1 The Linear Constitutive Equations And Its Dynamics Applications Of Viscoelastic Materials 2 The Mechanical Problems Research For Rotary Steering Drilling Tool

Viscoelastic material constitutive equations and its forms must be taken into account for analyzing vibration of visco-elastic composite structure. The forms of viscoelastic material constitutive equations are very important to the dynamic characteristics of visco-elastic composite structure. For different relaxation modulus, the viscoelastic material constitutive equations are of different forms. The study on linear constitutive equations of viscoelastic material is summarized. The five typical models in common use are recommended and discussed. They are complex modulus model, the standard model, fractional derivative model, fractional exponential model and mini-oscillator model, respectively. The dynamic applications of these models are briefly discussed. The dynamic equations of visco-elastic composite structure are second order linear Volterra differential-integral equations. It is difficult to analyze the modes of composite structure by using Volterra differential-integral equations. The extended order state variable forms of dynamic equations of visco-elastic composite structure are given. For three parameters standard model, the dynamic equations of visco-elastic composite structure are transformed into third order ordinary differential equations. The eigenvalue of visco-elastic composite structure can be calculated based on ordinary modal analysis theory and state space method. An analysis method for dynamic response of visco-elastic composite structure is presented by using extended order state variable method. By introducing Runge-Kutta integration method and the high-precision integration, the complicated problems of dynamic responses can be solved simply. By comparing the obtained results with the results of existing method, it is shown that the present method is accurate enough and efficient. The extended order state variable forms of dynamic equations of visco-elastic composite structure have many advantages, such as simple in formulation, easy in programming, and fast in calculating. In particular, the method can be applied easily to practical engineering problems. The estimation of model parameters of a viscoelastic material constitutive equations is a key problem in analyzing visco-elastic composite structure dynamics. The principle and method for fitting and estimation of constitutive equation model parameters are discussed. Based on the experimental data of energy storage module and loss factor for viscoelastic materials in a given frequency span, the model parameters of three constitutive equations, the standard model, the fractional derivative model, and the mini-oscillator model, are confirmed in using an optimization algorithm. Numerical examples are given to show the effectiveness of the present method. The closed loop control of stabilized platform is a key problem of modulated rotary steering drilling system. The stabilized platform control axes, which must be longer and slender, is subject to larger dynamic loads. The mechanical strength and stiffness of control axes are very important. The mechanical models of control axes designed by authors are established for mechanical strength and stiffness analysis .The mechanical strength and stiffness of the control axes are calculated by means of ANSYS, finite element analytical software. The theoretic basis for designing correctly a stabilized platform for a modulated rotary steering drilling system is put forward. The one of key problems of designing the control valve of a modulated rotary steering drilling tool (MRST) is the design of high pressure hole of upside disk valve. The work principle and mechanical model of the control valve of MRST are investigated. The best central angle parameters of high pressure hole of upside disk are given by theory analysis and simulation. The influence of the liquid lag on the force of palms is discussed. The theoretic basis for designing correctly the control valve of MRST is provided. The mechanical model of drilling string with modulated rotary steering drilling tool and resolving methods are new mechanical problems. In order to realize designing exactly and operating the down-hole closed-loop control system of well bore trajectory, the mechanical problems of bottom hole assembly (BHA) with modulated rotary steering drilling tool must be studied. The actual forces on BHA with modulated rotary steering drilling tool are investigated. Calculating formulas for the steering forces of bit are derived. The steering forces of bit are the summation of two parts. The one is called deformation steering force that is created by the elastic deformation of whole BHA, the other is called tool steering force that is created by rotary steering drilling tool. The application for calculating steering forces is programmed based on MATLAB. Numerical examples are given. The analysis results may be as theoretic basis for calculating the steering forces of bit and the prediction or control of well bore trajectory.