rigid mechanism, it has shown many advantages because it eliminates the assembly and friction and wear between moving pairs, so it has become a research hot spot in the field of mechanism at home and abroad in recent years. Compliant mechanism has unique performance and wide application prospect, but it is very difficult to analyze and design compliant mechanism because of geometric nonlinear caused by large deformation. The pseudo-rigid body model method proposed by Howell converts the nonlinear problem of compliant mechanism into the linear problem of equivalent rigid mechanism, which lays a foundation for the research of compliant mechanism. Later, scholars put forward 2R, PR pseudo-rigid body model one after another, but these pseudo-rigid body models have insufficient degree of freedom, which leads to the limited simulation accuracy and range, which limits its further application. In order to solve the above problems, a multi-degree-of-freedom PRR pseudo-rigid body model with axial deformation is proposed by adding the degrees of freedom of the pseudo-rigid body model on the basis of the existing models. Considering a variety of complex loads, a new pseudo-rigid body model is established. The model is also studied. The main contents are summarized as follows: 1. The PRR pseudo-rigid body model of large deformation compliance mechanism is established for the compliant rod loaded with moment at the end. The torque load is applied to the end of the model, and the three-dimensional search process of the characteristic radius coefficient of the model is established by using the parameter approximate method, and the proportion of the axial displacement caused by the moving pair in the pseudo-rigid body model to the whole axial movement is quantitatively analyzed. The results show that the axial displacement of the moving pair almost does not occur under torque load, and the PRR model is basically consistent with the 2R pseudo-rigid body model. 2, the PRR pseudo-rigid body model of large deformation compliant mechanism is established for the compliant rod loaded at the end of the force. The numerical expression of the characteristic parameters of the model is obtained by the forward kinematic solution, the program block diagram is established by using the parametric approximate method, and the stiffness coefficient of the model is fitted by the linear regression method. By using the numerical analysis software, the simulation accuracy of the PRR pseudo-rigid body model is further improved by comparing with the existing pseudo-rigid body model and the end trajectory characteristics of the compliant rod. 3, for the compliant rod in the form of composite load at the end, The PRR pseudo-rigid body model of large deformation compliant mechanism is established. The load ratio is extreme treated, and the mathematical expressions of the pseudo-rigid body model under two extreme load forms are derived. The characteristic parameters of the model are solved by establishing three-dimensional search program and linear fitting method, and the superiority of PRR model under compound load is verified by comparing with other models. The PRR pseudo-rigid body model under different loads is applied to the plane compliant mechanism, and the PRR pseudo-rigid body model of compliant four-bar mechanism and compliant crank-slider mechanism is established. Through force-deformation analysis, the curve diagram of the relationship between slider displacement and crank angle and the pose change diagram at the end of flexible four-bar mechanism are obtained, and the results are compared with those of finite element analysis. The effectiveness of PRR pseudo-rigid body model in practical compliance mechanism is verified.
【學位授予單位】：中北大學
【學位級別】：碩士
【學位授予年份】：2016
【分類號】：TH112
本文編號：2491554
[Abstract]:Compliance mechanism is a new type of mechanism which can transform motion, force and energy by using the elastic deformation of its own flexible components. Compared with the traditional rigid mechanism, it has shown many advantages because it eliminates the assembly and friction and wear between moving pairs, so it has become a research hot spot in the field of mechanism at home and abroad in recent years. Compliant mechanism has unique performance and wide application prospect, but it is very difficult to analyze and design compliant mechanism because of geometric nonlinear caused by large deformation. The pseudo-rigid body model method proposed by Howell converts the nonlinear problem of compliant mechanism into the linear problem of equivalent rigid mechanism, which lays a foundation for the research of compliant mechanism. Later, scholars put forward 2R, PR pseudo-rigid body model one after another, but these pseudo-rigid body models have insufficient degree of freedom, which leads to the limited simulation accuracy and range, which limits its further application. In order to solve the above problems, a multi-degree-of-freedom PRR pseudo-rigid body model with axial deformation is proposed by adding the degrees of freedom of the pseudo-rigid body model on the basis of the existing models. Considering a variety of complex loads, a new pseudo-rigid body model is established. The model is also studied. The main contents are summarized as follows: 1. The PRR pseudo-rigid body model of large deformation compliance mechanism is established for the compliant rod loaded with moment at the end. The torque load is applied to the end of the model, and the three-dimensional search process of the characteristic radius coefficient of the model is established by using the parameter approximate method, and the proportion of the axial displacement caused by the moving pair in the pseudo-rigid body model to the whole axial movement is quantitatively analyzed. The results show that the axial displacement of the moving pair almost does not occur under torque load, and the PRR model is basically consistent with the 2R pseudo-rigid body model. 2, the PRR pseudo-rigid body model of large deformation compliant mechanism is established for the compliant rod loaded at the end of the force. The numerical expression of the characteristic parameters of the model is obtained by the forward kinematic solution, the program block diagram is established by using the parametric approximate method, and the stiffness coefficient of the model is fitted by the linear regression method. By using the numerical analysis software, the simulation accuracy of the PRR pseudo-rigid body model is further improved by comparing with the existing pseudo-rigid body model and the end trajectory characteristics of the compliant rod. 3, for the compliant rod in the form of composite load at the end, The PRR pseudo-rigid body model of large deformation compliant mechanism is established. The load ratio is extreme treated, and the mathematical expressions of the pseudo-rigid body model under two extreme load forms are derived. The characteristic parameters of the model are solved by establishing three-dimensional search program and linear fitting method, and the superiority of PRR model under compound load is verified by comparing with other models. The PRR pseudo-rigid body model under different loads is applied to the plane compliant mechanism, and the PRR pseudo-rigid body model of compliant four-bar mechanism and compliant crank-slider mechanism is established. Through force-deformation analysis, the curve diagram of the relationship between slider displacement and crank angle and the pose change diagram at the end of flexible four-bar mechanism are obtained, and the results are compared with those of finite element analysis. The effectiveness of PRR pseudo-rigid body model in practical compliance mechanism is verified.
【學位授予單位】：中北大學
【學位級別】：碩士
【學位授予年份】：2016
【分類號】：TH112
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