Analysis of fluid-structure interaction vibration based on the detection principle of SI-FLAT flatness measurement systems
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摘要: 為從力學本質上揭示SI-FLAT非接觸式板形儀的檢測原理,基于薄板流固耦合振動理論,建立了薄板振幅與殘余應力關系的數學模型.在非協調Föppl-von Kármán方程組的平衡方程中引入慣性項與流體壓強項,利用氣動載荷在時間上的周期性將流體速度函數、流體壓強函數、薄板撓度函數和薄板應力勢函數的時間變量分離出來,得到描述SI-FLAT板形儀穩定工作狀態的偏微分方程組.進一步利用分離變量法求解該方程組,最終建立起薄板振幅與殘余應力的數學關系.同時結合實測殘余應力數據,利用Siemens提出的振幅-殘余應力模型反算得到實際薄板振幅分布,并將其與流固耦合振動模型計算的振幅進行對比,驗證了提出的數學模型的可靠性.進一步利用流固耦合振動模型分析了氣泵進風口流體速度、檢測距離和激振頻率對振幅的影響,為SI-FLAT板形儀科學合理的利用提供了理論依據.Abstract: In order to reveal the mechanical essence of the detecting principle of SI-FLAT flatness measurement systems, the mathematical model of the relationship between amplitude and residual stress was established, based on the theory of fluid-structure interaction vibration of thin plates. The terms of inertia and fluid pressure were introduced to the equilibrium equation in incompatible Föppl-von Kármán equations. The time variables were separated out from the velocity function of fluid, pressure function of fluid, deflection function of thin plates and stress potential function of thin plates with consideration of periodic aerodynamic load. Therefore, the partial differential equations aiming at steady state of SI-FLAT flatness measurement systems was obtained. Solving the equations by using the method of separation of variables, the mathematical relationship between amplitude and residual stress was established. Combined with measured residual stress, the distribution of actual amplitude of thin plates could be calculated by the Siemens'amplitude-residual stress model, which coincided with the amplitude calculated by the fluid-structure interaction vibration model. The influences of fluid velocity at air pump's inlet, detecting distance and excitation frequency on amplitude were analyzed by using the fluid-structure interaction vibration model, which provides a theoretical basis for application of SI-FLAT flatness measurement systems.
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Key words:
- flatness measurement systems /
- residual stress /
- vibration /
- thin plates /
- fluid-structure interaction
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參考文獻
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