| The precision or ultra-precision machine tool is matter of a vital strategic equipment having deep influence on the national economy and people’s livelihood, which is specially used in the precision or ultra-precision processing for the key parts in the field of national defense industry and civil optical industry. spindle is the core functional part of the precision or ultra-precision machine tool, whose rotational accuracy has a decitional influence on machining accuracy. However, as a result of the dynamic unbalance of the spindle, journal profile error, electromagnetic excitation due to inclination and eccentricity of the spindle, it is very difficulty to analyze and predict the rotational accuracy of the spindle. At present, the research is not systematic and profound in the respect mentioned above at home and abroad. It is urgent to research the rotational accuracy of the hydrodynamic and static spindle influenced by the profile error and electromagnetic force.(1) A dynamic model for predicting the rotational accuracy which is based on Timoshenko beam theory is constructed. It considers the factors of the journal bearing, unbalance magnetic pull, grinding force and the spindle. Element matrixes including mass, stiffness and damping are deduced by using the Timoshenko beam theory and Lagrange dynamics equation. Element load vectors including gravity and unbalanced force are derived by applying symbolic integration function module in the software named’Matlab’. An united dynamic model is constructed based on Timoshenko beam theory with global matrix including mass, stiffness, damping, also with global load vector, which considers the factors of the journal bearing, unbalance magnetic pull, grinding force and the spindle. Using the absolutely convergent numerical algorithm named Wilson-9, the dynamic model constructed above is solved by the code programmed independently in Matlab software platform. The characteristics and applicable scopes for assessing the rotational accuracy are clarified. The assessment indexes contain three types, such as difference of radius between the circum circle and inscribed circle whose circle center is fitted by the axis orbit, radius of the envelop circle, peak-peak value of sensitive direct synchronous error. Through comprising with the natural frequency provided by the present references, the effectiveness of the model constructed and the program algorithm proposed in this paper is verified.(2) According to the parallel plate flow diffusion model and the physical phenomena that the relative movement between the two flats produces the extrusion flow, a method belonged to the finite volume method is proposed to calculate the nonlinear oil film force for a kind of deep-shallow recess bearing hydrodynamic and static journal bearing. In order to solve the problem that the fixed grid is difficult to effectively eliminate the low frequency iterative error, the multi-grid iterative technology is used to accelerate the convergent speed and improved calculating efficiency. The equilibrium position of the spindle is found by Euler iterative method, the eight bearing dynamic characteristic coefficient is deduced by the small disturbance conditions of displacement, speed. The method is used to study the bearing characteristics with the different structure parameters and working parameters, such as supply pressure, spindle speed, oil inlet aperture, shallow depth and initial oil film thickness. An engineering experience that the shallow recess depth of the deep-shallow recess bearing should be about twice the initial oil film thickness is validated rationally by the numerical calculation. After an experimental platform is established, the pressure values of oil cavity are measured with different rotational speed and supplying pressure. The correctness of the method for calculating the nonlinear oil film force belonged to the finite volume method is verified.(3) According to the present situation that the calculate model of unbalanced magnetic pull (UMP) with rotor tilt and eccentricity is not perfect, a semi-analytical solution is provided to calculate the UMP by using air gap magneto resistance of each node in the air domain and applying Maxwell stress. By contrast with the existing references, the results showed that the semi-analytical method mentioned in this paper for calculating the UMP is right and has higher efficiency than the finite element method. Under the same conditions for other electro magnetic parameters, in order to minimize rotational error due to UMP, the motor pole-pair numbers should be no less than two. The electro magnetic parameters of a type of motor in this paper are verified reasonably by using Ansoft 2D transient simulation module. The law that the UMP and magnetic stiffness vary with eccentricity and inclination angle of the rotor is studied with the method mentioned above. The result shows that the level of the UMP is the same with the dynamic unbalance force’s, and the effect due to the UMP can not be ignored.(4) The law that profile error of journal affects the rotary accuracy of journal bearing is studied quantitatively. A model is constructed to explain how the roundness error causes the rotary accuracy movement. The mechanism that rotary accuracy is affected by the roundness error is revealed. The laws could be explained by the model as follows:without considering the gravity, the dynamic unbalanced force and other external force, under concentric condition, the roundness error with odd frequency per period does not produce rotary motion, whereas the roundness error with even frequency per period does not produce it. After considering all the above external force, the roundness error with odd frequency per period has more significant impact on rotary accuracy than the roundness error with even frequency per period. Rotary accuracy decreases with speed and magnitude of the roundness error increasing. The component of odd frequency per period in the composite journal roundness error plays a dominant role in affecting the rotary accuracy.(5) The effect of a combination of factors such as journal profile error, UMP, and grinding force affecting the rotary accuracy is revealed. The result showed that the UMP with two pair poles and the grinding force belongs to step-change type change the equilibrium position only and have little affect on the rotary accuracy. In the same conditions, when the amplitude of journal roundness error with odd frequency per period is small enough, the rotary accuracy of the front node of spindle can achieve precis ion-grade. Journal cylindrical error(tapered cylindrical error, drum-shape cylindrical error and saddle cylindrical error) has little effect on the rotary accuracy of the front node of spindle.(6) The liquid hydrodynamic-static spindle experimental bench is settled up, the rotary accuracy of the spindle and the natural frequency are tested. The results showed that the calculate values agree well with the experimental ones. Both the experimental values and the theoretical values of synchronous rotary error are below 1 um, and have the same trend varying with speed. The correct nesses of the model constructed, the algorithm provided and the results studied are validated.This thesis offers an important theoretical method and effective implementation way for realizing the simulation of the dynamic transition process of the spindle from the origin to the equilibrium position quantitatively, and for revealing the mechanism that the journal profile error affects the rotary accuracy, provided a strong technical support to design new type of high precision liquid hydrodynamic-static spindles and grinding equipments... |
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