基于汽車輪轂軸承自動線生產線輔助系統(tǒng)設計
基于汽車輪轂軸承自動線生產線輔助系統(tǒng)設計,基于汽車輪轂軸承自動線生產線輔助系統(tǒng)設計,基于,汽車,輪轂,軸承,自動線,生產線,輔助,系統(tǒng),設計
附錄
有限元素分析與設計42（2006）298 - 313
大型軸承螺栓接頭數值模式的發(fā)展
作者：奧里安 韋迪納，*，迪米特里 尼瑞巴 ，讓 癸樂特布
加拿大H3C公司3A7,魁北克，蒙特利爾，沙田，車站中心，蒙特利爾Ecole理工學院，機械工程系，P.O 6079信箱
摘要：
螺栓接頭的傳統(tǒng)理論并沒有考慮到外部負載的復雜性，既沒有其相關連接的不靈活性，也沒有接觸的非線性。本文論述了可以快速，精確的計算直徑軸承上承受很大傾覆力矩的緊固螺栓的二維數值模型。該模型的獨特性是在于一個特殊的有限元素的使用，像一環(huán)，除了在軸向方向。其軸向剛度是控制螺栓組裝方式的局部剛度。該模型調整為三維有限元的模擬，并在幾種類型的軸承中表現了優(yōu)異效果。
關鍵詞：螺栓接頭;數值模式;轉盤軸承;有限元分析
1、 介紹
提供快捷，準確的結果，是對實際工程的挑戰(zhàn)之一，主要是在設計過程的早期階段。涉及不同的螺栓接頭的機械系統(tǒng)的制造商需要合適的計算模型，該計算模型需要考慮整體解決方案。大量的模型近似的部件和螺栓剛度使用錐體，球體，相當于瓶裝或其他分析模型[1-4]。 根據傳統(tǒng)理論，最初是為那些居中或稍微偏離中心的負荷發(fā)展，該負荷的剛度為常數。然而，有限元模擬以及實驗結果顯示出強勁的非線性由于接觸面積的變化[5-7]與外部負載。剛度非線性特性進行了研究格洛斯[8]和吉洛[9]，他們提出了一個非線性模型，但只有板樣的配置。
另一個傳統(tǒng)理論的弱點在于所謂的負載系數的計算方法。負荷因素試圖測量傳送到螺栓上面的外在的力量。在外部力量的成員上應用所在地管轄的負載因子和剛度成員的方式分配。張[10]開發(fā)了一種新的螺栓接頭分析模型，并考慮到剛性還原會與殘余力量有關，壓縮變形和尺寸變化的外力是因為成員輪換造成的。這種模式有它的局限性，并不適用于螺栓裝配時的成員有不同的幾何形狀，或在外部勢力不是在成員接口對稱的。
對于具體模型，我們提出對大型軸承可以看作為一個圓形法蘭盤，考慮到不同的非線性特性以及不同的配置或通過適當的幾何剛度分布的通用模型的基礎。
2、 回轉支承
本文提出的模型是對特定的大直徑螺栓軸承合適。這些大型軸承（高達13米（43英尺））也被稱為“回轉支承”，是用起重機，雷達菜，隧道掘進機，軸承套圈等。二是夾在主框架由高強度的螺栓預裝。一個或兩個環(huán)是提供齒，使擺動驅動器進行運轉。連接就像大量的一個個又厚又狹小的螺栓固定一個非常嚴格的框架圓柱法蘭。
該系統(tǒng)的另一個特殊性是重要的和可變的傾覆力矩。軸承是遭受同樣重要徑向和軸向負荷。軸承所研究的三個類型，球軸承，交叉滾子軸承和三排滾子軸承，如圖 1所示。
由于結構的復雜性和特殊性，螺栓聯合負荷，既不是傳統(tǒng)的模式也不是非線性模型是合適的。
圖 1 回轉軸承
因此，我們已經開發(fā)出一種新的模式，同時考慮到在與框架單元的軸向方向，并與管狀分子徑向方向的彎曲剛度。此外，管內容進行了修改，涉及螺栓裝配的預裝行為特征。此外，在建模過程是一個原始的“混合”有限元素的定義。這個元素有一個除了在其軸向剛度有關，局部剛度，支配行為的螺栓裝配環(huán)的一般行為。嚙合同幾個元素的環(huán)狀物可以考慮到非線性剛度分布，特別是對高負荷的應用效果。不斷演變的接觸面積是仿照通過接觸彈簧和使用迭代求解的技術。
3、 建模和假設
對這些系統(tǒng)的具體負荷是一個偏離中心的軸向載荷（正常起重機載荷型）在一個大的傾覆力矩造成的。這將建立在軸承槽（如圖1內部負載1）。在這個發(fā)展階段，外部負荷強度并不重要。這足以適用于兩種型號相同的載荷：二維數值模型和三維有限元模型用于調整的第一個步驟。
要構建數學模型，我們提出了一些簡化：
?建模的目的，我們只考慮負載最重的螺栓和相關零件;
?外圈不僅是為模型。因此，外部勢力所取代滾動體負荷，等效負載增加螺栓的工作負荷;
?加載，以及有關的具體內容的制定被認為是軸對稱;
?安裝被認為是非常嚴格的。
圖 2 基本原則提出了新的建模。在左邊的是素描和數值模型;右側的是等效有限元模型。
圖2 建模原理
正如圖 2顯示，軸承環(huán)模型包括三個要素的類型：
A：盤子模型是以由沃代安[11]提出和羅克解析式[12]發(fā)展的圓板模型為基礎的。他們有兩個自由度/節(jié)點（是翻譯和z旋轉軸對稱元素）及其作用：
?為代表的環(huán)的彎曲度是根據OY軸的方向;
?表征移位，尤其是環(huán)狀物的邊界不斷增長和它的分離。聯系彈簧元素它們能夠模擬環(huán)變量之間的接觸帶和安裝根據預安裝和外部負載的應用。因此，以不同的接觸狀態(tài)，物體的剛度矩陣將被調整和它們對螺紋元件的非線性負荷將增大。
B：所謂的混合物原理使人們有可能考慮到物體的部分壓縮剛度，以及具體的彎曲沿徑向方向的撓度。每個節(jié)點的三個自由度使鐵元素的結構與系統(tǒng)的受力相當于外部負載。
C: 元素的彎曲和分裂是由于模型的接觸與安裝。它們的行為特征的彈性表現在該接口和單方面的接觸。彈簧剛度模型可作為一個調諧參數。
螺栓有一個等效梁的制定在本文件的以后會有講述。
3.1 確定軸承的軸向剛度位置
為了計算軸承的軸向剛度位置，我們已經使用MASSOL[13]根據拉斯穆森[14]提出的一個基本圓柱集會（圖3）所作的改進。本節(jié)計算的等效部分,記為Ap,使我們能夠確定零件剛度的Kp值。所用的關系式為
（1）
圖3 一個基本部件的尺寸
圖 4 軸向剛度部門尺寸計算
用下面的無量綱量：
對我們的知道軸承而言，有一部分不圓。外型尺寸X和Y是考慮如圖4所示。
如果直徑
Dp=3*Da (3)
不是該扇形面的部分上，下面的表達式。那么就使用
Dp=(x+y)/2 (4)
該扇形面的總軸向剛度計算是用 等式（1）和（2）。考慮LP的長度等于軸承圈的高度。軸向剛度Kp值以及相當于相等的面積Ap，從而得到考慮整個扇形的角度。
3.2 混合元素
如圖2所示 ，嚙合的軸承環(huán)使用的三個混合元素與三個主要部件有關：一個元素指定為環(huán)之間的上表面和軌道上負載生效的起點之間的區(qū)域;第二個元素是指定減少的區(qū)域是由軸承滾道和在軸承滾道及其安裝之間的下部區(qū)域的三分之一所決定。中間節(jié)點面對滾動體接觸點，使外部力量應用到其中之一。
v1
θ1
R - 元素的平均半徑
T - 元素的徑向厚度
L - 元素的高度
u，v，θ - 局部自由度
圖 5 管（圓柱表面）元素的參數
圖6 圓柱表面單元矩陣
3.2.1 混合單元剛度矩陣
由于相比于外徑和高度相對較低的徑向厚度，在外圈的運動方式是和其內表面裝載的管子相似的。該管的基本自由度以及主要參數顯示如圖 5。其代表性是以圓柱表面的基本公式[15]為基礎。
對于我們軸承，重要的是要考慮到一個具體的圓柱表面彎曲，以及由一個徑向力（或壓力）造成的徑向位移。這種根據羅基[15]如圖6所示的元素的剛度矩陣很普遍。在圖6中，所有的表達方式kij都使用R，T，L參數（圖5），E-電子楊氏模量和-泊松數字來表達。
混合元素的剛度矩陣是以圓柱表面元素公式為基礎的。為了準確的在軸向剛度建模，與圓柱表面單元矩陣的拉伸力的表達方式對應的行和列已被等效剛度的梁的公式所取代。因為輕微的影響力，所以連接表達方式設置為零，正如數值試驗表明。在圖 6（給予部分坐標）采用的坐標轉換程序根據整個模型的坐標系統(tǒng)和編號矩陣圖控制的原因提出來的。
在全球CS的管狀物元素矩陣的拉伸自由度是（行和列）六方面。該矩陣轉換得到的最后形式是如圖 7 介紹的雜交元矩陣。
在新的條件下截面積Ap和以前提出的橫截面計算使用改進的RAS -穆森公式[14]是相等的。
此外，為了考慮負載點的應用高度，總軸向剛度（或相反的靈活性）必須用不同的元素在非均勻模式下來分配，正如在3.3節(jié)中討論的。
圖 7 管狀物元素矩陣轉化成雜交元矩陣
上部靈活的Sp1
銻螺栓的靈活性
下部靈活的Sp2
圖 8 螺栓裝配示意圖
3.3 考慮外在負載應用程序的起源
正如Guillot[9]和最近以來的張[10]所示的外負載應用這個地方,對螺栓裝配行為,計算拉力的標準及帶有螺紋部件的彎曲瞬間補充度有極其重大影響。對于一個軸向載荷,螺栓的裝配可以按照圖8所示來代表。
圖 9 實際區(qū)域的壓縮
圖 10 自適應的靈活性
眾所周知,和初始狀態(tài)的預加負荷Q比較,外力導致螺栓受力增大。螺栓所受總力Fb為
Fb=Q+Sp2*Fe/(Sp+Sb) (5)
全部零件的靈活性
Sp=Sp1+Sp2 (6)
是什么讓零件的靈活性不均勻分布的厚度的計算復雜化了，事實上,在壓縮條件下的頭螺栓的模樣,取決于裝配的水平,看起來就像一個體積接近于被切去頂端的形狀的圓錐(圖9)。
符合標準的實際情況是通過合理的算法來計算一個壓縮零件的靈活性。零件可由兩個或多個分區(qū)分開?？紤]一個兩部分組裝零件隔斷案例(圖10),這個方法如下:
1、 通過改良的拉斯穆森的[14]計算橫截面面積Ap,然后全部零件的靈活性。
Ap?Sp=Lp/ApEp (7)
Finite Elements in Analysis and Design 42 (2006) 298–313
Bolted joints for very large bearings—numerical model development
Aurelian Vadean ?, Dimitri Leray , Jean Guillot
aDepartment of Mechanical Engineering, Ecole Polytechnique de Montreal, P.O. Box 6079, Station Centre-Ville,Montreal, Québec, Canada H3C 3A7
bLaboratoire de Genie Mecanique de Toulouse - COSAM, INSA Toulouse, 135 Avenue de Rangueil,Toulouse Cedex 4, 31077, France
Abstract
The conventional theory of bolted joints does not take the complexity of external loads into account, neither its related joint stiffness nor the contact non-linearities. This article deals with a 2D numerical model allowing fast and precise calculation of the fastening bolts for very large diameter bearings subjected to an overturning moment. The originality of the modelling lies in the use of a particular ?nite element that behaves like a ring, except in the axial direction. Its axial stiffness is the local stiffness that governs the behaviour of the bolted assembly. The model was tuned upon 3D ?nite elements simulations and provides excellent results for several types of bearings.
Keywords: Bolted joints; Numerical model; Slewing bearings; Finite elements analysis
1. Introduction
Providing fast and accurate results is one of the challenges of practical engineering mainly during the early stages of the design process. The manufacturers of different mechanical systems involving bolted joints need suitable calculation models that allow integrated solutions. Numerous models approximate the parts and bolt stiffness using cones,spheres, equivalent cylinders or other analytical models [1–4].
According to the conventional theory, which was originally developed for loads that are centred or slightly off-centre, the stiffness of the member is constant. However, ?nite elements simulations as well as experimental results showstrong non-linearities due to the changing contact area [5–7]with the external load. Stiffness non-linearities were studied by Grosse [8] and Guillot [9] and they propose a non-linear model but only for plate-like con?gurations.
Another weakness of the conventional theory lies in the way the so-called load factor is calculated. The load factor tries to measure the amount of the external force which is transmitted to the bolt. The location where external forces are applied on themember governs the load factor and the way themember stiffness is distributed. Zhang [10] developed a new analyticmodel of bolted joints and takes into consideration the stiffness reduction associated with the residual force on the assembly, compression deformation caused by external force and dimensions changing due to member rotation. This model has its limitation and is not applicable to bolted assemblies when the members are of different geometry or when the external forces are not symmetric about the member interface.
The speci?cmodel we are proposing for large bearings can serve as base for a genericmodel of circular ?anges which can take into account the different non-linearities as well as different con?gurations or geometries by appropriate stiffness distribution.
2. The slewing bearings
The model this article proposes is suitable for speci?c bolted joints for large diameter bearings. These large bearings (up to 13m(43 ft)) also called “slewing bearings”, are used for cranes, radar dishes, tunnel-boring machines, etc. The two bearing rings are clamped to the main frame by preloaded high strength bolts. One or both rings are provided with gear teeth to enable the swing drive to operate. The connection is like a thick and narrow cylindrical ?ange on a very rigid frame fastened with a large number of bolts.
Another particularity of the system is the important and variable overturning moment. The bearings are subjected to radial and axial loads of same importance. The three types of bearings under study, ball bearings, crossed-roller bearings and three-row roller bearings, are presented in Fig. 1.
Due to the complexity of structure and the particularity of bolted joint loading, neither traditional models nor non-linear models are appropriate.
Thus we have developed a new model that takes into account simultaneously the bending stiffness in the axial direction with shell elements and in radial direction with tube-like elements. Furthermore, the tube elements were modi?ed to consider the characteristics related to the behaviour of preloaded bolted assemblies. Therefore, the modelling process lies in the de?nition of an original “hybrid” ?nite element.This element has the general behaviour of a ring except for the axial direction where its stiffness is related to the local stiffness that governs the behaviour of the bolted assembly. Meshing the ring with several elements allows taking into account non-linear stiffness distribution in the assembly and in particular the effect of the load application height. The evolving contact area is modelled by contact springs and using
an iterative solving technique.
Fig. 1. Slewing bearings.
3. Modelling and assumptions
The speci?c loading on these systems is an off-centre axial load (a normal crane loading type) resulting in a large overturning moment. This will build up an internal load on the bearings grooves (as shown in Fig. 1). At this stage of development, the intensity of the external load is not important. It is suf?cient to apply the same loading on both models: the 2D numerical model and the 3D ?nite elements model used to tune the ?rst one up.
To build the numerical model, several simpli?cations were made:
? for modelling purposes, we consider only the most loaded bolt and the associated sector;
? the outer ring only is modelled. Thus the external forces are replaced by the rolling elements load as
an equivalent load which increase the working load on bolts;
? the loading as well the formulation of the speci?c elements are considered axisymmetric;
? the mounting is considered extremely rigid.
Fig. 2 presents the principle underlying the new modelling. On the left-hand side is the sketch of the numerical model and on the right-hand side is the equivalent ?nite elements model.
Fig. 2. Modelling principle.
As Fig. 2 shows, the bearing ring model consists of three types of elements:
a. The plate elements based on the circular-plate model as described byVadean [11] and developed from Roark’s analytical formulas [12]. They are axisymmetric elements with two DOFs/node (y translation and z rotation) and their role is
? to represent the ring bending according to the axial direction OY;
? to characterize displacements and particularly the boundary separation of the ring from its mount-ing. Coupled to springs elements they are able to model the variable contact zone between the ring and the mounting according to the preload installed and the external load applied. Consequently to different contact status, the stiffness matrix will be adjusted and a non-linear loading of the threaded element is produced.
b. The so-called hybrid elements which make it possible to take into account the part compression stiffness, as well as the speci?c bending stiffness of a tube along radial direction OX. The three DOFs per node enable the structure to be loaded with a force system equivalent to the external load Fe.
c. The spring elements that model the contact with the mounting. They characterize the elastic behaviour of the interface and the unilateral contact. Springs stiffness will be a parameter of the model tuning.
The bolt has the formulation of an equivalent beam as described later in this paper.
3.1. Determining the axial stiffness of the bearing sector
In order to calculate the axial stiffness of the bearing sector we have used the improvement made by MASSOL [13] to the formulation of Rasmussen [14] for an elementary cylindrical assembly (Fig. 3).
The calculation of the equivalent section, noted Ap, makes it possible to determine the Kp stiffness of the parts. The relations used are
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