Gear table for gear splitting and differential exchange
In gear and thread machining, tooth splitting and differential motion are key to ensuring workpiece indexing accuracy and helix precision, and an exchange gear table is a crucial tool for achieving this. A tooth splitting exchange gear controls the workpiece’s indexing motion, enabling precise indexing at a specific angle. Differential exchange gears compensate for workpiece motion errors during helix machining, ensuring helix accuracy. A tooth splitting and differential exchange gear table is developed based on the machine tool’s transmission ratio and the workpiece’s machining requirements. It includes a variety of commonly used exchange gear combinations, making it easy for operators to select the appropriate exchange gear.
The function of a tooth-splitting gear is to transmit the motion of the machine tool spindle to the workpiece, enabling precise indexing. In gear machining, when machining a gear with a tooth count of z, the tooth-splitting gear is required to maintain a certain proportional relationship between the workpiece speed and the tool speed. That is, for every spindle revolution, the workpiece rotates 1/z revolutions. The transmission ratio of a tooth-splitting gear is i tooth = z tool / z work, where z tool is the number of teeth on the tool (for gear milling cutters, z tool is the nominal number of teeth on the tool) and z work is the number of teeth on the gear being machined. The tooth-splitting gear table lists gear combinations corresponding to different transmission ratios. For example, for a transmission ratio of 1/2, gear combinations with 20 and 40 teeth are available (20/40 = 1/2). For a transmission ratio of 2/3, gear combinations with 20, 30, 40, and 60 teeth are available (20 × 40) / (30 × 60) = 800 / 1800 = 2/3). The operator can quickly complete the installation of the exchange gears by looking up the corresponding gear combination from the gear exchange gear table according to the required transmission ratio, ensuring the gear exchange accuracy.
Differential interchanging gears are primarily used in the machining of parts with helical structures, such as helical gears and worms. Their function is to compensate for the additional rotational motion generated by the workpiece during axial feed, thereby ensuring the lead accuracy of the helical line. In helical machining, the workpiece’s rotational motion includes not only the inter-tooth motion but also the additional rotational motion caused by axial feed. This additional rotational motion is accommodated by differential interchanging gears. The transmission ratio i diff of differential interchanging gears is related to parameters such as the workpiece’s helix angle β, module m, and lead S. Its calculation formula is i diff = S/(πmz) or i diff = tanβ, with the specific formula determined by the machine tool type and machining method. The differential interchanging gear table lists gear combinations corresponding to different transmission ratios. For example, for a transmission ratio of 0.577 (corresponding to a helix angle of 30°, tan30° ≈ 0.577), the appropriate gear combination can be selected. By using the differential interchanging gear table, operators can quickly find the gear combination that meets the required transmission ratio and ensures helical machining accuracy.
The compilation of interchanging gear tables for split and differential gears is based on the machine tool’s transmission system and the principle of gear meshing. Factors such as the gear tooth count range, transmission ratio accuracy, and gear installation space must be considered. Gear tooth counts typically range from 16 to 120. Too few teeth can lead to undercutting, compromising gear strength; too many teeth increase gear size and take up too much installation space. Transmission ratio accuracy is crucial for compiling interchanging gear tables. To ensure transmission ratio accuracy, multiple gear combinations are often used, approximating the desired transmission ratio using the gear ratios. For example, a transmission ratio of π (≈3.1416) cannot be represented by a simple integer ratio. Multiple gear combinations can be used, such as (63×75)/(25×25)=4725/625=7.56. This is clearly not π. In practice, more accurate combinations are used, such as (100×127)/(40×100)=127/40=3.175, which have a smaller error from π. The gear combination in the gear exchange table should be as simple as possible to reduce the number of gears and the difficulty of installation. At the same time, it is necessary to ensure good meshing between gears to avoid interference.
The selection and installation of split teeth and differential exchange gears need to follow certain principles to ensure the accuracy and stability of the transmission. First, the appropriate gear combination should be selected from the exchange gear table according to the required transmission ratio. When selecting, priority should be given to combinations with high transmission ratio accuracy and a small number of gears. Secondly, when installing the gears, it is necessary to ensure that the axes of the gears are parallel and the center distance is accurate to avoid additional force and wear when the gears are engaged. The installation order of the gears should be carried out according to the transmission route. The driving gear should be installed first, and then the driven gear should be installed to ensure that the meshing clearance between the gears is appropriate. If the clearance is too large, it is easy to generate impact and noise, and if the clearance is too small, it will increase friction and wear. After the installation is completed, the gears should be manually rotated to check whether the transmission is smooth and whether there is any jamming. If there is any abnormality, it should be adjusted in time.
The use of tooth-splitting and differential exchange gear tables not only improves processing efficiency, but also ensures processing accuracy, and is widely used in mechanical processing. With the development of CNC machine tools, the use of exchange gears has gradually decreased, replaced by servo motors and CNC systems to achieve precise indexing and differential motion, but on some old machine tools and special equipment, exchange gears still play an important role. Mastering the use of tooth-splitting and differential exchange gear tables is of great significance for understanding the transmission principle of machine tools, improving processing quality and solving practical processing problems. Operators should be familiar with the compilation principles and use methods of exchange gear tables, and be able to correctly select and install exchange gears according to processing requirements to ensure that the processing accuracy of the workpiece meets the design requirements.
