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During the manufacturing process, certain parts may present unique challenges. As shown in Figure 1, this part has a small outer shape with five φ25H9 holes evenly distributed along an arc. The center of each hole coincides with the center of the arc. Machining these angled holes accurately and efficiently is a complex issue that needs to be addressed.
Figure 1
2. Problem Analysis
Traditionally, there are three methods used for such machining: the scribing method, where the position of each hole is marked and then machined accordingly. However, due to the large radius of the arc, scribing becomes difficult and accuracy is hard to maintain. Another approach involves aligning the arc's center with the machine table's rotational center, but this requires a large machine tool and precise alignment, which is challenging. A third option is using a five-axis CNC machine, which simplifies the process but is costly and not always available. Therefore, finding a solution for conventional machines remains a pressing need.
When placing the part on the workbench, the straight edge must be perpendicular to the machine spindle, and the part is clamped so it rotates with the table. As a result, the holes are no longer directly under the spindle, creating an offset in the X-direction. Determining this compensation distance can be tricky without proper tools or calculations.
3. Solution Approach
(1) Using Drawing to Determine Compensation Distance By using AutoCAD software, we can simulate the position of the table and the rotating center. By measuring values A and B based on the clamping position (ensuring the straight edge is perpendicular to the spindle), we can draw the exact location of the part on the workbench, as shown in Figure 2. This allows us to calculate the necessary X-axis compensation for machining the central hole.
Figure 2
After rotating the table clockwise by 4°, as shown in Figure 3, we measure the X1 value. In actual machining, compensating for X1 along the X-axis allows us to process the hole at the 4° position. Similarly, when rotating 8°, we measure X2 and use that for compensation, as shown in Figure 4. The same method applies to counterclockwise positions.
Figure 3
Figure 4
(2) Calculating the Compensation Distance Taking a concave arc as an example, when the table rotates β degrees clockwise, two right triangles are formed. Knowing the angle β/2 and using trigonometric functions, we can calculate the required X-axis compensation. The formula for compensation after a clockwise rotation is: X = [C + Atan(β/2)] × sinβ, where C = R + B. For a counterclockwise rotation, the formula becomes: X = [C - Atan(β/2)] × sinβ, with C = R + B. The calculation method for convex arcs is similar, with only the sign of B changing. For convex arcs, the formula becomes: X = [C + Atan(β/2)] × sinβ, where C = R - B. And for counterclockwise rotation: X = [C - Atan(β/2)] × sinβ, with C = R - B.
4. Conclusion
Accurate measurement of A and B values is crucial for both drawing and calculation. These values can be measured by installing a checker bar in the positioning hole of the table’s rotational center. To ensure precision, the part should be finely milled, with all surfaces controlled within 0.02mm of parallelism and perpendicularity, and surface roughness maintained at Ra ≤ 1.6µm.
Using the described method, this part was successfully manufactured on our TH6350 horizontal machining center (with a 500mm × 500mm worktable). Post-testing confirmed that the accuracy meets design specifications, proving the method to be cost-effective, simple, and reliable. It is highly recommended for similar applications.
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