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論文題目
手推式草坪修剪機設(shè)計
一 選題背景和意義:
草坪是高度培育的特殊草地,隨著草坪面積的擴大,品質(zhì)的提高,草坪業(yè)逐漸由單一的人工作業(yè)向半自動化﹑機械化﹑自動化過度,草坪作業(yè)的機械化已經(jīng)成為十分重要的課題。
大部分的草坪一直到19世紀(jì)中葉還在使用鐮刀來割草或放牧牛羊以保持草地的整齊性。隨著高爾夫球﹑網(wǎng)球以及足球等運動的興起,保持完整的草地做運動場便成為當(dāng)務(wù)之急。從20世紀(jì)起出現(xiàn)以機器代替手工的趨勢,于是好的修剪機遂成為草坪管理的必需品。
草坪修剪機分滾切式﹑旋刀式﹑剪切式三類,按動力又可分為手動與機動兩類。機動有乘坐式與手推式,北京園林機修廠JUS—420型旋刀式修剪機系單缸四沖程汽油機驅(qū)動,功率2.6Kw,一把旋刀,幅寬420mm,每班可修剪2000m2,整機質(zhì)量40Kg。上海園林機械廠JCG540Ⅱ型滾切式草坪修剪機,乘坐手推兩用式,有兩個前進檔,IE50F—2汽油機功率2.3kw,5片滾刀,幅寬540mm,該機 高,但用于坡地時機組穩(wěn)定性較差。小庭院的草坪可用上海生產(chǎn)的JCG—250Ⅱ型手推草坪修剪機,人推動前進并使6個滾刀旋轉(zhuǎn)切割草坪,幅寬250mm。德國SOLO522型草坪修剪機為手推式,動力系單缸四沖程汽油機,功率為2.3kW,刀片為剪切式,幅寬800mm。該產(chǎn)品的特點是刀片耐磨,機具噪聲低,振動小,對坡地適應(yīng)性好。改換工作部件可作掃雪工具。
旋刀式剪草機適用于草高25~80mm低要求的草坪,剪幅在0.5~20.m之間。滾切式剪草機適用于草高3~80mm的高要求草坪,剪幅0.5~5.0m之間。
修剪是維持優(yōu)質(zhì)草坪的重要作業(yè),它主要是定期除掉草坪草枝條的土表部分。在特定的草坪上,根據(jù)所需要的培育強度,修剪的目的是在特定的范圍內(nèi)保持頂端生長,控制不理想的、不耐剪的營養(yǎng)生長,維持一個觀賞和游息草坪,產(chǎn)生一個真實的擊球表面或發(fā)展草坪作物。
修剪的質(zhì)量由所使用的剪草機的類型和割時草地的狀況決定。因此,隨各種特殊功能的開發(fā),應(yīng)重視修剪機具的發(fā)展。
我國幅原廣闊,地區(qū)差異很大。草坪的功能不同,對機具的要求也不同,加之各地區(qū)經(jīng)濟發(fā)展不平衡,用戶的購買能力也有差異,因此草坪機械只有開發(fā)系列產(chǎn)品才能滿足不同市場的需要。
另外,有些草坪機具一年只用幾次,因此草坪機具在以草坪作業(yè)為主項的同時,應(yīng)配備一些附加裝置,擴大其使用功能,提高機具的利用率。
二 難點和關(guān)鍵問題:
(1) 圍繞著零件圖紙進行分析,做出綜合性的分析。
(2) 對零件進行綜合布局,畫出總設(shè)計的圖紙。
(3) 在設(shè)計中應(yīng)合理的選擇材料,減少應(yīng)力集中(如尖角、銳邊、表面;粗糙度等).控制尺寸公差。
(4)本課題的難點是,根據(jù)電機的功率和人行走的速度換算出三級變速齒輪的傳動比,電機和人力兩種動力間的轉(zhuǎn)換。
三 文獻總述
從地球有了人類開始,我們就磨削石塊,制造工具,開始了工具革命的過程,一直延續(xù)至今,最早的剪草工具是小鐮刀和手剪。但是I803年美國專利機構(gòu)公布了剪草機的第一個專利。然而未形成商品。在大西洋披岸 ,一位名叫Edwin Budding的英國人發(fā)明了滾刀式剪草機他是一個紡織工人,監(jiān)視旋轉(zhuǎn)式機械用于修剪呢絨絨毛。他決定將這一工作原理應(yīng)用于割草 。
1855年 Budding的剪草機在英國問世并受到歡迎,Henxy將它引入美國。
1877年在 Richmond,McGuin試圖發(fā)展這種剪草機使其容易推動更加實用 1855年美國公司一年生產(chǎn)近50000臺草坪剪草機.其構(gòu)造與今天的手推式剪草機類似 。
1890年還是在英國開始設(shè)計有動力驅(qū)動的剪草機。第一個成功的動力剪草機由LeyLandMotors制造,為蒸汽動力型,然而,另一個技術(shù)革命使它不久即被淘汰。
1885年德國工程師 Gottlieb Daimler 發(fā)展了一種小型內(nèi)燃機,并首先應(yīng)用在自行車上。建立第一個摩托車。適用的動力源導(dǎo)致發(fā)展汽車,飛機甚至洗衣機,隨之應(yīng)用于動力剪草機和園藝機具,另一個英國公司1902年皇家農(nóng)業(yè)協(xié)會舉辦的展覽會上展出了6馬力的動力剪草機.
美國工程師和革新家在本世紀(jì)初的十年中,也致力于動力剪草機的研究1909年Leoni取 到了動力型機械式剪草機專利Leoni的動力型剪草機由汽油機驅(qū)動。整個裝置行走由馬拉。大約在第1次世界大戰(zhàn)前不久 ,動力型剪草機開始用于家庭。George 是一位實業(yè)家和開發(fā)者。他最早開始經(jīng)營商業(yè),他的馬達剪草機公司曾定名為“立即成功 ”。他設(shè)計的發(fā)動機安裝在滾刀式剪草機上。一直保持到1950年。
接著又有其他廠家生產(chǎn)類似的機械。到1927年Hardware Age“年度消費者目錄”登出了近21家公司生產(chǎn)動力型草坪剪草機其中的兩家廠商一波倫 (Bolens)和蔣索波森(Jacobsen)存在至今,并成為著名廠商 。
美國克里夫蘭市的聯(lián)合鑄造供應(yīng)公司制造的草坪剪草機備有集草袋和自動離臺器當(dāng)?shù)镀龅酵饨缱枇r即與傳動裝置自動分離。
美國費拉德爾菲亞(費城)的草坪剪草機公司在廣告上登出了全系列的手動馬拉和動力驅(qū)動的剪草機,從1922年開始推出30和40英時的可乘式剪草機。
事實上,旋刀式剪草機是在戰(zhàn)前發(fā)展的,然而直到1次世界大戰(zhàn)之后才推廣。1933年 ,Bolen提出的旋刀式剪草機專利與今天使用的類似 ,有跡象表明,在 1920年之前此種旋刀式剪草機只是為私人使用。1938年出現(xiàn)的旋刀式剪草機獲得了商業(yè)上的成功Howard為 了解決大面積雜草的修剪問題 一 他立即在他的地下車間開始了研制工作。
Gravely是個花匠,為了解決他花園的耕作問題,使用手推犁刀,1920年他開始生產(chǎn)園藝用拖拉機,并 取得動力犁的專利,更早的園藝拖拉機是在1919年 GiLson Brothers制造 ,Beeman拖拉機公司銷售。1927年Hardware Age列出11個園藝拖拉機制造商。包括克里夫蘭市的Barcer~ Raulang公司,該公司推出了電動型園藝拖拉機。
1910年瑞士Konrad應(yīng)用除根的耕作機具。該裝置不是第一個轉(zhuǎn)子式中耕機 (早在1857年就有此種機型),但是早期的機型重量大,達數(shù)噸,其動力為蒸氣機式,與現(xiàn)代機型完全不同。
1911年德國的Siemens—Sehckert~ Werk公 司 ,在它的專利基礎(chǔ)上制造了最早的電動機驅(qū)動的中耕機。但是沒有得到發(fā)展。不久被汽油機所取代 。
1930年Siemens決定將機器引入美國,他來到美國同費城的Kol sey合作。Kelsey 建立 了Rototiller公司,銷售從歐州引進的機器。1934年Kelsey的Rototiller公司生產(chǎn)了它的第一臺美國制造的中耕機 。
Rototiller公司早期競爭對手之一是 Arien公司,Arien和他的兒子成立了一個公司,聲稱為美國第一家生產(chǎn)轉(zhuǎn)子式中耕機的公司。Arien公司的第一臺轉(zhuǎn)子式中耕機重900磅,未獲得成功。隨著 1次世界大戰(zhàn)爆發(fā),園藝機械的生產(chǎn)也隨之停頓。
應(yīng)該指出,無論是 Ariens公司或 Rototiller公司的中耕機都是后齒型一1936年 Roto--Hoe公司生產(chǎn)了前齒型中耕機 ,在戰(zhàn)爭初期,它們銷售很慢,而前齒型中韉機在戰(zhàn)爭之后作為家用設(shè)備獲得成功 。
鏈鋸的發(fā)展也要追溯到 Ⅱ次世界大戰(zhàn)爆發(fā)之前 。第一具鏈鋸是在1904年。直到戰(zhàn)爭之后才形成商業(yè)產(chǎn)品。Sfihl的鏈鋸重105 磅 .是在1927年。由兩人操作。
動力草坪清掃機也出現(xiàn)在戰(zhàn)爭之前。創(chuàng)建者是 Parker Pattern。他的兒子 Edwin Parker于1919年進一步發(fā)展 。1931年 Edwin作為公司董事長推出公司第一臺動力草坪清掃機 。
在園林機械發(fā)展的歷 史上 。2次世界大戰(zhàn)是一個轉(zhuǎn)折點,2次世界大戰(zhàn)之后 ,整個國家得到復(fù)興,園林機械也得到重大發(fā)展。允許復(fù)役軍人低價買房不付現(xiàn)金,大批建設(shè)房屋并 出售。促使園林設(shè)備得到空前發(fā)展。
戰(zhàn)后,鏈鋸也得到改進。1944年Claude—Poulan監(jiān)視德國人—戰(zhàn)爭囚犯在東德克薩斯州砍樹。兩人操縱鏈鋸。尚需第三個人控制撬扛。戰(zhàn)后,他立即著手建立裝有發(fā)動機的鏈鋸 。生產(chǎn)鏈鋸的公司也在不斷增長。橫過大西洋,Solo(在1948年 )和 Stihl(在1950 年)是首批生產(chǎn)一人操縱鏈鋸的公司 Stihl承認。最初的一人操縱的鏈鋸重量較重。直到1954年才生產(chǎn)了輕重量級的鏈鋸(重31 磅)。與此同時,其他廠商也發(fā)展了輕重量級的鏈鋸。例如1961年Iombard Governor 公司出售一種16英寸,27磅鏈鋸 Steve和Dave HOH試圖清除他家占地面積為240畝的莊園雜草。這促使他建立了一個大鐮刀。1949年曾形成商品。銷售灌木切割機 。
在同一時期,人們利用內(nèi)燃機為動力驅(qū)動掃雪裝置,1948年Henry Ariens發(fā)展了一種拋雪機的工作樣機。直到1960年初才進入市場。
1959年隨著園林機械工業(yè)的發(fā)展。人們意識到需要興辦一個雜志。Bill Qu Jnn.自行車 雜志的發(fā)行人開始創(chuàng)辦草坪設(shè)備期刊 ,1969年,該雜志更名為戶外動力設(shè)備 (OPE)。
在雜志創(chuàng)辦時,按照產(chǎn)品銷售的型號與今天幾乎差不多。但是隨著工業(yè)的發(fā)展,操作者 的要求在改變,必須考慮操作安全,環(huán)境污染及其他關(guān)心的問題。
1971年George Ballas為了控制自已莊園樹根周圍的雜草,他制造了多頭帶式修剪機 (繩索式割灌機)。達到了理想的效果。1977年 Weed Eater公司推出了單繩帶式修剪機 。
當(dāng)然.園林機械設(shè)備的歷史沒有結(jié)束.如同沒有明顯的起點一樣,沒有終點它將繼續(xù)擴大領(lǐng)域為人類作出新的貢獻。
四 方案論證
根據(jù)電機的功率和人行走的速度換算出三級變速齒輪的傳動比,電機和人力兩種動力間的轉(zhuǎn)換。
傳動裝置是大多數(shù)機器或機組的主要組成部分。實驗證明,傳動裝置在整臺機器的質(zhì)量和成本中占有很大比例。機器的運轉(zhuǎn)性能和運轉(zhuǎn)費用在很大程度上決定了傳動系統(tǒng)的優(yōu)劣。因此,不斷提高傳動裝置的設(shè)計和制造水平具有極其重要的作用。
(1)剪切裝置
剪切裝置由滾刀和底刀組成,滾刀和底刀結(jié)構(gòu)如下圖所示。底刀用六角螺栓固定在底刀架上,剪草時位置不動,刀刃為直線型。滾刀的刀片形狀為螺旋曲面,刀刃為螺旋線,五片刀片均勻分布固定在刀架上。剪草時,滾刀向前轉(zhuǎn)動,刀刃由一端開始與底刀刃逐點組成剪口,草隨著滾刀刀片螺旋面的旋轉(zhuǎn)被卷進剪口內(nèi),并被剪斷。上下刀刃剪草過程始終為點接觸。
圖4.1滾刀和底刀外形圖
(2)離合器裝置
離合器裝置是為了使剪草機正向剪草反向停止旋轉(zhuǎn)而特意設(shè)置的工作裝置,它是由齒輪和其內(nèi)的彈簧和鋼球組成。剪草時,鋼球在彈簧的作用下壓緊齒輪內(nèi)壁迫使起和其他齒輪嚙合,從而帶動滾刀旋轉(zhuǎn)然后與底刀相切剪草的,當(dāng)手扶手拉動剪草機向后運動時,由于該齒輪的轉(zhuǎn)速大于與之聯(lián)結(jié)的軸的轉(zhuǎn)速,這樣在超越離合器作用下該齒輪將相對軸做超越運動,使得滾刀軸靜止不動,不與齒輪軸發(fā)生干涉。
五、進度安排
第1、2周 調(diào)查查閱 收集查閱資料
第3、4周 資料翻譯 總體方案擬定、開題
第5、6周 畢業(yè)實習(xí)
第7、8周 詳細設(shè)計
第9、10周 詳細設(shè)計
第11、12周 詳細設(shè)計
第13、14周 詳細設(shè)計
第15、16周 詳細設(shè)計
第17周 撰寫畢業(yè)設(shè)計說明書
第18周 畢業(yè)答辯
六 指導(dǎo)教師意見:
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七 教研室(或開題審查小組)意見:
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外文文獻及譯文
文獻、資料題目:A new analytical–experimental method for the identification of stability lobes in high-speed milling
文獻、資料來源:國外金屬加工2OO5年第26卷
第3期
文獻、資料發(fā)表(出版)日期:2005.3
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外文文獻
A new analytical–experimental method for the identification of stability lobes in high-speed milling
There is a pressing economic need for efficient machine-tool operation. A wide range of research has been conducted to determine the optimal parameters for machining (i.e. feed of rate, depth of cut, and spindle speed). Studies have focused on cost minimization, machining time minimization and metal-removal rate (MRR) maximization. Most optimization methods seek to increase the MRR and are oriented towards optimizing cutting speeds and accelerations. Even so, thesemethods do not guarantee the optimal solution, since they are developed in a space conspicuously free fro mall the restrictions entailed in real machining.
Some attempts at finding the optimal values of cutting parameters consider different objective functions , including production-cost minimisation [1], production time minimisation [2] and a combination thereof [3,4].
However, the limiting factor for most optimization methods is the instability involved in milling operations. Instability is a vibratory phenomenon and can be measured and described in a quantitative form. Diverse studies of the vibratory phenomenon have been made for machine tools and with the help of technology, it is now in a certain way scientifically possible to quantify the characteristics of the vibration in machining processes, to predict chatter and to make pertinent recommendations to avoid it.
Tobias, in ‘‘Vibrations in Machine-Tools’’ [5], discusses the principles of vibration theory applicable to machine tools and offers a critical overview of the main theoretical and experimental results in the investigation of chatter. Nevertheless, since 1961, the year when the original manuscript of the book was finished, machine-tool research has made great strides. New techniques for predicting machine-tool instability have been developed and have been applied successfully. Other aspects of chatter theory, however, have not changed; the way the cutting process under chatter conditions is conceptualised has not altered, nor has the exceptional importance of the regenerative effect as the main physical cause of instability been questioned.
In 1983, Tlusty et al. [6] examined machining stability, especially in high-speed machining (HSM). They applied an approach using a time-domain simulation in order to analyze chatter and thus to enhance the knowledge of the effect of cutting speed on milling operations. In this paper, stability lobe diagrams, based on the axial depth of cut and speed (Fig. 1), are obtained.
Another study of Ismail and Soliman [8] introduces a method for identifying stability lobes in milling operations. This method depends on ramping the spindle speed while monitoring the behavior of a chatter indicator. Based on patterns shown by this indicator, stability lobes can be identified on line. The proposed technique makes it viable to locate stable regions during practical tests while avoiding chatter.
In 1998, Abrari et al. [7] presented a dynamic-force model and a stability analysis for ball-end milling. The concept of equivalent orthogonal cutting conditions, which they applied to modeling the mechanics of ball-end milling, can be extended to include the dynamics of cutting forces. The model thus developed can generate forces very similar to the data from the experiments.
A more recent study from Naterwalla [9] has been published on how to perform machining operations without chatter and maximise MRR for the metal industry.
As a result of technological advances in tools and machine tools, operations are taking place at increasingly higher speeds and accelerations. The terms ‘‘high-speed machining’’, ‘‘high speed of cut’’ (HSC) and ‘‘high-speed performance’’ (HSP) have become more common over the last few years for describing the process of machining at high speeds.
Because machining operations are taking place at increasingly higher speeds, studies in the area of vibrations have branched off into researching the stability of HSM. One of Tlusty’s studies [10] describes HSM applications in facing for airplane structures and introduces a case of ‘‘high-speed grilling’’.
Fig.1 Example of a stability diagram
In the year 2000, Altintas [12] published a paper focusing on the foundations of metal-cutting mechanisms, static and dynamic deformations, principles for the design of CNC, sensor-assisted machining and technology for programming numerical-control machines. He proposes a method for determining the chatter vibrations in orthogonal cuts and introduced a technique for considering chatter in complex milling operations. In the article, Altintas explained the technique with the help of the results of machining simulations and tests.
Insperger and Ste′pe′n [11] proposed and applied a new criterion for delaying the parametric excitation of the milling model wherein stability diagrams are constructed and the non-conventional regions of instability are identified together with the vibration frequencies.
1. A method to identify the stability lobes
1.1. The chatter problem
In the milling process, material is removed from a work piece by a rotating cutting tool. While the tool rotates, it translates in the feed direction at a certain speed. A schematic representation of the milling process is shown in Fig. 2.
One of the most common problems in machining is dynamic deformations, which are structural vibrations between the cutting tool and the work piece. The most common vibrations are the self-excited vibrations of chatter, which grow until the tool leaves its cutting zone due to the exponential increase of the dynamic displacements between the tool and the work piece (regenerative chatter).
Chatter occurs in machining operations due to the interaction between the tool-work piece structure and the force process. Regenerative chatter is so named because of the closed-loop nature of this interaction (Fig. 3). Each tooth pass leaves a modulated surface on the work piece due to the vibrations of the tool and work piece structures, causing a variation in the expected chip thickness.
Under certain cutting conditions (i.e. feed of rate, depth of cut, and spindle speed), large chip thickness variations and hence force and displacement variations occur and chatter is present. The results of chatter include a poor surface finish due to the chatter marks, excessive tool wear, reduce dimensional accuracy, and tool damage. Machine-tool operators often select conservative cutting conditions to avoid chatter, thus, decreasing productivity.
Different studies have been developed to avoid operations with chatter. One of these studies is the analytical prediction of chatter presented by Altintas and Budak. In the next subsection, a summary of this stability analysis is presented.
Fig.2 Mechanical model for milling
1.2. Analytical prediction of chatter vibrations in milling
In the articles ‘‘Analytical predictions of stability lobes in milling’’ and ‘‘Analytical prediction of chatter stability in milling. Part I: General formulation and Part II: Application of the general formulation to common milling systems’’ published by Altintas and Budak, and described in the book ‘‘Manufacturing Automation. Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design’’ [12], the analytical chatter prediction model was presented and provide practical guidance to machine-tool users for optimal process planning of depth of cuts and spindle speeds in milling operations.
The tool vibrations are assumed to occur at a chatter frequency, when a marginally stable depth of cut is taken. The forces (F) are described as harmonic functions and the closed-loop equation of the face milling operation is written as:
(1)
where is the stiffness of the work piece material, is the axial depth of cut, T is the tooth passing period, is the most simplistic approximation of the average component of the Fourier series expansion. The transfer function matrix [ is defined at the cutter work piece contact zone as
= (2)
where and are the direct transfer functions in the x and y directions, where and are the cross transfer functions, which has a nontrivial solution if its determinant is zero:
(3)
The eigenvalue of the characteristic equation is:
(4)
where N is the number of the tool teeth. The final expression for chatter-free axial depth of cut is found as:
(5)
The spindle speed n is simply calculated by finding the tooth passing period:
(6)
In summary, the transfer functions of the machinetool system are determined, and the dynamic cutting coefficients are evaluated from the derived equations for a specific cutter, workpiece material, and radial immersion of the cut.
(7)
However, the transfer function for multi degree systems can be identified experimentally using a piezoelectric force transducer and it can simplify this analytical method to determine the stability lobes in milling. One methodology to determine experimentally the transfer function is the experimental modal analysis for multi degree-of-freedom systems, which is described in the next subsection.
2.3. Experimental modal analysis for
Multi degree-of-freedom systems
Transfer functions of existing multi degree-of-freedom systems are identified by a structural dynamic test. An impact hammer instrumented with a piezoelectric transducer and a accelerometer can be used (Fig. 4). With this method, we try to excite a range of frequencies that contain the natural modes of the system. In order to obtain our objective, we need to generate an impulse and this can be given with a short impact. To choose the appropriate hammer and sensor, we have to consider the mass, the stiffness and the material of the structure.
Once the response and impulse signals are acquired, an analysis takes place to detect and eliminate signals with double impact and overload; and a ponderation in frequency is made. The modals parameters must be estimated. It is possible to use several systems.
The excitation and the answer contains very few data, but our precision is improved using order analysis methods different as the traditional frequency response function (FRF). Because the order analysis uses models, the coefficients that we needed are adjusted to a similar model of the obtained
signal. A damped sinusoidal signal can be described as a lineal combination of the different damped signals with the following expression:
(8)
where are the amplitudes of the damping factor and indicates the complex amplitudes. Written as a matrix form:
(9)
Baron de Prony discovered that are roots of the polynomial equation:
(10)
that facilitates the resolution using mathematical models. In general, these models solve the coefficients of auto-regression (AR) using diverse regression methods.
Then, the complex roots of the polynomial in (10) are found. The phase of indicates the frequency and the amplitude is the damping factor. Finally, to solve Ck, the values of must be inserted in Eq. (9). Considering that the amplitude and the phase of the sinusoidal component is equal to the amplitude and the phase of Ck, respectively.
The characteristics of damping, natural frequency and stiffness of the present vibration mode in the systemare obtained. These methods are sensible to the noise, reason why the measurement must be made without noise and properly treated.
1.4. The new method to obtain the stability lobes for high-speed milling
The method to generate the stability lobes for a certain vibration mode identifies the transfer function of the system with the experimental analysis. The natural frequency, damping factor and stiffness of the mechanical system are determined experimentally.
Once these values are found, the real and the imaginary components of the transfer function for a certain chatter frequency can be calculated using:
(11)
where and is a chatter frequency.
It is necessary also to consider the average number of teeth during the cut (m):
(12)
where is the tool diameter, N the number of teeth of the tool and the radial depth of cut. The axial depth of cut limit of stability is calculated with the following equation:
1 (13)
where l is directional orientation factor and Km the cutting stiffness. To calculate the spindle speed using Eq. (7) is necessary to identify the phase shift (e) between the inner and outer modulations (present and previous vibrations marks), with the equation:
(14)
The new proposed method to identify the stability lobes for high-speed milling using a combination between the analytical prediction of chatter and the experimental modal analysis for multi degree-off reedom systems is:
Step 1: Obtain the characteristics of the tool, material to mechanise and milling process, and obtain the characteristics of the systemusing the experimental analysis of the system;
Step 2: Calculate the real and imaginary component of the transfer functions (KR, KI), Eq. (11);
Step 3: Select a chatter frequency from the transfer function around a dominant mode;
Step 4: Calculate the critical depth of cut from
Eq. (13);
Step 5: Calculate the spindle speed from n