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研究生:張煌權
研究生(外文):Huang-cheng Chang
論文名稱:考慮磨粒隨機分佈之磨削力、振動及包含振動效應之表面粗糙度模式建立
論文名稱(外文):The establishment of stochastic grinding force and vibration model considering random grit distribution and ground surface roughness model with the effect of vibration
指導教授:王俊志
指導教授(外文):J-J Junz Wang
學位類別:博士
校院名稱:國立成功大學
系所名稱:機械工程學系碩博士班
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:2008
畢業學年度:96
語文別:中文
論文頁數:115
中文關鍵詞:磨削振動隨機磨削力模式隨機磨粒分佈功率密度頻譜表面粗糙度
外文關鍵詞:grinding vibrationsurface roughnessstochastic grinding force modelpower spectrum densityrandom grit distribution
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本文考慮磨削過程中磨粒隨機分佈特性,建立一套統合隨機磨削力、振動以及磨削表面粗糙度之磨削系統。首先考慮磨粒在砂輪上隨機分佈推導出隨機磨削力模式,進而將此模式與機台結構動態特性結合,建立磨削振動預測模式。最後利用變異分析將振動效應對表面粗糙度之影響。
在時域中,隨機磨削力可表示為單磨粒磨削力以及隨機磨粒密度函數兩者之捲積;在頻域中,總磨削力之功率密度頻譜(power spectrum density, PSD)則可表示為單磨粒磨削力之能量密度頻譜以及磨粒密度之PSD之乘積。根據隨機理論,平均磨粒密度與動態磨粒密度PSD與加工寬度及單位面積平均作用磨粒數呈正比;磨削力變異反而與單位面積平均作用磨粒數值呈反比。另外根據實驗結果,在本文之條件操作下磨削深度對於磨粒密度函數並不會有影響。在磨削振動模式建立方面,一開始建立考慮主要回饋項之閉迴路系統,而在一般平面研磨條件可將系統簡化為開迴路系統;磨削力強迫振動PSD解析式可表示為磨削力PSD以及結構動態撓性能量密度頻譜兩者相乘。透過此解析式可分析加工條件對磨削強迫振動之影響,並且透過特別設計之平板工件進行實驗,以驗證振動預測模式及分析結果之正確性。在考慮振動效應之磨削表面粗糙度模式中,均方根表粗度之平方可表示為磨粒隨砂輪轉動及振動之軌跡變異數相加。其中機台振動對於磨削振動之影響取決於隨著砂輪接觸剛性增加;並隨著工件磨耗剛性下降。其中尤以磨削深度變大時,會導致砂輪接觸剛性也會增加,而工件磨削剛性卻會減小之傳遞因子。因此傳遞係數會隨著磨削深度而增加,再加上磨削力上升激發較大之振動量,所以磨削深度對於表面品質之影響比磨削寬度以及床台進給速度更為顯著。
Considering the random nature of grit distribution, this thesis establishes a grinding system, incorporating the stochastic grinding force, vibration and ground surface roughness model. First, a closed form expression for the stochastic grinding force as a function of the grinding conditions and grit distribution is presented. With the grinding force model, further analytical study can then be carried out to investigate the effects of wheel properties, machine dynamics and process parameters on the resulting grinding vibration, as well as in characterizing the effect of vibration on the ground surface topology.
The stochastic grinding force model is formulated as the convolution of a single grit force and the grit density function in time domain, while the power spectrum density (PSD) of the total grinding force can be expressed as a product of the energy spectrum density of the single grit force and the PSD of the grit density function. A series of grinding experiments were performed and their results discussed to validate this model. Incorporating with the dynamics of the machine structure and the established force model, a closed loop grinding system was established. The system can be further simplified to an open loop system, thus the analytical expression for the PSD of grinding vibration can be derived. The effects of grinding conditions on the machine vibration can be analyzed based on the analytical expression machine vibration, and the results were verified by the experiments. By the variance analysis of kinematic grit and machine vibration profiles, an analytical ground surface roughness model representing their explicit effects on the ground surface was developed. The surface profile is treated as the superposition of the kinematic grit and vibration profiles. By the variance analysis of the two profiles, the root-mean-square ground surface roughness model can be derived. The transmitting factor, which defines the partition of power transmitted from spindle vibration to the ground surface, was derived from the dynamic grinding system and is related to the stiffness of the process, namely the workpiece cutting stiffness and wheel contact stiffness. An experimental procedure for identifying the stiffness in surface grinding was also developed. Discussions regarding the grinding conditions for the surface roughness based on experimental and model analysis results are presented. The model predictions and experimental results support the finding that a greater grinding depth and width increases the grinding force and hence deteriorates the ground surface.
摘要 I
Abstract III
誌謝 V
總目錄 VI
表目錄 IX
圖目錄 X
符號說明 XIV
第一章 緒論 1
1.1 前言 1
1.2 研究動機與目的 2
1.3 文獻回顧 3
1.3.1 磨削力分析及模式建立相關研究 3
1.3.2 磨削系統建立及振動、穩定性分析相關研究 6
1.3.3 磨削表面形貌分析及粗糙度預測模式相關研究 7
1.4 研究範疇與論文架構 9
第二章 隨機動態磨削力模式之建立與驗證 13
2.1 前言 13
2.2 隨機動態磨削力模式之建立 14
2.2.1 單一磨粒磨削力模式之推導 14
2.2.2 磨粒密度函數 17
2..2.3 總磨削力之合成 19
2.3總磨削力模式功率強度頻譜分析 20
2.3.1 基本磨削函數之能量密度頻譜分析 21
2.3.2 磨粒密度函數之功率密度頻譜分析 22
2.4 磨削常數之判認 24
2.5 實驗驗證與討論 26
2.5.1 模式正確性之驗證 27
2.5.2 磨削條件對磨粒密度函數及磨削力影響之分析 28
2.6 結語 31
第三章 磨削振動預測模式之建立 49
3.1 前言 49
3.2 隨機磨削振動系統之建立 49
3.2.1 隨機磨削力模式對磨削深度之線性化 51
3.2.2 線性磨削振動系統方塊圖之建立 53
3.2.3 磨削強迫振動之功率頻率密度分析 56
3.3 實驗驗證及結果討論 57
3.3.1 實驗設備配置及條件規畫 57
3.3.2 實驗結果及討論 59
3.4 結語 62
第四章 考慮機台振動之磨削表面粗糙度模式之建立 77
4.1 前言 77
4.2 磨削磨痕(lay)方向均方根磨削粗糙度解析模式之建立 78
4.2.1 磨削表面形貌之合成 78
4.2.2 磨削表面貌形變異數分析及均方根表面粗糙度 80
4.2.3 磨削表面磨粒運動效應之均方根表粗度 81
4.3 磨削製程剛性之判認 82
4.4 實驗步驟及結果討論 84
4.4.1 實驗方法及步驟 84
4.4.2 實驗結果 85
4.4.3 實驗結果討論 86
4.5振動預測模式之結合 88
4.6 結語 89
第五章 結論與建議 102
5.1 結論 102
5-2 建議 105
參考文獻 109
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