METHOD FOR PRECISION FORMING BY CONTINUOUS FREE BENDING

Abstract

A method for precision forming by continuous free bending starts with establishing a correlation equation of a continuous axis f(x) to a bending radius R and determining a bending radius R at a real-time location in the axis. Based on the free bending technique, the method further involves establishing a correlation model of a real-time bending radius R of a tube to an eccentric distance U of a bending die and hence correlations of the equation of the axis to free bending parameters, and constructing a complete correlation model among f(x), R, U, and t based on a relational equation of an eccentric distance U to movement time t of the bending die to enable the precision forming of a complex component by continuous bending. Accordingly, the production efficiency can be improved.

Claims

1. A method for precision forming by continuous free bending, comprising the following steps: (1) extracting a curved axis from a bent component, establishing a correlation equation of the continuous curved axis f(x) to a bending radius R, and determining a bending radius R at a real-time location in the curved axis; (2) establishing a correlation model of a bending radius R to an eccentric distance U of a bending die to obtain correlations of f(x) to bending parameters; and (3) constructing a complete correlation model among f(x), R, U, and t based on a relational equation of an eccentric distance U to movement time t of the bending die to enable the precision forming of the bent component by continuous free bending.

2. The method for precision forming by continuous free bending according to claim 1, wherein the f(x) is a parabolic axis function.

3. The method for precision forming by continuous free bending according to claim 1, wherein the correlation equation of f(x) to a bending radius R in step (1) is expressed as: $R_n=\frac{{\left(1+{f\left(x\right)}^2\right)}^{\frac{3}{2}}}{\left|{f\left(x\right)}^{\text{"}}\right|},$ wherein n represents a point n in the curved axis, while R.sub.n a bending radius corresponding to the point n.

4. The method for precision forming by continuous free bending according to claim 1, wherein the correlation model of a bending radius R to an eccentric distance U of a bending die in step (2) is expressed as: $t_{sn}=\frac{\Delta S_n}{v},$ $t_{\mathrm{kn}}=\frac{\pi \times R_n\times \arcsin \frac{A}{R_n}}{180°\times v};$ $U_n=R_n-R_n\cos \frac{v{t}_{k𝔫}\times 180}{\pi \times R_n}+\tan \frac{{\mathrm{vt}}_{\mathrm{kn}}\times 180}{\pi \times R_n}\left(A-R_{𝔫}\sin \frac{v{t}_{k𝔫}\times 180}{\pi \times R_n}\right),$ wherein U.sub.n represents an eccentric distance corresponding to the point n, while A a distance from a front end of a guide mechanism to the center of the bending die, v an axial feed velocity of a tube, t.sub.sn a time taken for forming of an arc length ΔS.sub.n, and t.sub.kn a time taken for the bending die to reach an eccentric distance U.sub.n.

5. The method for precision forming by continuous free bending according to claim 2, wherein n is 6.

6. The method for precision forming by continuous free bending according to claim 2, wherein the correlation equation of f(x) to a bending radius R in step (1) is expressed as: $\begin{array}{cc}{R}_n=\frac{{\left(1+{f\left(x\right)}^{\text{'}2}\right)}^{\frac{3}{2}}}{.Math.{f\left(x\right)}^{\text{"}}.Math.},& \end{array}$ wherein n represents a point n in the curved axis, while R.sub.n a bending radius corresponding to the point n.

7. The method for precision forming by continuous free bending according to claim 2, wherein the correlation model of a bending radius R to an eccentric distance U of a bending die in step (2) is expressed as: $t_{\mathrm{sn}}=\frac{\Delta S_n}{v},$ $t_{\mathrm{kn}}=\frac{\pi \times R_n\times \arcsin \frac{A}{R_n}}{{180}^{\circ }\times v};$ $U_n=R_n-R_n\cos \frac{{\mathrm{vt}}_{\mathrm{kn}}\times 180}{\pi \times R_n}+\tan \frac{v{t}_{\mathrm{kn}}\times 180}{\pi \times R_n}\left(A-R_n\sin \frac{v{t}_{\mathrm{kn}}\times 180}{\pi \times R_n}\right),$ wherein U.sub.n represents an eccentric distance corresponding to the point n, while A a distance from a front end of a guide mechanism to the center of the bending die, v an axial feed velocity of a tube, t.sub.sn a time taken for forming of an arc length ΔS.sub.n, and t.sub.kn a time taken for the bending die to reach an eccentric distance U.sub.n.

8. The method for precision forming by continuous free bending according to claim 3, wherein the correlation model of a bending radius R to an eccentric distance U of a bending die in step (2) is expressed as: $t_{sn}=\frac{\Delta S_n}{v},$ $t_{\mathrm{kn}}=\frac{\pi \times R_n\times \arcsin \frac{A}{R_n}}{180^{\circ }\times v};$ $U_n=R_n-R_n\cos \frac{v{t}_{\mathrm{kn}}\times 180}{\pi \times R_n}+\tan \frac{v{t}_{kn}\times 180}{\pi \times R_n}\left(A-R_n\sin \frac{v{t}_{k𝔫}\times 180}{\pi \times R_n}\right),$ wherein U.sub.n represents an eccentric distance corresponding to the point n, while A a distance from a front end of a guide mechanism to the center of the bending die, v an axial feed velocity of a tube, t.sub.sn a time taken for forming of an arc length ΔS.sub.n, and t.sub.kn a time taken for the bending die to reach an eccentric distance U.sub.n.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0017] FIG. 1 is a flowchart of a method for precision forming of a tube by continuous free bending.

[0018] FIG. 2 is a schematic diagram analytically illustrating a parabolic axis of a complex component.

[0019] FIG. 3 is a schematic diagram analytically illustrating a custom axis of a complex component.

[0020] FIG. 4 is a schematic diagram illustrating simulation of three-dimensional free bending of a tube component.

DETAILED DESCRIPTION

Example 1

[0021] As shown in FIG. 1 to FIG. 4, a complex bent component having a parabolic axis f(x).sub.1=x.sup.2 (−3≤x≤3) is taken for example in this Example. Firstly, a curved axis is extracted from the complex bent component. In the axis, n points are designated, and each point corresponds to a single bending radius R.sub.n, and corresponds to a single eccentric distance U.sub.n and time t.sub.n during free bending. That is, at each time, there is a corresponding eccentric distance present to control the free bending forming of the parabolic component. In this Example, 6 control points are chosen in the parabolic axis. The coordinates of the 6 control points are determined according to the function f(x).sub.1=x.sup.2 to be P1 (−3,9), P2 (−2,4), P3 (−1,1), P4 (1,1), P5 (2,4), and P6 (3,9), and each corresponding bending radius R.sub.n is calculated. An eccentric distance and a movement velocity of a bending die are calculated by analytic equations for the free bending forming process, whereby a movement locus is determined. The free bending die is then allowed to move along the planned locus to form the complex component having a parabolic axis.

[00003]$R_n=\frac{{\left(1+{f\left(x\right)}^{\text{'}2}\right)}^{\frac{3}{2}}}{|f\left(x\right)\text{"|}}$$t_{s𝔫}=\frac{\Delta S_n}{v},$$t_{kn}=\frac{\pi \times R_n\times \arcsin \frac{A}{R_n}}{180^{\circ }\times v},$$U_n=R_n-R_n\cos \frac{v{t}_{kn}\times 180}{\pi \times R_{𝔫}}+\tan \frac{v{t}_{\mathrm{kn}}\times 180}{\pi \times R_{𝔫}}\left(A-R_n\sin \frac{v{t}_{kn}\times 180}{\pi \times R_n}\right)$

[0022] The bending radius of the six points are calculated to be R.sub.1=1125.3 mm, R.sub.2=350.4 mm, R.sub.3=55.9 mm, R.sub.4=55.9 mm, R.sub.5=350.4 mm, and R.sub.6=1125.3 mm, respectively, and the eccentric distances and times are obtained accordingly as follows: t.sub.s1=7.07 s, t.sub.k1=3.0 s, U.sub.1=0.400071131 mm; t.sub.s2=5.10 s, t.sub.k2=3.004 s, U.sub.2=1.288082569 mm; t.sub.s3=3.17 s, t.sub.k3=3.165 s, U.sub.3=8.713600553 mm; t.sub.s4=3.17 s, t.sub.k4=3.165 s, U.sub.4=8.713600553 mm; t.sub.s5=5.10 s, t.sub.k5=3.004 s, U.sub.5=1.288082569 mm; and t.sub.s6=7.07 s, t.sub.k6=3.0 s, U.sub.6=0.400071131 mm. The free bending forming of the parabolic axis is controlled precisely based on the calculated real-time eccentric distances and times. The simulated result is illustrated in FIG. 4, in which a spherical bearing 1, the bending die 2, a guide mechanism 3, a hold-down mechanism 4, a tube 5, and a feed mechanism 6 are shown.

Example 2

[0023] A custom continuous curve f(x).sub.2 is taken for example herein. Firstly, a curved axis is extracted from a complex bent component, with a bending radius varies with increasing arc length. In particular, the bending radius will increase or decrease by 20 mm for each increase of 50 mm in arc length. At an initial point of the extracted curve, the bending radius is 260 mm. In the axis, n points are designated, and each point corresponds to a single bending radius R.sub.n, and corresponds to a single eccentric distance U.sub.n and time to during free bending. That is, at each time, there is a corresponding eccentric distance present to control the free bending forming of the complex component. For example, 6 control points are chosen in the custom complex axis. The bending radii R.sub.n of the 6 control points are determined according to the function f(x).sub.2 to be R.sub.1=260 mm, R.sub.2=240 mm, R.sub.3=220 mm, R.sub.4=200 mm, R.sub.5=180 mm, and R.sub.6=160 mm, respectively. An eccentric distance and a movement velocity of a bending die are calculated by analytic equations for the free bending forming process, whereby a movement locus is determined. The free bending die is then allowed to move along the planned locus to form the complex component having a custom continuous curve.

[00004]$R_n=\frac{{(1+{f\left(x\right)}^{\text{'}2}\}}^{\frac{3}{2}}}{|f\left(x\right)\text{"|}}$$t_{\mathrm{sn}}=\frac{\Delta S_n}{v},$$t_{\mathrm{kn}}=\frac{\pi \times R_n\times \arcsin \frac{A}{R_n}}{180^{\circ }\times v},$$U_n=R_n-R_n\cos \frac{v{t}_{\mathrm{kn}}\times 180}{\pi \times R_{𝔫}}+\tan \frac{v{t}_{k𝔫}\times 180}{\pi \times R_n}\left(A-R_n\sin \frac{v{t}_{\mathrm{kn}}\times 180}{\pi \times R_n}\right)$

[0024] By calculation, the eccentric distances and times are obtained as follows: t.sub.s1=5 s, t.sub.k1=3.007 s, U.sub.1=1.88238105 mm; t.sub.s2=5 s, t.sub.k2=3.009 s, U.sub.2=2.055052734 mm; t.sub.s3=5 s, t.sub.k3=3.011 s, U.sub.3=2.262800196 mm; t.sub.s4=5 s, t.sub.k4=3.014 s, U.sub.4=2.517601851 mm; t.sub.s5=5 s, t.sub.k5=3.018 s, U.sub.5=2.837662091 mm; and t.sub.s6=5 s, t.sub.k6=3.023 s, U.sub.6=3.252052344 mm. The free bending forming of the custom axis f(x).sub.2 is controlled precisely based on the calculated real-time eccentric distances and times.