segment one by one in order to generate the smooth circular path. 切削是沿着每一小线段一个一个的进行以产生光滑曲线路径。 A limitation of circular interpolation is that the plane in which the circular are exists must be a plane defined by two axes of the NC system. 圆弧差补的局限性是圆弧路径所在平面是由数控系统中两轴所决定的平面。
Helical interpolation combines the circular interpolation scheme for two axes described above with linear movement of a third axis. This permits the definition of a helical path in three-dimensional space. 螺旋线差补结合了环形差补两轴在第三轴上做线性运动这样来定义空间三维螺旋路径。
Parabolic and cubic interpolation routines are used to provide approximations of free-form curves using higher-order equations. 抛物线差补和立方差补法通过高次高程来实现自由曲线。 They generally require considerable computational power and are not as common as linear and circular interpolation. 这通常需要有强的计算能力，正因如此，他不如直线差补和环形差补常见。Their applications are concentrated in the automobile industry for fabricating dies for car body panels styled with free-form designs that cannot accurately and conveniently be approximated by combining linear and circular interpolations. 他们主要用于汽车工业中具有自由风格的车身面，而这是线性差补和圆弧差补不能精确容易得到的
The most common application of numerical control is for machine tool control. This was the first application of NC and is today the most important commercially. 数控技术运用于数控机床，这是数控的主要应用。现在主要用于商业。 In this section we discuss the machine tool applications of NC with emphasis on metal machining. 我们仍讨论数控系统特别是金属数控车床。
Machine Tool Technology for NC 数控车床技术
Each of the five machining processes is carried out on a machine tool designed to perform that process. Turning is performed on a lathe, drilling is done on a drill press, milling on a milling machining, and so on. 每种加工过程都可以在设计的专门车床上来实现加工。在车床上车削，在钻床上钻，在铣床上加工。 There are several different type of grinding operations with a corresponding variety of machines to perform them. 有几种类型的磨削方法也要有相应种类的磨床。
Numerical control machine tools have been designed for nearly all of the machining processes. The list includes: 被设计的数控磨床可以进行下列加工包括：
? Drill presses钻加工
? Milling machines, vertical spindle and horizontal spindle铣床立式和卧式主轴
? Turning machines, both horizontal axis and vertical axis车床卧式主轴和立式主轴
? Horizontal and vertical boring mills卧式和立式镗床 ? Profiling and contouring mills仿形铣床
? Surface grinders and cylindrical grinders平面磨和圆柱磨
In addition to the machining process, NC machine tools have also been developed for other metalworking processes. These machines include: 除了上述几种机械加工方法，数控机床可用于其他金属加工过程包括：
? Punch presses for sheet metal hole punching用于薄片板的金属板上冲孔的冲压机
? Presses for sheet metal bending用于薄片金属弯曲的折弯机。
The introduction of numerical control has had a pronounced influence on the design and operation of machine tools. 数控技术的介入到机加工对机床的设计和运用有着显著的影响。One of the effects of NC has been that the proportion of time spent by the machine cutting metal under program control is significantly greater than with manually operated machines. 数控影响之一在程序控制下切削金属的时间与传统手动机床大得多。This causes certain components, such as the spindle, drive gears, and feed screws, to wear more rapidly. These components must be designed to last longer on NC machines。所以对于一些零件如主轴驱动主轴丝杠磨损更快，这些零件要设计成持续时间长的。 second, the addition of the electronic control unit has increased the cost of the machine, therefore requiring higher equipment utilization. 第二，增加电子控制单元后设备成本也随之增加，因此需要更高的利用率。 Instead of running the machine on only one shift, which was the convention with manually operated machines, NC machines are often operated two or even three shifts to obtain the required payback. 取代传统手工操作的一班制，数控机床通常采用两班或三班制来获得更多的回报。Also, the NC machines are designed to reduce the time consumed by the non-processing
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elements in the operation cycle, such as loading and unloading the workpart, and changing tools. 数控机床的设计中减少了非操作过程的时间如装卸工件和换刀时间。Third, the increasing cost of labor has altered the relative roles of the operator and the machine tool. Consider the role of the human operator. 第三，增加的劳动成本由人工成本变为设备成本。Instead of being the highly skilled worker who controlled every aspect of the part production, the tasks of the operator have been reduced to part loading and unloading, tool changing, chip clearing, and the like. In this way, one operator can often run two or three automatic machines. The role and functions of the machine tool have also changed. 考虑到人工操作的角色，角色由技术熟练的工人控制，工件生产的每一个过程变为只控制装卸换刀和清除碎屑和类似的操作，这样一个工人可以同时操作两台或三台车床，机床的角色和功能也改变了。 NC machines are designed to be highly automatic and capable of combining several operations in one setup that formerly required several different machines. These changes are best exemplified by a new type of machine that did not exist prior to the advent and development of numerical control: the machining center. 数控需要设计成高度自动化具有需要在不同车床加工几种操作联合在一起一定加工的能力，这些变化是通过一种新型车床在数控技术存在之前是不存在的，他丰富了数控加工中心
The machining center, developed in the late 1950s, is a machine tool capable of performing several different machining operations on a workpart in one setup under program control. 加工中心是在20 世纪50 年代发展起来的具有在程序控制下在一个工件上一次裝夹完成几种不同的加工能力的机床。
The machining center is capable of milling, drilling,reaming, tapping, boring, facing, and similar operations. 加工中心能完成铣，钻，铰屑，攻丝，镗，车端面及一些类似机加工工作。 In addition, the features that typically characterize the NC machining center include the following: 另外数控加工中心的典型特征包括以下方面：
(1) Automatic tool-changing capability (1)自动换刀能力:
A variety of machining operations means that a variety of tools is required. 多种机加工工作一位着需要多种刀具。 The tools are contained on the machine in a tool magazine or drum. 刀具贝安装在刀库或多刀刀库中。 When a tool needs to be changed, the tool drum rotates to the proper position, and an
automatic tool changing mechanism, operating under program control, exchanges the tool in the spindle and the tool in the drum. 当一把刀需要被调换时，多刀刀座自动旋转到相应的位置上。自动化的换刀机构。在程序控制下进行，把主轴上需换下的刀和多刀刀座上的刀调换
(2) Automatic workpart positioning (2)工件的自动定位:
Most machining centers have the capability to rotate the job relative to the spindle, thereby permitting the cutting tool to access four surfaces of the part. 大多数加工中心都可以使工件沿着主轴旋转因此允许刀具达到工件的四个表面
(3) Pallet shuttle
(3)托架滑动装置（平板架）:
Another feature is that the machining center has two (or more) separate pallets that can be presented to the cutting tool. 加工中心另一个特点是有两个或多个独立拖板每个拖板都可以调整在刀具上。 While machining is being performed with one pallet in position in front of the tool, the other pallet is in a safe location away from the spindle. 在加工过程中，一个拖板在刀具的前部，另一个拖板在远离主轴的安全位置。In this way, the operator can unload the finished part from the prior cycle and fixture the raw workpart for the next cycle while machining is being performed on the current workpiece. 这样当机床正在加工当前的零件时。操作人员就可以从上一个工作循环中卸下最终加工好的零件，同时加紧毛坯用于下一个工作循环。
Machining centers are classified as vertical or horizontal. 加工中心可以分为立式和卧式。 The descriptor refers to the orientation of the machine tool spindle. 这是参照机床主轴方向来划分的。 A vertical machining center has its spindle on a vertical axis relative to the worktable, and a horizontal machining center has its spindle on a horizontal axis. 立式加工中心具有轴线相对工作台垂直的主轴，卧式车床的主轴轴线是水平方向的。 This distinction generally results in a difference in the type of work that requires tool access from the top. 这种区别通常会导致在这些加工中心加工的零件类型不同。 A horizontal machining center is used for cube-shaped parts where tool access can best be achieved on the sides of the cube. 立式加工中心用于以上进刀的平面工作。卧式加工中心用于立体形状，刀具在立体侧面可以进刀。An example of an NC horizontal machining center,
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capable of many of the features described above, is shown in Fig.2.2. 一台数控卧式加工中心，例子如图2.2 所示，具有上面提到的一些特征。
The success of the machining center has resulted in the development of similar machine tools for other metal working processes. 加工中心的成功应用导致了其他类似金属加工机床的发展。 One example is the turning center, designed as a highly automated and versatile machine tool for performing turning, facing, drilling, threading, and related operation. 例如：在车削中心，把车削加工设计成一个高度自动化万能机床可以完成车削，刨，钻，螺纹加工和类似的操作.
DNC and CNC
The development of numerical control was a significant achievement in batch and job shop manufacturing, from both a technological and a commercial viewpoint. 数控的发展在分批生产和小批量生产中有着重要意义，从技术和商业角度来说都有着重要意义。There have been two enhancements and extensions of NC technology, including: 数控有两方面的提高和扩展，包括：
? Direct numerical control直接数据控制
? Computer numerical control计算机数字控制
(1) Direct numerical control直接数据控制
Direct numerical control can be defined as a manufacturing system in which a number of machines are controlled by a computer through direct connection and in real time. 直接数据控制定义为一个制造系统，一定数量的机床有一台计算机通过直接硬件连线实时控制。The tape reader is omitted in DNC, thus relieving the system of its least reliable component. Instead of using the tape reader, the part program is transmitted to the machine tool directly from the computer memory. 相应的磁带播放机忽略在直接数控中，这样就消除系统中最不可靠的环节。不用磁带播放机而用电脑信息传给车床。 In principle, one computer can be used to control more than 100 separate machines. (One commercial DNC system during the 1970s boasted a control capability of up to 256 machine tools.) The DNC computer is designed to provide instructions to each machine tool on demand When the machine needs control commands, they are communicated to it immediately. 原则上说一台计算机可以控制100 台独立机器（DNC 系统在1970 年称为可控制26
台机床）直接数控（DNC）电脑设计成在需要的时候提供指令给每一台机床，当机床需要控制指令时，计算机立即发送指令给机床。
Fig.2.3 illustrates the general DNC configuration. 图2.3 说明了DNC 的基本配置。The system consists of four components: 这个系统包括4 部分：
? Central computer中央计算机
? Bulk memory, which stores the NC part programs大量内存，用于存放数控程序
? Telecommunication lines通信线 ? Machine tools机床刀具
The computer calls the part program instructions from bulk storage and sends them to the individual machines as the need arises. 计算机从海量内存中取出部分程序指令送入到需要的独立机床中。 It also receives data back from the machines. 相应的计算机也接受机床反馈信息。This two-way information flow occurs in real time, which means that each machine‘s requests for instructions must be satisfied almost instantaneously. 这种双工的信息流在实时控制加工系统中出现意味着每台机床需要指令的请求能立即得到回应。 Similarly, the computer must always be ready to receive information from the machines and to respond accordingly. 类似的，计算机必须总是要准备要接受信息和进行回应。The remarkable feature of the DNC system is that the computer is servicing a large number of separate machine tools all in real time. Depending on the number of machines and the computational requirements that are imposed on the computer, it is sometimes necessary to make use of satellite computers, as shown in Fig.2.4. DNC 系统显著特点是：可以实时控制大量机床。更具机器数量和所需的计算机程度化。有时需要使用卫星计算机如图2.4 所示。These satellites are smaller computers, and they serve to take some of the burden off the larger central computer. 卫星计算机是更小的计算机，可以分担中央计算任务，减轻其负担。Each satellite controls several machines. 每台卫星控制几台机床。 Groups of part program instructions are received from the central computer and stored in buffers. 零件加工指令程序由计算机接受，储存在内存中。They are then dispensed to the individual machines as required Feedback data from the machines are also
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stored in the satellite‘s buffer before being collected at the central computer. 当需要时卫星计算机发送指令程序到每个独立机床中。来自机床的反馈数据在电脑中央存储接受之前存储在卫星内存中。
（2）Computer numerical control计算机数字控制
Since the introduction of DNC, there have been dramatic advances in computer technology. 由于DNC 技术的介入，在计算机技术上得到了很大的发展。 The physical size and cost of a digital computer have been significantly reduced at the same time that its computational capabilities have been substantially increased. 计算机在尺寸和成本显著减少的同时，计算机的能力却有很大的提高。 In numerical control, the result of these advances has been that the large hard-wired MCU of conventional NC have been replaced by control units based on the digital computer. Initially, minicomputers were utilized in the early 1970s. 在数控中，这些发展使得由硬件布置的MCU变为数字电脑控制的控制单元。最早，小型机在1970 年使用。 As further miniaturization occurred in computers, minicomputers were replaced by today‘s microcomputers. 随着计算机进一步小型化，小型机被当今的微型机取代。
Computer numerical control is an NC system using dedicated microcomputer as the machine control unit. 计算机控制也是一种数字控制，它采用微型计算机作为控制单元。Because a digital computer is used in both CNC and DNC, it is appropriate to distinguish between the two types of system. There are three principal differences: 由于数字电脑用于CNC 和DNC 中，只近似区分两种类型。有三个区分原则：
? DNC computers distribute instructional data to, and collect data from, a large number of machines. CNC computers control only one machine, or a small number of machines. DNC 电脑接受和发送指令数据都是来自许多机器，CNC 电脑控制只是一个机器或多个机器。
? DNC computers occupy a location that is typically remote from the machines under their control. CNC computers are located very near their machine tools. DNC 电脑占有一个位置通过控制来实现机器的旋转。CNC 电脑要非常靠近车床。
? DNC software is developed not only to control individual pieces of
production equipment, but also to serve as part of a management information system in the manufacturing sector of the firm. DNC 软件的发展不经可以控制生产设备的每个单独零件，还可以在生产坚固性方面提供主要控制信息。 CNC software is developed to augment the capabilities of a particular machine tool. CNC 的提高可以提高特殊车床的能力。
The general configuration of a computer numerical control system is pictured in Fig.2.5. 电脑数控系统的大体配置如图2.5 所示。As illustrated in the diagram, the controller has a tape reader for initial entry of a part program. 如图中所示，最初进入控制器的是磁带播放机。In this regard, the outward appearance of a CNC system is similar to that of a conventional NC machine. 这样，CNC 的外部系统与传统的NC机相似。However, the way in which the program is used in CNC is different. 似。然而CNC 中的程序使用方法是不同的。With a conventional NC system, the punched tape is cycled through the tape reader for each workpart in the batch. The MCU reads in a block of instructions on the tape, executing that block before proceeding to the next block. 与传统的数控系统比，纸带通过纸带阅读机对每个批次的工件循环。MCU读取磁带上的指示块，执行该块，然后进行下一个块。In CNC, the entire program is entered once and stored in computer memory.在数控中，整个程序一旦进入并储存在电脑的存储器中。 The machining cycle for each part is controlled by the program contained in memory rather than from the tape itself.每个零件的加工周期控制在内存中，而不是来自磁带本身的程序。
Control algorithms contained in the computer convert the part program instructions into actions of the machine tool (or other processing equipment). 在计算机中的控制算法转换成机床（或其他加工设备）的行动的一部分程序指令。Certain functions are carried out by hard-wired components in the MCU. MCU中进行硬连接组件的某些功能。For example, circular interpolation calculations are often performed by hard –wired circuits rather than by stored program. Also, a hardware interface is required to make the connections with the machine tool servo systems. 例如，圆弧插补计算往往是通过硬连接的电路，而不是由存储程序执行。另外，硬件接口需要与机床伺服系统连接。
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(3) Features of CNC control CNC的控制特点
In previous the important features and functions of the machine control unit in numerical control were described. 在前面，对数控机床控制单元的重要特征和功能进行了描述。CNC has made possible additional features beyond what is normally found in a conventional hard-wired MCU. Some of these features include the following: 数控已经超出了通常在传统的硬连线的单片机中可能发现的附加功能。其中一些功能包括以下内容：
1) Storage of more than one part program. 存储多个零件程序With improvements in computer technology, many of the newer CNC controllers have a large enough capacity to store more than a single program. 随着计算机技术的改进，许多新的CNC控制器有一个足够大的容量来存储大于一个单一的程序。This translates into the capability to store either one very large program or several small and medium-sized programs.这能力意味着存储成功其中一个非常大的程序或几个小型和中型项目。
2) Use of diskettes. 使用软盘There is a growing use of floppy disks for part programs in manufacturing. The capacity of an 8-in. 有越来越多的软盘制造业中的部分程序使用，8合一的能力。 diskette is the approximate equivalent of 8,000 ft of punched tape. Because of this more modern storage technology, many CNC controllers have the optional capability to read in programs stored on disks as well as punched tape. 软盘是大致相当于8000英尺纸带。因为这更现代的存储技术，许多CNC控制器可选的阅读能力在磁盘上以及纸带存储方案。
3) Program editing at the machine tool site.机床网站编辑计划 To deal with the mistakes in part programming, CNC systems permit the program to be edited while it is in computer memory. 为了解决部分编程的错误，数控系统允许程序编辑，而它是在计算机内存中。 Hence, the process of testing and correcting the program can be done entirely at the machine site rather than returning to the programming office in the shop to make the tape corrections. 因此，完全可以在机器网站中测试和纠正计划的过程，而不是去店里的编程办公室进行磁带更正。In
addition to part program corrections, editing can also be done to optimize the cutting conditions of the machining cycle. 除了部分程序更正，编辑也可以进行对切削条件下加工周期的优化。 After correcting and optimizing the program, a tape punch can be connected to the CNC controller in order to obtain a revised version of the tape for future use. 纠正和优化方案后，纸带穿孔机可以连接到CNC控制器，以获得供将来使用的磁带的修订版本。
4) Fixed cycles and programming subroutines. 固定周期和编程子程序The increased memory capacity and the ability to program the control computer in CNC provides the opportunity to store frequently use machining cycles in memory that can be called by the part program Instead of writing the instructions for the particular cycle into every program, a code is written into the program to indicate that the cycle should be execute. 增加内存容量和能力，在数控编程控制计算机提供了机会来存储经常使用在记录中的加工，而是写入到特定周期的指令，每一个程序的一部分程序，可以称为周期，写入代码到程序表明周期应当执行。Some of these cycles require the definition of certain parameters in order to execute. 这些周期需要通过某些参数的定义来执行。An example is a bolt hole circle, in which the diameter of the bolt circle, the spacing of the bolt holes, and other parameters must be specified. In other cases, the particular machining cycle used by the shop would not require parameter definition. 例如螺栓孔圆形，螺栓圈的直径，其中必须指定螺栓孔和其他参数的间距。在其他情况下，特别是加工店使用的周期并不需要参数的定义。
5) Interpolation.插值 Some of the interpolation schemes are normally executed only on a CNC system because of the computational requirements. 一些插值计划通常仅由于数控系统计算的要求而执行。Linear and circular interpolation are often hard-wired into the control unit.直线和圆弧插补往往很难连接到控制单元。 Helical, parabolic, and cubic interpolations are usually executed in a stored program algorithm.螺旋线，抛物线，立方插值通常作为存储程序的算法。
6) Positioning features for setup. 定位功能设置Setting up the
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