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Stiffness of multipoint servo presses: Mechanics vs. control
G Model
CIRP-1611; No. of Pages 4 CIRP Annals - Manufacturing Technology xxx (2016) xxx–xxx
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er . com /ci r p/ def a ult . asp
Stiffness of multipoint servo presses: Mechanics vs. control Peter Groche (1)*, Florian Hoppe, Julian Sinz Institute for Production Engineering and Forming Machines, Technische Universita¨t Darmstadt, Darmstadt, Germany
A R T I C L E I N F O
A B S T R A C T
Keywords: Stiffness Control Servo press
The accuracy of metal-formed products is strongly affected by the stiffness of the machine used. Therefore, huge efforts to increase moments of inertia and reduce backlash were made in conventional press design. Multipoint servo presses allow for an alternative approach: increasing the position accuracy with respect to the press stroke direction and the ram tilting by controlling deflections. Necessary models and parameters as well as the effectiveness of such a control are discussed in this paper. The proposed method is validated by experiments using a 3D servo press. ß 2017 Published by Elsevier Ltd on behalf of CIRP.
1. Introduction Presses actuate tools along predefined paths. As they are heavily loaded, accurate positioning is challenging. Inaccuracies can cause dimensional deviations from the required product geometry or tool damage. Possible reasons for the inaccuracies are varying conditions of the press or the tools as well as load variations caused by fluctuating process conditions, e.g., temperature, material, and lubrication. Due to the elastic behavior of the press components, varying loads lead to different deflections of the press. High stiffness values are desirable, since they reduce deviations from the targeted tool paths. Therefore, stiffness is one of the most important characteristics of presses [1]. High values should guarantee ram parallelism and accurate tool guidance. Two approaches are commonly known to influence the stiffness of presses. These are the adaption of the mechanical press design on the one hand [2], and the active compensation of the ram deflections using a closed-loop control on the other hand. Different frame and gear drive designs vary with respect to the achievable press stiffness [1]. One important design restriction in the optimization of the mechanical press stiffness is the necessary accessibility of the working space [3]. Increasing stiffness by control requires active components and methods for stiffness identification. So far, measurements of press stiffness focus on the stroke direction and the rotational stiffness around the horizontal axes of the ram [4]. Although complete 6 by 6 compliance matrices have already been identified in experiments for both hydraulic [5] and mechanical [6] presses, only single operation points of a press have been considered. This follows DIN 55189 [4], which suggests that the compliance has to be measured at the bottom dead center. Numerical press models, e.g., finite element models, are often used in press design to evaluate the
* Corresponding author. E-mail address: [email protected] (P. Groche).
press behavior, but can only be used offline due to their high computing time. Even though reduced order models are required for control, their effectiveness for the stiffness determination has still to be examined. The possibility to control the ram position and thus to influence the stiffness of the press has been enabled by servo presses through a feedback of the slide positions [7]. Servo presses feature an adjustable bottom dead center. Therefore, position-dependent values of the press compliance are necessary for a position control. Since a direct measurement of the ram position is often impracticable during forming processes, an observer might be required. In case of using a single point servo press, only the stiffness in stroke direction can be controlled. For multipoint servo presses with several independent drive systems, the tilting of the ram can also be manipulated, thus boosting the rotational stiffness. Due to the risk of press damage, ram tilting has to be compensated in conventional spindle-driven multipoint servo presses with respect to the guidance. Contrary to this, the 3D Servo Press [8] shown in Fig. 1 is equipped with special linkage mechanisms and ram bearings resulting in two additional degrees of freedom in the ram movement. Thus, this press type is less sensitive to ram tilting and position control is not limited by the ram bearings. Assuming the press stiffness to be controllable corresponding to the driven degrees of freedom of the ram, the effect of a closed-loop control on the stiffness values is of high interest. In the present study, the compliance of the 3D Servo Press is determined for different operation points. In addition, a complete 6 by 6 compliance matrix is evaluated with and without position control of the ram. The effect of control, measurement position and the usage of adequate observers will be compared by means of the measured compliance matrices. With that, the coupling behavior between the controlled and uncontrolled 3D Servo Press is investigated and the dependency between the linking mechanism’s position of the 3D Servo Press and its stiffness is shown.
http://dx.doi.org/10.1016/j.cirp.2017.04.053 0007-8506/ß 2017 Published by Elsevier Ltd on behalf of CIRP.
Please cite this article in press as: Groche P, et al. Stiffness of multipoint servo presses: Mechanics vs. control. CIRP Annals Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.053
G Model
CIRP-1611; No. of Pages 4 P. Groche et al. / CIRP Annals - Manufacturing Technology xxx (2016) xxx–xxx
2
positions u, an efficient simulation technique is required. For this purpose, a multibody simulation based on a mixed truss and beam model has been developed for the 3D Servo Press and implemented in Matlab. All bodies of the linkage mechanism have been modeled with their corresponding cross-sectional area, material parameters and geometrical moment of inertia. The connections between the bodies are modeled as frictionless springs whose stiffness values represent their bearing behavior. As outlined by Chodnikiewicz [6] and Arentoft [10], the press deflection behavior can be described by measuring a 6 by 6 compliance matrix L. This matrix describes the dependency between the translational and rotational ram positions x and the process loads l such that Dx = Ll. Due to the variability of the linkage mechanism of the 3D Servo Press, a nonlinear compliance matrix L(u) is considered. The elements lij of the compliance matrix 2 3
l11 l12 l22 l32 l42 l52 l61 l62
6 l21 6 6 l31 LðuÞ ¼ 6 6 l41 6 4 l51
Fig. 1. Linkage mechanism of the 3D Servo Press.
2. Mechanics In the following, the press used for the investigations as well as the compliance model and test setup will be explained. 2.1. 3D Servo Press Multipoint servo presses driven by multiple servo motors can perform an asynchronous movement. The 3D Servo Press has three independent drive systems and special bearings, which allow intentional tilting up to 38 in ux and uy. As shown in Fig. 1, three eccentric drives in a 1208 arrangement and two spindle motors allow for a combined actuation of the ram. Besides three spatial degrees of freedom at the ram z, ux, uy (stroke, pitch, roll), adjustable mounting height and stroke length are provided. To control the ram position, the eccentric drives wecc,i as well as the upper spindle xSU and lower spindle xSL work together simultaneously. Therefore, the press system can be described by the drive positions as press input u, the ram positions x as press output 2 3 2 3 x ’ecc;1 6 y 7 6 ’ecc;2 7 6 7 6 7 6 z 7 6 7 7 x¼6 6 ux 7; u ¼ 6 ’ecc;3 7: 4 xSU 5 6 7 4 uy 5 xSL
l13 l23 l33 l43 l53 l63
l14 l24 l34 l44 l54 l64
l15 l25 l35 l45 l55 l65
l16 l26 7 7 l36 7 7 l46 7 7 l56 5 l66
describe the quantitative influence of the loads on the ram deflection and are significant characteristics of the press accuracy under loaded conditions. For instance, the compliance l33 has to be reduced to increase stiffness in stroke direction. The deflections of the tilting angles are specified by the elements in the fourth and fifth row (l4j, l5j), mainly by l44, l55. For the stiffest design of presses, all elements have to be as low as possible. By evaluating the compliance for the operation area, a positiondependent compliance matrix L(u) can be generated. Especially for the mechanical and control design of parallel kinematic machines, such stiffness or compliance models are very helpful to predict the machine’s behavior [11]. As the kinematic shown in Fig. 1 has a highly nonlinear transfer function f(u), no explicit solution for L(u) can be given. Therefore, the compliance was calculated implicitly for the operation area of the machine. The influence of the upper and lower spindle positions xSU, xSL at constant wecc,i on the compliance in z direction l33 is presented in Fig. 2. Simulating the compliance matrix at a reference point uref results in the following values unequal to zero: mm mm mm ; l22 ¼ 1:5 ; l33 ¼ 1:5 ; l44 ¼ l55 kN kN kN mm : ; l66 ¼ 0:3 ; l16 ¼ 0:8 ¼1 kNm kNm kNm
l11 ¼ 0:6
uz
and the kinematic transfer function f(u) [9], which represents the kinematic model. It has to be noted that the drive system allows for ram movements with a bottom dead center not coinciding with the bottom dead centers of all eccentric drives. Process forces and torsional moments lead to a deflection of the ram and therefore to a deviation from the desired position. These loads can be represented as a load vector l = [Fx, Fy, Fz, Mx, My, Mz]T. As stated before, it is suggested that the deflection of the ram position Dx depends on the drive positions. 2.2. Compliance model The compliance of a press can either be determined through measurements or a press model. When evaluating the compliance for different positions of the linkage mechanism, the effort put into measurements increases significantly. Numerical simulation methods are widely used to evaluate the behavior of presses. In order to obtain the press compliance for all
Fig. 2. Simulated compliance map for l33 at constant wecc,i = 2708 over the operation area of xSU, xSL.
Please cite this article in press as: Groche P, et al. Stiffness of multipoint servo presses: Mechanics vs. control. CIRP Annals Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.053
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CIRP-1611; No. of Pages 4 P. Groche et al. / CIRP Annals - Manufacturing Technology xxx (2016) xxx–xxx
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to induce forces and torsional moments. Based on the measured acting forces and the resulting lever lengths, the applied torsional moments are determined. Dial gauges are employed to measure the displacement at the three ram bearings and thus z, ux and uy. Additionally, three measurements in x and y direction yield the tool center point displacements x, y and uz. Solving the equation system, the following compliance matrix for the uncontrolled (passive) press arises: 2 3 0 0 0 0 730 860 6 101 1617 0 207 29 360 7 6 7 6 60 1632 12 153 88 7 3 6 25 7 Lp ¼ 10 6 1 2 7 994 7 2 7 7 6 4 13 42 3 31 1046 1 5 122 0 0 0 0 188
Fig. 3. Comparison of simulated (lines) and experimentally (cross markers) determined compliance of l33, depending on synchronous eccentric positions wecc,i.
The limits of the operation area of the upper and lower spindle represent the kinematic singularities as well as the installation space limitations. It can be concluded that the press compliance highly depends on the operation point of the upper and lower spindle. In order to validate the elastic model and investigate the influence of the eccentric drives’ positions, the compliance of the 3D Servo Press has been measured at different positions 1, 2, 3 (see Fig. 2) and compared to the model. Exemplary kinematic illustrations visualize the linkage mechanism in the corresponding positions. Fig. 3 shows the dependency of l33 on the position of the eccentric drives wecc,i in comparison to the measured compliance for the positions 1, 2 and 3. A model uncertainty due to the reduction of the press model is visible. Nevertheless, the reduced order model is able to represent the characteristics and dimension of compliance in a computationally efficient way. Therefore, the reduced order model is valuable for online closed-loop control. In order to rate the influence of a closed-loop control on the compliance in all ram coordinates, a test setup has been installed through which the full compliance matrix can be determined. 2.3. Test setup and compliance matrix By applying loads l on the ram while measuring its displacements Dx, the compliance matrix can be determined. The measurements were performed at the reference point uref (see Fig. 2) without a position control of the ram. To determine both coupled and decoupled elements of the compliance matrix, the 6 by 6 matrix has been determined using the method of least squares solving the equation system Dx1 ; Dx2 ; . . .; Dxn ¼ L½l1 ; l2 ; . . .; ln based on n = 18 measurements. The test setup shown in Fig. 4 contains a pneumatic cylinder with a load cell for applying the loads. A load of 30% of the nominal force is applied horizontally and vertically at six different positions
Fig. 4. Load and measurement positions of the test setup.
Deflections are stated in mm, rotations in8, forces in kN and torsional moments in kNm. The compliance matrix shows that the highest influence on the deflections Dx is given by the corresponding diagonal elements lii. The effect of ram deflection on part quality is well known, see Doege and Behrens, p. 873 [12]. For a ram, perfectly positioned in a particular direction, the corresponding row of the compliance matrix has to become zero. Two effects lead to asymmetric values in the compliance matrix. Due to a higher rotational stiffness of the upper bearing, the center of rotation deviates from the tool center point. This leads to large values in l16, l26 and l61. Furthermore, the ram bearing bolts can freely slide in the direction of their axes. This causes a larger compliance in y direction than in x direction. Comparing the matrix with results from other works, e.g., Arentoft [5], it becomes apparent that some coupled values like l15, l42 and l51, representing the influence of the horizontal forces on the tilting of the ram, differ from the values in the matrix shown above. Because the ram guidance is not axisymmetric, these deviations refer to the difference in mechanical press designs. The characteristics of the diagonal elements are in good agreement compared to other matrices. In any case, the influence of a closedloop control of the ram movement has not been investigated yet. 3. Control Servo presses in combination with a closed-loop control of the slide position are characterized by an excellent accuracy of the ram positioning [7]. Moreover, multipoint servo presses with such a control are able to keep tilting to a minimum. This requires a reliable and robust measurement of the ram position. Robust sensor placement is challenging, as they should not be damaged in a production environment. A direct measurement of the ram position often is infeasible or involves a high risk of sensor damage. In order to determine the actual position, models and observers are required to estimate the ram position based on measurements at protected locations. Therefore, displacement sensors have been located behind the frame to determine actual positions of the drive bars xB = [xB,1, xB,2, xB,3]T (see Fig. 1) and combined with an observer. This allows for a robust and accurate measurement of the ram position. The measured ram position is used to control z, ux, uy through adaption of the servo drive positions u. In most presses, only the drive’s position and velocity is controlled without feedback of the actual ram position and therefore, compliance cannot be compensated. By using sensors near the ram and observers, a deflection of the ram position can be handled and compensated by a closed-loop control. Fig. 5 illustrates the structure of the control system consisting of an inverse kinematic model that converts the desired ram positions xdes into drive positions udes and a closed-loop control with an observer. While the observer estimates the ram position based on the measurements xB, the closed-loop control continuously corrects the ram movement based on that information. In order to investigate the influence of the observer, an observer with an inelastic kinematic model has been used to control the ram at first. The same test setup as described in Section 2.3 was carried
Please cite this article in press as: Groche P, et al. Stiffness of multipoint servo presses: Mechanics vs. control. CIRP Annals Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.053
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compared to the previous observer, l33 becomes negative. This means that the observer overshoots at estimating the z position because of uncertainty in the compliance model. Nevertheless, reduced order models are valuable for both predicting the press behavior and estimating unmeasurable states of control. 4. Conclusion
Fig. 5. Control loop for a servo press with position feedback.
out to measure loads and displacements. The compliance matrix with active control but without knowledge of the elastic behavior of the structure between sensor and ram shows that the compliances l33, l44 and l55 can be reduced significantly: 2
860 6 104 6 6 0 La ¼ 103 6 6 3 6 4 0 129
0 1624 1 8 1 0
0 0 364 2 2 0
0 150 12 269 7 0
0 28 161 23 291 0
3 737 371 7 7 2 7 7 12 7 7 1 5 165
Due to the adaption of the drive positions in case of a loadinduced deviation in xB, the active controller is able to compensate the compliance of the linkage mechanism. A reduction l35 is also expected since any notable deflection in z direction should be compensated by the control. However, a nearly constant l35 shows that a deflection caused by My does not reach the sensors and therefore might be caused by unconsidered backlash. Furthermore, the closed-loop control has no effect on the remaining compliances which therefore should be considered in the mechanical design of the ram guidance. While a high mechanical stiffness is required in the guidance of the ram, a combination with a closed-loop control allows for a compliant linkage mechanism. As the closed-loop control highly depends on the quality of the measurement and observer, accurate sensors and models are required. The spatial distance between the sensor position and the tool center point causes small compliance values to remain in La for l33, l44 and l55. By combining the position measurement with the elastic machine model in the observer, a robust and more accurate online estimation of the ram position is achieved. This requires computing the compliance matrix for the press L(u) as well as the compliance matrix for the drive bar and the ram LB(u). In a second test series for the active press, a more accurate observer model for the ram positions x ¼ f ðuÞLðuÞðLðuÞLB ðuÞÞ ˆ
1
ðf ðuÞf B ðxB ÞÞ
is used. As the elastic model improves the accuracy of the observer, the compliance matrix with the same closed-loop results in 2
La;m
732 6 139 6 6 0 ¼ 103 6 6 0 6 4 0 97
0 1670 0 0 6 0
0 0 24 4 9 0
0 0 20 69 10 0
0 0 106 2 71 0
3 706 497 7 7 0 7 7; 0 7 7 0 5 165
which shows a further decrease of the compliance in z, ux, uy. While the rotational compliance values l44, l55 are reduced by 75%
The compliance of multipoint servo presses can mainly be influenced in two ways: adaption of the mechanical design on the one hand, and the control of the ram position on the other hand. An extremely low mechanical compliance often is demanded, but not mandatory. By comparing the compliance of an uncontrolled press to a press with an active ram control, it becomes evident that a closed-loop control is capable of influencing relevant factors of the press compliance. Compliances corresponding to the degrees of freedom of the ram are controllable. For a profound decision on which components are to be designed stiff and where to implement a closed-loop control, an accurate model of the press is required. As the assumption of a constant and position-independent compliance is not generally valid, the model has to consider nonlinear compliance. For the 3D Servo Press, a highly nonlinear stiffness behavior has been identified by using a reduced order model. Such models can be incorporated into online observers, in order to improve the closedloop system’s accuracy. Especially if a direct measurement is infeasible, accurate observers for the estimation of relevant quantities are mandatory. It has been shown that the observer has a large influence on the quality of the control. It becomes apparent that the knowledge of the compliance at all operation points is essential for the quality of both press design and press control. Acknowledgements The results of this paper are achieved within the Collaborative Research Centre (SFB) 805 ‘‘Control of uncertainty in load-carrying mechanical systems’’ in subproject ‘‘B2: Forming – Production families at equal quality’’ funded by the German Research Foundation (DFG). The authors wish to thank for funding and supporting the project.
References [1] Doege E, Lange K (1980) Static and Dynamic Stiffness of Presses and Some Effects on the Accuracy of Workpieces. Annals of the CIRP 29(1):167–171. [2] Doege E, Silberbach G (1990) Influence of Various Machine Tool Components on Workpiece Quality. Annals of the CIRP 39(1):209–213. [3] Groche P, Schneider R (2004) Method for the Optimization of Forming Presses for the Manufacturing of Micro Parts. Annals of the CIRP 53(1):281–284. [4] 55189 DIN (1988) Machine Tools; Determination of the Ratings of Presses for Sheet Metal Working Under Static Load, German Institute for Standardization. [5] Arentoft M, Wanheim T (2005) A New Approach to Determine Press Stiffness. Annals of the CIRP 54(1):265–268. [6] Chodnikiewicz K, Balendra R (2000) The Calibration of Metal-forming Presses. Journal of Materials Processing Technology 106(1–3):28–33. [7] Osakada K, Mori K, Altan T, Groche P (2011) Mechanical Servo Press Technology for Metal Forming. Annals of the CIRP 60(2):651–672. [8] Groche P, Scheitza M, Kraft M, Schmitt S (2010) Increased Total Flexibility by 3D Servo Presses. Annals of the CIRP 59(1):267–270. [9] Scheitza M (2010) Konzeption eines flexiblen 3D-Servo-Pressensystems und repra¨sentative Basisanwendungen. Berichte aus Produktion und Umformtechnik, vol. 80. . [10] Arentoft M, Eriksen M, Wanheim T (2000) Determination of Six Stiffnesses for a Press. Journal of Materials Processing Technology 105(3):246–252. [11] Gosselin C (1990) Stiffness Mapping for Parallel Manipulators. IEEE Transactions on Robotics and Automation 6(3):377–382. [12] Doege E, Behrens B-A (2010) Handbuch Umformtechnik, Springer.
Please cite this article in press as: Groche P, et al. Stiffness of multipoint servo presses: Mechanics vs. control. CIRP Annals Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.053
CIRP-1611; No. of Pages 4 CIRP Annals - Manufacturing Technology xxx (2016) xxx–xxx
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er . com /ci r p/ def a ult . asp
Stiffness of multipoint servo presses: Mechanics vs. control Peter Groche (1)*, Florian Hoppe, Julian Sinz Institute for Production Engineering and Forming Machines, Technische Universita¨t Darmstadt, Darmstadt, Germany
A R T I C L E I N F O
A B S T R A C T
Keywords: Stiffness Control Servo press
The accuracy of metal-formed products is strongly affected by the stiffness of the machine used. Therefore, huge efforts to increase moments of inertia and reduce backlash were made in conventional press design. Multipoint servo presses allow for an alternative approach: increasing the position accuracy with respect to the press stroke direction and the ram tilting by controlling deflections. Necessary models and parameters as well as the effectiveness of such a control are discussed in this paper. The proposed method is validated by experiments using a 3D servo press. ß 2017 Published by Elsevier Ltd on behalf of CIRP.
1. Introduction Presses actuate tools along predefined paths. As they are heavily loaded, accurate positioning is challenging. Inaccuracies can cause dimensional deviations from the required product geometry or tool damage. Possible reasons for the inaccuracies are varying conditions of the press or the tools as well as load variations caused by fluctuating process conditions, e.g., temperature, material, and lubrication. Due to the elastic behavior of the press components, varying loads lead to different deflections of the press. High stiffness values are desirable, since they reduce deviations from the targeted tool paths. Therefore, stiffness is one of the most important characteristics of presses [1]. High values should guarantee ram parallelism and accurate tool guidance. Two approaches are commonly known to influence the stiffness of presses. These are the adaption of the mechanical press design on the one hand [2], and the active compensation of the ram deflections using a closed-loop control on the other hand. Different frame and gear drive designs vary with respect to the achievable press stiffness [1]. One important design restriction in the optimization of the mechanical press stiffness is the necessary accessibility of the working space [3]. Increasing stiffness by control requires active components and methods for stiffness identification. So far, measurements of press stiffness focus on the stroke direction and the rotational stiffness around the horizontal axes of the ram [4]. Although complete 6 by 6 compliance matrices have already been identified in experiments for both hydraulic [5] and mechanical [6] presses, only single operation points of a press have been considered. This follows DIN 55189 [4], which suggests that the compliance has to be measured at the bottom dead center. Numerical press models, e.g., finite element models, are often used in press design to evaluate the
* Corresponding author. E-mail address: [email protected] (P. Groche).
press behavior, but can only be used offline due to their high computing time. Even though reduced order models are required for control, their effectiveness for the stiffness determination has still to be examined. The possibility to control the ram position and thus to influence the stiffness of the press has been enabled by servo presses through a feedback of the slide positions [7]. Servo presses feature an adjustable bottom dead center. Therefore, position-dependent values of the press compliance are necessary for a position control. Since a direct measurement of the ram position is often impracticable during forming processes, an observer might be required. In case of using a single point servo press, only the stiffness in stroke direction can be controlled. For multipoint servo presses with several independent drive systems, the tilting of the ram can also be manipulated, thus boosting the rotational stiffness. Due to the risk of press damage, ram tilting has to be compensated in conventional spindle-driven multipoint servo presses with respect to the guidance. Contrary to this, the 3D Servo Press [8] shown in Fig. 1 is equipped with special linkage mechanisms and ram bearings resulting in two additional degrees of freedom in the ram movement. Thus, this press type is less sensitive to ram tilting and position control is not limited by the ram bearings. Assuming the press stiffness to be controllable corresponding to the driven degrees of freedom of the ram, the effect of a closed-loop control on the stiffness values is of high interest. In the present study, the compliance of the 3D Servo Press is determined for different operation points. In addition, a complete 6 by 6 compliance matrix is evaluated with and without position control of the ram. The effect of control, measurement position and the usage of adequate observers will be compared by means of the measured compliance matrices. With that, the coupling behavior between the controlled and uncontrolled 3D Servo Press is investigated and the dependency between the linking mechanism’s position of the 3D Servo Press and its stiffness is shown.
http://dx.doi.org/10.1016/j.cirp.2017.04.053 0007-8506/ß 2017 Published by Elsevier Ltd on behalf of CIRP.
Please cite this article in press as: Groche P, et al. Stiffness of multipoint servo presses: Mechanics vs. control. CIRP Annals Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.053
G Model
CIRP-1611; No. of Pages 4 P. Groche et al. / CIRP Annals - Manufacturing Technology xxx (2016) xxx–xxx
2
positions u, an efficient simulation technique is required. For this purpose, a multibody simulation based on a mixed truss and beam model has been developed for the 3D Servo Press and implemented in Matlab. All bodies of the linkage mechanism have been modeled with their corresponding cross-sectional area, material parameters and geometrical moment of inertia. The connections between the bodies are modeled as frictionless springs whose stiffness values represent their bearing behavior. As outlined by Chodnikiewicz [6] and Arentoft [10], the press deflection behavior can be described by measuring a 6 by 6 compliance matrix L. This matrix describes the dependency between the translational and rotational ram positions x and the process loads l such that Dx = Ll. Due to the variability of the linkage mechanism of the 3D Servo Press, a nonlinear compliance matrix L(u) is considered. The elements lij of the compliance matrix 2 3
l11 l12 l22 l32 l42 l52 l61 l62
6 l21 6 6 l31 LðuÞ ¼ 6 6 l41 6 4 l51
Fig. 1. Linkage mechanism of the 3D Servo Press.
2. Mechanics In the following, the press used for the investigations as well as the compliance model and test setup will be explained. 2.1. 3D Servo Press Multipoint servo presses driven by multiple servo motors can perform an asynchronous movement. The 3D Servo Press has three independent drive systems and special bearings, which allow intentional tilting up to 38 in ux and uy. As shown in Fig. 1, three eccentric drives in a 1208 arrangement and two spindle motors allow for a combined actuation of the ram. Besides three spatial degrees of freedom at the ram z, ux, uy (stroke, pitch, roll), adjustable mounting height and stroke length are provided. To control the ram position, the eccentric drives wecc,i as well as the upper spindle xSU and lower spindle xSL work together simultaneously. Therefore, the press system can be described by the drive positions as press input u, the ram positions x as press output 2 3 2 3 x ’ecc;1 6 y 7 6 ’ecc;2 7 6 7 6 7 6 z 7 6 7 7 x¼6 6 ux 7; u ¼ 6 ’ecc;3 7: 4 xSU 5 6 7 4 uy 5 xSL
l13 l23 l33 l43 l53 l63
l14 l24 l34 l44 l54 l64
l15 l25 l35 l45 l55 l65
l16 l26 7 7 l36 7 7 l46 7 7 l56 5 l66
describe the quantitative influence of the loads on the ram deflection and are significant characteristics of the press accuracy under loaded conditions. For instance, the compliance l33 has to be reduced to increase stiffness in stroke direction. The deflections of the tilting angles are specified by the elements in the fourth and fifth row (l4j, l5j), mainly by l44, l55. For the stiffest design of presses, all elements have to be as low as possible. By evaluating the compliance for the operation area, a positiondependent compliance matrix L(u) can be generated. Especially for the mechanical and control design of parallel kinematic machines, such stiffness or compliance models are very helpful to predict the machine’s behavior [11]. As the kinematic shown in Fig. 1 has a highly nonlinear transfer function f(u), no explicit solution for L(u) can be given. Therefore, the compliance was calculated implicitly for the operation area of the machine. The influence of the upper and lower spindle positions xSU, xSL at constant wecc,i on the compliance in z direction l33 is presented in Fig. 2. Simulating the compliance matrix at a reference point uref results in the following values unequal to zero: mm mm mm ; l22 ¼ 1:5 ; l33 ¼ 1:5 ; l44 ¼ l55 kN kN kN mm : ; l66 ¼ 0:3 ; l16 ¼ 0:8 ¼1 kNm kNm kNm
l11 ¼ 0:6
uz
and the kinematic transfer function f(u) [9], which represents the kinematic model. It has to be noted that the drive system allows for ram movements with a bottom dead center not coinciding with the bottom dead centers of all eccentric drives. Process forces and torsional moments lead to a deflection of the ram and therefore to a deviation from the desired position. These loads can be represented as a load vector l = [Fx, Fy, Fz, Mx, My, Mz]T. As stated before, it is suggested that the deflection of the ram position Dx depends on the drive positions. 2.2. Compliance model The compliance of a press can either be determined through measurements or a press model. When evaluating the compliance for different positions of the linkage mechanism, the effort put into measurements increases significantly. Numerical simulation methods are widely used to evaluate the behavior of presses. In order to obtain the press compliance for all
Fig. 2. Simulated compliance map for l33 at constant wecc,i = 2708 over the operation area of xSU, xSL.
Please cite this article in press as: Groche P, et al. Stiffness of multipoint servo presses: Mechanics vs. control. CIRP Annals Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.053
G Model
CIRP-1611; No. of Pages 4 P. Groche et al. / CIRP Annals - Manufacturing Technology xxx (2016) xxx–xxx
3
to induce forces and torsional moments. Based on the measured acting forces and the resulting lever lengths, the applied torsional moments are determined. Dial gauges are employed to measure the displacement at the three ram bearings and thus z, ux and uy. Additionally, three measurements in x and y direction yield the tool center point displacements x, y and uz. Solving the equation system, the following compliance matrix for the uncontrolled (passive) press arises: 2 3 0 0 0 0 730 860 6 101 1617 0 207 29 360 7 6 7 6 60 1632 12 153 88 7 3 6 25 7 Lp ¼ 10 6 1 2 7 994 7 2 7 7 6 4 13 42 3 31 1046 1 5 122 0 0 0 0 188
Fig. 3. Comparison of simulated (lines) and experimentally (cross markers) determined compliance of l33, depending on synchronous eccentric positions wecc,i.
The limits of the operation area of the upper and lower spindle represent the kinematic singularities as well as the installation space limitations. It can be concluded that the press compliance highly depends on the operation point of the upper and lower spindle. In order to validate the elastic model and investigate the influence of the eccentric drives’ positions, the compliance of the 3D Servo Press has been measured at different positions 1, 2, 3 (see Fig. 2) and compared to the model. Exemplary kinematic illustrations visualize the linkage mechanism in the corresponding positions. Fig. 3 shows the dependency of l33 on the position of the eccentric drives wecc,i in comparison to the measured compliance for the positions 1, 2 and 3. A model uncertainty due to the reduction of the press model is visible. Nevertheless, the reduced order model is able to represent the characteristics and dimension of compliance in a computationally efficient way. Therefore, the reduced order model is valuable for online closed-loop control. In order to rate the influence of a closed-loop control on the compliance in all ram coordinates, a test setup has been installed through which the full compliance matrix can be determined. 2.3. Test setup and compliance matrix By applying loads l on the ram while measuring its displacements Dx, the compliance matrix can be determined. The measurements were performed at the reference point uref (see Fig. 2) without a position control of the ram. To determine both coupled and decoupled elements of the compliance matrix, the 6 by 6 matrix has been determined using the method of least squares solving the equation system Dx1 ; Dx2 ; . . .; Dxn ¼ L½l1 ; l2 ; . . .; ln based on n = 18 measurements. The test setup shown in Fig. 4 contains a pneumatic cylinder with a load cell for applying the loads. A load of 30% of the nominal force is applied horizontally and vertically at six different positions
Fig. 4. Load and measurement positions of the test setup.
Deflections are stated in mm, rotations in8, forces in kN and torsional moments in kNm. The compliance matrix shows that the highest influence on the deflections Dx is given by the corresponding diagonal elements lii. The effect of ram deflection on part quality is well known, see Doege and Behrens, p. 873 [12]. For a ram, perfectly positioned in a particular direction, the corresponding row of the compliance matrix has to become zero. Two effects lead to asymmetric values in the compliance matrix. Due to a higher rotational stiffness of the upper bearing, the center of rotation deviates from the tool center point. This leads to large values in l16, l26 and l61. Furthermore, the ram bearing bolts can freely slide in the direction of their axes. This causes a larger compliance in y direction than in x direction. Comparing the matrix with results from other works, e.g., Arentoft [5], it becomes apparent that some coupled values like l15, l42 and l51, representing the influence of the horizontal forces on the tilting of the ram, differ from the values in the matrix shown above. Because the ram guidance is not axisymmetric, these deviations refer to the difference in mechanical press designs. The characteristics of the diagonal elements are in good agreement compared to other matrices. In any case, the influence of a closedloop control of the ram movement has not been investigated yet. 3. Control Servo presses in combination with a closed-loop control of the slide position are characterized by an excellent accuracy of the ram positioning [7]. Moreover, multipoint servo presses with such a control are able to keep tilting to a minimum. This requires a reliable and robust measurement of the ram position. Robust sensor placement is challenging, as they should not be damaged in a production environment. A direct measurement of the ram position often is infeasible or involves a high risk of sensor damage. In order to determine the actual position, models and observers are required to estimate the ram position based on measurements at protected locations. Therefore, displacement sensors have been located behind the frame to determine actual positions of the drive bars xB = [xB,1, xB,2, xB,3]T (see Fig. 1) and combined with an observer. This allows for a robust and accurate measurement of the ram position. The measured ram position is used to control z, ux, uy through adaption of the servo drive positions u. In most presses, only the drive’s position and velocity is controlled without feedback of the actual ram position and therefore, compliance cannot be compensated. By using sensors near the ram and observers, a deflection of the ram position can be handled and compensated by a closed-loop control. Fig. 5 illustrates the structure of the control system consisting of an inverse kinematic model that converts the desired ram positions xdes into drive positions udes and a closed-loop control with an observer. While the observer estimates the ram position based on the measurements xB, the closed-loop control continuously corrects the ram movement based on that information. In order to investigate the influence of the observer, an observer with an inelastic kinematic model has been used to control the ram at first. The same test setup as described in Section 2.3 was carried
Please cite this article in press as: Groche P, et al. Stiffness of multipoint servo presses: Mechanics vs. control. CIRP Annals Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.053
G Model
CIRP-1611; No. of Pages 4 P. Groche et al. / CIRP Annals - Manufacturing Technology xxx (2016) xxx–xxx
4
compared to the previous observer, l33 becomes negative. This means that the observer overshoots at estimating the z position because of uncertainty in the compliance model. Nevertheless, reduced order models are valuable for both predicting the press behavior and estimating unmeasurable states of control. 4. Conclusion
Fig. 5. Control loop for a servo press with position feedback.
out to measure loads and displacements. The compliance matrix with active control but without knowledge of the elastic behavior of the structure between sensor and ram shows that the compliances l33, l44 and l55 can be reduced significantly: 2
860 6 104 6 6 0 La ¼ 103 6 6 3 6 4 0 129
0 1624 1 8 1 0
0 0 364 2 2 0
0 150 12 269 7 0
0 28 161 23 291 0
3 737 371 7 7 2 7 7 12 7 7 1 5 165
Due to the adaption of the drive positions in case of a loadinduced deviation in xB, the active controller is able to compensate the compliance of the linkage mechanism. A reduction l35 is also expected since any notable deflection in z direction should be compensated by the control. However, a nearly constant l35 shows that a deflection caused by My does not reach the sensors and therefore might be caused by unconsidered backlash. Furthermore, the closed-loop control has no effect on the remaining compliances which therefore should be considered in the mechanical design of the ram guidance. While a high mechanical stiffness is required in the guidance of the ram, a combination with a closed-loop control allows for a compliant linkage mechanism. As the closed-loop control highly depends on the quality of the measurement and observer, accurate sensors and models are required. The spatial distance between the sensor position and the tool center point causes small compliance values to remain in La for l33, l44 and l55. By combining the position measurement with the elastic machine model in the observer, a robust and more accurate online estimation of the ram position is achieved. This requires computing the compliance matrix for the press L(u) as well as the compliance matrix for the drive bar and the ram LB(u). In a second test series for the active press, a more accurate observer model for the ram positions x ¼ f ðuÞLðuÞðLðuÞLB ðuÞÞ ˆ
1
ðf ðuÞf B ðxB ÞÞ
is used. As the elastic model improves the accuracy of the observer, the compliance matrix with the same closed-loop results in 2
La;m
732 6 139 6 6 0 ¼ 103 6 6 0 6 4 0 97
0 1670 0 0 6 0
0 0 24 4 9 0
0 0 20 69 10 0
0 0 106 2 71 0
3 706 497 7 7 0 7 7; 0 7 7 0 5 165
which shows a further decrease of the compliance in z, ux, uy. While the rotational compliance values l44, l55 are reduced by 75%
The compliance of multipoint servo presses can mainly be influenced in two ways: adaption of the mechanical design on the one hand, and the control of the ram position on the other hand. An extremely low mechanical compliance often is demanded, but not mandatory. By comparing the compliance of an uncontrolled press to a press with an active ram control, it becomes evident that a closed-loop control is capable of influencing relevant factors of the press compliance. Compliances corresponding to the degrees of freedom of the ram are controllable. For a profound decision on which components are to be designed stiff and where to implement a closed-loop control, an accurate model of the press is required. As the assumption of a constant and position-independent compliance is not generally valid, the model has to consider nonlinear compliance. For the 3D Servo Press, a highly nonlinear stiffness behavior has been identified by using a reduced order model. Such models can be incorporated into online observers, in order to improve the closedloop system’s accuracy. Especially if a direct measurement is infeasible, accurate observers for the estimation of relevant quantities are mandatory. It has been shown that the observer has a large influence on the quality of the control. It becomes apparent that the knowledge of the compliance at all operation points is essential for the quality of both press design and press control. Acknowledgements The results of this paper are achieved within the Collaborative Research Centre (SFB) 805 ‘‘Control of uncertainty in load-carrying mechanical systems’’ in subproject ‘‘B2: Forming – Production families at equal quality’’ funded by the German Research Foundation (DFG). The authors wish to thank for funding and supporting the project.
References [1] Doege E, Lange K (1980) Static and Dynamic Stiffness of Presses and Some Effects on the Accuracy of Workpieces. Annals of the CIRP 29(1):167–171. [2] Doege E, Silberbach G (1990) Influence of Various Machine Tool Components on Workpiece Quality. Annals of the CIRP 39(1):209–213. [3] Groche P, Schneider R (2004) Method for the Optimization of Forming Presses for the Manufacturing of Micro Parts. Annals of the CIRP 53(1):281–284. [4] 55189 DIN (1988) Machine Tools; Determination of the Ratings of Presses for Sheet Metal Working Under Static Load, German Institute for Standardization. [5] Arentoft M, Wanheim T (2005) A New Approach to Determine Press Stiffness. Annals of the CIRP 54(1):265–268. [6] Chodnikiewicz K, Balendra R (2000) The Calibration of Metal-forming Presses. Journal of Materials Processing Technology 106(1–3):28–33. [7] Osakada K, Mori K, Altan T, Groche P (2011) Mechanical Servo Press Technology for Metal Forming. Annals of the CIRP 60(2):651–672. [8] Groche P, Scheitza M, Kraft M, Schmitt S (2010) Increased Total Flexibility by 3D Servo Presses. Annals of the CIRP 59(1):267–270. [9] Scheitza M (2010) Konzeption eines flexiblen 3D-Servo-Pressensystems und repra¨sentative Basisanwendungen. Berichte aus Produktion und Umformtechnik, vol. 80. . [10] Arentoft M, Eriksen M, Wanheim T (2000) Determination of Six Stiffnesses for a Press. Journal of Materials Processing Technology 105(3):246–252. [11] Gosselin C (1990) Stiffness Mapping for Parallel Manipulators. IEEE Transactions on Robotics and Automation 6(3):377–382. [12] Doege E, Behrens B-A (2010) Handbuch Umformtechnik, Springer.
Please cite this article in press as: Groche P, et al. Stiffness of multipoint servo presses: Mechanics vs. control. CIRP Annals Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.053