立式銑床升降工作臺設(shè)計含9張CAD圖
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附錄一：英文文獻翻譯
非圓齒輪與機械壓力機運動學(xué)優(yōu)化
1997年1月8日研制
摘要：使用金屬成形方法來加工生產(chǎn)零件的質(zhì)量很大取決于壓力桿。在機械壓力傳動時，有一種依賴于驅(qū)動旋轉(zhuǎn)角度速度比的非圓齒輪，提供了一種獲得這么動作時間的新途徑，我們致力于為不同的優(yōu)化金屬成型運作的制造。本文闡述了由漢諾威的大學(xué)研究所建成的金屬成形和金屬成形加工機床的使用原型原則，它就是目前運動學(xué)以及在原型產(chǎn)生的力和力矩。此外，本文展示了如何使用拉深和鍛造的一個例子，幾乎所有的金屬成形操作可有利用于機械傳動機構(gòu)的非圓齒輪。
關(guān)鍵詞：壓力，齒輪，運動學(xué)。
1. 簡介
提高質(zhì)量的要求在生產(chǎn)工程制造，所有的金屬成形以及在鍛造，有必要去攜手制定生產(chǎn)經(jīng)濟。日益增長的市場定位要求技術(shù)和經(jīng)濟條件都得到滿足。提高質(zhì)量、生產(chǎn)力、生產(chǎn)手段的創(chuàng)新解決方案,是一種用來維持和擴大的市場地位的關(guān)鍵所在。
所生產(chǎn)的金屬部件,我們需要分清期間所需的形成過程和處理零件所需的時間。隨著我們必須添加一些必要的額外工作，例如冷卻或潤滑的模具一次成型過程。根據(jù)質(zhì)量和產(chǎn)量兩個方面，產(chǎn)生了兩個最優(yōu)化方法。為了滿足這兩個方面，我們的任務(wù)是設(shè)計運動學(xué)形成過程中考慮到該進程的要求，也考慮到的是改變部分以及與一個優(yōu)先線輔助運作所需的時間短周期的時間。
2. 壓力機的要求
一個生產(chǎn)周期,這相當(dāng)于一個沖程來回壓的過程,大致經(jīng)歷了三個階段:加載、成型和移除零件。相反,在加載和移除零件階段，我們經(jīng)常發(fā)現(xiàn)送料的薄板,尤其是在純粹的切割時候。為此，壓力泵必須要一個確定時間的最小高度。成型周期中桿應(yīng)該有一個特別速度曲線,它將會降到最低。這個轉(zhuǎn)變期之間應(yīng)盡快來確保短周期時間。
短周期的要求是事件的原因,以確保通過高產(chǎn)量低成本的部分?；谶@個原因，關(guān)于對大型汽車車身沖壓片機和自動1200/min、拉深24/min的沖程數(shù)是標準的做法。增加沖程數(shù)是為了減少設(shè)計的周期變化導(dǎo)致增加的壓實機械應(yīng)變率, 然而，這對成形過程有很明顯影響,使它必須考慮參數(shù)確定過程和被它所影響。
在拉深成形過程中,當(dāng)敲打板塊時的撞擊速度應(yīng)盡量避免產(chǎn)生了深遠影響。一方面,速度成形時必須充分潤滑。另一方面,我們必須要考慮提高產(chǎn)量的相應(yīng)的壓力來增加造成更大的應(yīng)變速率力,這可能導(dǎo)致沖床半徑一側(cè)的一部分過渡疲勞而導(dǎo)致斷裂。在鍛造時，停留時間短的壓力是可取的。隨著停留時間的壓力下降了模具的表面溫度將降低，其結(jié)果是熱磨損。這是提高抵消了由于機械磨損形成更大的力量，但由于增加的應(yīng)變率是較低的，因為較低的部分冷卻屈服應(yīng)力補償。目前，最佳短住壓力可以用有限元分析法萊分析。此外,避免由于成本降低磨損、短壓住時間也是一個重要的技術(shù)要求的精密鍛造，近凈形部分有一個光明的未來。
高質(zhì)量的要求和高產(chǎn)量將只能通過一個機技術(shù),考慮到金屬成形過程的考察要求等同于減少工作的目標成本。以前按設(shè)計已經(jīng)不能同時滿足這些技術(shù)要求和經(jīng)濟的充分程度，或他們是非常昂貴的設(shè)計和制造，例如鏈接驅(qū)動壓力機。這就需要尋找對泵創(chuàng)新設(shè)計的解決方案，它的設(shè)計應(yīng)主要標準化，模塊化，以降低成本。
3．非圓齒輪的壓力傳動
3.1 原則
使用非圓齒輪傳動機械曲柄壓力機，它提供了一種新方式的技術(shù)和經(jīng)濟需求的壓力桿運動。一對非圓齒輪有不變的中心距, 因此采用了電動馬達，或由飛輪、曲柄和驅(qū)動機制本身。制服驅(qū)動器的速度傳送是通過一對非圓齒輪傳遞給非均勻的偏心軸。如果非圓齒輪的適當(dāng)設(shè)計，從動齒輪的非均勻驅(qū)動器會導(dǎo)致泵所需的行程時間行為。調(diào)查中心的金屬成形和金屬成型機床(IFUM)漢諾威的大學(xué)已經(jīng)表明,在這個簡單的方式所有相關(guān)的壓力桿的連續(xù)運動，可以達到各種成形過程。
此外從運動學(xué)和縮短生產(chǎn)周期，驅(qū)動概念導(dǎo)致新的驅(qū)動器的優(yōu)點被以下的良好性能所區(qū)分。因為它是一個機械壓力機，它具有高可靠性、低維護性和可預(yù)期性。對連桿壓力機的數(shù)量和軸承零件顯然是減少。首先，一個基本泵類型可以通過安裝不同的齒輪而進一步改變設(shè)計，它根據(jù)客戶的要求而設(shè)計。不同環(huán)節(jié)的驅(qū)動器，軸承的安裝位置不會隨著單一載荷方向的不同運動而改變。因此，上述要求的模塊化和標準化是考慮到時間和成本，它降低了設(shè)計和沖壓生產(chǎn)成本。
3.2 原型
在金屬成型和金屬成型工具機（IFUM）1架的c型泵，它已經(jīng)進行了修整和安裝了非圓齒輪副。為達到這種目的，先前的背輪背一個行星齒輪組做取代。這項工作表明了存在的新型傳動印刷機是可能的，在最后對標準壓力泵的改造在Fig. 1中進行說明。
圖表1 壓力機設(shè)計是為了所受1000KN的柱塞力和200KN的沖壓模具緩沖力。 這一對非圓齒輪傳動比平均為1，每個齒輪輪齒有59，直齒，模數(shù)10mm（圖2）齒面寬是150mm，這些齒輪有漸開線輪齒。我假設(shè)了非圓曲線設(shè)計是以側(cè)面幾何設(shè)計為基礎(chǔ)。因此，一個非圓齒輪的齒形沿齒輪圓周而改變。盡管如此,它可以來自知名的梯形齒條. 然而[4.5],提出了一種計算方法，它精確地把齒頂高和齒根高考慮在內(nèi)，進行相應(yīng)的調(diào)整。
壓力機是為了在單一沖程模式下對零件進行深拉而設(shè)計的。最高滑塊行程為180mm，行程數(shù)32/min。在140毫米的沖壓速度幾乎保持71mm/s不變，它是靜點中心線到靜點中心線之前的速度。見圖3。這種速度就相當(dāng)于液壓機工作的速度。這個速度影響到曲柄機構(gòu)，使其與擊打具有相同的數(shù)目相比較，速度都是220m/。為了跟一個曲柄壓力機具有相同的平均速度擊打的數(shù)目不得不將減少一半。短周期內(nèi)的機械改造將導(dǎo)致最后的向上運動。由于壓力機是運行在單一的操作模式,在設(shè)計時對其做相關(guān)的處理沒有提出特別的要求。
驅(qū)動機制的原型與非圓齒輪有另外一個有利的影響及其驅(qū)動力矩（圖4）。對于一個曲柄壓力機的公稱力通?？梢越档挽o點之前把曲柄軸按正常方式旋轉(zhuǎn)。這對應(yīng)于公稱力作用下相對于擊打力的75%。若要達到1000kN標準力，該驅(qū)動器已提供45 kNm 的曲柄軸扭矩。該原型只要求對非圓齒輪傳動增加額外的30kNm力矩。他們被傳送一個循環(huán)，非均勻的曲柄轉(zhuǎn)矩，將導(dǎo)致一個標準力在靜點范圍內(nèi)變化。這相當(dāng)于27.5%的行程。如果非圓齒輪副是在壓力機的工作范圍，我們總能找到類似的條件。這幾乎總是與板料成形及沖壓件有關(guān)。這樣可以設(shè)計一些較弱的機器零件，而且節(jié)約成本。
4. 進一步的設(shè)計實例
利用二沖程時間行為的設(shè)計實例說明了以下幾點。假設(shè)一系列的零件時通過壓力機來加工的。為了達到這一目的，壓力桿所需的速度和擊打成形速度要求假設(shè)成立必須量化。再者，處理零件所需的時間必須確定，而且必須假設(shè)在處理時壓力桿的最小高度。由此，我們設(shè)計動作的順序，我們用數(shù)學(xué)含義來描述它。在IFUM中，由該研究所開發(fā)使用軟件程序。從這個數(shù)學(xué)描述的沖程運動,我們可以計算出所需要的非圓齒輪速度比，從這我們可以得到齒輪的圓周曲線[1.2.7]。
在第一個例子，在深拉伸沖壓速度應(yīng)該是在靜止點前，金屬板材成形保持在至少超過100mm，它的速度應(yīng)該是約400m/s。讓行程數(shù)定為30/min。第450mm以上擊打的地方，讓處理零件時間和曲柄壓力機在25min/n的擊打時間相同。圖5表明了沖程運動情況，這是由一對齒輪的描繪所獲得。該齒輪是通過他們的圓周率所描繪。在25/min傳統(tǒng)的余弦曲線作為比較。除了生產(chǎn)周期時間減少了20％，應(yīng)把桿速度的影響也大大減少。下靜點前110mm，當(dāng)使用曲柄機構(gòu)時，沖擊速度為700mm/s，而當(dāng)使用非圓齒輪時僅僅只有410mm/s。
第二個例子顯示了驅(qū)動裝置是用于鍛造。在圖6中，常規(guī)鍛造曲軸的行程時間是相對于在圖片中說明非圓齒輪壓力運動學(xué)。曲柄壓力機的周期時間是0.7s、行程數(shù)是85/min和標準力是20mn。它的保壓時間為86ms與50mm的成形部份時間。非圓齒輪壓力機描繪的保壓描繪時間67%減少至28ms。因此，它達到了和錘子一樣的幅度。通過增加1.5倍的沖程數(shù)，周期時間縮短至46mm。盡管如此,處理時間依舊與常規(guī)非圓齒輪曲柄壓力機的運動學(xué)相同。在這種情況下為了實現(xiàn)這些運動,傳統(tǒng)的圓弧齒輪可以作為驅(qū)動裝置，安排偏心。這為齒輪制造降低了成本。
這些例子表明，不同的運動可以通過使用非圓齒輪驅(qū)動裝置實現(xiàn)。在同一時間內(nèi)，這個驅(qū)動器的實用潛力用實現(xiàn)理想的運動學(xué)變得清晰，而且生產(chǎn)周期時間減少。例如，通過不同的例子，如果運動的順序?qū)σ幌盗袎毫C生產(chǎn)零件有利，可能增加拉深成形后的速度。
5．總結(jié)
高生產(chǎn)率，降低成本和保證產(chǎn)品質(zhì)量的高要求，這時所有制造公司所期望的，特別適用于公司的金屬加工領(lǐng)域。這種情況導(dǎo)致我們重新考慮壓力傳動機的使用。
對曲柄與非圓齒輪傳動壓力機的描述，使我們能夠優(yōu)化簡單的機械壓力機運動學(xué)。這意味著周期時間縮短,以達到高生產(chǎn)率和運動學(xué)的成形工藝的要求。這個設(shè)計工作需要很低。相對于多連桿壓力機驅(qū)動器，可以實現(xiàn)其他運動學(xué)在其他齒輪軸承位置不改變時的壓力機構(gòu)建使用。這使壓力機模塊化和標準化。
6．致謝
作者想表達他們的謝意，感謝德國機床制造商協(xié)會(VDW),位于德國法蘭克福，其經(jīng)濟援助以及一些成員，感謝他們的支持。
7. 參考文獻
[ I ] Bernard, J., 1992, Optimization of Mechanism Timing Using Noncircular Gearing, Mechanical Design and Synthesis, Vol. 46, p. 565-570.
[2] Doege, E., Hindersmann, M., 1996, Fertigungsgerechte Kurbelpressenkinematik durch Unrundzahnrader. VDI-Z Special Antriebstechnik 1/96, p. 74-77.
[31 Doege, E., Nagele, H., 1994, FE-Simulation of the Precision Forging Process of Bevel Gears, Annals of the CIRP, Vol. 43, p. 241-244.
[4] Hindersmann, M., Betke, V., 1996, Unrunde Zahnrader- ein wiederentdecktes Maschinenelement, Konstruktion, Vol. 48, p. 256-262.
[5] Litvin, F. L.: 1994, Gear qeometrv and applied theory,PTR Prentice Hall, Englewood Cliffs (NJ, U.S.A.).
[6] Niemitz, D., 1992, Anforderungen an Grof3raumstufenpressen;Pflichtenheft fur die Auftragsvergabe. In:Blechbearbeitung '92, Int. Congress 27 -28.0ct.1992,VDI-Bericht, Vol. 946, p.231-253.
[7] Ogawa. K., Yokoyama, Y., Koshiba, T., 1973, Studies on the Noncircular Planetary Gear Mechanisms with Nonuniform Motion, Bulletin of the JSME, Vol. 16. p. 1433-1442.
附錄二:英文文獻原文
Optimized Kinematics of Mechanical Presses with Noncircular Gears
E. Doege ( l ) , M. Hindersmann
Received on January 8, 1997
Abstract：The quality of parts manufactured using metal forming operations depends to a large degree on the kinematics of the press ram. Non-circular gearsy to obtain those stroke-time behaviours we aim at as an optimum for the various metal forming ope with a rotational-angle-dependent speed ratio in the press drive mechanism offer a new wa rations in terms of manufacturing. The paper explains the principle using a prototype press which was built by the Institute for Metal Forming and Metal Forming Machine Tools at Hanover University. It will present the kinematics as well as the forces and torques that occur in the prototype. Furthermore, the paper demonstrates using one example of deep drawing and one of forging that the press drive mechanism with non-circular gears may be used advantageously for virtually all metal forming operations.
Keywords: Press, Gear, Kinematics
1 lntroductior
Increasing demands on quality in all areas of manufacturing engineering, in sheet metal forming as well as in forging, go hand in hand with the necessity to make production economical. Increasing market orientation requires that both technological and economic requirements be met. The improvement of quality, productivity and output by means of innovative solutions is one of the keys to maintaining and extending one's market position.In the production of parts by metal forming, we need to distinguish between the period required for the actual forming process and the times needed to handle the part.
With some forming processes we have to add time for necessary additional work such as cooling or lubrication of the dies. This yields two methods of optimization, according to the two aspects of quality and output. In order to satisfy both aspects, the task is to design the kinematics taking into account the requirements of the process during forming; also to be considered is the time required for changing the part as well as for auxiliary operations in line with the priority of a short cycle time.
2 Pressing Machine Requirements
One manufacturing cycle, which corresponds to one stroke of the press goes through three stages: loading,forming and removing the part. Instead of the loading and removal stages we often find feeding the sheet, especially in sheer cutting. For this, the press ram must have a minimum height for a certain time. During the forming period the ram should have a particular velocity curve,which will be gone into below. The transitions between the periods should take place as quickly as possible to ensure short cycle time. The requirement of a short cycle time is for business reasons, to ensure low parts costs via high output. For this reason stroke numbers of about 24/min for the deep drawing of large automotive body sheets and 1200/min for automatic punching machines are standard practice.Increasing the number of strokes in order to reduce cycle times without design changes to the pressing machine results in increasing strain rates, however. This has a clear effect on the forming process, which makes it necessary to consider the parameters which determine the process and are effected by it.
In deep drawing operations, the velocity of impact when striking the sheet should be as low as possible to avoid the impact. On the one hand, velocity during forming must be sufficient for lubrication. On the other hand, we have to consider the rise in the yield stress corresponding to an increase in the strain rate which creates greater forces and which may cause fractures at the transition from the punch radius to the side wall of the part.
In forging, short pressure dwell time is desirable. As the pressure dwell time drops the die surface temperature goes down and as a result the thermal wear This is counteracted by the enhanced mechanical wear due to the greater forming force, but the increase due to the strain rate is compensated by lower yield stress because of the lower cooling of the part. The optimal short pressure dwell can nowadays be determined quantitatively using the finite element method [3]. In addition to cost avoidance due to reduction in wear, short pressure dwell time is also an important technological requirement for the precision forging of near net shape parts, which has a promising future.
The requirements of high part quality and high output will only be met by a machine technology which takes into account the demands of the metal forming process in equal measure to the goal of decreasing work production costs. Previous press designs have not simultaneously met these technological and economical requirements to a sufficient extent, or they are very costly to design and
manufacture, such as presses with link drives [6]. This makes it necessary to look for innovative solutions for the design of the press. Its design should be largely standardized and modularized in order to reduce costs [6].
Fig 1. Prototype press
3 Press Drive with Noncircular Gears
3.1 Principle
The use of non-circular gears in the drive of mechanical crank presses offers a new way of meeting the technological and economic demands on the kinematics of the press ram. A pair of non-circular gears with a constant center distance is thus powered by the electric motor, or by the fly wheel, and drives the crank mechanism itself.The uniform drive speed is transmitted cyclically and
non-uniformly to the eccentric shaft by the pair of noncircular gears. If the non-circular gear wheels are suitably designed, the non-uniform drive of the driven gear leads to the desired stroke-time behaviour of the ram. Investigations at the Institute for Metal Forming and Metal Forming Machine Tools (IFUM) of Hanover University have shown that in this simple manner all the relevant uninterrupted motions of the ram can be achieved for various forming processes [2].
Apart from, the advantages of the new drive, which result from the kinematics and the shortened cycle time, the drive concept is distinguished by the following favourable propertties. Because it is a mechanical press, high reliability and low maintenance may be expected. In comparision to linkage presses the number of parts and bearings is clearly reduced. Above all, a basic press type can be varied without further design changes by installing different pairs of gears, designed according to the demands
of the customer. Unlike link drives, bearing locations and installations do not change within one load
class as a result of different kinematics. Thus the above mentioned requirement of modularization and standardization is taken into account Reductions in time and costs are possible for the design and press manufacture.
3.2 Prototype
At the Institute for Metal Forming and Metal Forming Machine Tools (IFUM) a C-frame press has been remodeled and a pair of non-circular gears was installed. The previous backgears were replaced by a planetary gear set for this purpose. The work carried out shows that remodeling of existing presses for the new drive is possible. The state of the press at the end of the remodelling is shown in fiqure 1. The press is designed for a nominal ram force of 1,000 kN and 200 kN of the die cushion. The center distance of the non-circular gears is 600 mm. The pair of non-circular gears has an average transmission ratio of 1.Each gear wheel has 59 gear teeth, straight-toothed,module 10 mm (fiaure 2). The face width is 150 mm. The gears have involute gear teeth. We assume a non-circular base curve for the design of the flank geometry. As a result the tooth geometry of a non-circular gear varies along the circumference. In spite of this, it can be derived from the well-known trapezium rack, however [4, 51. An algorithm for the computation, which takes the addendum and dedendum into account exactly, has been developed.
Fig. 2 View of the gears from the rear
The press is designed for deep drawing of flat parts in single stroke operation mode. The maximum ram stroke is 180 mm, the number of strokes 32/min. At a stroke of 140 mm the ram velocity almost remains constant 71 mmls from 60 mm before lower dead center until lower dead center, see fiqure 3. Thus the velocity corresponds to the working velocity of hydraulic presses. The velocity of incidence of a crank mechanism with the same number of strokes would be 220 mmls, in comparison. In order to keep the same average velocity with a crank press, the number of strokes would have to be halved. The short
cycle time of the remodelled machine results from the fast upward motion. Because the press is run in single stroke operation mode, no particular requirements were made concerning handling time during design.
The drive mechanism of the prototype with non-circular gears has in addition a favourable effect on the ram forces and the driving torques (ficlure 4). For a crank press the nominal force is normally available at 30" rotation of the crank shaft before the lower dead center. This corresponds to a section under nominal force of only 7 5% relative to the stroke. To reach the nominal force of 1,000 kN, the drive has to supply a torque of 45 kNm at the crank shaft. The prototype only requires 30 kNm on account of the additional transmission of the non-circular gears. They are transmitted to a cyclic. non-uniform crank shaft torque, resulting in a nominal force range from 60" to the lower dead center. This corresponds to 27.5% of the stroke. We always find similar conditions if the pair of non-circular gears is stepped down in the operating range of the press. This will almost always be the case with sheet metal forming and stamping. It is thus possible to design some machine parts in a weaker form and to save costs this way.
4 Further Design Examples
Using the examples of two stroke-time behaviours the design is illustrated in the following. A range of parts is assumed which are to be manufactured by the press. For this purpose the ram velocity requirements and the forming section of the assumed stroke need to be quantified.Furthermore, the time needed for the handling of the part needs to be determined, and also the minimum height which the ram has to assume during the handling. From this, we design the sequence of movements, and we describe
it mathematically. At the IFUM, a software program developed by the institute is used. From this mathematical description of the stroke-time behaviour we can calculate the speed ratio of the non-circular gears needed.From this we obtain the rollcurves of the gears [l, 2, 7].
In a first example the ram velocity in deep drawing is supposed to be constant during the sheet metal forming at least over 100 mm before the lower dead center and it is supposed to be about 400mm/s. Let the number of strokes be fixed at 30/min. Above 450mm section of stroke, let the time for the handling of the part be the same as for a comparable crank press with 25 strokes per minute. Fiqure 5 shows the stroke-time behaviour , which is attained by the sketched pair of gears. The gear wheels are represented by their rollcurves. The conventional cosine curve at 25/min is given for comparison. In addition to the reduction of cycle time by 20%, the ram velocity of impact onto the sheet is also considerably reduced.110 mm before the lower dead center, the velocity of impact is 700 mmls when using the crank mechanism and only 410 mm/s when operated with non-circular gears.
A second example shows a drive mechanism as is used for forging. In fioure 6, stroke-time behaviour of a conventional forging crank press is compared with the kinematics of the press with non-circular gears illustrated in the picture.The cycle time of the crank press is 0.7 s, the number of strokes is 85/min and the nominal force is 20 MN.Its pressure dwell time is 86 ms with a forming section of 50 mm. The pressure dwell of the press depicted with non-circular gears decreases by 67% to 28 ms. It thus reaches the magnitude familiar from hammers. By increasing the number of strokes by a factor of 1.5, the cycle time decreases by 33% to 46 ms. In spite of this,the handling time remains the same compared to conventional crank press on account of the kinematics of the non-circular gears. In order to achieve these kinematics in this case, a conventional circular gear may be used as driving gear, arranged eccentrically. This reduces the costs for gear manufacture.These examples show that different kinematics can be achieved by using non-circular gears in press drives At the same time the potential of this drive with respect to the realization of the desired kinematics becomes clear as does the reduction of cycle times in production. By varying the examples it is also possible to increase the velocity after inpact in deep drawing operations if :his sequence of motions is advantageous for the range of pans to be produced on the press, for reasons of lubrication, for example.
5 Conclusions
The requirements of high productivity, reduced costs and the guarantee of high product quality to which all manufacturing companies are exposed, applies particularly to companies in the field of metal working. This situation leads us to reconsider the press drive mechanism in use up to now.
The new drive for crank presses with non-circular gears described here allows us to optimize the kinematics of simple mechanical presses. This means that the cycle time is shortened to achieve high productivity and the kinematics follows the requirements of the forming process.The design effort needed is low. In contrast to presses with link drives, other kinematics can be achieved during the construction of the press by using other gears without changing bearing locations This allows the modularization and standardization of presses.
6 Acknowledgement
The authors would like to express their appreciation to the German Machine Tool Builders Association (VDW), located in FrankfurVGermany, for its financial assistance and to some members for their active support.
7 References
[ I ] Bernard, J., 1992, Optimization of Mechanism Timing Using Noncircular Gearing, Mechanical Design and Synthesis, Vol. 46, p. 565-570.
[2] Doege, E., Hindersmann, M., 1996, Fertigungsgerechte Kurbelpressenkinematik durch Unrundzahnrader. VDI-Z Special Antriebstechnik 1/96, p. 74-77.
[31 Doege, E., Nagele, H., 1994, FE-Simulation of the Precision Forging Process of Bevel Gears, Annals of the CIRP, Vol. 43, p. 241-244.
[4] Hindersmann, M., Betke, V., 1996, Unrunde Zahnrader- ein wiederentdecktes Maschinenelement, Konstruktion, Vol. 48, p. 256-262.
[5] Litvin, F. L.: 1994, Gear qeometrv and applied theory,PTR Prentice Hall, Englewood Cliffs (NJ, U.S.A.).
[6] Niemitz, D., 1992, Anforderungen an Grof3raumstufenpressen;Pflichtenheft fur die Auftragsvergabe. In:Blechbearbeitung '92, Int. Congress 27 -28.0ct.1992,VDI-Bericht, Vol. 946, p.231-253.
[7] Ogawa. K., Yokoyama, Y., Koshiba, T., 1973, Studies on the Noncircular Planetary Gear Mechanisms with Nonuniform Motion, Bulletin of the JSME, Vol. 16. p. 1433-1442.
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