摘要
接触是普遍存在的力学问题,由于其问题的复杂性,它一直是工程学与力学两门学科所共同面临的难题。对于多体接触,即使是弹性光滑接触问题,由于其边界非线性,采用数值方法分析求解也有很大的难度。正是由于该问题的普遍性和复杂性,也使得该问题的计算分析显得极为重要。
本文以某型号固体火箭发动机轴承类接头多体接触的关键问题为研究背景,基于滚动轴承,采用接触问题的非线性有限元方法,在额定载荷下进行全尺寸三维多体非线性有限元分析。
作为滚动轴承工程学基础的轴承力学分析与轴承的设计和应用技术密切相关。而作为评定滚动轴承实际工作状态下的各项技术因素如负荷能力、疲劳寿命、变形与刚度、振动与噪声等都与这种弹性接触问题有着密切的联系。通过寻求合适的数值计算方法并借助高速电子计算技术对这种接触问题进行局部乃至整体的接触应力和弹性变形分析求解,将成为滚动轴承及轴承类零部件进行优化设计和可靠性分析的关键。
传统计算轴承的方式是采用力平衡方法及Hertz接触理论。由于这类问题受负荷作用情况复杂,且Hertz接触理论的前提假设在简单形状的单体规则体接触,在半无限空间的边界条件下,对于多体及三维复杂几何及载荷边界条件,其解析解尚未建立。
本研究在进行轴承分析之前,先根据Hertz接触理论的解析解,验证滚动体与钢板有限元接触模型的分析结果,同时它也是某型号固体火箭发动机喷管接头单项预研的基础。然后分别对二维和三维接触模型的分析,进行边界条件、接触参数及单元尺寸、形状、离散网格方式的预测,以确立适合滚动轴承全尺寸三维有限元接触分析的有限元模型,从而得到更为精确的计算分析结果。
对61801深沟球轴承,在其接触角为零,不考虑游系的情况下,分别对局部和整体进行静态有限元计算分析。基于有限元分析软件ANSYS,建立了滚动轴承接触分析的三维有限元模型,对轴承的接触问题进行了数值模拟,得到了轴承承载过程中的应力和变形分布趋势。通过与Hertz理论计算结果对比分析,两者结果比较接近。在此基础上进行了某型号固体火箭发动机喷管接头的三维弹性接触应力及摩擦分析( f =0.003),其结果有待于实验进一步验证。
滚动轴承及某型号全轴摆动喷管接头处接触问题的计算分析结果,为轴承的动力学仿真及高性能材料的某型号固体火箭发动机类轴承接头的接触问题的进一步分析研究奠定了理论基础。
The contact is a universal mechanics question, as a result of its complexity; it is always a difficult problem to both the engineering and mechanics. Regarding polysome contact, even if it is the elastic smooth contact question, as a result of its boundary non-linearity, it is very difficulty to analysize with numerical method. Just for its universality and complexity, it appears extremely important.
In this article taking the attachment polysome contact key question of bearing which is used for some model solid propellant engine as the research background, based on the rolling bearing, applying the non-linear contact question in finite element method, the whole size 3D polysome non-linear finite element analysis under the work load is carried on.
As the basis of engineering theory of the Bearings, the mechanics analysis of the Bearing is closely involved in the Bearings' design and application technical. Several main technical factors used to evaluate the practical working states of the Bearing such as capacity to load, fatigue life, tolerance life, deformation and rigidity, vibration and noise should be related to the contact problem. It’s a key for the optimization design and reliability analysis of the Bearing to calculate and analyze the partial or entire contact stress and elastic deformation through seeking accurate algorithm approach based on the computer.
Static force balancing and Hertz contact theory are adopted to calculate the bearing; however it is difficult to obtain the accurate stiffness value due to the complicated loading of the bearing. In addition Hertz contact theory is only applied to the simple shape and semi-infinite boundary condition. Therefore the penalty method has been adopted here to solve the contact problem with the consideration of large deformation and the friction. The finite element method also has been employed to establish and analyze the bearing model built with ANSYS to estimate the relative displacement of inner and outer ring and bearing stiffness under various boundary conditions.
According to Hertz contact theory, its analysis result can be applied to verify the contact model of a steel ball and a plate in numerical techniques. Then the optimum contact analysis model is built for finite element in elementary mesh way to estimate the normal stiffness. The result of this investigation proofs the finite element method is more suitable.
Based on the software of ANSYS, the finite element contact model of the bearing 61801 was established. The bearing of contact deform process was numerically simulated with ANSYS. The direction of the stress and strain of the bearing contact was founded. Compared with the results which were calculated by Hertz theory, there were nearly equal. That means the finite element analysis is feasible. And the simulation applied precondition for the dynamic study in theory. Based on which the contact stress and the friction analysist to some solid propellant engine nozzle contacts is carried on, and the result waits to be confirmed furtherly by experiment. The computation and analysis of the contact question to the bearing and this model nozzle attachment place has laid the rationale for the bearing dynamics simulation and the further analysis of attachment contact question to the bearing which is used for some solid propellant engine and made with high performance materiall.
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