The accurate shaping curve for forming inside small right-angle step using cross-wedge rolling
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摘要: 內直角臺階的軋齊一直是楔橫軋的關鍵技術之一，一般內直角臺階的軋齊曲線公式和算法不適合小臺階的生產應用。為了解決這一問題，通過改進幾何模型，針對內直角小臺階的螺旋體體積提出一種新的計算方法。根據楔橫軋工藝的特點，比較軋件初始半徑與對應輔助圓半徑的大小關系，指出了二輥軋齊過程中內直角小臺階的判斷條件。根據軋件大端半徑與旋轉角度的關系，將軋齊過程分成了三個階段。通過對小臺階螺旋體的分塊，將其近似成三個規則體積的組合，推導出了軋齊過程中各個階段的體積公式。依據體積平衡原理和楔橫軋模具特點，得到了二輥楔橫軋內直角小臺階隨軋件旋轉角度變化的軋齊曲線。最后采用剛塑性有限元軟件Deform-3D對一定斷面收縮率范圍內的軸類件進行楔橫軋數值模擬，驗證了本文所提出的軋齊曲線計算方法的適用性。同時通過對比分析，發現在小斷面收縮率軸類件直角臺階成形時展寬角應盡量取小。Abstract: Cross-wedge rolling (CWR) die generally has three parts: a knifing section, a stretching section, and a finishing section. When forming an inside step, to avoid generating spiral steps, a new transitional section is introduced between the knifing and finishing sections, during which the surface is cut in the same shape as the inside step. The resulting surface is called the shaping surface, and its intersection with the base surface of the die is called the shaping curve. The rolling of the inside right-angle step has long been a key technology of CWR. The general formula and algorithm for the rolling alignment curve are not suitable for producing small right-angle steps. To solve this problem, we improve the geometric model and propose a new method for calculating the volume of the spiral cone of the small right-angle step. Based on the characteristics of the CWR process, the initial radius of the rolled product is compared with the radius of the corresponding auxiliary circle to preliminarily determine the conditions required for the small inside right-angle step. Based on the relationship between the radius of large section and the rotation angle, the shaping process is divided into three phases, the volume formulas for which are deduced by dividing the spiral cone into three regular volumes. Based on the volume fixedness theory, an accurate shaping curve of the small right-angle step is obtained by changing the rotation angle of the rolled piece. Finally, the finite element software Deform-3D is used to simulate the large diameter part within a certain area reduction range, the results of which verify the applicability of the proposed calculation method. The results of a comparative analysis also reveal that the stretching angle should be as small as possible when producing large-diameter shaft parts with small right-angle steps.
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Key words:
- cross-wedge rolling /
- small right-angle steps /
- volume of helix /
- shaping curve /
- FEM
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圖 1 不同情況下軋輥與軋件接觸面形狀。（a）大斷面收縮率工況；（b）小斷面收縮率工況
Figure 1. Shape of the contact surface between the roll and rolled part under different conditions: (a) large area reduction; (b) small area reduction
圖 3 內直角小臺階軋齊過程示意圖。 （a）第一階段；（b）第一階段和第二階段的臨界狀態；（c）第二階段；（d）第二階段和第三階段的臨界狀態；（e）第三階段
Figure 3. Diagrams of rectangular small steps in the rolling process: (a) the first stage; (b) the critical state of the first and second stages; (c) the second stage; (d) the critical state of the second and third stages; (e) the third stage
圖 12
$ {V_{{\rm I}{\rm I}{\rm I} - 1}} $ 示意圖Figure 12.
$ {V_{{\rm I}{\rm I}{\rm I} - 1}} $ schematic
圖 13
$ {V_{{\rm I}{\rm I}{\rm I} - 3}} $ 示意圖Figure 13.
$ {V_{{\rm I}{\rm I}{\rm I} - 3}} $ schematic
圖 15 不同斷面收縮率仿真結果。（a）
$ \psi = 27.75\% $ ，$ \beta = {6^ \circ } $ ；（b）$ \psi = 19\% $ ，$ \beta=4^\circ $ ；（c）$ \psi = 9.75\% $ ，$ \beta = {2^ \circ } $ Figure 15. Simulation results obtained using different sectional shrinkage rates: (a)
$ \psi = 27.75\% $ ,$ \,\beta = {6^ \circ } $ ; (b)$ \psi = 19\% $ ，$ \,\beta=4^\circ $ ; (c)$ \psi = 9.75\% $ ,$ \,\beta = {2^ \circ } $ 
圖 17 臺階角度和半徑尺寸變化圖。（a）
$ \psi = 27.75\% $ ，$ \,\beta = {6^ \circ } $ ；（b）$ \psi = 19\% $ ，$ \,\beta=4^\circ $ ；（c）$ \psi = 9.75\% $ ，$ \beta = {2^ \circ } $ Figure 17. Results obtained with changes in step angle and radius values: (a)
$ \psi = 27.75\% $ ，$ \beta = {6^ \circ } $ ; （b）$ \psi = 19\% $ ，$ \beta=4^\circ $ ; (c)$ \psi = 9.75\% $ ，$ \beta = {2^ \circ } $ 
圖 18 簡單軋齊曲線實例。（a）斷面收縮率43.75%；（b）斷面收縮率19%
Figure 18. Examples of the simple shaping curve: (a) the area reduction is 43.75%; (b) the area reduction is 19%
表 1 斷面收縮率與直角小臺階軋齊展寬角的關系
Table 1. Relationship between the area reduction and stretching angle
Area reductions rate, ψ/% Stretching angle/(°) <10 1–3 10–20 2–4 20–30 4–6 
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