虛擬制造在齒輪生產(chǎn)中的應用外文翻譯、中英文翻譯、機械類外文文獻翻譯

外文原文： Application of virtual manufacturing in generation of gears Received: 29 November 2004 / Accepted: 5 May 2005 / Published online: 24 November 2005 Spfinger-Verlag.London Limited 2005 Abstract The manufacturing process of gears is fairly complicated due to the presence of various simultaneous motions of the cutter and the job. In this paper, an attempt is made to generate meaningful design data for spur and helical gears and the corresponding rack form cutter necessary for the manufacturing. Using this information, solid models for the cutter and blank are developed and finally gear-manufacturing processes are simulated in a virtual manufacturing environment. The user has the option to choose between designs and manufacture mode at will. The integrated process may also help to develop an optimized product. For better understanding of the operational principle, an animation facility in the form of a movie is included in the package. Keywords Virtual manufacturing； Animation； Gear generation 1 Introduction A gear is a very common machine element in mechanical engineering applications. However, manufacturing of the gear seems to be fairly complicated even to the person having thorough technical knowledge in the related field. The conventional gear generation processes like forming, shaping, hobbing, etc. are usually represented in two-dimensional sketch. There may be some components that are not adequately described by the two-dimensional approach. In the case of gear generation, it may be difficult to understand the complex geometries and the manufacturing arrangement with the help of 2D models. These limitations can be partially overcome and understanding will be more meaningful if one uses 3D solid models instead. However, the development of the models using 3D solids may not always ensure the clarity of the complex gear generation process unless one uses animation to represent tile motion of the gear blank and the gear cutter. This can be achieved very efficiently with the help of the virtual manufacturing technique. It is a technology to create a virtual environment on the computer screen to simulate the physical world. The knowledge base and expertise gained from the work in the virtual environment enables the user to apply them more meaningfully in real life situations. A host of literature is available on virtual manufacturing in different areas among which some of the recent and important works are referred below. Tesic and Baneljee 1 have worked in the area of rapid prototyping, which is a new technology for design, visualization and verification. Graphical user interfaces, virtual reality technologies, distillation, segregation and auto interpretation are some of the important features of their work. Balyliss et al. 2 dealt with the development of models in a virtual environment using the virtual reality technologies providing an outstanding 3D visualization of the object. In 1994, G.M. Balyliss et al. 3 presented theoretic solid modeling techniques using the VM tools, like VP, MI, (virtual reality manufacturing language) and 3D Sludio Max. They have developed different parts of an automobile and through the special effect of animation imparted all possible motion to the model. The technology is further enhanced by Kiulera 4, who treated product and process modeling as a kernel for the virtual manufacturing environment. In his work, Kimura has incorporated significant modeling issues like representation, representation language, abstraction, standardization, configuration control, etc. Arangarasau and Gadh 5 contributed towards the virtual prototyping that are constructed using simulation of the planned production process using virtual manufacturing on a platform of MAYA,3D Studio Max and VRML, etc. At .Jadavpur University, research work 6, 7 is being carried out to simulate the gear manufacturing processes using A I Ill)CAD and 31) Studio Max as platforms. Software has been developed that helps the design engineers to understand the problems related to spur gear operation and its manufacturing process. A study of the state of tile art and literature review reveal that the scope of virtual manufacturing is wide open for simulating spur gear generation processes. Computer simulation can be very effectively used for viewing along with aiding subsequent analysis of different complicated manufacturing processes using the concept of design centered virtual manufacturing. With this objective in mind, an attempt is made to virtually manufacture spur and helical gears from the blank using a rack cutter. The scope of the work includes the generation of design data for the spur and helical gears and the rack form cutter, the generation of solid models for the cutter and blank, and finally to simulate gear-manufacturing process through animation. The main motivation of the work is to simplify the task of designing, and to study the gear generation process that can be understood by a layman and to present a realistic view of it. All the processes are developed on the platform of the 3D Studio Max, which is one of the most important virtual tools. The software is developed using max-script, an object contained programming language that can be run in 3D Studio Max environment. 2 Description of the software The max-script language is basically an image processor that creates the visual effects in 3D Studio Max. In addition, it can be used for design calculation and subsequent checking. An attempt is made to develop the entire package in modular form so that any further improvement can be implemented easily without affecting the others. The entire work is carried out in a 3D environment. The modular structure of the entire package is presented in Fig. l. The major modules are: input module, gear design module, virtual manufacturing module and special module. A brief description of these modules is mentioned below. 2.1 Input module This module is developed to provide input parameters that are essential for (tie design and development of the spur and helical gears and the corresponding cutters. In order to make the software user friendly, the process of inputting the data is specifically done through an input dialogue-box created by the max-script-language. A sample dialogue box is shown in Fig.2. Some fields have some restrictions like predefined lower or upper limits or predefined steps for increment or decrement. This is done purposively to make the environment more user friendly and to restrict the user from entering invalid data, for example, a user cannot make the number of gear teeth less than 18. 2.2 Gear-design module Before going for the generation of the gears, one should evaluate the various design parameters of the gears to be manufactured based on the input parameters. In order to design a gear pair, the following data are essential. I Rpm at which the gear is running 2. The power being transmitted 3. The transmission ratio of the assembly In addition, users may specify the following operational conditions/parameters: 1. Precision of the gear assembly 2. Pressure angle of the gear 3. Material of the pinion 4. Type of shock load required for the pinion to take up 5. Helix angle in case of helical gear If the user is not satisfied with the output, he can modify the input to obtain desired output. In this module, the entire design procedure for the gears has been treated. The different aspects of design calculations, for example, dynamic load, static load (fatigue load) and the wear load have been calculated in separate programs, and are displayed through the output dialog box. While designing the gear, it has been kept in mind that the gear has to form mesh with that of the rack, so care has been taken to avoid the interference of the mating pair. 2.2.1 Methodology Varieties of gear cutting processes are available and are generally being followed in the industries during their manufacturing. In this paper, Focus is given on gear manufacturing through generation. The underlying principle of gear design is based on the fact that the profiles of a pair of gear teeth bear a definite relationship to each other such that the pair of teeth have a predetermined relative motion and contact at every instant. Therefore, if the relative motion of the profiles and the form of one of them is known, the determination of the form of the other may be regarded as tile problem capable of solution by either graphical or analytical means. The actual production of gear tooth represents a solution to the above problem by mechanical means known as generation. The generation is a method that follows the following principles. 1. A cutting edge (basically a gear with cutting edges) is given a motion. As a result, it is caused to sweep out the surface corresponding to the actual teeth surfaces of the known member of a pair of conjugate gears. 2. A blank is mounted at an appropriate relationship to the cutter. It is given a motion that the finished gear must have relative to that of the cutter. As a result of the simultaneous movement and the cutting action of the cutter, teeth are formed on the blank conjugate to that represented by the cutter. In fact due to the addition of the relative motion, the profile given to the work piece is different from that of the cutter. This differentiates the generating from the forming operation. 2.2.2 Spur gear Generation of spur gear by means of cutter corresponding in form to the mating gear is well known. Cutter may be in the form of a rack. For an involute system of tooth profiles, the cutter corresponding to the rack will have straight sides. The arrangement of such a cutter relative to the blank is shown in Fig. 3. The cutter is adjusted radially with respect to the axis of the work. It is reciprocated so that its edges may sweep out the surface of the teeth of the imaginary rack forming the basis of the design of the tooth profile of the blank. In addition to this reciprocation, the cutter is advanced in the direction of the pitch line and at the same time the work is rotated about its axis at a speed such that it is pitch point has the same linear veloc ity as that of the rack. In other words, the pitch circle of the blank and the pitch line of the rack roll together. In consequence the straight cuttings edges generate the involute profile in the blank. For such a process to be continuous, The length of the cutter should be somewhat longer than the pitch circumference of the work； since this is usually impracticable The cutter is withdrawn from the work after it has advanced a distance equal to all integral number of pitches and return to its starting point， the blank in the meantime remains stationary This is repeated until all the teeth are cut 2.2.3 Helical gear It is well known that a helical involute gear is conjugate to a straight rack having inclined teeth Therefore， the same method described above can be employed to manufacture a helical gear However, the direction of reciprocation of the rack cutter must be inclined to the axis of the blank at all angle equal to the helix angle of the gear The cutter must roll over the blank in a direction similar to that described earlier The simultaneous motion involved and the orientation of the cutter relative to the blank during the cutting operation is shown in Fig.4 2.3 Virtual manufacturing module This module has been divided into two sub sections： (a) cutter generation， and (b) gear generation 2.3.1 Cutter generation In this section of the virtual manufacturing， a solid model of the rack form cutter is developed. This cutter is used in the later stage to animate the gear generation process in the virtual environment The cutter with all its cutting geometry such as rack and clearance angles have been provided Figure 5 exhibits a 3D solid model view of the cutter developed by the software 2.3.2 Gear generation This module is further subdivided into two parts， namely, (i) spur gear generation module，and (ii) helical gear generation module. (i) Spur gear generation In this sub module, spur gear is generated. In order to simulate the actual machining operation, the blank, which is to be used for the generation of spur gear, is bolted on the movable tabletop. The required washer and back-plate are also tied with the same so that it will have a firm support and be ready for the machining purpose. The cutter is positioned at a desired location. Afterwards, the cutter is given requisite motion to generate involute profile tooth. Generation by means of such a tool is called copy-generation. The arrangement of such a cutter relative to the blank is illustrated in the Fig, 6. The kinematics of the gear shaping process involve the following motions. 1. Reciprocation of the cutter 2. Tangential feed of the cutter and rolling of the gear blank 3. The advanced and reliving motion of the gear-blank 4. Radial feed of the cutter 5. Indexing of the gear-blank All of the above input parameters can be entered through tile input dialog box. In the software, provision is made to display the following motions of the system in the animation mode so that the users have the feeling of a virtual environment created in 3D. (ii) Helical gear generation In the case of helical gears, as the cutter reciprocates up and down over the gear blank. It makes a definite angle with the vertical, equal to the helix angle of the cutter (Fig. 7). As a result, a few teeth that are inclined to the axis of the blank will be partially generated on the gear blank at one time. None of the teeth will be complete in first phase following the principle of gear generation . 2.4 Special module One of the major objectives of the software is to simulate the various simultaneous movements involved in a gear generation process. In the special module, additional features are provided for better understanding of the gear generation process. They are (a) camera views (snap shot), (b) camera views (animated), and (c) movie files. 2.4.1 Camera views (snap shot) The software provides the facility to place the camera at different coordinate positions and thus display different camera views of the cutting process. These are the still pictures taken in render form at successive intervals of the machining process. Still pictures of the partially cut pinion along with that of the cutter at every step of cutting is recorded and enable the user to feel the reality in a virtual environment, 2.4.2 Animation and movie Animation is the backbone of virtual manufacturing as it gives life to already created stationary objects, in other words, it simulates the dynamic behavior of different components. In order to create the effect of animation, a series of still pictures are first generated with a little change of position of the objects from the previous one. When these pictures are displayed in proper sequence at successive interval, they create the impression of moving objects. Each of these pictures is known as flame. For the animation, time interval between successive frames is very important. Generally, the human eye can perceive a frame rate between 60 frames per sec (fps) and I0 fps. The illusion of continuous motion as opposed to a fast paced slide show starts to break down under 1 2 fps. So, frame rate is to be kept above this limit. Generally the frame rate for films becomes standardized at 24 fps. In addition, the animator has to decide whether a given motion has to be shot on ones or on twos. For simple motion it is better to shoot on twos in which case each frames would be shot tw ice, making the effective playback rate 12 fps. For a very swift or intricate motion, the frames of shooting on ones are generally recommended to keep continuity. The cutter and the gear blank occupy different positions in each of the frames depending on the kinematics relationship of the cutting process. This is achieved through the max-script programming environment of 3D Studio Max. They are stored in the hard disk as rendered views of the objects so that whenever necessary they can be run efficiently with the help of Windows media player: 2.4.3 Animated camera view The software has the additional facility to pan the camera as the gear generation process is in progress. The procedure is quite simple and is described below in brief. As mentioned in the earlier section, a first snap shot of the machining process is taken with the camera situated at a particular position. The next frame is taken with the camera position shifted a little bit from its original location. This process continues until the camera comes to the pre-determined end position. The number of frames to be created within the interval is decided as per the visual requirement. Each of the frames captures the progressive development of the cutting process, while the camera moves along definite path. When these frames are projected on the screen successively, it creates the effect of panning the camera. This facility is very useful to understand the complex mechanism of the gear generation process. However, setting of camera locations requires a thorough understanding of 3D co-ordinate systems. 3 Results and discussions It is not possible to present all the feature of the software. Some of the salient features are highlighted below. As the cutter reciprocates up and down over the gear blank, a few teeth will be partially generated on the gear blank at a time. None of the teeth will be in complete shape in the first cut following the principle of gear generation. It should be noted that the cutter teeth profile is straight edge whereas, in the case of gear, it has an involute profile. In order to create the impression of cutting, a large number of frames are generated, each one exhibiting a different amount of material removal from the gear blank. The downw ard motion of the cutter is assumed to be the cutting stroke. The requisite depth of cut is introduced by bringing the cutter to the predetermined position above the blank. The gear blank below the cutter is not yet cut. This is one frame and is shown to the viewer. The next frame shows the sequence when the cutter just finishes the cutting motion and a few partial teeth are developed on the blank. The successive frames illustrate the withdrawal of the cutter, its backward movement, indexing of the gear blank, and positioning of the cutter for the next cutting action. When all these frames are shown one after another, the observer will have the impression of virtual manufacturing of the gear. This process continues until all the teeth successively pass on the pitch circumference of the gear-blank. Figures 8, 9 show a few of the frames during the cutting process of spur and helical gears, respectively. The software has the facility of creating movie files in which a user can control projection of frame rates. Therefore, it is very useful for demonstration purpose as well. The user can change the camera view as per his requirement for better understanding of the operational principal. 4 Conclusion A user-friendly software package has been developed that can tackle the problem of gear design and subsequent visualization of the gear generation process in a virtual environment. It also focuses the development of a rack form cutter, which in the later stage is used for the generation of the gear. All the models are developed in a 3D environment. Additional features like camera views, movie files, etc. are incorporated for better understanding of a fairly difficult subject. Provisions are made to enter the input data through dialog box. If there is incorrect data, a warning message is given by the software indicating what step to be followed next. The results of all the design calculation are indicated in the output dialog box. For a designer these values are very useful information. Using the above output, a designer may have an overall idea about the gear to be manufactured. Once the designer is sure about the output results of the design calculation, he can proceed forward for subsequent virtual manufacturing operations. He can also switch between design module and manufacture module at will, thus leading to an optimized product. References 1. 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Proceedings of 20th AIMTDR, conference, BIT Mesra, Ranchi, India, 13-15 Dec 7. Pattanayak RK, Pohit G, Saha KN (2003) Application of solid modeling in virtual manufacturing of spur gear. Proceedings of 11th national conference on machines and mechanism (Nacomm), I.I.T. Delhi, Delhi, 18 19 December, pp 683 688 譯文： 虛擬制造在齒輪生產(chǎn)中的應用 摘要 齒輪的制造過程相當?shù)膹碗s，這歸結于各種各樣的刀具和工件同時運動的出現(xiàn)。 在本文，為了使直齒圓柱齒輪、斜齒圓柱齒輪以及相應機架形式的車刀成為制造的必需品而產(chǎn)生了有意義的設計數(shù)據(jù)。 使用這個信息，刀具和毛胚的實體模 型開始發(fā)展，并且最后齒輪制造過程應用于虛擬制造環(huán)境當中。 用戶有權在設計和制造方式之間任意選擇。 這個綜合過程也有利于開發(fā)一個優(yōu)化產(chǎn)品。 為了對操作原則有更好的理解，動畫設施以電影的形式也包含于其中。 關鍵詞 虛擬制造 動畫 齒輪滾銑法 1 介紹 在機械制造應用中，齒輪是非常常見的機械零件。然而 , 齒輪制造似乎相當?shù)膹碗s，甚至對于那些在相關領域有廣泛技術知識的人也是如此。常規(guī)齒輪滾銑生成過程如鑄造、塑造、滾銑等，通常是在二維草圖里表示。有些零件可能是由二維模型途徑所不能充分描述的。在齒輪滾銑生成情況下，借 助于二維模型可能很難了解復雜的幾何形狀和制造過程。如果你改為使用 3D 實體模型，這些限制可能會部分地被克服并且更有助于理解。但是 ,除非你使用動畫代替齒輪輪胚和刀具的運動，否則使用三維實體模型可能并不總是保證復雜齒輪滾銑生成過程的清晰。在虛擬制造技術的幫助下，這可能非常有效地達到。這種技術是在電腦屏幕上去模仿實際世界而創(chuàng)建的一個虛擬環(huán)境。在虛擬環(huán)境里獲得信息庫和專門技術，這使用戶更加有意義地應用于現(xiàn)實生活中。 在不同的領域中，虛擬制造被許多文章提到，一些最新并且重要的文章如下：Tesic 和 Baneljee 曾經(jīng) 致力于快速原型法，這種方法對于設計、可視化、檢驗是一項新技術。圖形用戶界面、虛擬現(xiàn)實技術、蒸餾、偏析和自動分析是他們工作的重要對象。 Balyliss et al 處理了模型發(fā)展在虛擬環(huán)境里使用三維可視化對象的虛擬現(xiàn)實技術 。 1994 年， Balyliss et al 發(fā)表了使用 VM 工具設計的實體模型技術理論，如 VRML（虛擬現(xiàn)實制造語言）和 3D Studio Max。他們開發(fā)了汽車的不同零件，并且通過動畫的特殊效果對模型給予所有可能的運動。這項技術有Kiulera 進一步提高，他把產(chǎn)品模型和過程視為虛擬制造環(huán)境的核心 。在他的工作中， Kimura 合并了主要模型的表示法、表示法語言、抽象、標準化、結構控制等等。在 MAYA 平臺， 3DStudio Max 和 VRML 等等上面， Arangarasau 和 Gadh致力于虛擬原型，它是對使用虛擬制造的計劃生產(chǎn)過程的模擬。在 Jadavpur 大學，研究工作是使用 AUTOCAD 和 3D Studio Max 作為平臺去模擬齒輪制造過程完成的。幫助設計師了解關于直齒圓柱齒輪的運動問題和它的制造過程的軟件已經(jīng)開發(fā)了。 對文獻資料的調(diào)查情形表明虛擬制造的范圍擴大是為了模仿直齒圓柱齒輪的生成過程。計算機模 擬為了觀看變得身份有效，并使用了虛擬制造的集中設計，這有助于不同制造過程的隨后分析。有了這個目標，就企圖在毛胚上面使用齒條刀具虛擬制造直齒圓柱齒輪和斜齒圓柱齒輪。工作的范圍包括直齒和斜齒以及機架形式車刀的設計數(shù)據(jù)的產(chǎn)生，車刀和毛胚實體模型的產(chǎn)生，以及最后通過動畫模擬齒輪的制造過程。 工作的主要目的是簡化設計任務和齒輪虛擬制造過程的研究，這樣可以是一個外行人所理解，并表現(xiàn)出它的現(xiàn)實意義。所有的過程都是基于 3D Studio Max平臺開發(fā)的，它是一個非常重要的模擬工具。軟件的發(fā)展使用最大的腳本，這個對象包括可 以在 3D Studio Max 環(huán)境中運行的語法語言。 2 軟件的描述 最大的腳本語言基本上是在 3D Studio Max 上面創(chuàng)建一個視覺效應的圖像處理機。另外，它可以為設計演算和隨后檢查所使用。以模塊形式開發(fā)整個部件，以便使任何的改善在不影響其他部件的情況下都能容易的貫徹。整個工作都是在3D 環(huán)境下實現(xiàn)的。整個部件的模塊結構在表現(xiàn)如圖 1，主要模塊是：輸入模塊、齒輪設計模塊、虛擬制造模塊和特殊模塊。這些模塊的一個簡要說明敘述如下。 2.1 輸入模塊 這個模塊的發(fā)展是提供輸入?yún)?shù)，這些參數(shù)是設計和發(fā)展直齒、斜齒和 相應刀具的基礎。為了是軟件用戶更親和，輸入?yún)?shù)的過程是通過由最大腳本語言創(chuàng)建的輸入對話框完成的。例如在圖 2 中所表示的對話框。一些領域有一定的限制，如：預定義的上下限、增量或減量步驟的預定義。這樣有目的的做法是環(huán)境更加的親和，并且阻止用戶輸入不合法的數(shù)據(jù)，例如：用戶不能輸入齒數(shù)少于 18 的齒輪。 2.2 齒輪設計模塊 在生成齒輪之前，基于輸入?yún)?shù)，你應該評估制造齒輪的各種各樣的設計參數(shù)。為了設計成對齒輪，以下參數(shù)是重要的： 1. 齒輪運行每分鐘的轉(zhuǎn)數(shù)。 2. 力的轉(zhuǎn)換。 3. 裝配的傳動比。 此外，用戶也可以指定以下操作的 情況 /參數(shù)： 1. 齒輪的裝配精度。 2. 齒輪的壓力角。 3. 小齒輪的材料。 4. 小齒輪所能承受的沖擊載荷的類型。 5. 斜齒輪的螺旋角。 如果用戶對輸出結果不滿意，他可以修改輸入?yún)?shù)以獲得理想的輸出結果。在這個模型中，齒輪的整個設計步驟是固定好的。設計計算的不同方面，如動載荷、靜載荷（疲勞載荷）和欠載荷在不同程序里已經(jīng)計算好了，通過輸出對話框展示出來。當設計齒輪時，你必須知道齒輪和機架的嚙合情況，這樣就可以避免一對齒輪嚙合的干涉。 2.2.1 方法論 在工廠的加工過程中，各種各樣的切齒過程是有用的，并且通常被從事。在本文中， 重點是通過“生成”來說明齒輪的制造。 齒輪設計的根本原則是基于一定的事實，那就是一對齒輪的齒廓具有一定的關系，如：一對輪齒有預定好的相對運動和每一瞬間的接觸情況。因此，如果齒廓的相對運動和其中一個的運動形式是已知的，那么另外一個所定義的形式就可以被認為是通過繪畫或分析的手段可以解決的問題。齒輪輪廓的實際生成是通過機械方法表示了解決上面問題的一種方法，就是大家所知道的“生成”。生成是根據(jù)以下原則的一種方法。 1. 一個切削刃給定一個運動（基本上每個齒輪都有切削刃）。因此，這就是計算一對共軛齒輪已知部分的表面所對應的 實際齒廓表面的原因。 2. 一個“毛胚”裝配在一個相對于刀具的合適位置，精加工的齒輪必須相對于刀具有一個給定的運動。作為同時運動和刀具切齒運動的結果，輪齒是在相對于刀具變化的毛胚上形成的。 實際上由于相對運動，工件的給定輪廓是不同于刀具的。這種“生成”不同于“成形”操作。 2.2.2 直齒圓柱齒輪 直齒圓柱齒輪的生成是依靠刀具相對于嚙合齒輪的形式，刀具可能是齒條的形式。因為一個齒廓的漸開線規(guī)律，就是刀具相對于齒條有直的邊。 這樣的刀具相對于毛胚的排列如圖 3 所示。刀具相對于工件的軸線做徑向調(diào)整，這種往復運動以至于 它的刀刃可能破壞虛擬齒條的表面，虛擬齒條是根據(jù)毛胚齒廓設計的。除了這種往復運動，刀具在節(jié)線方向上，并且同時工件以一定的速度相對于軸轉(zhuǎn)動，以至于作為齒條的每個節(jié)點都具有一定的線速度。換句話說，毛胚的節(jié)圓和齒條的節(jié)線重合，因此直的切削刃在毛胚上面形成了漸開線齒形。 這樣來說，刀具應該比工件的節(jié)圓長點。因為這樣是不可能的，所以刀具在前進了等于整個節(jié)距的距離并返回起始點之后開始遠離工件，同時毛胚是固定的，這個運動不斷重復直到所有的輪齒加工完。 2.2.3 斜齒圓柱齒輪 總所周知，斜齒漸開線齒輪有與其共軛的齒條傾斜的 輪齒，因此，采用上面描述的方法同樣可以制造一個斜齒圓柱齒輪。然而，齒條刀具的往返方向必須傾斜與毛胚的軸線，這個角度等于齒輪的螺旋角。刀具的轉(zhuǎn)向必須與上面描述的方向一致。與同時動作有關的以及在加工操作時相對于毛胚的刀具方向表四如圖4 所示。 2.3 虛擬制造模塊 這個模塊可以分為 2 個部分：（ a）刀具的生成，（ b）齒輪的生成 2.3.1 刀具的生成 在虛擬制造的這一部分，一個齒條刀具的實體模型正在發(fā)展。在虛擬環(huán)境中，這個刀具是在后面的步驟中用來模擬動畫齒輪的生成過程。刀具和它所有的幾何學，例如刀架和后角，圖 5 表 示的就是通過軟件制作的 3D 實體模型。 2.3.2 齒輪的生成過程 這個模塊被細分為 2 部分 （ ）直齒圓柱齒輪滾銑生成模型（ ）斜齒圓柱齒輪滾銑生成模型 （ ）直齒圓柱齒輪滾銑生成模型 在這個小模塊里，生成的是直齒。為了模擬實際的機器操作，用來生成直齒圓柱齒輪的毛胚鎖定在可移動的桌面上。必須的墊片和支承板都約束在一起，這樣不但可以使它有牢靠的支承，而且還為了加工的需要。刀具放置在一個重要位置，然后給予刀具必備的運動去產(chǎn)生漸開線齒廓，這樣的生成是依靠一個仿形生成工具，與毛胚相關的刀具排列如圖 6 所示。 齒輪成 形過程的運動學包括一下運動： 1. 刀具的往復運動。 2. 刀具的切向進給運動和齒