论文部分内容阅读
一、轴的扭转振动的研究在工程中有着实际意义。工程中轴的扭转振动常简化成直轴的扭转振动。在轴的线性扭转振动中,为避免“共振”需求出轴扭振的固有频率。直轴扭振固有频率可列成为一个二阶线性常微分方程组(文献〔1〕)。二阶线性常微分方程组的求解在数学理论上是早已解决了的,然而由于具体求解时计算的繁杂,因而在工程中对轴的扭振固有频率的计算提出各种方法。其中在工程中应用较广的是Holzer在1921年所提出的剩余扭矩表格法(残矩法)〔1〕。Klotter,K.〔2〕全面总结、比较过1947年以前提出的各种主要方法。但由于简化它的计算,使能迅速求出轴扭振的固有频率,在工程设计中有实际意义,所以直到最近还有方法提出来〔4、6〕。其中有对〔4〕的讨论〔5、6〕。Holzer法虽可按一定表格,逐次假设频率,重复循环计算,最后从剩余扭矩为零时得到固有频率,但计算量大。尤对于经验较少的计算者,按表格法进行计算,要得到一个固有频
First, the torsional vibration of the shaft has a practical significance in engineering. The torsional vibration of the shaft in the engineering is often simplified to the torsional vibration of the straight shaft. In the linear torsional vibration of the shaft, the natural frequency of torsional vibration of the shaft is required to avoid “resonance”. The natural frequency of torsional vibration of straight shaft can be listed as a second-order linear ordinary differential equation (Reference [1]). The solution of second-order linear ordinary differential equations is already solved in the theory of mathematics. However, due to the complicated calculation in the concrete solution, various methods are proposed to calculate the natural frequency of the torsional vibration of the shaft in engineering. One of the more widely used in the project is the residual torque table method (residual moment method) proposed by Holzer in 1921 [1]. Klotter, K. [2] A comprehensive summary of the main methods proposed before 1947. However, until recently, methods have been proposed because of simplifying its calculation and enabling rapid determination of the natural frequency of shaft torsional vibration, which is of practical significance in engineering design [4,6]. There are discussions of [4] [5,6]. Although the Holzer method can be based on a certain form, one after another assuming the frequency, repeat the cycle of calculation, the final residual torque to zero when the natural frequency, but a large amount of computation. Especially for less experienced calculators, according to the table method to calculate, to get a natural frequency