Design of a fuzzy controller to prevent wrinkling during rotary draw bending

Linda Borchmann. Forming Technology, Institute of Production Technologies at the University of Siegen, Breite Strasse 11, 57076 Siegen, Germany Corresponding author: linda.borchmann@uni-siegen.de Dominique Schneider. HJS Emission Technology GmbH & Co. KG, Dieselweg 12, 58706 Menden, Germany Bernd Engel. Forming Technology, Institute of Production Technologies at the University of Siegen, Breite Strasse 11, 57076 Siegen, Germany

Rotary draw bending (RDB) is preferably used for small wall thicknesses and small bending radii. With appropriate tool and machine technology, bending ratios of less than 1 can be represented.The tool assembly of the RDB is shown in Fig. 1. The tools bend die (1), clamp dies (2.1, 2.2) and pressure die (3) are necessary for the bending. Bending mandrel (4), wiper die (5) and collet (6) are used optionally.
The tube is clamped with the inner (2.1) and outer (2.2) clamp die in order to transfer the rotation from the machine to the tube. [6] The bending moment is applied by supporting the tube on the pressure die (3). The collet (6) clamps the tube at its end. The bending mandrel (4) supports the inner wall of the outer bend and thus reduces the cross-sectional deformation. To counteract wrinkling, a wiper die (5) can be used in addition to the bending mandrel.  [4] and (b) influence of the pr ocess [4] and (b) influence of the pressur essure die inf e die infeed and the collet eed and the collet speed on the f speed on the formation of wrinkles [5]. ormation of wrinkles [5].
Practical experiments show that the process parameters pressure die infeed and collet speed have a significant influence on the wrinkles [5]. The wrinkle height is reduced when the pressure die is moved towards the tube, see Fig. 1 b). In case of contact between pressure die and tube, a positive infeed causes an increase in force. If the collet speed is reduced so that tensile stresses are superimposed, this can also lead to a reduction in wrinkle height.

F Fuzzy uzzy-Contr -Control ol
In forming technology, the change in tool forces and axis paths triggers a non-linear change in the material flow in the bending component. According to [3,7,10], the effort to solve a nonlinear control problem can be significantly reduced by using fuzzy logic. Fuzzy controllers are robust and can be realized with a comparatively small amount of data [8].

Application case Application case
The central elements of a fuzzy controller are the fuzzy sets of inputs and outputs and the control base [17]. To determine the fuzzy sets of the input values, the measurement results of the bending tests are evaluated according to [4]. A laser line sensor and a load cell on the wiper die as well as a tension-compression force sensor on the mandrel  (LLT 2900-50 2D  T 2900-50 2D, short w  , short wa av ve laser f  e laser for pr  or precise and stable cont  ecise and stable contour our  measur measurement ement, sampling fr , sampling frequency: 5 Hz) of the Micr equency: 5 Hz) of the Micro-Epsilon measur o-Epsilon measurement t ement technology echnology GmbH & Co. K GmbH & Co. KG G From the measured data of the laser line sensor, wrinkle heights are determined, which serve as input variables for the controller. The measured wrinkle heights of the line sensor consist of the actual wrinkle height and a displacement which is caused by the mobility of the tube due to a certain clearance between the tube and the tools. The maximum value of the determined wrinkle heights defines the wrinkle height of the respective time step used for evaluation (see Fig. 2). To generate the fuzzy sets, the wrinkle evaluation factor ΩVDI3431 was determined for each sample of the experimental plan according to [18] and to the procedure described in [5]. The wrinkle evaluation factor is determined from the topographic height profile of the inner tube bend, whereby a comparison of the target and actual contour takes place [18]. All tests for which ΩVDI3431 = 0 are valid are assigned to the category "no wrinkles". The tests in the category "small wrinkles" have a wrinkle evaluation factor of 0 < ΩVDI3431 < 0.002. Correspondingly, the bending tests in the category "large wrinkles" have been assigned a rating of 0.002 ≤ ΩVDI3431. During the tests, the longitudinal force of the mandrel was recorded over the bending angle. The derivation of the force course i.e. the course of force change has the ability to make well-founded statements about the occurrence of wrinkles. The courses of force change are subject to fluctuations. In order to reduce the fluctuations while preserving the characteristic course over time, the evaluation of every tenth data point has proven to be appropriate.
Typically, the force progression of a wrinkle-free tube has force increases and areas with an approximately constant force, as shown in Fig. 3. During the bending process, the mandrel elements are individually "taken along" by the tube, whereby the mandrel longitudinal force increases and then reaches a plateau. During the withdrawal of the mandrel 5°b efore the end of the bend, the longitudinal force of the mandrel decreases.

Pr Production rules and char oduction rules and charact acteristic diagr eristic diagrams ams
The empirical values from the bending tests according to [4] serve as the foundation for the rule base which comprises 27 rules. An extract from the rule base is shown in Table 1. In order to avoid crack formation, the adjustment of the setting values with regard to wrinkling is only made as much as necessary and as little as possible.
T Tabelle 1. Extr abelle 1. Extract fr act from the pr om the production rules de oduction rules dev veloped on the basis of the e eloped on the basis of the ev valuation of pr aluation of practical bending t actical bending tests. ests.
Using collet speed as a manipulated variable to prevent the occurrence of wrinkles is generally more critical for the tube with regard to crack formation if tensile forces are induced. Therefore the use of the pressure die infeed is to be preferred, see also  As soon as the fuzzy controller has calculated a required infeed with the help of all input variables, DIAdem determines the new pressure die position to be set in connection with the current position of the pressure die. DIAdem then causes the cylinder of the pressure die axis to move to the new target position. This overall control process is run through until a termination criterion is met (e.g., reaching a specified bending angle).
Design of a fuzzy controller to prevent wrinkling during rotary draw bending 2742/6

Experimental pr Experimental procedur ocedure e
Practical tests were carried out on the TN 120 bending machine from Tracto Technik GmbH. The bending angle is set to 90°for each test in order to ensure comparability. The specimens have the material X5CrNi18-10 (1.4301) with an outer diameter of 40 mm and wall thicknesses of 2 mm, 1 mm and 0.8 mm. The pressure die was moved in transverse direction a normal force of 10 kN on the tube. In the longitudinal direction, the pressure die was adjusted to move with the tube to minimize the relative speed. The wiper die was positioned conventionally. The tube end was clamped in the inner and outer clamp dies.
Since the TN 120 bending machine does not allow any intervention in the collet axis, only the manipulated variablepressure die infeed was adjusted by the controller. The output values calculated by the controller for the collet axis were recorded and evaluated. The experimental setup can be seen in Fig. 7. Fig. 7.R Fig. 7.Repr epresentation of the e esentation of the experimental setup. The numbering is the same as in Fig. 1 a). xperimental setup. The numbering is the same as in Fig. 1 a).
Similar to the bending tests according to [4], the sensors described in Section 2.1 were installed. The laser line sensor is placed behind the holder of the wiper die so that the laser line strikes the tube surface in the area of the wiper die. The wiper die and its holder are provided with a slot in longitudinal direction of the tube, as shown in Fig. 7. To position the laser line close to the forming zone, the sensor is placed at an angle α > 30° to the longitudinal axis of the tube.
To validate the fuzzy control, the semi-finished product with a wall thickness of 1 mm was first bent without activating the control, see also Fig. 8. In the subsequent bends with closed-loop control, adjustments were made to the transmission frequencies, to the speed of the pressure die and to integrated force and displacement limits in order to avoid collisions and sensor damage. When three successive tube bends were bent without wrinkles (see also Fig. 9), the control was transferred to the wall thicknesses 0.8 mm and 2 mm without making any further changes to the fuzzy control except for the maximum limit of the pressure die travel spd. It was increased from 1.0 mm to 1.3 mm (see Table   2). The tube bends were scanned with the Faro Edge 2.7 M coordinate measuring arm with FARO Laser Line Probe ES and processed with the software Poly-Works 2016. The evaluation was done with the software MATLAB R2016b according to [1]. The higher the wrinkle evaluation factor, the more the actual contour of the inner arc deviates from the target contour due to the resulting wrinkles.

R Results esults
In order to evaluate the performance of the controller in advance, first "theoretical" experiments are carried out. The input variables are sampled and the output variables are calculated by the controller, but the output variables are not implemented on the tools (controller does not intervene in the process). This allows to assess the results of the controller at different wrinkle levels. The bending of the semi-finished product with a wall thickness of 1 mm shows an increasing course of the wrinkle height, see Fig. 8 a). The course of the mandrel force change is mostly in a range that does not indicate wrinkles. The course of the force change of the wiper die detects wrinkles from a bending angle of approx. 65°. The input variables are converted by the fuzzy controller into manipulated variables for the pressure die infeed. The result is the increasing course of the pressure die infeed Δspd shown in Fig. 8 b). The manipulated variable, change of collet speed factor, remains largely unchanged, as it is dominated by the mandrel force change, which does not indicate a significant course for wrinkles. When bending the semi-finished product with a wall thickness of 1 mm with activation of the fuzzy control, the pressure die is actively fed during the bending process, see Fig. 9. The fuzzy controller determines by which amount (Δspd) the pressure die is to be moved towards the tube. Figure 9 shows that the wrinkle height always shows wrinkles for a short period of time, but then returns to the wrinkle-free area. The courses of the force changes do not indicate wrinkles. The progression of the pressure die feed matches the input value, wrinkle height. The pressure die is repeatedly advanced by a small amount, but then returns to the wrinkle-free area.  In summary, the most important bends of the test series are listed in Table 2. The wrinkle evaluation factor shows that wrinkle-free tube bends were bent by the automatic adjustment of the pressure die by the fuzzy controller without the operator having to make adjustments to the bending program.
T For the bends of the semi-finished product with a wall thickness of 0.8 mm, larger infeeds were required than for the wall thickness of 1 mm. The input variable, wrinkle height, dominated in this bending task similar to the 1 mm wall thickness. In the bends with a wall thickness of 2 mm, which are thick-walled tubes, the wrinkles were detected less by the laser line sensor, but mainly by the course of the normal force change of the wiper die.

Conclusion Conclusion
In this manuscript, a fuzzy control is presented that uses the tools pressure die and collet to reduce wrinkles without the need for operator intervention in the process. The automation optimizes the manipulated variables in such a way that the formation of wrinkles is just avoided, which reduces the acting forces and thus the wear of the machine to a minimum. At the same time, these optimal conditions significantly reduce the probability of cracking.
Thin-walled tubes with an outer diameter of 40 mm and wall thicknesses of 1 mm and 0.8 mm formed wrinkles in front of the bend area. This area could be detected by the in situ measurement of the tube contour by means of a laser line sensor through a narrow slot in the wiper die. This input variable dominated for the thin-walled tubes. Wrinkle-free tubes could be produced using fuzzy controllers.
Thick-walled tubes with an outer diameter of 40 mm and a wall thickness of 2 mm formed wrinkles in the transition plane. These wrinkles were detected early by the force change of the wiper die. Wrinkles in the comparatively thick tube wall seem to have applied enough force to cause a force change at the wiper die. Wrinkle-free tube bends could be produced by means of fuzzy control.
The input variable, mandrel force change, detected wrinkles in the bend area. According to the fuzzy control, this has an influence on the collet speed as manipulated variable. For software reasons, the collet speed could not be adjusted automatically on the bending machine during the validation tests. However, the recorded target values of the collet Design of a fuzzy controller to prevent wrinkling during rotary draw bending 2742/10