Gear transmission has the advantages of large transmission power, high efficiency and accurate transmission ratio, and is widely used in mechanical transmission. In the involute tooth profile meshing transmission, due to the advantages of constant meshing transmission ratio, constant meshing angle, and separability of center distance, the involute gear has good meshing characteristics, and is relatively easy to manufacture and install.
The design and manufacture of standard involute spur cylindrical gears and helical gears have been standardized, and they are the most widely used in mechanical transmission. In the process of meshing transmission of involute straight cylindrical gears, the load is suddenly added or removed along the full tooth width when the tooth surfaces of the two wheels are in contact, so the impact and noise are large and the transmission stability is poor.
The helical cylindrical gear tooth profile surface is an involute spiral surface, and the contact line is inclined to the axis when the tooth surface of the two wheels is in contact, and its advantage is that the gear teeth gradually enter and exit the meshing when they are meshed, so the meshing transmission bearing capacity is large, the degree of overlap is large, and the transmission is stable, but the disadvantage is that there is a large axial force in the transmission process. Therefore, the research on the meshing transmission of arc-toothed cylindrical gears has received extensive attention from scholars at home and abroad.
The tooth structure of the arc tooth cylindrical gear is similar to that of herringbone gear, so it has the advantages of herringbone gear, that is, high gear transmission coincidence, small axial load and strong bearing capacity. At the same time, in the process of meshing cylindrical gears of arc teeth, the meshing and meshing of each pair of teeth are carried out gradually, compared with the cylindrical gears and helical gears, it has neither the meshing impact phenomenon of the spur gear, nor the axial force when the helical gear meshing transmission, so its transmission performance is better. In addition, because the tooth direction of the arc tooth cylindrical gear is the arc tooth line, the arc tooth cylindrical gear can rotate along the tooth line at a small angle without affecting its meshing transmission when installed, and the gear pair installation parallelism error adaptability is strong. Shanghai Huanyue Machine Tool shares an article with you, on the basis of studying the basic rack of arc-toothed cylindrical gears, introducing the design and manufacturing methods of arc-toothed cylindrical gears.
In general, the study of cylindrical gears with arc teeth is based on the basic rack of the cylindrical gear. Fig. 1 is the basic rack of arc tooth cylindrical gear, respectively, the convex and concave surfaces of the gear teeth, they are part of the two cones p and q, r is the radius of the conical cone at the indexing circle, t 2 is the spacing between the two conical axes, is the width of the rack, the a-a section is the middle section of the rack, the b-b section is the indexing plane of the rack, and the rack at the section a-a has an involute tooth shape. It is found that the tooth shape of the arc tooth cylindrical gear in the middle section of the gear tooth is the same as that of the involute spur cylindrical gear, so the design and calculation of the arc tooth cylindrical gear can be carried out with reference to the involute spur cylindrical gear, and its basic geometric parameters are modulus, number of teeth, pressure angle, tooth top height coefficient and top clearance coefficient, and the geometric size calculation is the same as that of the involute spur cylindrical gear, and the calculation formula is shown in Table 1.
The design process of arc-toothed cylindrical gears can be carried out with reference to involute spur-toothed cylindrical gears, and the design criteria are the same as those of spur-toothed cylindrical gears. In the design process of spur cylindrical gears, because the main failure modes of gears are tooth surface fatigue pitting and gear tooth fatigue fracture, according to different gear transmission applications, the tooth surface contact fatigue strength or tooth root bending fatigue strength design calculation criteria can be selected for design calculation. Therefore, in the design and calculation process of arc-toothed cylindrical gears, the design and calculation process of involute spur-toothed cylindrical gears can be referred to, and the gear material, heat treatment method and accuracy level can be selected first, and then the corresponding design criteria are determined according to the working conditions, and the number of teeth and modulus of the pinion can be determined by calculation. Because the number of pinion teeth is small, considering the undercut problem, the number of pinion teeth should be satisfied when selecting Once the number of teeth of pinion is determined, the number of teeth of pinion can be determined according to the gear transmission ratio, i.e., then, according to the geometric size calculation formula in Table 1, the main size of arc tooth cylindrical gear is calculated; Finally, the strength of the arc-toothed cylindrical gear can be checked.
Table 1 Calculation of basic parameters and geometric dimensions of arc-toothed cylindrical gears.
The cutting of arc cylindrical gears is different from that of straight cylindrical gears, and the more typical cutting methods mainly include rotary cutter head method and parallel connecting rod method. Because the rotary cutterhead method is highly efficient and easy to realize in the process of tooth cutting, this method is widely used in the machining of arc tooth cylindrical gear, and its principle is shown in Figure 2. When the rotary cutter head method is used to cut the arc tooth cylindrical gear, the cutting cutter head and the gear tooth blank are precisely normalized motion relationship, that is, the linear velocity of the segment of the processed gear tooth blank is equal to the linear velocity of the cutting cutter head section. In the process of cutting the arc gear teeth, in addition to the main rotation motion, the cutting cutter head also has a radial plunge feed movement along the tooth blank. When the fan method is adopted, because only one cogging can be cut at a time, the precise indexing of the tooth blank must be controlled after each gear tooth coagulation is cut, and then the second cogging is cut, and the processing of the arc gear can be completed after all the cogging is cut in turn. Theoretically speaking, the arc tooth cylindrical gear cogging can use the double-sided edge cutter to cut out a complete cogging at a time, form the convex and concave surface of the gear teeth, but, because the double-sided edge cutter is full-edge cutting in the tooth cutting process, the cutting amount when cutting the tooth groove is larger, the tool wears quickly, and the tooth surface accuracy that is cut out is not high, and it is difficult to cut the arc gear that meets the requirements when the actual tooth is cut. Therefore, on the basis of the practice of using double-sided edge cutter tooth cutting, the single-sided edge tool tooth cutting method is proposed, and the arc tooth cylindrical gear cutting tool is shown in Figure 3. In Fig. 3, and are the cutterhead radii of the inner and outer side edge cutters, respectively, and the tool pressure angle. Combined with the practical experience of tooth cutting of double-sided edge tools, in the process of arc gear cogging, the double-sided tool can be used to roughly cut out the tooth groove, and then the single-sided edge tool can be used to fine-cut the convex and concave surfaces of the arc tooth cylindrical gear respectively to ensure the accuracy of tooth cutting.
The advantage of using single-sided edge cutters to fine-cut the convex and concave surfaces of arc teeth cylindrical gears is that the inner and outer single-sided edge tools can be designed as tools with equal radius, and the convex and concave surfaces of the teeth are cut with high accuracy. However, because the convex and concave surfaces need to be cut separately, it is necessary to consider the problem of tooth blank installation and tool replacement in the machining process, once the tool needs to be replaced or disassembled and assembled in the machining process, it will inevitably affect the machining accuracy of the gear teeth. To this end, the single-sided double-milling processing method of arc tooth cylindrical gear is proposed, and its processing principle is shown in Fig., in the process of arc tooth cylindrical gear tooth cutting, two stations are designed on the special gear milling machine tool to cut the convex and concave surface of the gear tooth respectively. In Fig. 4, the convex and concave single-edge gear milling cutters located at the left and right stations respectively represent the machined arc teeth cylindrical gear blanks when milling the convex and concave tooth surfaces are convex and concave single-edge milling tools. It can be seen that the cutting of arc teeth cylindrical gears requires special CNC gear milling equipment to complete.
In the process of milling arc cylindrical gears, special tools are used for milling tools. In order to design and manufacture special gear milling tools, the tooth surface equation of the tooth cutting tool can be studied and established based on the principle of rotary cutter head method tooth cutting tool. The figure is the coordinate system of the cutter and the gear to be processed, and the coordinate system is established first and is fastened on the gear tooth blank to be processed, and the coordinate system is fixed with the milling tooth cutter, and they rotate with the processed gear tooth blank and the milling tooth cutter head respectively; Then establish a fixed coordinate system, for the auxiliary coordinate system, if the pitch radius of the gear blank is the average radius of the milling cutter, then the radius of the inner cutting edge of the milling cutter is
The radius of the outer blade is
In addition, in the figure, and are the angular velocity of the tool and the blank, respectively, and the angle of rotation of the blank.
It can be seen that in the coordinate system fixed with the cutter, the parameter equation of the cutter surface can be established as follows:
Wherein: is the distance between the point on the surface of the tool along the conical bus and the reference point; is the angle of the tool holder from the ** section of the tooth blank to the end face.
Combined with the analysis of the above-mentioned tooth cutting process, the arc tooth cylindrical gear cutting process can be divided into three steps: the first step is to cut down in the middle of the arc tooth cylindrical gear cogging, and the tooth groove is milled out by using a three-sided edge tooth slotting milling cutter to remove most of the tooth blank material; The second step and the third step use a single-sided edge tool to process the concave and convex tooth surfaces of the arc tooth cylindrical gear respectively. When machining on the special gear milling machine tool, the indexing of the machining process is programmed in two ways: absolute indexing and relative indexing, such as the gear is δ according to the number of teeth indexing angle, and the first step of the starting angle of the machining program starts from δ 2, that is, the cogging is roughened from the middle of the gear tooth groove; The second step starts from δ=0, and the third step starts from the δ, and two single-sided edge tools are used respectively to carry out the corresponding concave and convex tooth surface processing; When each tool completes the entire cogging and tooth shape processing of the gear one week, the processing of the entire arc cylindrical gear can be completed. Since the cutter plunge is made according to the involute, the plunge trajectory of the cutter is fed according to the involute. For example, the basic parameters for machining arc-toothed cylindrical gears are as follows: modulus m=3, number of teeth z=25, tooth top height coefficient 10, the top clearance coefficient is 025, a cogging cutting cycle macro program is compiled as follows:
The milling process of arc tooth cylindrical gear is fed in the direction of the involute, and the retract is also retracted in the direction of the involute. When the tool moves along the involute direction, it is necessary to pay attention to avoid the overcutting of the unmachined tooth surface, so as to ensure that the surface to be processed has enough machining allowance, so as to ensure the machining quality of the arc tooth surface. Fig. 6 is the arc tooth cylindrical gear obtained by trial cutting, and the meshing transmission test proves that the cut arc tooth cylindrical gear meets the expected requirements.
The meshing transmission performance of arc-tooth cylindrical gears is good, but because the tooth-cutting processing requires special processing equipment and gear milling tools, the arc-tooth cylindrical gears cannot be popularized and applied in a large area in mechanical transmission. In this paper, on the basis of the design and calculation of arc cylindrical gears, the in-depth study of the cutting of arc cylindrical gears is carried out, and the convex and concave surfaces of arc gear teeth are cut by using a single-sided double-milling method, and the gear milling is carried out based on special gear milling equipment. In the tooth convex and concave milling process of arc tooth cylindrical gear, the cutter is driven along the involute trajectory when cutting in and out, and after adjusting the machine tool to complete the convex or concave machining of the first gear tooth, the milling of the subsequent gear tooth only needs the accurate indexing of the tooth blank, and then repeats the previous cutting feed. By compiling the CNC machining macro program, the arc gear is tried to be cut on the special gear milling equipment, and the accuracy of the cut arc tooth cylindrical gear is basically at the level, and the cut arc gear meets the expected requirements through the meshing transmission inspection. In addition, if the accuracy of the arc gear needs to be further improved, the gear grinding machine can be used to further grind the tooth surface to improve the accuracy of the gear.