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研究生:陳恩傑
研究生(外文):En-Chieh Chen
論文名稱:大域模態假設法應用於轉軸在斜向移動負載下之動態分析
論文名稱(外文):Dynamic Analysis of Rotating Shaft under a Moving Skew Force with Global Assumed Mode Mthod
指導教授:蕭庭郎
指導教授(外文):Ting-Nung Shiau
學位類別:碩士
校院名稱:國立中正大學
系所名稱:機械系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2001
畢業學年度:89
語文別:英文
論文頁數:72
中文關鍵詞:斜向移動負載大域模態假設法
外文關鍵詞:moving sjew forceglobal assumed mode methodgeneral boundary condition
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高速化技術是近幾年工具機重要的發展趨勢,在高速切削發展已漸趨成熟的今日,進給系統若無法配合高速切削之需求,加工效率則無法提升;由此可見高速進給系統的研究實為重要之工作。現今進給系統的傳動方式可分為線性馬達及滾珠導螺桿兩類,其動態特性一般皆以一旋轉軸受移動負載來模擬,然而無論是線性馬達或是滾珠導螺桿,其在進給過程中均會受到斜向力的作用。因此,為了更有效率地分析高速進給系統的動態行為,本論文將應用大域模態假設法(Global Assumed Mode Mthod)探討旋轉軸受斜向移動負載動態特性。
經由理論分析得知,大域模態假設法相較於一般模態假設法,可建構更精簡的運動方程式,並能適用於不同邊界條件的系統。本研究將應用拉格朗至法(Lagrangian Approach)結合大域模態假設法,針對兩種常見的邊界條件─簡支撐(simply-supported)和固定支撐(Clamped-Clamped)推導出旋轉軸受斜向移動負載的運動方程式,再由朗吉─庫塔(Runge-Kutta Mthod)逐步積分法求得系統在移動負載下的暫態響應。有關系統的自然頻率則藉由解系統的特徵值問題求得。
數值結果顯示,斜向負載的傾斜角明顯影響著系統的自然頻率:傾斜角度越大,自然頻率會相對的變小。而由系統的暫態響應得知,簡支撐系統側向位移的振幅較小於固定支撐系統側向位移的振福;軸向位移的振福則是固定支撐的系統較簡支撐系統小。
High-speed technique has been an emphasis on machine tools for many years.
Especially the High-Speed Cutting is tending to maturity. To raise the efficiency of manufacture certainly, it should be paid much attention to the research of high-peed feed drive system. In general, the dynamic behaviors of a feed drive system can be modeled as a rotating shaft subjected to a moving force that is assumed as a skew force under high-speed operation. Thus, the Global Assumed Mode Method (GAMM) is used to investigate the dynamic behavior of a rotating shaft under a moving skew force in this study for more efficient purpose.
Comparing the GAMM with the assumed mode method (AMM), the theoretical analysis shows that the GAMM can not only construct simpler system equations of motion, but also be employed to analyze different system models combined distinct geometric boundaries. Hence, the system equations of motion in connection with two general geometric boundaries, i.e. simply-supported and clamped-clamped, are derived by Lagragian approach combined with GAMM in this study. The system natural frequencies are obtained by solving the system eigenvalue problem. Furthermore, the transient response of the system due to a moving skew force is evaluated by applying Runge-Kutta method.
From the numerical results, it is shown that the natural frequency is significantly affected by the skew angle of skew force. As long as the large skew angle is taken into account, the natural frequency will decrease. In addition, it is also indicated that the lateral deflections due to the skew force in the case of simply-supported boundary are smaller than that in the case of clamped-clamped boundary. And the axial deflections due to the skew force are larger in the case of simply-supported boundary.

ABSTRACT
LIST OF TABLES
LIST OF FIGURES
NONMENCLATURES
CHAPTERS
1 INTRODUCTION
1-1 Motivation of Research
1-2 Literature Review
1-3 Outline
2 FORMULATION OF EQUATION OF MOTION
2-1 Basic Assumptions
2-2 Lagrangian Approach
2-3 Transformation Matrix for Boundary Conditions
3 DYNAMIC ANALYSIS
3-1 Transient Response Analysis
3-2 Natural Frequency Analysis
4 NUMERICAL RESULTS AND DISCUSSION
4-1 Comparison of Numerical Results between GAMM and AMM
4-1.1 Comparison of Natural Frequency
4-2.2 Comparison of Transient Response
4-2 Dynamic Analysis of Clamped-Clamped Beam
4-2.1 Natural Frequency
4-2.2 Transient Response
5 CONCLUSIONS AND FUTURE STUDY
REFERENCE

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