论文部分内容阅读
为从力学本质上揭示SI-FLAT非接触式板形仪的检测原理,基于薄板流固耦合振动理论,建立了薄板振幅与残余应力关系的数学模型.在非协调F9ppl-von Kármán方程组的平衡方程中引入惯性项与流体压强项,利用气动载荷在时间上的周期性将流体速度函数、流体压强函数、薄板挠度函数和薄板应力势函数的时间变量分离出来,得到描述SI-FLAT板形仪稳定工作状态的偏微分方程组.进一步利用分离变量法求解该方程组,最终建立起薄板振幅与残余应力的数学关系.同时结合实测残余应力数据,利用Siemens提出的振幅-残余应力模型反算得到实际薄板振幅分布,并将其与流固耦合振动模型计算的振幅进行对比,验证了提出的数学模型的可靠性.进一步利用流固耦合振动模型分析了气泵进风口流体速度、检测距离和激振频率对振幅的影响,为SI-FLAT板形仪科学合理的利用提供了理论依据.
In order to reveal the detection principle of SI-FLAT non-contact profiler from mechanics, the mathematical model of the relationship between the amplitude of thin plate and the residual stress was established based on the fluid-solid coupling vibration theory of sheet metal.In the non-equilibrium F9ppl-von Kármán equation The inertia term and fluid pressure term are introduced into the equation, and the temporal variations of fluid velocity, fluid pressure, sheet deflection and sheet stress potential are separated by periodicity of the aerodynamic load. The system of partial differential equations with stable working conditions is further solved by using the method of separating variables to establish the mathematical relationship between the amplitude and the residual stress of sheet metal.At the same time the measured residual stress data are used to calculate the amplitude-residual stress model proposed by Siemens The amplitude distribution of actual thin plate is compared with the calculated amplitude of the fluid-solid coupling vibration model to verify the reliability of the proposed mathematical model.Furthermore, fluid-solid coupling vibration model is used to analyze the fluid velocity, detection distance and vibration The influence of frequency on the amplitude provides a theoretical basis for the scientific and rational utilization of the SI-FLAT shape analyzer .