提高數控機床幾何精度使用生產過程分析技術外文文獻翻譯、中英文翻譯、外文翻譯

提高數控機床幾何精度使用生產過程分析技術外文文獻翻譯、中英文翻譯、外文翻譯,提高,數控機床,幾何,精度,使用,生產過程,分析,技術,外文,文獻,翻譯,中英文 附錄一： 提高數控機床幾何精度使用生產過程分析技術 文摘 現代數控設備的精度要求越來越高,加工制造工藝和裝配的結構組件是一個越來越重要的因素建立幾何糾正機床。具體來說,平面度,垂直度、并行性和連接表面的平直度確定機床的基本精度。表現出更少的幾何誤差允許其他錯誤,如熱增長,滾珠絲桿螺距誤差和控制更容易被孤立和糾正錯誤。 幾何誤差具有較高的機床加工和裝配過程的一個因素。多個方向在夾具裝配和加工導致顯著的扭曲最終組裝產品。這是由于切削力,夾具變形,重力變形,螺栓力變形。通過詳細分析每個進程使用虛擬仿真技術,高保真模型相應的錯誤可以實現在每個生產步驟,不是身體上的可衡量的由于測量設備的約束。使用模擬數據作為抵消數據加工過程中以及在夾具及固定裝置設計確保了幾何準確的最終產品。 關鍵詞:仿真;加工精度;機床制造;有限元法 1. 介紹 實際上，精密機床制造業(yè)是在飛速發(fā)展的。增量經驗基礎的改進正在穩(wěn)步實現機械本身精度的進步,機器的組件,這些組件構成了下一代也提高。再加上附加值由技術熟練的工匠導致機床精度不斷增加。[1]然而,降低產品生命周期時間和機床行業(yè)競爭力的本質要求改進機床精度是不夠的。此外,成本效益的實際限制機械與高精度生產零部件將物理限制的精度水平,可用于制造過程。[2]過程產生更嚴格的公差比傳統(tǒng)加工和磨削往往是成本高昂,無法廣泛采用到流程鏈。因此找到一種方法來改進過程是很重要的使用現有的設備。機器檢查是 NHX4000,400 毫米托盤臥式數控加工中心由 DMG Mori 精在戴維斯,CA。 1.1 在機床虛擬建模使用 在過去的的五年里,計算能力已經足夠成熟來處理完整的機床系統(tǒng)的復雜模型。作為一個例子,DMG Mori 精數字技術實驗室(迪泰)購買了 32 節(jié)點 Linux 集群運行仿真,桌面 PC 的 30 天的時間來解決。集群計算機的時間縮短到一天! 今天,桌面可以擊敗,性能幾乎任何級別的機床系統(tǒng)的計算機模擬現在是可能的。 重要研究已經做了關于如何使用虛擬測試機床設計性能和造型是 Altintas CIRP 主題的一篇論文中總結,等人一個非常有前途的方法,可以用來分析制造過程有限元建模和其他形式的虛擬仿真。在過去在 2005 年。[2]研究成功完成從組件級別的完全模擬機床虛擬樣機來證明傳統(tǒng)的設計周期可以現實地縮短消除物理原型迭代。從簡單的靜態(tài)分析完成復雜的動態(tài)模型和熱模型剛度模型。雖然仍有改進,這種方法的機床虛擬仿真已迅速成為成熟。 已經被充分研究過的另一個方面是使用有限元法對微觀的各個組件的性能復雜的內部行為(滾珠絲桿接觸模型和阻尼運動組件的行為。健壯的組件模型可用于改善 產品質量,也為開發(fā)更高的帶寬控制算法。[3]詳細接觸模型被用來協(xié)助經驗測試的組件發(fā)現阻尼值被回收用于整體機動態(tài)模型。[4] 另一個相當大的研究領域的仿真應用到模擬切削過程本身。這些類型的物理現象往往很難添加儀器,因此模擬的交互是非?？扇〉摹Ｊ怯脕砟M切削過程的表面光潔度的決心,毛刺的形成,芯片形成溫度分散,刀具磨損等等。[5][6]中使用喋喋不休和切削穩(wěn)定性的預測也可以不去。[7] 很明顯,計算機模擬技術廣泛用于機床和加工的好處。然而,這項技術還沒有部署到研究機床本身的制造過程。這可能是由于精密機床的所有權性質。無論如何,有足夠的機會,應用仿真技術以提高機床的精度。為了實現更大的精度,分析將顯示改善的領域。這包括集成的切削力、夾具設計、組裝順序,等等。夾具和夾具一起把機器精度高和重復精度也非常重要,檢查。這將是一個自然的結果上面的分析進行的。 1.2 幾何測量誤差來源 進行機床分析使用虛擬造型本身適用于只有某些錯誤。具體來說,可以糾正的錯誤本質上是幾何和大量地重復。許多論文清晰地闡明幾何錯誤。它們通常依賴。在旋轉的軸的情況下,線性幾何誤差可以認為是比旋轉式軸誤差極小。然而,[8]的方法改善的準確性機床生產過程機器適用于任何配置的工具。此外,直線運動誤差復合回轉軸線的不確定性誤差補償[9],建議盡可能降到最低。本研究將集中在錯誤的生產過程,可以糾正一次確認。 2. 生產過程鏈的統(tǒng)計分析 在制造精密數控設備,它是極其困難的,大大降低成本,同時保持產品質量。因此,分析生產周期中的變量系統(tǒng)和識別改進的重點領域有潛力提供最大限度的改善,在成本和精度/質量,同時保持最小中斷生產。試圖分析和優(yōu)化每個測量和寬容將是理想的,但實際上是不可行的。也非常希望建立一個統(tǒng)計鏈接關鍵領域在生產過程的最終精度機床。 為此,XY 平面的統(tǒng)計分析。機床是一個復雜的機器與數以百計的測量和檢驗點,只有最相關的常見的切割操作需要分析。大多數削減在 XY 平面二維輪廓線測量,直接影響到 XY 運動鏈的精度被用來調查統(tǒng)計關系。為了得到一個合理的樣本量,30 臺取樣人口大約 150 臺機器生產。 為了進行統(tǒng)計分析,數據的形式。就是做出假設依賴于正態(tài)分布的數據,數據必須檢查正常。使用 Z 分數正常的情節(jié)是一個可接受的方式建立一個正態(tài)分布。[10]的正常情節(jié)雙球棒循環(huán)測量有線性回歸與一個高度線性 R2 值為 0.96。其他數據集有類似的行為,所以是假設 30 機器的數據樣本正態(tài)分布和基本假設可以應用正態(tài)分布。 比較每個參數的方法是獲取原始加工結果之間的相關系數和最終的精度測試。因此,發(fā)展關聯矩陣的測量。這允許一個快速查看的參數可能有強壯的,溫和,弱,或根本沒有關系。系數超過 0.4 是強大而超過 0.3 是溫和的。[10] 是決定之間有很強的相關性的切圓和直線度測試組裝機器單獨的鑄造精度。x 軸有強烈的相關性。y 軸的頂端安裝軸和錯誤的軸通過這個運動鏈傳播工具提示。此外, 大型移動質量上的軸原因地方變形的初始精度軸直接增加了局部變形。此外,x 軸鑄造(床)上加工大東芝龍門磨(MPC),y 軸(列)是一個緊湊的臥式加工中心上加工(NHX10000)。NHX10000 展品更高程度的精度和可重復性比東芝 MPC。統(tǒng)計分析的結論是,提高幾何特性的 X,Y,Z 軸的鑄造加工重點是X 軸將導致最終直接提高機床精度。 3 .加工過程 加工過程包括各種變量。摘要進行密切的兩個變形由于夾具設計和變形由于切削力本身。重力是一組默認的加載,應用在整個制造過程。 3.1 夾具的影響 加工中使用的設備有四個標準,必須分析 1. 鑄件由于變形大的夾緊力 2. 足夠的支持在加工鑄造的最小變形 3. 中立的定位,以避免彈簧后切割和夾具釋放。 4. 足夠的支持和取向的引力誘導變形降到最低。 對于 NHX4000、夾具主要發(fā)現足夠的設計方面的支持和夾緊的一個例外。圖 3 所示的右下方夾從支持導致幾乎抵消 2 點位移顯示在圖 4。 由于機器的限制,鑄造組件可能需要加工的方向不同的定向組裝。這可能導致過度的重力變形的部分鑄件。的列所示,水平夾具定位結果在 y 軸的直線度誤差大于 4 點。 床上鑄有類似的結果,而是因為它是加工組裝、定位 self-gravitational 效果取消,加工夾具是更健壯的床上。 3.2. 貢獻的力量 切削力可以很容易地預測和仿真。Altintas 提出了一個廣義切削力模型適用于各種刀具與給定的幾何和切削條件。[11][12],值得注意的是,切削力的影響很小引力效應相比,決定研究中被認為可以忽略不計。 4. 裝配過程 4.1. 夾具及固定裝置設計 部分機床組裝在不同單位盡可能以最佳效率。X 和 Z rails 是直接安裝在床上,但 y 軸 rails 安裝到列在一個獨立的車站。裝配工人的有效的地方和測量 rails 在安裝和調整,列必須放置在夾具上的水平方向與 rails 面臨向上。穩(wěn)定性和安全性,四點固定最初被設計為在圖 7 中。 分析顯示嚴重靈敏度調整夾具。只有增加 4 點一個夾具的高度支持導致 Y-rails 平行度誤差為 3.5 點。在這種情況下,夾具的腿沒有微米級別的調整能力作為他們的高度調整是由普通 SAE 機線程。因此,裝配調整并行的人為變形狀態(tài)。釋放后的變 形狀態(tài)列從夾具中移除并設置直立導致 y 軸失去并行性。由于并行性高依賴于夾具調整,變形也非可重復加工期間,不能得到補償。 找到的解決方案是使用三個點支持列在鐵路修復。雖然列仍然變形由于重力,rails 近對稱變形和沒有靈敏度小夾具的高度變化。這是在 4.2 節(jié)詳細討論。結果是一個可重復的重力變形,可以補償在加工步驟。 4.2. 取向的結構 當一個組件如列是聚集在一個取向有利于有效的裝配工作正如上一節(jié)所討論的,重力將發(fā)揮作用的測量步驟。這種引力效應可以有效地抵消了理解存在變形,隨后裝配調整過程中占了。當使用三個點支持,列會變形,但這將是可預測的,依賴于三個點的位置。因此,有必要總是使用相同的三個點位置每次測量列,以確保測量重復性。此外,因為它是可取的 Y Rails 準確測量并行性,指出應選擇導致平衡 Rails 的 z 三個方向變形。同時,Y rails 變形在等量所以并行性是保存列時調整。下圖顯示了三個點位置選擇基于有限元分析重力變形。關鍵是抵消略向電機支架的一面。這抵消抵消更大的質量。在質量控制和裝配使用了相同的位置。 4.3. 裝配順序和群眾不移動 組件的順序獲得機體創(chuàng)建大型機床結構的局部變形由于大質量的每個組件。當緊公差的軸運動系統(tǒng)已經在早期階段獲得,然后會產生大量添加二級精度設置,每個軸的保真度的準確性可以完全丟失。這可能并不總是會在最后的精度測試整機信封通常不是測試和局部變形可能只影響局部的信封。然而,詳細檢查整個機器的信封將揭示缺陷在不同工作信封的位置。因此,建議檢查添加的效果通過有限元質量在每個裝配步驟。 減少這種影響的一個方法是解決運動組件安裝后沉重的子單元的裝配過程。然而, 在很多情況下這是不可行的,因為進入工作區(qū)域時抑制子單元連接,也因為鑄件本身仍然看到了變形。 一種更有效的解決方案是模擬裝配順序,并記錄產生的變形。因為這是高度可重復的,可以直接做鑄件加工補償抵消變形,組裝后獲得一個中立的變形子單元。 4.4. 影響移動組件 最后分析執(zhí)行檢查裝配機軸運動的影響下重力加載。軸,相對工具在中間沖程位置較高,由于不同的變形前后 X-rails 之間在床上。后方 X-rail 有積極弓雖然前面 Xrail 負弓沿著 Xstroke 隨著列。的微分軌道高度傳播到 2.3 點誤差在 Y 的工具提示結束行程的中間!調整方法是一種積極的皇冠后方鐵路。下圖所示的數據。 5. 最終的加工結果 5.1. 加工計劃 每個組件有一個加工計劃開發(fā)基于前面的分析結果。這個計劃是累積的。的列,加冕應該相反的變形形狀在 Y 中風。在質檢過程中測量應仰臥位時重力變形直立時加上加冕變形減去重力變形。一個表面加工補償目標的一個例子是提供在圖 14。 5.2。與其他工廠相比 生產過程的分析是在戴維斯進行的,日本。在 Iga DMG Mori 精也有工廠,日本生產NHX4000 機相同。理解如果戴維斯的方法真的不同,戴維斯和Iga 的箱線圖結果了。結果不僅顯示出近似從戴維斯Iga 的平均提高20%,戴維斯數據變化少,一些極端的異常值,表明分析過程不僅增加了最終產品的精度,但一致性。 重要的是要注意,所有最終機器測量改進是基于國際 ISO 標準。ISO 230 是用于最后的質量控制測量和 ISO 10791 用于最終的質量控制測試。循環(huán)的最大公差 5 微米和 8 微米直線度測量。 6. 結論 一個創(chuàng)新的使用現有的虛擬仿真技術已被提出和實施。一系列削減概要文件為每個部分是計算累計添加所有先前解釋的影響。這些是有效的,一個特定的順序和方向裝配過程質量控制步驟和計劃也交付。累積的結果完成機器是表明 20%的整體改進最后 NHX4000 產品。 引用 [1] D. A. Dornfeld, 精密的道路:機床和他們創(chuàng)造的產品,First. Mori Seiki Co., Ltd., 2008. [2] Y.Altintas,C.Brecher,M.Weck,and s.Witt,“虛擬機床”,CIRP Ann.-Manuf.technol,vol.54，no.2,pp.115-138,2005. [3]M.F.Zaeh,T.Oertli,and J.Milberg,“有限元建模的滾珠絲桿進給驅動系統(tǒng),”CIRP Ann.-Manuf.technol,vol.53,no.1,pp.289-292,2004. [4] C.Brecher,M.Fey,and S.Ba,“阻尼模型線性軸機床組件,” CIRP Ann.-Manuf.technol,vol.62,pp.399-402,2013. 附錄二： Improving CNC Machine Tool Geometric Precision Using Manufacturing Process Analysis Techniques Abstract With the ever increasing demands for higher and higher accuracy on modern CNC equipment, the manufacturing processes for machining and assembling the structural components are an increasingly important factor in establishing a geometrically correct machine tool. Specifically, flatness, perpendicularity, parallelism, and straightness of interfacing surfaces determine whether the machine tool’s basic accuracy. Exhibiting less geometric error allows other errors such as thermal growth, ballscrew pitch error, and control error to be isolated and more easily corrected. The geometric errors are predominately a factor of the machine tool machining and assembly process. Multiple orientations during fixturing in both assembly and machining result in significant distortions to the final assembled product. These are a result of cutting forces, fixturing deformations, gravity deformations, and bolt force deformation. By analyzing each process in detail using virtual simulation techniques, a high-fidelity model of the corresponding error at each manufacturing step can be achieved that is not physically measurable due to constraints of measurement equipment. Using simulated data as offset data in the machining process as well as in the jig and fixture design ensures a geometrically accurate final product. Keywords: Simulation; machining accuracy; machine tool manufacturing; FEM 1. Introduction Precision manufacturing of machine tools is very evolutionary in nature. Incremental experience based improvements are steadily achieved and as the machinery itself advances in precision, the components that make up the next generation of machines also improve. This, together with value added by skilled craftsman results in ever increasing accuracy of machine tools.[1] However, decreasing product life cycle times and competitive nature of the machine tool industry dictate that incremental improvements to machine tool accuracy are not sufficient. Moreover, the practical limit of cost effective machinery to produce parts with high precision puts a physical limit on the level of precision that can be used in the manufacturing process.[2] Processes that produce tighter tolerances than conventional machining and grinding tend to be cost prohibitive and are not able to be widelyadopted into the process chain. It therefore becomes important to find a way to improve the process using equipment that is currently available. The machine checked is the NHX4000, a 400 mm pallet horizontal CNC machining center produced by DMG Mori Seiki in Davis, CA. 1.1. Virtual modeling uses in machine tools A very promising method that could be used to analyse the manufacturing process is Finite Element Modelling and other forms of virtual simulation. In the last five years, computing power has become mature enough to handle full complex models of machine tool systems in a very short amount of time. As an example, DMG Mori Seiki’s Digital Technology Laboratory (DTL) purchased a 32 node Linux cluster for running simulation’s that took a desktop PC 30 days to solve. That cluster computer shortened the time to one day! Today, a desktop is able to beat that performance so virtually any level of computer simulation is now possible for machine tool systems. Significant research has been done on how to use virtual modelling to test machine tool designs performance and is well summarized in a CIRP keynote paper by Altintas, et al. in 2005.[2] Research successfully accomplished has modelled machine tools from component level to full virtual prototype to prove that the traditional design cycle could be realistically shortened by eliminating physical prototype iterations. Analyses completed range from simple static rigidity models to complex dynamic models and thermal models. While there is still improvement to be made, this method of machine tool virtual simulation has rapidly become mature. Another area that has been well studied is the use of FEM for the micro performance of individual components that have complex internal behaviour such contact models for ballscrews and damping behaviour of motion components. Robust component models are useful for improved product quality and also for developing higher bandwidth control algorithms. [3] Detailed contact models have been used to assist empirical testing of components to find damping values which are recycled for use in overall machine dynamic models.[4] Another considerable research area simulation is applied toward is simulation of the cutting process itself. These types of physical phenomena are often very difficult to add instrumentation and thus simulating the interaction is highly desirable. It is used to model cutting processes for surface finish determination, burr formation, chip formation, temperature dispersion, tool wear, and so on. [5] [6] Use in the prediction of chatter and cutting stability can also not go unmentioned. [7] It is clear that computer modelling techniques are widely used for the benefit of machine tools and machining. However, this technology has not been deployed to study the manufacturing process of the machine tool itself. This is perhaps due to the proprietary nature of precision machine tools. Regardless, there is ample opportunity to apply simulation technology in order to improve the accuracy of machine tools. To achieve greater accuracy, the analysis will show areas of improvement to be made. This includes integration of cutting forces, fixture design, assembly order, and so on. The fixtures and jigs to put the machine together for high accuracy and repeatable accuracy are also very important and are examined. This will be a natural result of the analysis carried out above. 1.2. Geometric measurable error sources Carrying out a machine tool analysis using virtual modelling applies itself to only certain errors. Specifically, the errors that can be corrected for are geometric in nature and measurably repeatable. Many papers articulate geometric errors clearly. They are generally position dependent. In the case of rotating axes, the linear geometric errors may be assumed to be negligibly small compared to rotary axes error. [8] However, the methods of improving the accuracy of the machine tool production process are applicable to machines tools of any configuration. Furthermore, linear motion errors compound the uncertainty of rotary axis error compensation [9] and are advisable to minimize as much as possible. This research will focus on errors that are a result of the manufacturing process and can be corrected once identified. 2. Manufacturing process chain statistical analysis In manufacturing precision CNC equipment, it is extremely difficult to significantly reduce cost while maintaining product quality. Therefore, analysing the variables in the production cycle systematically and identifying key focus areas for improvement has potential to provide maximum improvement, both in cost and accuracy/quality, while maintaining minimal disruption to production. Attempting to analyse and optimize every measurement and tolerance would be ideal, but practically it is not feasible. It is also highly desirable to establish a statistical link to key areas in the manufacturing process to the final accuracy of the machine tool. To do so, a statistical analysis of the XY plane was carried out. A machine tool is a complex machine with hundreds of measurements and inspection points, only the most relevant for common cutting operations need be analysed. Most cutting is 2D contouring in the XY plane so the measurements that directly affect the XY accuracy in the kinematic chain were used to investigate a statistical relationship. In order to get a reasonable sample size, 30 machines were sampled out of a population of approximately 150 machines produced. In order to conduct a statistical analysis, the form of the data had to be established. That is, to make assumptions relying on the normal distribution of data, the data had to be checked for normalcy. A normal plot using the Z score is an acceptable way to establish a normal distribution.[10] The normal plot of the double ball bar circularity measurement has a linear regression line with an R 2 value of 0.96 which is highly linear. Other data sets had similar behaviour so it was assumed that the data sample of 30 machines had a normal distribution and basic assumptions regarding a normal distribution can be applied. The method used to compare each parameter was to obtain correlation coefficients between the initial machining results and the final accuracy tests. Thus, developing correlation matrices among the measurements was done. This allowed a quick view of what parameters may have strong, moderate, weak, or no relationship. Coefficients over 0.4 are strong while those over 0.3 are moderate. [10] It was determined that there is a very strong correlation between the circularity and straightness in the cutting tests of the assembled machine to the individual casting accuracy. The X-axis had the strongest correlations. The Y-axis sits on top of the X-axis and errors of the X-axis are propagated through this kinematic chain to the tool tip. Additionally, the large moving mass on top of the X-axis causes local deformations so the initial accuracy of the X-axis directly adds to this local deformation. Furthermore, the X-axis casting (bed) is machined on a large Toshiba Gantry mill (MPC) while the Y-axis (column) is machined on a compact horizontal machining center (NHX10000). The NHX10000 exhibits a higher degree of accuracy and repeatability than the Toshiba MPC. The conclusion of the statistical analysis was that improving the geometric qualities of the X, Y, and Z axes of the casting machining with an emphasis on the X-axis would result in directly improved final machine tool accuracy. 3. Machining Process The machining process involves a variety of variables. The two that are examined closely in this paper are the deformations due to the fixture design and also the deformation due to the cutting force itself. Gravity is a default load set that is applied across the entire manufacturing process. 3.1. Effect of fixturing The fixtures used in machining have four criteria that must be analysed 1. Deformation of casting due to large clamping force 2. Sufficient support of the casting for minimal deformation during machining 3. Neutral positioning to avoid spring back after cutting and fixture release. 4. Adequate support and orientation to minimize gravitationally induced deformations. In the case of the NHX4000, the fixtures were largely found to be of sufficient design in terms of support and clamping with one exception. The lower right clamp shown in Fig. 3 is offset from the support which results in an almost 2μm displacement indicated in Fig. 4. Due to machine constraints, casting components may need to be machined in orientations differing from the assembled orientation. This can result in excessive gravitational deformation for some sections of the casting. In the case of the column shown below, the horizontal fixture orientation results in a Y-axis straightness error of greater than 4μm. The bed casting had similar results, but because it is machined in the orientation of assembly, the self-gravitational effect is cancelled and the machining fixture is more robust for the bed. 3.2. Contribution of cutting forces Cutting forces can be fairly easily predicted and added to the simulation. Altintas proposed a generalized cutting force model suitable for a wide range of cutters with given geometry and cutting conditions. [11], [12] Notably, the cutting force effect was small in comparison to the gravitational effect and was decided to be assumed negligible in the study. 4. Assembly Process 4.1. Jig and fixture design Parts of the machine tool are assembled in separate units as much as possible for optimal efficiency. X and Z rails are installed directly onto the bed, but the Y-axis rails are installed to the column in an independent station. For assembly workers to efficiently place and measure the rails during installation and adjustment, the column must be placed in the horizontal orientation on a jig with the rails facing upward. For stability and safety, a four point fixture was originally designed as in Fig. 7. Analysis showed a severe sensitivity to jig adjustment. Only a 4 ?m increase in the height of one jig support resulted in a parallelism error of 3.5 ?m for the Y-rails. In this case, the jig legs do not have micron level adjustment capability as their height adjustment is determined by regular SAE machine threads. Therefore, assembly adjusts for parallelism in an artificially deformed state. The deformed state releases after the column is removed from the jig and set upright resulting in the Y-axis losing parallelism. Since parallelism is highly dependent on the fixture adjustment, the deformation is also non repeatable and cannot be compensated during machining. The solution found was to use a three point support for the column during rail fixing. Although the column still deforms due to gravity, both rails deform nearly symmetrically and there is no sensitivity to small height changes of the fixture. This is discussed in more detail in section 4.2. The result is a repeatable gravitational deformation that can be compensated in the machining step. 4.2. Orientation of structure When a component such as the column is assembled in an orientation conducive to efficient assembly work as discussed in the previous section, gravity will play a role in the measurements of that step. This gravitational effect can be effectively cancelled out by understanding what deformations are present and subsequently accounted for during the assembly adjustment process. When using three point support, the column will deform, but it will be predictable, dependent on the locations of the three points. Therefore, it is necessary to always use the same three point locations each time measuring the column to ensure measurement repeatability. In addition, since it is desirable to measure parallelism of the Y Rails accurately, points should be selected that cause a balanced Z-direction deformation of the rails. Also, both Y rails deform in equal amounts so parallelism is preserved when the column is reoriented. The diagram below shows the three point locations selected based on FE analysis g