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关键词：: 数控车床主轴参数建模分析

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数控车床主轴参数化建模及频域分析

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外文翻译--齿轮和轴的介绍.doc

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齿轮.dwg

数控车床主轴参数化建模及频域分析

摘要：

　　　本毕业设计是对CKA6140数控车床主轴进行参数化建模及频域分析，将现代化的设计方法应用于机床的设计，以数控系统设计方案的拟定为主线，通过对数控车床主轴伺服系统机械部分进行参数化设计，理论强度基础计算及其关键零件的校核，对车床进给伺服系统进行数学建模，然后使用ANSYS软件进行频域仿真，简要论述了频域方法和动力学分析的基本求解过程，建立机床主轴频域模型，合理的确定了载荷、轴承支承刚度和约束条件，选定了单元类型。采用Lanczos法对其进行自由模的具体研究内容，总结了机床、动态设计方法研究和机床主轴动静态研究的发展状况和发展趋势，在总结前人研究成果的基础上，结合当前的技术发展趋势，采用频域方法来进行研究，简要论述了模态分析，得到主轴的固有频率和振型，找出工作时容易发生共振的频率域，为进一步提高精度和转速提供理论依据。通过毕业设计进行了机电结合的全方面训练，从而培养设计计算的能力以及分析和处理生产过程中所遇到的问题的综合能力。

关键词：频域分析；模态分析；机床主轴；振动

1 绪论1

1.1 课题研究的背景及意义1

1.2 数控机床主轴国内外研究现状1

1.3 本课题的研究内容2

2 总体设计方案4

2.1 设计要求4

2.2 设计参数5

2.3 总体设计方案图5

3 数控系统选择6

3.1 简介西门子802S数控系统6

3.2 802S数控系统的组成6

3.3数控机床伺服系统的选择7

4 主轴计算及校核8

4.1 主轴设计8

4.1.1 电动机的选择8

4.1.2 带传动设计8

4.2 主轴的校核10

4.2.1 传动组齿轮模数的确定和校核10

4.2.2 齿轮强度校核11

4.2.3 主轴挠度的校核12

4.2.4 主轴弯曲变形的校核13

4.2.5主轴扭转变形校核13

4.3 主轴最佳跨距的确定14

4.3.1选择轴颈直径,轴承型号和最佳跨距14

4.3.2求轴承刚度14

4.4 主轴支承处轴承的选择15

4.5 主轴图16

5 参数化建模17

5.1理论基础17

5.1.1 主轴的动力学模型17

5.2 建立目标函数18

5.3约束条件19

5.3.1 刚度约束19

5.3.2 强度约束19

5.3.3 转角的限制20

5.3.4 扭转变形的限制20

5.3.5 切削力的限制20

6 数控车床主轴的频域分析21

6.1 频域简介及ANSYS软件应用21

6.1.1 频域概述21

6.1.2 ANSYS软件应用22

6.2 机床主轴频域分析模型22

6.2.1 构建几何模型22

6.2.2 频域模型建立22

6.2.3 单元类型选择和网格划分23

6.3 机床主轴振动模态分析25

6.3.1 ANSYS动力分析25

6.3.2 模态分析25

结论30

致谢31

参考文献32

附录33

1.1 课题研究的背景及意义

制造业是体现一个国家综合实力的重要方面，是国家财富的主要创造者世界上凡是发达国家都拥有高水平的制造业。而装备制造业作为整个国家工业部门的装备提供者，其水平的高低决定了我国制造业的国际竞争力，特别是我国加入到WTO以后，行业竞争更加激烈，已经关系到我们国家现代化的进程和民族的复兴，因此提高我国装备制造业的整体技术水平具有重大的理论和现实意义。在当前的振兴过程中，我们应该清醒的认识到我国装备制造业和发达国家的差距，不能只看到眼前的一时繁荣。特别是机床行业，在设计水平上与发达国家有着比较大的差距，缺少创新和突破，掌握核心技术较少，特别在高端的产品领域，竞争力还不够强大。

　　　动态设计的原则：目标是保证机械满足其功能前提要求的条件下具有较高的动刚度，使其经济合理、运转平稳、可靠。要从总体上把握机械结构的固有频率、振型和阻尼比。具体为：避开共振，避开率应在15%-20%；降低机器运行过程中的振动幅度；结构各阶模态刚度最大且尽量相等；结构的各阶模态阻尼比要尽量高；避免结构疲劳破坏；提高振动稳定性。

设计步骤：

　　　（1）建立机械结构或机械系统的动力学模型，根据设计图纸建立力学模型，也可以应用试验模态分析技术建立结构的试验模型；

　　　（2）利用数学模型求解自由振动方程得到结构振动的固有特性，引入外部激励可以进行动力响应分析；

　　　（3）动态性能评定；

　　　（4）结构修改和优化设计[1]。　　　机床主轴的动静态特性主要就是固有频率、受力变形、临界转速、动态响应等，在60年代以前，一般采用经验模拟法设计，方法繁琐，精度低。60年代以后由于计算机技术和计算方法的进步，出现了有限差分法、结构分析法、频域法、结构修正法，模态法等大量方法。本课题就是要研究机床主轴的动静态特性，其主要任务是计算轴承的刚度、建立合理有效的模型，特别是轴承部分的简化，再对模型进行静变形、模态及响应等各方面的分析，得到固有频率、振型等参数。其中轴承刚度的计算较复杂，静刚度可用经验公式计算得出[12]；而动刚度的计算部分则要考虑主轴高速运转条件下对轴承的影响。

2.1 设计要求

　　　1）数控车床应具有性能：

（1）数控代码制：ISO

（2）输入方式：增量值、绝对值通用

（3）同时控制坐标轴数：2坐标轴（纵向Z，横向X）

（4）纵向脉冲当量值：0.01mm/puls

（5）刀具补偿量：0~99.99mm

（6）自动升降速性能：有

（7）数控系统选连续控制系统。

（8）进给伺服系统采用步进电机开环控制系统。

（9）一般采用8位微机。在8位微机中，MCS—51系列单片机具有集成度高、可靠性好、功能强、速度快、抗干扰能力强、具有很高的性价比，因此，可选 MCS—51系列单片机扩展系统。

（10）设计自动回转刀架及其控制电路。

（11）为了保证进给伺服系统的传动精度和平稳性，选用摩擦小、传动效率高的滚珠丝杠螺母副，并应有预紧机构，以提高传动刚度和消除间隙，齿轮副也应有消除齿侧间隙的机构。

（12）采用贴塑导轨，以减小导轨的摩擦力。

　　　2）数控车床的工艺范围：具有快速定位，直线插补，顺、逆圆插补，暂停，循环加工。

　　　3）对微机数控系统的要求：

　　　微机控制系统要有可靠性好、功能强、速度快、抗干扰能力强，具有很高的性能价格比等特点。控制系统的加工程序和控制命令通过键盘操作实现，显示器采用数码管显示加工数据及机床状态等信息。2.2 设计参数

表2.1 机床基本参数

　　项目单位　　参数

　　型号　　CKA6140

　　床身回转直径mm　　400mm

　　刀架上回转直径mm　　210mm

　　主轴最高转速r/min　　1920r/min

　　主电机功率KW　　7.5KW

　　数控系统　　西门子802S

尾座主轴直径行程及主轴孔锥度mmmm75mm150mm；莫氏圆锥5号

丝杠螺距mm12mm

系统环境工作条件℃ %温度-10~+40℃；湿度为40% ~80%

输入电网电压V交流(220±22)V；频率为50Hz；电流为1.5A

2.3 总体设计方案图

数控车床主轴参数化建模及频域分析.gif

内容简介：: 附录2 外文翻译THE INTRODUCTION OF GEAR AND SHAFTAbstract: The important position of the wheel gear and shaft cant falter in traditional machine and modern machines. The wheel gear and shafts mainly install the direction that delivers the dint at the principal axis box. The passing to process to make them can is divided into many model numbers, used for many situations respectively. So we must be the multilayer to the understanding of the wheel gear and shaft in many ways. Key words: Wheel gear; ShaftIn the force analysis of spur gears, the forces are assumed to act in a single plane. We shall study gears in which the forces have three dimensions. The reason for this, in the case of helical gears, is that the teeth are not parallel to the axis of rotation. And in the case of bevel gears, the rotational axes are not parallel to each other. There are also other reasons, as we shall learn. Helical gears are used to transmit motion between parallel shafts. The helix angle is the same on each gear, but one gear must have a right-hand helix and the other a left-hand helix. The shape of the tooth is a volute. If a piece of paper cut in the shape of a parallelogram is wrapped around a cylinder, the angular edge of the paper becomes a helix. If we unwind this paper, each point on the angular edge generates a volute curve. The surface obtained when every point on the edge generates a volute is called helicoids. The initial contact of spur-gear teeth is a line extending all the way across the face of the tooth. The initial contact of helical gear teeth is a point, which changes into a line as the teeth come into more engagement. In spur gears the line of contact is parallel to the axis of the rotation; in helical gears, the line is diagonal across the face of the tooth. It is this gradual of the teeth and the smooth transfer of load from one tooth to another, which give helical gears the ability to transmit heavy loads at high speeds. Helical gears subject the shaft bearings to both radial and thrust loads. When the thrust loads become high or are objectionable for other reasons, it may be desirable to use double helical gears. A double helical gear (herringbone) is equivalent to two helical gears of opposite hand, mounted side by side on the same shaft. They develop opposite thrust reactions and thus cancel out the thrust load. When two or more single helical gears are mounted on the same shaft, the hand of the gears should be selected so as to produce the minimum thrust load.Crossed-helical, or spiral, gears are those in which the shaft centerlines are neither parallel nor intersecting. The teeth of crossed-helical fears have point contact with each other, which changes to line contact as the gears wear in. For this reason they will carry out very small loads and are mainly for instrumental applications, and are definitely not recommended for use in the transmission of power. There is on difference between a crossed helical gear and a helical gear until they are mounted in mesh with each other. They are manufactured in the same way. A pair of meshed crossed helical gears usually have the same hand; that is a right-hand driver goes with a right-hand driven. In the design of crossed-helical gears, the minimum sliding velocity is obtained when the helix angle are equal. However, when the helix angle is not equal, the gear with the larger helix angle should be used as the driver if both gears have the same hand. Worm gears are similar to crossed helical gears. The pinion or worm has a small number of teeth, usually one to four, and since they completely wrap around the pitch cylinder they are called threads. Its mating gear is called a worm gear, which is not a true helical gear. A worm and worm gear are used to provide a high angular-velocity reduction between nonintersecting shafts which are usually at right angle. The worm gear is not a helical gear because its face is made concave to fit the curvature of the worm in order to provide line contact instead of point contact. However, a disadvantage of worm gearing is the high sliding velocities across the teeth, the same as with crossed helical gears.Worm gearing are either single or double enveloping. A single-enveloping gearing is one in which the gear wraps around or partially encloses the worm. A gearing in which each element partially encloses the other is, of course, a double-enveloping worm gearing. The important difference between the two is that area contact exists between the teeth of double-enveloping gears while only line contact between those of single-enveloping gears. The worm and worm gear of a set have the same hand of helix as for crossed helical gears, but the helix angles are usually quite different. The helix angle on the worm is generally quite large, and that on the gear very small. Because of this, it is usual to specify the lead angle on the worm, which is the complement of the worm helix angle, and the helix angle on the gear; the two angles are equal for a 90-deg. Shaft angle. When gears are to be used to transmit motion between intersecting shaft, some of bevel gear is required. They may be produced for almost any shaft angle. The teeth may be cast, milled, or generated. Only the generated teeth may be classed as accurate. In a typical bevel gear mounting, one of the gear is often mounted outboard of the bearing. This means that shaft deflection can be more pronounced and have a greater effect on the contact of teeth. Another difficulty, which occurs in predicting the stress in bevel-gear teeth, is the fact the teeth are tapered. Straight bevel gears are easy to design and simple to manufacture and give a very good results in service if they are mounted accurately and positively. As in the case of gears, however, they become noisy at higher values of the pitch-line velocity. In these cases it is often good design practice to go to the spiral bevel gear, which is the bevel counterpart of the helical gear. As in the case of helical gears, spiral bevel gears give a much smoother tooth action than straight bevel gears, and hence are useful where high speed are encountered. It is frequently desirable, as in the case of automotive differential applications, to have gearing similar to bevel gears but with the shaft offset. Such gears are called hypoid gears because their pitch surfaces are hyperboloids of revolution. The tooth action between such gears is a combination of rolling and sliding along a straight line and has much in common with that of worm gears. A shaft is a rotating or stationary member, usually of circular cross section, having mounted upon it such elements as gears, pulleys, flywheels, cranks, sprockets, and other power-transmission elements. Shaft may be subjected to bending, tension, compression, or torsion loads, acting singly or in combination with one another. When they are combined, one may expect to find both static and fatigue strength to be important design considerations, since a single shaft may be subjected to static stresses, completely reversed, and repeated stresses, all acting at the same time. The word “shaft” covers numerous variations, such as axles and spindles. axle is a shaft, wither stationary or rotating, nor subjected to torsion load. A shirt rotating shaft is often called a spindle. When either the lateral or the torsion deflection of a shaft must be held to close limits, the shaft must be sized on the basis of deflection before analyzing the stresses. The reason for this is that, if the shaft is made stiff enough so that the deflection is not too large, it is probable that the resulting stresses will be safe. But by no means should the designer assume that they are safe; it is almost always necessary to calculate them so that he knows they are within acceptable limits. Whenever possible, the power-transmission elements, such as gears or pullets, should be located close to the supporting bearings, this reduces the bending moment, and hence the deflection and bending stress.Although the von Mi-Hen Goodman method is difficult to use in design of shaft, it probably comes closest to predicting actual failure. Thus it is a good way of checking a shaft that has already been designed or of discovering why a particular shaft has failed in service. Furthermore, there are a considerable number of shaft-design problems in which the dimension are pretty well limited by other considerations, such as rigidity, and it is only necessary for the designer to discover something about the fillet sizes, heat-treatment, and surface finish and whether or not shot peen is necessary in order to achieve the required life and reliability. Because of the similarity of their functions, clutches and brakes are treated together. In a simplified dynamic representation of a friction clutch, or brake, two inertias I1 and I2 traveling at the respective angular velocities W1 and W2, one of which may be zero in the case of brake, are to be brought to the same speed by engaging the clutch or brake. Slippage occurs because the two elements are running at different speeds and energy is dissipated during actuation, resulting in a temperature rise. In analyzing the performance of these devices we shall be interested in the actuating force, the torque transmitted, the energy loss and the temperature rise. The torque transmitted is related to the actuating force, the coefficient of friction, and the geometry of the clutch or brake. This is problem in static, which will have to be studied separately for geometric configuration. However, temperature rise is related to energy loss and can be studied without regard to the type of brake or clutch because the geometry of interest is the heat-dissipating surfaces. The various types of clutches and brakes may be classified as follows: 1. Rim type with internally expanding shoes.2. Rim type with externally contracting shoes.3. Band type.4. Disk or axial type.5. Cone type.6. Miscellaneous type.The analysis of all type of friction clutches and brakes use the same general procedure. The following steps are necessary: 1. Assume or determine the distribution of pressure on the frictional surfaces.2. Find a relation between the maximum pressure and the pressure at any point3. Apply the condition of static equilibrium to find (a) the actuating force, (b) the torque, and (c) the support reactions.Miscellaneous clutches include several types, such as the positive-contact clutches, overload-release clutches, overrunning clutches, magnetic fluid clutches, and others. A positive-contact clutch consists of a shift lever and two jaws. The greatest differences between the various types of positive clutches are concerned with the design of the jaws. To provide a longer period of time for shift action during engagement, the jaws may be ratchet-shaped, or gear-tooth-shaped. Sometimes a great many teeth or jaws used, and they may be cut either circumferentially, so that they engage by cylindrical mating, or on the faces of the mating elements. Although positive clutches are not used to the extent of the frictional-contact type, they do have important applications where synchronous operation is required. Devices such as linear drives or motor-operated screw drivers must run to definite limit and then come to a stop. An overload-release type of clutch is required for these applications. These clutches are usually spring-loaded so as to release at a predetermined toque. The clicking sound which is heard when the overload point is reached is considered to be a desirable signal.An overrunning clutch or coupling permits the driven member of a machine to “freewheel” or “overrun” because the driver is stopped or because another source of power increase the speed of the driven. This type of clutch usually uses rollers or balls mounted between an outer sleeve and an inner member having flats machined around the periphery. Driving action is obtained by wedging the rollers between the sleeve and the flats. The clutch is therefore equivalent to a pawl and ratchet with an infinite number of teeth. Magnetic fluid clutch or brake is a relatively new development which has two parallel magnetic plates. Between these plates is a lubricated magnetic powder mixture. An electromagnetic coil is inserted somewhere in the magnetic circuit. By varying the excitation to this coil, the shearing strength of the magnetic fluid mixture may be accurately controlled. Thus any condition from a full slip to a frozen lockup may be obtained.齿轮和轴的介绍摘要：在传统机械和现代机械中齿轮和轴的重要地位是不可动摇的。齿轮和轴主要安装在主轴箱来传递力的方向。通过加工制造它们可以分为许多的型号，分别用于许多的场合。所以我们对齿轮和轴的了解和认识必须是多层次多方位的。关键词：齿轮，轴在直齿圆柱齿轮的受力分析中，是假定各力作用在单一平面的。我们将研究作用力具有三维坐标的齿轮。因此，在斜齿轮的情况下，其齿向是不平行于回转轴线的。而在锥齿轮的情况中各回转轴线互相不平行。像我们要讨论的那样，尚有其他道理需要学习，掌握。斜齿轮用于传递平行轴之间的运动。倾斜角度每个齿轮都一样，但一个必须右旋斜齿，而另一个必须是左旋斜齿。齿的形状是一溅开线螺旋面。如果一张被剪成平行四边形（矩形）的纸张包围在齿轮圆柱体上，纸上印出齿的角刃边就变成斜线。如果我展开这张纸，在血角刃边上的每一个点就发生一渐开线曲线。直齿圆柱齿轮轮齿的初始接触处是跨过整个齿面而伸展开来的线。斜齿轮轮齿的初始接触是一点，当齿进入更多的啮合时，它就变成线。在直齿圆柱齿轮中，接触是平行于回转轴线的。在斜齿轮中，该先是跨过齿面的对角线。它是齿轮逐渐进行啮合并平稳的从一个齿到另一个齿传递运动，那样就使斜齿轮具有高速重载下平稳传递运动的能力。斜齿轮使轴的轴承承受径向和轴向力。当轴向推力变的大了或由于别的原因而产生某些影响时，那就可以使用人字齿轮。双斜齿轮（人字齿轮）是与反向的并排地装在同一轴上的两个斜齿轮等效。他们产生相反的轴向推力作用，这样就消除了轴向推力。当两个或更多个单向齿斜齿轮被在同一轴上时，齿轮的齿向应作选择，以便产生最小的轴向推力。交错轴斜齿轮或螺旋齿轮，他们是轴中心线既不相交也不平行。交错轴斜齿轮的齿彼此之间发生点接触，它随着齿轮的磨合而变成线接触。因此他们只能传递小的载荷和主要用于仪器设备中，而且肯定不能推荐在动力传动中使用。交错轴斜齿轮与斜齿轮之间在被安装后互相捏合之前是没有任何区别的。它们是以同样的方法进行制造。一对相啮合的交错轴斜齿轮通常具有同样的齿向，即左旋主动齿轮跟右旋从动齿轮相啮合。在交错轴斜齿设计中，当该齿的斜角相等时所产生滑移速度最小。然而当该齿的斜角不相等时，如果两个齿轮具有相同齿向的话，大斜角齿轮应用作主动齿轮。蜗轮与交错轴斜齿轮相似。小齿轮即蜗杆具有较小的齿数，通常是一到四齿，由于它们完全缠绕在节圆柱上，因此它们被称为螺纹齿。与其相配的齿轮叫做蜗轮，蜗轮不是真正的斜齿轮。蜗杆和蜗轮通常是用于向垂直相交轴之间的传动提供大的角速度减速比。蜗轮不是斜齿轮，因为其齿顶面做成中凹形状以适配蜗杆曲率，目的是要形成线接触而不是点接触。然而蜗杆蜗轮传动机构中存在齿间有较大滑移速度的缺点，正像交错轴斜齿轮那样。蜗杆蜗轮机构有单包围和双包围机构。单包围机构就是蜗轮包裹着蜗杆的一种机构。当然，如果每个构件各自局部地包围着对方的蜗轮机构就是双包围蜗轮蜗杆机构。着两者之间的重要区别是，在双包围蜗轮组的轮齿间有面接触，而在单包围的蜗轮组的轮齿间有线接触。一个装置中的蜗杆和蜗轮正像交错轴斜齿轮那样具有相同的齿向，但是其斜齿齿角的角度是极不相同的。蜗杆上的齿斜角度通常很大，而蜗轮上的则极小，因此习惯常规定蜗杆的导角，那就是蜗杆齿斜角的余角；也规定了蜗轮上的齿斜角，该两角之和就等于90的轴线交角。当齿轮要用来传递相交轴之间的运动时，就需要某种形式的锥齿轮。虽然锥齿轮通常制造成能构成90轴交角，但它们也可产生任何角度的轴交角。轮齿可以铸出，铣制或滚切加工。仅就滚齿而言就可达一级精度。在典型的锥齿轮安装中，其中一个锥齿轮常常装于支承的外侧。这意味着轴的挠曲情况更加明显而使在轮齿接触上具有更大的影响。另外一个难题，发生在难于预示锥齿轮轮齿上的应力，实际上是由于齿轮被加工成锥状造成的。直齿锥齿轮易于设计且制造简单，如果他们安装的精密而确定，在运转中会产生良好效果。然而在直齿圆柱齿轮情况下，在节线速度较高时，他们将发出噪音。在这些情况下，螺旋锥齿轮比直齿轮能产生平稳的多的啮合作用，因此碰到高速运转的场合那是很有用的。当在汽车的各种不同用途中，有一个带偏心轴的类似锥齿轮的机构，那是常常所希望的。这样的齿轮机构叫做准双曲面齿轮机构，因为它们的节面是双曲回转面。这种齿轮之间的轮齿作用是沿着一根直线上产生滚动与滑动相结合的运动并和蜗轮蜗杆的轮齿作用有着更多的共同之处。轴是一种转动或静止的杆件。通常有圆形横截面。在轴上安装像齿轮，皮带轮，飞轮，曲柄，链轮和其他动力传递零件。轴能够承受弯曲，拉伸

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