英语翻译Firstly,spindle system in Fig.1 is divided into the number of elements given in Table 1.Then,from the Lagrange equation and the rotor dynamics,the dynamic model of the elements is established using the Timoshenko beam element.Finally,the

英语翻译Firstly,spindle system in Fig.1 is divided into the number of elements given in Table 1.Then,from the Lagrange equation and the rotor dynamics,the dynamic model of the elements is established using the Timoshenko beam element.Finally,the
英语翻译
Firstly,spindle system in Fig.1 is divided into the number of elements given in Table 1.Then,from the Lagrange equation and the rotor dynamics,the dynamic model of the elements is established using the Timoshenko beam element.Finally,the dynamic model of the drilling
system is developed using the element model,the bearing model,and the corresponding boundary conditions.3.1.Model of Timoshenko beam element Since the stiffness of micro-drills is small and there is eccentricity in the drilling system,the micro-drill and spindle bend when the axial drilling force acts.The bend causes the drill and spindle to deform elastically although the spindle deformation is very small.The elastic deformation makes the drill and spindle displace in radial and axial directions,respectively.Since the radial displacement is larger than axial one,axial displacement of the drill and spindle is neglected in this work[6–8].Fig.2 shows that a shaft element subject to axial force P is rotating at a constant speed O.Assume that the deformed displacements at any position of the element axis in x-and y-directions are x(s,t)and y(s,t),respectively,and that angle displacements of any cross-section of the element are yx(s,t)around the x-axis and yy(s,t)around the y-axis.

英语翻译Firstly,spindle system in Fig.1 is divided into the number of elements given in Table 1.Then,from the Lagrange equation and the rotor dynamics,the dynamic model of the elements is established using the Timoshenko beam element.Finally,the
怎么没有分?
首先,在图1主轴系统分为若干要素中给出表1.Then ,从拉格朗日方程和转子动力学,动态模型的内容是建立使用Timoshenko梁element.Finally ,动态模型在钻井
系统开发利用的因素模型,同时模型,以及相应的边界条件.3.1.Model Timoshenko梁自元的刚度微小型和演习是有偏心的钻探系统,微型钻头和主轴弯曲时的轴向钻削力acts.The弯曲原因演练和主轴虽然弹性变形主轴变形是非常small.The弹性变形使演习和主轴取代径向和轴向方向,respectively.Since的径向位移大于轴向之一,轴向位移的演习及主轴忽视这方面的工作[ 6-8 ] .图2表明,轴元素受轴向力P是一个不断旋转的速度我国假设变形位移在任何位置的元素轴的X和Y方向的第十章（秒,T ）和肽Y （秒,吨） ,分别与角位移的任何截面的元素是一心（秒,吨）在x轴和年（秒,吨）在y轴上.