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研究生:蘇威守
研究生(外文):Wei-Shou Su
論文名稱:交叉滾子軸承負載分析
論文名稱(外文):Load Analysis of Cross Roller Bearing
指導教授:蔡錫錚
指導教授(外文):Shyi-Jeng Tsai
學位類別:碩士
校院名稱:國立中央大學
系所名稱:機械工程學系
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:2019
畢業學年度:107
語文別:中文
論文頁數:113
中文關鍵詞:交叉滾子軸承接觸負載分析滾子輪廓修整加工誤差分析
外文關鍵詞:Cross roller bearingLoad contact analysisRoller corwningMachining error analysis
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交叉滾子軸承的應用非常廣泛,適用於高精度及高負載之傳動上,然而因交叉滾子軸承之滾子交叉排列,在不同負載的交互作用下滾子的負載分配會較為複雜。因此本論文的研究目的即在建立交叉滾子軸承分析模型,分析軸承中各滾子之分配負載與接觸應力。在論文中先以等剛性接觸假設,利用軸承外環與滾子之位移關係求解軸承在承受綜合負載下各滾子之負載分配。而為求得滾子受載後之接觸應力分布,利用交叉滾子軸承在空間中的幾何特性,以影響係數法建立受載接觸分析模型,並以等剛性接觸方法作為預判接觸滾子,以加速計算流程。此模型除可得到各滾子負載分配,並可得到不同滾子修整輪廓與不同負載下滾子與滾道間的接觸應力分布。
在本論文中以大尺寸之旋轉齒輪軸承以及小尺寸之一般交叉滾子軸承等兩種案例進行分析,以了解軸承滾子受載下的接觸特性。分析中則考慮無修整、大圓、對數修整等三種修整輪廓,以及滾子接觸長度,滾子直徑誤差,滾子分布位置誤差對各滾子負載分配與接觸應力所造成的影響。
負載分配分析結果顯示,交叉滾子軸承因為相鄰滾子軸線交錯配置,在外環承受軸向負載時,僅相同軸線方向之滾子承受負載;承受正x方向之徑向負載時,由第二、三象限內所有滾子承受大小不等之負載;承受傾覆力矩時,力矩轉軸每側區域內所有相同軸線方向之滾子承受大小不等之負載。而無承受負載之滾子則因軸承外環位移而與滾道產生間隙,因此在綜合負載下,相同軸線之滾子有各自的負載分配曲線,其中某一軸線方向之滾子在部分區域內可能不受負載。
應力分布分析結果顯示,無修整滾子的接觸邊緣會出現應力集中的情形,而在大圓及對數修整的輪廓下,滾子應力集中的情形可以得到改善,使得應力在接觸面上分布的更加平均。而在接觸長度與迴轉半徑比值較大時,接觸長度對負載之影響較為顯著,其中又以受到傾覆力矩時影響較為顯著。滾子直徑誤差對於滾子負載分配整體趨勢大致相同,但因滾子直徑的不同而有不規則跳動。滾子因不同厚薄保持器之配置而造成的位置誤差,則僅會造成整體負載分配曲線之移動。
本研究同時建立旋轉齒輪軸承之承載能力界限圖,透過軸向及徑向負載交互影響之關係曲線,可快速挑選符合安全係數要求之對應軸向與徑向負載。
由分析結果可知本論文發展之分析方法,能夠快速並且準確的分析在不同幾何外形下,交叉滾子軸承整體的負載分配趨勢以及各滾子與滾道間接觸應力之分布情況。
Cross roller bearings are widely used in high-precision and high-load drives. However, due to the cross-arrangement of the rollers of bearings. The load distribution of rollers is complicated because of the interaction of different loads. Therefore, the purpose of this paper is to establish a cross roller bearing analysis model to analyze the distributed load and contact stress of each roller in the bearing. At first, use constant contact stiffness method to solve the load distribution of the bearings under the integrated load with the displacement relationship between the outer ring and the rollers. In order to obtain the contact stress distribution of loaded roller, the loaded contact analysis model is established by the influence coefficient method by using the geometric characteristics of the cross roller bearing, and the constant contact stiffness method is used for predicting contact roller in order to speed up the calculation process. In addition to the roller load distribution, the model can also obtain the contact stress distribution of different roller crowning profiles. And the contact stress distribution of rollers and raceways under different loads.
In this paper, two cases of large-sized slewing gear bearings and small-sized general cross roller bearings are analyzed. To understand the contact characteristics of bearing rollers under load. In the analysis, three crowning profiles such as non-crowning, circular, and logarithmic crowning are considered, as well as the effects of roller contact length, error of roller diameter, and error of roller position.
The result of load distribution analysis of each roller shows when the outer ring of cross roller bearings is subjected to the axial load, only the rollers in the same axial direction are subjected to the load due to the adjacent roller axes are staggered; when subjected to the radial load in the positive x direction, all the rollers between second and third quadrants are subjected to loads; when subjected to the overturning moment, all the rollers of the same axial direction in each side of the torque shaft are subjected to loads. Rollers that do not bear the load have gaps with the raceway due to the displacement of the outer ring. Therefore, under the integrated load, the rollers of the same axis have their respective load distribution curves, and the roller of one axial direction in a partial area may not be overloaded.
The result of stress distribution analysis shows that stress concentration occurs at the contact edge of the non-crowning roller, and under the circular and logarithmic crowning, the stress concentration of the roller can be improved, so that the stress is more evenly distributed on the contact surface. When the ratio of the contact length to the radius of bearing is large, the contact length has a significant influence on the load, and the influence is more significant when the overturning moment is applied. The error of roller diameter is roughly the same for the trend of roller load distribution, but there is irregular runout due to the difference in roller diameter. The error of roller position caused by different thickness holders only result in the load distribution curve to move.
This paper also establishes the limit diagram of the bearing capacity of the slewing gear bearing. Through the relationship between the axial and radial load, the corresponding axial and radial loads meeting the safety factor can be quickly selected.
From the analysis results, the analysis method developed in this paper can quickly and accurately analyze the load distribution trend of the cross roller bearing and the distribution of the contact stress between different geometric shapes of the rollers and the raceway.
摘要 i
Abstract iii
謝誌 vi
目錄 vii
圖目錄 x
表目錄 xv
符號說明 xvi
第 1 章 前言 1
1.1 研究背景 1
1.2 文獻回顧 4
1.3 研究目的 6
1.4 論文架構 7
第 2 章 交叉滾子軸承幾何 9
2.1 幾何接觸模型 9
2.2 內外環滾道數學模型 12
2.3 滾子輪廓數學模型 13
2.3.1 無修整 14
2.3.2 對數修整 14
2.3.3 大圓修整 15
2.3.4 滾子與滾道之接觸間距 16
2.4 外環與滾子等效位移 19
2.4.1 軸向位移 20
2.4.2 徑向位移 21
2.4.3 角度位移 23
第 3 章 交叉滾子軸承受載接觸分析模型 27
3.1 外環與滾子受力平衡 27
3.2 等剛性接觸負載計算模型 28
3.2.1 滾子之位移–變形關係 28
3.2.2 等剛性接觸分析模型 29
3.3 影響係數法計算模型 31
3.3.1 影響係數法基本分析模型 31
3.3.2 兩滾子接觸對受載分析模型 34
3.3.3 軸承完整受載分析模型 36
第 4 章 軸承分析案例 39
4.1 旋轉齒輪軸承 40
4.2 交叉滾子軸承 41
第 5 章 理想狀況下之負載分析結果 44
5.1 單一負載下滾子負載分配 44
5.1.1 旋轉齒輪軸承 44
5.1.2 交叉滾子軸承 46
5.1.3 輪廓修整對滾子負載分配之影響 48
5.2 綜合負載分析結果 50
5.2.1 旋轉齒輪軸承 51
5.2.2 交叉滾子軸承 54
5.2.3 考慮滾子接觸長度對負載分配影響 54
5.3 滾子應力分布 56
5.3.1 內外環與滾子接觸比較 56
5.3.2 滾子輪廓修整比較 59
5.3.3 考慮滾子接觸長度 61
第 6 章 誤差模擬分析 76
6.1 滾子加工誤差模擬 76
6.1.1 隨機取樣 76
6.1.2 滾子加工誤差分析結果 76
6.2 滾子分布誤差模擬 79
6.2.1 滾子分布模擬 79
6.2.2 滾子分布誤差分析結果 79
第 7 章 軸承之承載能力分析 81
7.1 額定靜負載與負載限值 81
7.2 旋轉齒輪軸承案例之承載能力界限 82
7.2.1 砲塔結構與負載關係 82
7.2.2 承載能力界限圖 82
第 8 章 結論與未來展望 87
8.1 結論 87
8.2 未來展望 89
參考文獻 90
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[9] 蔣旭君,「交叉滾柱迴轉支承載荷分布及游隙的影響」,重慶理工大學學報,第31卷,第7期,102-108頁,2017。
[10] Hartnett, M. J., “The Analysis of Contact Stresses in Rolling Element Bearings,” J. of Lubrication Tech, Transactions ASME, Vol. 101(1), pp. 105-109, 1979.
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[14] Harris, T. A. and. Kotzalas, M. N., “Rolling Bearing Analysis – Essential Concepts of Bearing Technology,” 5th edition. Wiley, New York, 2007.
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