In the machining of ordinary lathes, the turning of circular arcs is typically done manually using an experience-based method or with standardized turning tools (as shown in Figure 1). The former method often struggles to maintain precision, while the latter requires highly specialized tools that must match the workpiece shape exactly. This leads to high tooling costs, especially for low-volume, multi-standard production. With the rapid development of numerical control technology, CNC lathes have become a more efficient solution for machining arc-shaped contours on shaft parts. A standard external turning tool is commonly used (as shown in Figure 2), and this approach has proven effective. However, the profile produced by this method is limited in position—typically only the second quadrant can be machined because the lathe can only process the first two quadrants. If a cross-quadrant profile is required, the tool may interfere with the workpiece due to its relief angle, leading to rejection (as shown in Figure 3). Through analysis, we found that using a circular arc turning tool on a CNC lathe could improve results. Although the appearance of the machined workpieces looks good, several issues still exist. This article aims to address the problem of tool interference during arc machining through a programmed approach. Turning Trajectory Analysis To better understand the issue, let’s take the part shown in Figure 4 as an example. Normally, manual programming for arc machining might look like the following: N100 M06 T0101; N110 G00 X22 Z-16; N120 G01 X20 Z-16 F200 S500; N130 G02 X20 Z-34 I12 K-9; N140 G01 X22 Z-34; As seen in Figure 5, the arc appears smooth and visually appealing. However, when measured with a caliper, it becomes clear that the arc does not meet the drawing specifications. The distance between the start and end points along the Z-axis is consistently larger than expected. Upon investigation, it was found that the arc turning tool was interfering with the actual workpiece surface, which affected the accuracy of the final part. To resolve this, we replaced the arc turning tool with a sharp-edged tool (as shown in Figure 5). This approach met the design requirements more effectively. Under conditions of sufficient tool strength and acceptable surface finish, some arc surfaces can indeed be machined using a sharp-edged tool. However, there are limitations. The angle of the sharp tool plays a critical role in determining whether interference occurs. As shown in Figure 6, assume point A is the starting point, point B is the endpoint, and point C is the highest point on the arc. The cutting edge of the sharp tool follows the path ACB. Take any point D on this arc for analysis. When the tool touches the arc at point D, connect OD, draw tangent line L2 at point D, and then draw vertical line L3 from the Z-axis. The angle between L2 and L3 is denoted as 'a'. As the tool moves from A to C, the slope of the tangent L2 gradually decreases, and the angle between the tangents and L3 increases, meaning 'a' grows larger. The sharp tool has a specific angle, defined as the angle between the back of the tool and the vertical line of the Z-axis, denoted as 'b'. Once the tool is mounted, the value of 'P' remains fixed. The relationship between angles 'a' and 'b' determines whether the tool will interfere with the arc surface. From Figure 6, it is evident that when 'a' > 'b', the tool does not interfere with the arc surface. However, if 'a' < 'b', interference occurs, which can lead to errors in the final product. Understanding this relationship is crucial for optimizing the machining process and ensuring accurate results.

Electric Transmission Shifter

Electronic gear selector, automatic transmission switch, vehicle shifter module, electric shift actuator

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