Development of a technological post processor to improve the multi axis bending accuracy of furniture tubular components based on a process FEM simulation ? . – D. Bouzakis 1, ? . Korlos 1, A. Papapanagiotou2, D. Bitzionis 2 1. Laboratory for Machine Tools and Manufacturing Engineering, Mechanical Engineering Deparment, Aristoteles University of Thessaloniki, 54006, Greece Tel. 0030 31 996021, 0030 31 996021, Fax. 0030 31 996059,
[email protected] 2. DROMEAS S.A., Industrial Area of Serres, 62121,Greece
ABSTRACT. Complex metal tube elements of furniture, high quality demands, are formed mainly through digitally guided bending. The bent tube deforms plastically, resulting to inner hardening in its material. The generated inner hardening, the technological and geometrical characteristics of the tube and the characteristics of the bending tool affect the elastic springback of the tube after its bending. Thus, for the achievement of a specific geometry, the tube has to be over-bent, so that through the springback, the desirable geometry of a furniture element is achieved. The goal of the present research is the determination of the springback ratio, by estimating the influence of the various parameters of the bending. For this reason, with the help of the Finite Element Method (FEM), the whole bending procedure was simulated and the calculated results were evaluated and compared with the measured results of bent tube parts, formed by digitally guided bending. By applying the above procedure, an automatic correction of the NC code of a CNC bending machine is intended to achieve of high bending accuracy, with simultaneous assessment of the accuracy of the machine tool itself due to its and the bending tools’limited stiffness. KEYWORDS: tube bending FEM simulation, springback, plastic deformation
1. Introduction Multi axis bending is a modern industrial forming procedure of long metal elements. During this procedure, enhanced productivity and flexibility is achieved, in relation to the conventional forming procedures. A problem, which in this case effects on the quality of the final product, is the tube elastic springback, which leads to deviations related to the desirable geometry. These deviations in the case of sequential bending over the tube part are added making the quality of the procedure not acceptable. Many studies have been done for the deformation of a tube during its unloading [BAN 10], [KAR 11], [BRA 27]. Zhang and You [ZHA 87] have researched the elastic-plastic deformation of an infinite length tube section in pure bending. The analysis was based in energy principales. The created wall thickness change of the tube although, during the bending, is not taken under account. In the same admission Qureshi [QUR 99] based, while Stelson [STE 95] takes under account the wall thickness change, but not the friction that is generated between the tube and the bending tools. In bibliographies an analytical method of describing the finite length tube bending, that includes the wall thickness change, but also takes into consideration the limited stiffness of the bending tools and the friction that develops at the contact areas between them and the tube, is not found. Basic goal of the present study is to improve the accuracy of the multi axis tube bending, determining with an accurate way, the springback angle, so that the necessary test time is reduced and the productivity of the bending machine is increased. Traditionally the springback compensation is achieved through bending tests so that the correct springback compensation angle is found. In this way, though, the stage adjustment time of a bending procedure is increased with an immediate effect on the machine’s production time and generally on the time of a metal furniture production procedure. The developed at the present paper methodology, with the use of the Finite Element Method for the simulation of the part to be bent, as well as the bending procedure, allows the calculation of the springback. With the help of related calculated results and considering deviations due to the limited machine stiffness and existing gaps, an automatic correction of the information of CNC bending machines can be achieved so that the specified geometry of a product is attained.
2. Description of the multi axis bending procedure Multi axis CNC bending machines are widely used in industry and generally have greater accuracy related to conventional bending machines. The basic structure of the tools of such a machine is shown in Figure 1.
Collet B Seam welding Bending former C
Slide Tube X
Z
Clamp Y Figure 1. Basic structure of a typical bending machine During the bending procedure, the collet holds the tube, whose end is ahead. The collet has the ability to rotate about the tube’s axis. The goal of this function is the recognition of the seam position that is determined by an electronic sensor placed in the machine. The collet’s movement achieves the placing of the tube at the desired position so that the seam position is at the desired position according to the bending plane (angle B, Fig. 1). The two parts, the clamp and the bending former move in such a manner so that the tube is placed between them.
Figure 2. Tube bending layout with characteristic magnitudes The moment of the bending the bending former and the clamp, tangential to the tube, begin to rotate until the specified bending angle is achieved, while simultaneously the collet moves feeding the bending tools with the tube. During this whole procedure, the role of the slide is to prevent the formation of curvature behind
the bending former and restricting the bending in the desired area. In this way the tube is forced to change form, according to the curvature of the bending former’s surface, which in this case is circular. After the end of the above procedure the clamp and the bending former release the tube so that it can be ready for a new bending in a new area. Thus, three-dimensional structures are formed, which respond to the designing requests of the various elements.
3. Bending simulation by means of finite element method Multi axis bending, as aforementioned is a three dimensional procedure, difficult to be described by analytical methods, making necessary the use of numerical methodologies for the calculation of the displacements as well as the equivalent stresses that are created during the tube’s deformation. The last few years, the Finite Element Method (FEM) provides great potentials, especially for large material deformations, while in the case of multi axis bending large variation of displacement takes place.
X
Detail A
Z A
Y
Detail B
B Z Tube
X
Y
Bending area
A B Figure 3: Geometric simulation by means of Finite Element Method (FEM) of the tube
In Figure 2 the bending mechanism and the values that describe it, are presented. Initially the tube of outer diameter D, inner diameter d and thickness s is placed over the bending former of radius Rb. The collet holds the left side of the tube, while the slide is situated at a distance L from the bending former. The hidden line represents the initial bending angle a. However, because of the springback, the final bending angle is ar and the quotient between the angle ar to the angle a is defined as the springback ratio K. The FEM model, that was evolved in this case, takes under consideration with large accuracy the bending kinematics. The used interface allows the creation of three-dimensional surfaces in space with the use of three dimensional shell elements with four nodes per element [HAL 91]. Slide Clamp
Bending former
Figure 4: Geometric simulation by means of Finite Element Method (FEM) of the bending tools In Figure 3 is shown the simulated model of the tube. The finite element meshing in the bending area was made closer (Detail B) than the rest of the tube (Detail A).
This happens so that the desired accuracy of the simulation in the area of interest, the bending area, is larger. It is noted that although the seam welding exists on the tube, it is not taken under account into the initial simulation. Tube
Clamp
Slide
A Bending former Detail A Bending former
View A Slide
X A
Y
Z
Clamp
Z
Tube
Y X
Figure 5. Simulation of the tube bending procedure by means of Finite Element Method (FEM) The simulated models of the other bending tools are shown in Figure 4. The meshing here is closer in order to represent the actual bending tools better, resulting to more accurate calculations. This applies especially for the bending former due to his complex geometry. The position of tube and the bending tools at the beginning of the procedure are shown overall in Figure 5. In detail A different views of the critical bending area are also shown. The bending procedure was simulated by boundary conditions. The part of the tube that the collet holds can move only along the X-axis. On the other hand the slide holds its position by locking all degrees of freedom. The movement of the bending former and the clamp were described through motion equations.
During the bending procedure, the clamp holds along with the bending former the tube and the deformation is achieved by their simultaneous rotation, which is realised until the initial bending angle is achieved. During the Finite Element Method description of the various surfaces, interface algorithms were used, which ensure the movement transition from the bending tools to the tube. When the bending moment stops and the clamp is removed from the tube, the material has the tendency to regain its original shape, because of the material
springback. In this way, a small increase of the curvature radius of the bent tube is caused and a small decrease of the bending angle. Thus, for the springback compensation, the tube has to be bent at an angle larger than the desired. The compensation is calculated through the springback ratio. This ratio of the final over the initial (desired) angle is not constant but depends on various factors related to the adjustable procedure conditions, the machine stiffness, the geometric parameters and the mechanical properties of the material. These factors affect each and everyone separately on the value of the springback ratio and for this reason is necessary the determination of the influence they have on this ratio
4. Typical results of the FEM simulation The above analysis was performed for a specific bending case. For the better study of the phenomenon, is necessary the determination of the influence of the further parameters that affect the accuracy of the multi axis bending. Thus, using the model that was created with the help of the Finite Element Method and varying a different factor every time, conclusions are extracted for the procedure’s behaviour. Von Mises equivalent stress of the tube under loading 2 daN/mm 0.00 3.71 7.41 11.1 14.8 18.5 22.2 25.9 29.6 33.3 37.0
Von Mises equivalent stress of the tube under unloading 2 daN/mm 0.00 3.71 7.41 11.1 14.8 16.7 18.5 19.5 22.3 25.0 27.8
Variation of tube wall thickness
Data
Area of tube wall mm 1.62 thickness decrease
Area of tube wall thickness increase
1.70 1.78 1.86 1.94 2.01 2.09 2.17 2.25 2.32 2.40
aR
Rb
a
D = 22 mm Rb = 36 mm s = 2 mm 2
RE = 37 daN/mm o
aR = 118.2
Figure 6. Typical results of the bending simulation
St37 o
a = 120
The simulated models of the other bending tools are shown in Figure 4. The meshing here is closer in order to represent the actual bending tools better, resulting to more accurate calculations. This applies especially for the bending former due to his complex geometry. The position of tube and the bending tools at the beginning of the procedure are shown overall in Figure 5. In detail A different views of the critical bending area are also shown. The bending procedure was simulated by boundary conditions. The part of the tube that the collet holds can move only along the X-axis. On the other hand the slide holds its position by locking all degrees of freedom. The movement of the bending former and the clamp were described through motion equations. 1 St 37 Rb = 65 mm
Springback ratio K = aR / a
0.995
s = 2 mm
0.99
0.985 D = 16 mm
0.98
22 mm
0.975
D
26 mm
0.97
90 120 150 180o Initial bending angle a Figure 7. Effect of the tube’s outer diameter on the springback ratio 0
30
60
210
During the bending procedure, the clamp holds along with the bending former the tube and the deformation is achieved by their simultaneous rotation, which is realised until the initial bending angle is achieved. During the Finite Element Method description of the various surfaces, interface algorithms were used, which ensure the movement transition from the bending tools to the tube. When the bending moment stops and the clamp is removed from the tube, the material has the tendency to regain its original shape, because of the material springback. In this way, a small increase of the curvature radius of the bent tube is caused and a small decrease of the bending angle. Thus, for the springback compensation, the tube has to be bent at an angle larger than the desired. The compensation is calculated through the springback ratio. This ratio of the final over the initial (desired) angle is not constant but depends on various factors related to the adjustable procedure conditions, the machine stiffness, the geometric
parameters and the mechanical properties of the material. These factors affect each and everyone separately on the value of the springback ratio and for this reason is necessary the determination of the influence they have on this ratio Initial shape Final shape
Bending plane I
II Stress
Elastic springback II Bending former’s radius Rb
Elastic springback I
a4 a2a3 Strain
a1
Bending former
1 Springback ratio K = aR / a
0.995 0.99 buckling limit
0.985 0.98 0.975
Rb = 36 mm
St 37
0.97
50 mm 60 mm 65 mm
D = 22mm s = 2mm
0.965 0.96 0.955 0
30
60
90
120
150
o
180
210
Initial bending angle a Figure 8. Effect of the bending former’s radius on the springback ratio
In addition, the radius of the bending former affects the springback ratio as pictured in Figure 8. The stress – strain curve is also presented in the same figure. The smaller the bending former radius is, the larger the material deformation (e1 and e2 respectively) is for the same bending angle. Because during the unloading the slope of the stress – strain curve is the same in both cases, the springback will be larger in the first case, point I, resulting the springback ratio to be smaller when the process is performed with a smaller radius bending former. As shown in the same figure, for larger values of the bending former radius, the scatter of the calculated results of the springback ratio is small (case Rb = 65 mm). However, the opposite applies for smaller values of the bending former (case Rb =
35 mm). This is caused due to the large effect of the tube’s cross-section ovalization for small radius of the bending former. Too small bending former radius causes the tube to start buckling (Figure 9). Bending former diameter Rb = 20 mm
Contact area with bending former
Rb = 65 mm
Buckling Rb
Figure 9. Appearance of buckling in the contact area of the tube with the bending former In any bending case the tube’s cross-section deforms. In Figure 10 the part of the tube that touches the bending former does not change its outer diameter but only increases its wall thickness, while the other part becomes elliptical with simultaneous decrease of the wall thickness. As ovalization is defined the quotient of the difference between the maximum (Dmax) and the minimum (Dmin) diameter of the cross-section, after the bending, over the initial cross-section diameter (D0). The ovalization of the tube’s cross-section is an important factor because it affects negatively on the final form of the cross-section. It decreases the moment of inertia, resulting to the reduction of the strength of the final product (Figure 11). As a limit of the allowed ovalization in the international literature [MOR 97] is defined the percentage of 10%, since larger than that value creates problems not only in the strength of the final product, but creates variations on the springback ratio in relation to the initial bending angle.
smin
Initial shape Final shape
Dmin
Do smax Dmax
Bending plane
Figure 10. Initial and final shape of the tube cross-section 25
St 37 D = 22 mm s = 2 mm
Ovalization
% 15 10 5
R b = 36 mm 50 mm 60 mm 65 mm
ovalization limit
0 0
20
40
60
80 100 120 140 160 180 Initial bending angle a Figure 11. Effect of the bending former radius on the final tube cross-section
o
200
5. Results of the experimental–analytical determination of the springback ratio For the determination of the stress – strain curve a new procedure was used and is based on two steps [BOU 96a], [BOU 99b] (Figure 12). The first step concerns the imprinting on the tube and comparison with theoretic simulation of the procedure by the means of Finite element method. The whole procedure is based on the fact that the shape of the imprint that is taken depends on the material, that is, the springback [BOU 96b].
140 120 100 Stress
Seam welding material 80 Tube material 60 40 20
Chemical composition C 0.07% Mn 0.31% Fe 99.62%
tube material: St37
0 0
0.05
0.1
0.15
0.25
0.2
0.3
0.35
Strain Figure 12. Stress – strain curve calculated with a new procedure For the validity examination of the calculated with the Finite Element Method results, experiments were conducted with the use of a five-axis CNC bending machine (Figure 13).
? B C
? ?
Ammeter Controller
Motor
Figure 13. CNC tube bending machine The experimental measurements of the bending moment during the bending were performed with the arrangement shown the above figure. The whole procedure was based in the recording of the current intensity with an ammeter. In this way, by also knowing the machine’s voltage, the bending moment was derived for various
Bending moment
bending angles. The results are presented in Figure 14. Comparing the experimental with the calculated results it is found that they converge. The small deviation that is observed is owed to the existence of slippage in the bending machine 90 St37 Nm s = 2 mm measured 70 D = 22 mm R b = 65 mm 60 calculated
50
Bending former
M
40 30 20 10 0
0
30
120o
60 90 Initial bending angle
150
Figure 14. Comparison of the experimental and calculated bending moment 1
tube elastic springback
Springback ratio K = aR / a
0.99
calculated
required correction
0.98 0.97
measured 0.96
machine-tool-holders gaps and deflections
0.95 0.94
St37 s = 2 mm D = 22 mm Rb = 65 mm
0.93 0.92
0
30
60
90
120
o
150
180
Initial bending angle Figure 15. Comparison of the calculated and measured tube elastic springback ratios
The measurements of the tube parts’ final bending angles were performed in a CNC three-axis milling machine with the use of a touch probe. The tube is stabilised on the machine’s table and the touch probe is placed in such a manner, so that it is tangent to the tube’s surface. At the machines display, are shown every moment the co-ordinates of the tool’s position, which are recorded to a file. The above procedure was repeated several times recording point co-ordinates, so that the contour of the tube is formed. Knowing the initial bending angle adjustment and the co-ordinates of the contour, the final resultant bending angle is calculated and the springback ratio is determined. 4.5 St37 s = 2 mm D = 22 mm Rb = 65 mm
Correction of the bending angle
o
4
3.5 3 2.5
S 1 + 2 required correction according to measurements
2 1.5 1
(1.21)
0.5 0
1 correction due to calculated springback
correction due to determined 2 machine-tool-holder gaps and deflections
(1.28)
o 90 120 150 Final bending angle Figure 16. Correction of the NC machine code for various bending angles
0
30
60
180
The bending angle increase leads generally to an increase of the springback ratio [BOU 99c]. For large bending angles, the springback ratio converges to one, which is the ideal value of this ratio. In this case, adjustment of an unlimited stiffness machine for a specific bending angle will lead to the same angle to the bent part. Generally, though, due to the limited machine and the bending tool stiffness, as well as the springback of the tube part, a correction is necessary so that the desired bending angle is achieved (Figure 15). The correction angles that are determined based on the calculations and measurements on the tube parts are shown in the Figure 16. The distance between the relative curves represents the deviation, due to the deformation of the bending machine and the bending tools. It is clearly shown that the difference between the two corrections (experimental and calculated) is constant. This is result is extremely important for the correction of the NC code.
6. Development of a technological post processor For the automatic correction of the NC code of the tube-bending machine a technological post processor was developed. The aim is to reduce the time needed for the achievement of the desired geometry of the final product. Thus, with the use of a user friendly software is given the ability for the convenient correction of the NC code.
Figure 17. Correction of the NC code by means of a technological post processor In Figure 17 is presented the developed procedure for the compensation of the springback angle and the correction of the NC code. Knowing the geometry of the product, by using CAD/CAM software, the initial NC code is extracted. Next, the user loads the NC code from a specific file and inserts it in the technological post processor. The different bending parameters are selected from a list. The effect that the parameters have on the springback has already been calculated with the above procedure and corrected with experimental results. Finally, the corrected NC code is presented in electronic form so that it can be stored and used for the bending. A modified bending angle is presented highlighted.
7. Conclusions Multi axis bending is a forming procedure, among others, of metal tubes that is used widely in the industry, since it is able to create complex three-dimensional
structures. A problem, which in this case effects on the quality of the final product, is the springback, which leads to deviations related to the desirable geometry. Aiming the development of technological post processors for the automatic correction of the NC code of a CNC multi axis bending machine of structural furniture elements, in the present study was researched the influence of various parameters of the bending procedure over the resultant dimension accuracy due to the material springback. For this reason a simulated model was created with the Finite Element Method, while simultaneously experiments were held for the accuracy of the above procedure, which will be used in the continuance of research studies for the correction of the machine’s NC code, so that the desired geometry is achieved.
8. References [QUR 99] AL-QURESHI, H. A., “Elastic-plastic Analysis of Tube Bending”, International Journal of Machine Tools & Manufacture, 39 pp. 87-104, 1999. [BOU 99a] BOUZAKIS, K. - D., KORLOS, A., “Effect of the machining parameters during multi axis bending of tubes, structural elements of furniture, over the springback of the material and the bending accuracy”, Proceedings of the 5th conference, presenting the research activities of the Laboratory for Machine Tools and Manufacturing Engineering, pp. 261-273, 1999. [BOU 99b] BOUZAKIS, K. - D., VIDAKIS, N., “ Superficial plastic response determination of hard isotropic materials using ball indentations and a FEM optimisation technique”, Materials characterisation, Vol. 42, pp. 1-12, 1999. [BOU 99c] BOUZAKIS, K. - D., “Manufacturing processes with material deformation”, Laboratory for Machine Tools and Manufacturing Engineering, 1999. [MOR 97] MORI, SH., MANABE, K., “Experimental analysis of the flattening of the cross section, the springback and the moment of the clad tubes in uniform bending”, Journal of Materials Processing Technology, Vol. 66, pp.270 – 276, 1997. [BOU 96a] BOUZAKIS, K. - D., VIDAKIS, N., “Determination of plastic behaviour of hard materials using the Rockwell B test and a FEM simulation”, Proceedings of the 4th conference, presenting the research activities of the Laboratory for Machine Tools and Manufacturing Engineering, pp. 89-101, 1996. [BOU 96b] BOUZAKIS, K. - D., VIDAKIS, N., LONTOS, A., “ A CAE supported ball indentation method for the stress strain curves of hard materials, such as hardened and high speed steels”, Advanced Technology of Plasticity, Proceedings of the 6th ICTP, Vol II, pp. 1239-1300, 1999.
[STE 95] STELSON, K. A., ”On the Plastic Deformation of a Tube During Bending”, Transactions of the ASME, Vol. 117, pp 494-500, 1995. [HAL 91] HALLQUIST, J., LS-DYNA User Manual, 1991. [ZHA 87] ZHANG, L. C., YU, T. X., “An Investigation of the Brazier Effect of a Cylindrical Tube under Pure Elastic-plastic Bending”, Int. J Pres. Ves & Piping, Vol. 30, pp. 77-86, 1987. [BRA 27] BRAZIER, L. G., “On Flexure of Thin Cylindrical Shells and Other Thin Sections”, Proc. R. Soc. London, Ser. A, Vol. 116, pp. 104-114, 1927 [KAR 11] KARMAN, TH. V., “Ueber die Formaenderung Dunnwaendiger Roehre, insbesondere federner Ausgleichsroehre”, VDI Zeitschrift, Vol. 55, pp. 1889-1895, 1911. [BAN 10] BANTLIN, A., “Formaenderung und Beanspruchung federner Ausgleichsroehren,” VDI Zeitschrift, Vol. 54, pp. 43-49, 1910.
