Calculation of gear exchange during thread turning
Calculating the interchanging gear during threading is a critical step in lathe thread machining. Its purpose is to match the workpiece’s thread pitch with the lead screw’s pitch by adjusting the transmission ratio between the lathe’s spindle and lead screw, thereby producing threads that meet the requirements. Threading on a lathe is achieved by the spindle rotating the workpiece while the lead screw simultaneously drives the slide box and the turning tool axially. The transmission ratio between the spindle and lead screw is determined by the tooth ratio of the interchanging gear. Therefore, accurately calculating the number of teeth on the interchanging gear is a prerequisite for ensuring thread pitch accuracy, directly affecting the thread’s fit and performance.
The basic principle of interchanging gear calculation is based on the transmission relationship between the spindle and the leadscrew. That is, for each revolution of the workpiece, the turning tool moves axially a distance equal to the thread pitch (Pwork), while for each revolution of the leadscrew, the turning tool moves a distance equal to the leadscrew pitch (Pscrew). Therefore, the spindle-to-screw speed ratio (nmaster/nscrew) should be equal to the ratio of the leadscrew pitch to the workpiece pitch (Pscrew/Pwork). This speed ratio, in turn, is equal to the ratio of the number of teeth on the driven gear to the number of teeth on the driving gear of the interchanging gear (Zslave/Zmaster), namely, Zslave/Zmaster = Pscrew/Pwork. In actual calculations, the fixed-ratio transmission within the lathe’s transmission system (such as the transmission ratio ifixed in the feed box) must also be considered. In this case, the interchanging gear’s gear ratio should be: Zslave/Zmaster = (Pscrew/Pwork) × ifixed. For example, the screw pitch of a lathe is 12mm, the fixed ratio transmission ratio is 1, and when processing a thread with a pitch of 3mm, the tooth ratio of the exchange gear is 12/3 = 4, that is, the tooth ratio of the driving wheel to the driven wheel is 1:4. An exchange gear combination with 40 teeth on the driving wheel and 160 teeth on the driven wheel can be selected.
Commonly used threads can be categorized by thread type, such as triangular, trapezoidal, and sawtooth. While the principles for calculating interchangeable gears for these different thread types are the same, it’s important to note how the pitch is expressed. The pitch of a triangular thread typically refers to the axial distance between corresponding points on the mid-diameter line between two adjacent threads, while the pitch of an imperial thread is expressed in threads per inch. This calculation requires conversion to metric pitch (1 inch = 25.4mm, metric pitch P = 25.4 / threads per inch). For example, when machining an imperial thread with 12 threads per inch, the metric pitch is 25.4/12, which equals 2.117mm. If the lathe leadscrew pitch is 6mm, the gear ratio for the interchangeable gear is 6/2.117, which equals 2.834. The appropriate gear combination can be determined by factoring the fraction (e.g., 2.834 = 85/30, using a 30-tooth driving gear and an 85-tooth driven gear). For modular threads (such as worms), the pitch P = π × module m. When calculating, the module must be converted to pitch according to this formula before performing gear exchange calculations.
There are two main methods for calculating interchangeable gears: fractional decomposition and table lookup. The fractional decomposition method reduces the calculated gear ratio (Z slave / Z master = P silk / (P work × i fixed)) to its simplest form. The appropriate gear combination is then selected based on the gear table provided with the lathe, ensuring that the actual gear ratio does not exceed 0.001 of the theoretical value to ensure pitch accuracy. For example, for a gear ratio of 5/3, a driving gear with 60 teeth and a driven gear with 100 teeth can be used (60/100 = 3/5, meaning the ratio of driven gear to driving gear is 5/3). For a gear ratio of 7/4, a driving gear with 40 teeth and a driven gear with 70 teeth can be used. The table lookup method directly finds the gear combination corresponding to the desired pitch by consulting the interchangeable gear table in the lathe manual. This method is quick and accurate, making it suitable for beginners. For gear ratios that cannot be achieved with a simple gear combination, an intermediate gear (idler gear) or a triple gear combination can be used. The intermediate gear does not change the transmission ratio but is only used to change the transmission direction. The triple gear achieves a more precise transmission ratio by increasing the number of gears.
When calculating interchanging gears, the following considerations should be taken into account: First, the gear installation clearance: the center distance between interchanging gears should be appropriate, with the tooth side clearance controlled within 0.1-0.2mm. Excessive clearance will result in increased pitch error. Second, the number of gear teeth should be within the lathe’s permitted range, generally with a minimum of 16 teeth (to avoid undercutting) and a maximum of 120 teeth (due to installation space limitations). Third, for multi-start threads, the interchanging gears must be adjusted based on the number of starts. The pitch (lead) is the single-start pitch multiplied by the number of starts, and calculations should be based on the lead. Fourth, test cuts must be performed during machining to verify the correctness of the interchanging gear calculations by measuring the pitch of the test-cut threads. If the error exceeds the permitted range (generally ±0.05mm), the gear combination must be recalculated and adjusted. Furthermore, with the increasing popularity of CNC lathes, which directly control the transmission ratio of the spindle and feed through a servo system, manual interchanging gear calculations are no longer necessary. However, understanding the interchanging gear calculation principles of traditional lathes is still important for understanding the transmission relationships involved in thread machining.
The accuracy of the interchanging gear calculation directly impacts thread finish quality. For threads requiring high precision (such as machine tool lead screws and precision bolts), more precise calculation methods and gear combinations are required. In mass production, specialized gearboxes or gear racks can be used to quickly switch between various thread pitches, reducing gear change time. Interchanging gears should also be regularly inspected for wear. If tooth wear exceeds 0.2mm, they should be replaced promptly to avoid transmission ratio errors caused by variations in gear tooth thickness. Mastering the interchanging gear calculation method for threading allows operators to flexibly adjust the transmission system based on varying thread parameters, ensuring accurate thread processing and meeting the threaded connection and transmission requirements of mechanical products.
