旋轉式壓縮機之間隙對動態反應與性能影響之研究

Effect of clearance on dynamic response and performance of a rotary compressor

黃凱民(Kai-Min Huang)

指導教授 ： 黃元茂

國立臺灣大學/工學院/機械工程學研究所/碩士(2006年)

https://doi.org/10.6342/NTU.2006.01345

摘要

本研究探討單一滑動葉片旋轉式壓縮機的動態模擬和分析策略，並研究間隙對壓縮機的動態反應與性能之影響，同時提出精確、快速的接觸偵測與穿透深度的計算方法。本研究所考量的接觸分為葉片與滑槽的接觸，以及葉片前緣之半圓柱面與定子內壁之包絡線型曲面的接觸。研究方法主要是利用連續赫茲接觸力模型，模擬元件發生接觸時的正向接觸力，並考慮摩擦力的影響，再以多體動力學推導含拘束力的壓縮機系統動力方程式，而數值積分法則使用四階Adams預測-修正法配合四階Runge-Kutta法。為了更加感受其模擬結果的合理性，藉由計算機圖學的輔助，發展一般性之電腦動態模擬軟體，並將模擬結果以二維及三維動畫的方式呈現。由分析結果得知，在壓縮機於啟動狀態的初期或低轉速下，葉片的加速度將產生不穩定的情況。隨著轉速的提高，葉片運動的不穩定現象將會減少，而壓縮機的輸入功率、輸出功率和摩擦功率則會隨著轉速的提高而增大。當間隙存在時，壓縮機於運轉的過程中，葉片的運動會不平順，而此不穩定之現象，在葉片發生碰撞時最為明顯。隨著間隙的增大，壓縮機的輸入功率、輸出功率與機械效率則有明顯降低的趨勢，而葉片與定子及轉子將出現更多不同的接觸模式，且葉片的接觸力之最大值與平均值亦會明顯的變大。本研究中，以定子內壁之葉瓣數為3作為分析的基礎，轉速則設定為1500 rpm。當無間隙設定時，葉片的最大正向接觸力約為333 N，且葉片將出現10種不同的接觸模式，而壓縮機的機械效率約為75.7 %。當間隙設定為0.02 mm時，葉片的最大正向接觸力約為345 N，且葉片將出現16種不同的接觸模式，而壓縮機的機械效率約為74 %。當間隙設定為0.05 mm時，葉片的最大正向接觸力約為362.8 N，且葉片將出現19種不同的接觸模式，而壓縮機的機械效率約為70.8 %。當間隙值為0.1 mm時，壓縮機的機械效率約為65.12 %，當間隙值達0.2 mm時，壓縮機的機械效率則降為約54.2 %。由研究結果得知，本文之方法對於其它存在此二類接觸問題之壓縮機，亦可合理的應用。

關鍵字

壓縮機 ； 多體動力學 ； 間隙 ； 碰撞 ； 接觸偵測

並列摘要

This study develops dynamic simulation and analysis strategic of a single sliding-vane rotary compressor and analyzes effects of clearance on dynamic response and performance of the rotary compressor. It also provides accurate and fast solutions for contact detection and computing technology of penetration. Two types of contact are considered. One type is the contact between the vane and the vane slot, and the other type is the contact between the semi-cylindrical surface of the vane and the envelope surface of the stator. The continuous Hertzian contact force model is utilized to calculate contact forces of the compressor components with consideration of frictional forces. The dynamic equations including constrained forces of the compressor system are derived by using multibody dynamics. The numerical integration uses the fourth-order Adams predictor-corrector method incorporated with the fourth-order Runge-Kutta method. With two-dimensional and three-dimensional animations of computer graphics, it is easy to understand simulated results. When the compressor is turned on or it operated with low rotational speed, the unstable acceleration of the vane occurs. As the rotational speed increases, the unstability of the vane is reduced while the input power, the output power and the friction power of the compressor increase. The vane becomes unstable when the clearance exists. The unstability of vane is significant when impact happens. As the clearance increases, the input power, output power and mechanical efficiency of the compressor are decreased, and contact types of the vane with the stator and the rotor increase. The maximum and average contact forces of the vane also increase. A stator with three lobes and the rotational speed of 1500 rpm with and without clearance are studied. If there is no clearance, the vane has 10 kinds of contact modes, the maximum contact force of the vane is 333 N, and the mechanical efficiency of the compressor is 75.7 %. If the clearance is equal to 0.02 mm, the vane has 16 kinds of contact modes, the maximum contact force of the vane is 345 N, and the mechanical efficiency of the compressor is 74 %. If the clearance is equal to 0.05 mm, the vane has 19 kinds of contact modes, the maximum contact force of the vane is 362.8 N, and the mechanical efficiency of the compressor is 70.8 %. If the clearance is equal to 0.1 mm and 0.2 mm, the mechanical efficiency of the compressor is 65.1 % and 54.2 %, respectively. It is expected that the results of this study can also be applied to compressors with these two types of contact problem.

並列關鍵字

compressor ； multibody dynamics ； clearance ； collision ； contact detection

參考文獻

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