1附錄一PLC 模塊控制回轉(zhuǎn)工作臺(tái)在三軸數(shù)控銑床銑削螺旋傘齒輪中的應(yīng)用S. Mohsen Safavi (2) by this method, various types of gears can be manufactured with the industrial three-axis CNC milling machine; (3) this method is more economical than using the special machine tool. One of the main points which separate our work from previous ones is developing an automatic computer model in order to simulate the process entirely and obtain machining parameter. All previous studies have been engaged in calculating complicated mathematical equations and designing geometric models. In view of the above, special attention is given to experimental tests rather than presenting geometrical or mathematical model of SBGs. This is the first time that mechatronic tools and a three-axis CNC milling machine are being used simultaneously in manufacturing a special gear and even a mechanical element.2 Geometric specifications of the spiral bevel gearsMost of the time, the geometric parameters of a gear are provided with an engineering drawing. Some parameters (principal parameters) are required for defining the geometry. To calculate these parameters, we have used “drive component development software” called GearTrax. The design of spiral bevel gear requires high-accuracy mathematical calculations, and the generation of such gear drives requires not only high-quality equipment and tools for manufacturing of such gear drives but also the development of the proper machine-tool settings. Such settings are not standardized but have to be determined for each case of design (depending on geometric parameters of the gear drive and generating tools) to guarantee the required quality of the gear drives.3 Manufacturing the SBGAs it was discussed in the introduction, by machining, all types of gears can be made in all sizes, and machining is still unsurpassed for gears having very high accuracy. Form milling is one of the most common machining processes used to manufacture any types of gears. The cutter has the same form as the space between adjacent teeth. Standard cutters usually are employed in form-cutting gears. In the USA, these cutters come in eight sizes for each diametral pitch and will cut gears having the number of teeth indicated in standard tables. Gleason works used the face hobbing process that is based on the generalized concept of bevel gear generation in which the mating gear 10and pinion can be considered respectively, generated by the complementary generating crown gears. As it is shown in Eq. 1, velocity ratio of face hobbing process depends on tooth number of tool and generating gear: （1）tctNw?where, wt and wc denote the angular velocities of the tool and generating gear; Nt and Nc denote the number of the blade groups and the tooth number of the generating gear. The radii of the rolling circles of the generating gear and the tool are determined by Eqs. 2 and 3:（2 ）sNRctc???（3）cttwhere s is the machine radial setting.The generating crown gear can be considered as a special case of a bevel gear with 90° pitch angle. Therefore, a generic term “generating gear” is used. The concept of complementary generating crown gear is considered when the generated mating tooth surfaces of the pinion and the gear are conjugate. In practice, in order to introduce mismatch of the mating tooth surfaces, the generating gears for the pinion and the gear may not be complementarily identical. The rotation of the generating gear is represented by the rotation of the cradle on a hypoid gear generator. To manufacture the SBGs with the three-axis CNC milling machine, we first test the process by developing a CAD/CAM system composed of geometric modeling and graphic simulation modules. The commercial software Solidworks is used for creating CAD model and MSC. Visual NASTRAN 4D (CAE system of the kinematic analysis of the mechanisms by means of their 3D models) is used for simulating the process of gear manufacturing and its analytical results.As far as machine tool configuration is concerned, it is obvious that a rotational motion of the workpiece is required for NC machining of the SBGs. Based on the machinability analysis, at least four-axis controls are required for NC machining of SBGs by one setup. Thus, a rotary table to be interfaced with the three-axis milling machine is required. Form cutting or form milling is used in our tests. The tool is fed radially toward the center of the gear blank to the desired tooth depth, then across the tooth face, while the rotary table rotates the workpiece around its center to obtain the required tooth width. When one tooth space has been completed, the tool is withdrawn, the gear blank is indexed using a dividing head, and the next tooth space is cut. Basically, this method is a 11simple and flexible method of machining SBGs. The equipment and cutters required are relatively simple, and standard three-axis CNC milling machine is used. However, considerable care is required on the part of tool feed which should be a small value in each step to prevent any spoil. We used spiral bevel gear created in GearTrax in order to simulate operating sequence and then estimate some machining parameters such as initial height of end mill, location of proximity sensors, motor torque, motor speed, and rotation frequency. For example, in SolidWorks, distance between end mill and the apex of SBG was 14.7 mm which we used to locate the spindle vertically along the z-axis. Also, according to the graph report of CAE system which we used, motor angular velocity and motor torque are 1 rpm and 48 Nm, respectively. Mastercam is a mechanical software that can be used to generate toolpaths for machining. According to whole depth and face width of the gear, a rectangular contour was designed as toolpath in our cutting procedure. Other machining parameters and tool’s specifications were also submitted to the Tool Path menu of software. In contour window, there are two options which we use:1. Multipasses which enable multiple stepovers of the tool, allowing for greater control of stock removal.2. Lead in/out which extend or shorten the toolpath before making entry/exit moves without creating additional geometry, which is helpful when working with control compensation and makes it possible to program solid contours in less time.Although the form cutting of this kind of gears is currently done on universal milling machine, using an indexing head, the process is slow and requires skilled labor and operator. The cutter is mounted on an arbor, and a dividing head is used to revolve (required to cut the gear tooth) and index the gear blank. The table is set at an angle equals to the spiral angle (35°), and the dividing head is geared to the longitudinal feed screw of the table so that the gear blank will rotate as it moves longitudinally. In the presented method, we have used an alternating current (AC) motor interfaced with a worm gearbox. Worm gearbox is used to reduce the output speed of AC motor and also to set the angle between the tooth trace and the element of the pitch cone, known as spiral angle. Since synchronization between tool path planning and rotary motion of outward shaft of worm gearbox is required, a mechatronics system to control all the four axes (one-axis motion for the rotary table and three-axis motion for the cutting tool) was used simultaneously.At the same time we used ladder diagram, common program language to operate the PLC in the mechatronics system.12The operation of the PLC based on the ladder diagram is as follows:Step 1 Read the external input signal, such as the status of sensors or rotary encoder.Step 2 Calculate output signal, according to the value of the input signal in step 1 and send it to AC drive (Inverter) to run the AC motor in forward/reverse direction or turn the motor for a special angle (circular pitch) using a rotary encoder. Having set up the CNC milling machine, the procedure of the whole system is accomplished in five stages:Stage 1 Form cutter reaches the first proximity sensor. As soon as sensor 1 detects the form cutter, it sends a +5-V signal to the PLC. As it is mentioned before, PLC sends out an output signal to the AC drive to run the motor in forward direction.Stage 2 Form cutter machines the rotating workpiece with respect to the toolpath has been generated in Mastercam.Stage 3 Cutting tool reaches the second proximity sensor. Detecting form cutter by sensor 2, it sends the second signal to the PLC and PLC sends a stop command to the inverter.Stage 4 Milling tool withdraws the stopped workpiece and returns to its first place. Simultaneously, AC drive runs the motor in backward direction until the shaft reaches the first position which the receiver of photoelectric sensor sees the transmitted radiation passes through the longitudinal crack on the output shaft.Stage 5 Stages 1 through 4 continue until the first tooth space is cut. PLC counts a number for each of the above four stages until it reaches the predefined number of machining sequences. Then, it sends out a signal to the AC drive to index the gear blank equal to diametral pitch, and all the above stages will be repeated again. The diametral pitch is measured by a 1,024-pulse/revolution rotary encoder.In an advantageous embodiment of the method according to the present invention, machining time is one of the most factors which have been greatly noted. For example, it took only 2 min to cut one tooth space completely. While, in traditional method, it took more than half an hour to cut same tooth space.In a further advantageous embodiment of the present invention with respect to manual cutting, the instant for the angular compensation of the cutter head is set shortly before the end of the plunge process.4 Machining strategyThe workpiece is wood, and the blank material is premachined as a conic (face angle of the gear) form by turning operation. Standard cutter No. 5 used in our experiment is mounted on the machine spindle, and the gear blank is mounted on outward shaft of worm gearbox. The tool is fed subsequently (around 30 machining sequences to prevent spoiling work) toward the center of the 13gear blank to the desired tooth depth. When one tooth space has been completed, the tool is withdrawn; the gear blank is indexed using the AC motor based on explained procedure and then is followed by cutting the next tooth space. 5 ConclusionsIn this paper, we attempted to manufacture the spiral bevel gear using a three-axis CNC milling machine based on form milling method. For such a purpose, we investigated a CAD/CAM model of cutting procedure and also tool path computing algorithm. All previous works have been concerned with the design aspect using complicated mathematical procedure, and experimental manufacturing methods have not been explicitly focused. Basically, form cutting uses a simple and flexible method of machining of gears. The equipment and cutters required are relatively simple and inexpensive, and standard CNC milling machine is used. So, it does not need skilled operator to set up the system. Compared to the conventional gear cuttingmethod in which dedicated machine tools is required, the presented method can easily be modified to produce any type and size of SBGs or any other types of gears. In comparison to manual cutting machine, it is a complete automatic method in which all machining parameters are derived from the computer model. It is also a multideception system (use of mechatronic and CNC systems) which is a dynamic and constant evolving technology.References1. De Garmo EP, Black JT (1957) Materials and processes in manufacturing. Prentice–Hall, New York2. Shigley JE (1986) Mechanical engineering design. McGraw-Hill, New York3. Maitra GM(1994)Handbook of gear design. McGraw-Hill, New York4. Tsai Y, Chin P (1987) Surface geometry of straight and spiral bevel gears. ASME J Mech Trans Autom Des 109(4):443–4495. Al-daccak M, Angeles J, Gonzalez-Palacios M (1994) The modeling of bevel gears using the exact spherical involute. ASME J Mech Des 116:364–3686. 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