- Email: [email protected]
Energy optimized jerk-decoupling technology for translatory feed axes
CIRP Annals - Manufacturing Technology 58 (2009) 339–342
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology journal homepage: http://ees.elsevier.com/cirp/default.asp
Energy optimized jerk-decoupling technology for translatory feed axes B. Denkena (1), P. Hesse, O. Gu¨mmer * Institute of Production Engineering and Machine Tools (IFW), Leibniz Universita¨t Hannover, 30823 Garbsen, Germany
A R T I C L E I N F O
A B S T R A C T
Keywords: Machine tool Adaptronic Jerk-decoupling
Dynamic feed axes for machine tools are usually optimized for high jerk rates. This, however, might lead to excitations of the machine frame due to reaction forces of the linear motor. This paper describes the development of a jerk-decoupled feed axis with an innovative guidance system and energy-optimized spring-damper-elements. An accomplished system simulation is based on an energy observer applied to accomplish the energy-optimal design of an example jerk-decoupled feed axis. The simulatory results are verified at a test bed using adjustable adaptronic components. A concluding verification proves the positive effects of this technology without negative effect on the accuracy. ß 2009 CIRP.
1. Introduction
2. System simulation
High-dynamic feed axes are usually equipped with linear direct drives instead of ball screw drives. The quoted advantages are higher accuracy, reliability and attainable dynamics. One drawback concerning a robust control at load variations is described in [1]. Another disadvantage is the jerk dependent reaction force on the secondary part of the linear motor, which will act in the opposite direction and with the same magnitude as the active force on the primary part [2]. As a result, the maximum accelerations and jerks have to be limited due to dynamic reactions of the machine frame [3,4]. To decouple these reaction forces in critical frequency ranges from the machine frame, without substantially limiting the dynamics of the primary part at the same time, jerk-decoupling technologies [5,6] have been developed. The principle of jerkdecoupling is shown in Fig. 1. The jerk-decoupling technology is based on a linear motor’s secondary part which is not bolted to the machine frame, but mounted on a separate slide which again is linked to the machine frame with spring-damper-elements. As a result, a mechanical filtering of the dynamic forces is possible. Critical oscillations may clearly be reduced. The major disadvantage of known jerk-decoupling systems is the additional secondary part slide. For a complete feed axis, a minimum of four guideways is required, two for the table with primary part and two for the secondary part slide. Both have to be of high stiffness because they have to transmit the high normal forces of the linear motor. This requirement makes jerk-decoupling systems expensive, particularly when long feed strokes are necessary. On top, high pretension of the secondary part guideways and passive spring-dampersystems reduces the energy efficiency of the feed axes. The research described in this paper addresses these disadvantages and proposes a new solution design.
The basis of a system simulation with an energy observer is given by different models of the mechanics, the drive technology, respectively electro-technology and the control engineering. A simulation for different basic structures using jerk-decoupling (JDC) makes sense with regard to the expected costs of appropriate system realizations. A model of the linear motor and the control circuits has been developed. In order to get the best approximation of the linear synchronous motor, a model of a rotating main machine is applied. By way of control, a field orientated control is used. This control provides a smooth motion at low speeds as well as an efficient operation at high speeds. Moreover, it is used to control linear motors, especially in machine tools. The models of control engineering employed are described in more detail in [7] and the mechanics, as well as the drive technology, are given in [8]. The system simulation considers mechanical elements like the friction in all runner blocks and the energy losses in the damping elements. The friction in the runner blocks is illustrated with three effects of the Coulomb’s and viscous friction as well as the Stribeck-effect. Based on this simulation environment considering the primary and secondary part of the jerk-decoupled axis and the use of a model of a synchronous linear direct drive, an energy observer has been developed. This observer monitors the energies in the individual elements. The focus is here on the ‘‘energy sinks’’, as for example the friction effects or the damping losses. Hence this system simulation enables the comparison of different guiding systems and concepts. More details regarding different simulations of energy losses can be derived from [9]. The basis of the following analysis represents an assumed jerk-limited trapezoidal motion profile at the desired value of the simulation. This was published in [7] and contains the algorithm for the determination of the allocated times and the behaviour of the feed axis in the motion profile. For the following view the delimitation parameters were set to a maximum acceleration of 1 g, a maximum jerk of 500 m/s3 and to a maximum speed of 120 m/min.
* Corresponding author. E-mail address: [email protected] (O. Gu¨mmer). 0007-8506/$ – see front matter ß 2009 CIRP. doi:10.1016/j.cirp.2009.03.043
B. Denkena et al. / CIRP Annals - Manufacturing Technology 58 (2009) 339–342
340
Fig. 1. Principle of jerk-decoupling. Fig. 3. Classical separate guidance (top) versus new relative guidance (bottom).
At the top of Fig. 2 the prior mentioned motion profile of the primary part in horizontal feed direction is depicted. During this motion profile, an energy of 68 J is converted within the guidance of the primary part (Prim.). An energy loss of 63 J is added, which is converted in the linear motor (LM). In the lower third of Fig. 2 a supplemental diagram of the energies of the drive system with JDC is represented. In addition an energy loss of 27 J in the friction of the JDC carriage and 44.5 J in the damping occurs. It is to be recognized that more work is converted in the mechanics, which must be applied by the linear motor. However, the losses in the linear motor remain constant. This is justified in the allocation of the work in force and velocity. In JDC systems the applied force is the same as in classical drive systems. However, the velocity is larger, because an additional movable body has been integrated. Since the force is proportional to the current and the velocity is proportional to the voltage, a higher voltage is necessary to float the same current. So the energy losses in the synchronous motor remain approximately the same, since the energy losses are proportional to the square of the currents. Only the magnet wheel voltage and thereby the terminal voltage increase. 3. Relative guidance concept Previous constructions of jerk-decoupled feed axes have been designed using separated guiding system concepts (Fig. 3). In this case, the primary part and the secondary part are guided separately to the machine frame. Compared to this, a new relative guiding system has been developed. This new concept provides a serial first
guidance, the exterior, which guides the primary part relative to the machine frame. A serial second guidance, the interior, guides the secondary part relative to the primary part. A connection from the secondary part to the machine frame does not exist in this new design. A technical comparison of the prior mentioned guiding concepts shows an advancement of the relative guidance concerning the force path and the vibration behaviour. The attraction force of the linear motor is carried only by the interior guidance, so that the exterior precision guidance is not affected. Due to this comparison, in the following work the relative guidance concept is analyzed in more detail. Since in the course of the following verification described here, the developed relative guiding system presents itself as favourable and economically advantageous in comparison to the separate guidance, a patent by the Leibniz University of Hanover is pending [10]. On the basis of the system simulation in chapter 2, an energy observation of the relative guiding system has been performed. Therefore, two different system simulations were developed. On one hand the separate guiding system, which is characterised by the independence of the guidance frictions and on the other hand the relative guidance, which is characterized by the coupled guiding behaviour. Regarding a point-to-point motion of 100 mm (refer to Fig. 2), it is to be recognized that the friction of the relative guidance in both guidances, the primary part and the jerkdecoupling carriage, decreased. Here the energy loss converted by friction decreases in the primary guidance from 18.9 to 13.3 J, which equals 29.6%. At the same time the friction energy of the secondary guidance decreases from 8.0 to 3.1 J, thus around 61.3%. Because of the ‘‘shorter’’ force flow, the high attraction force of the linear motor is carried only by the second guidance. The primary guidance assumes the precision function in this new arrangement. Parallel to the reduction of the friction energy the energy loss in the damping of the JDC rises. This is justified by the fact that a smaller friction in the system permits more movement of the JDC carriage and thus more kinetic energy in the damping is converted. However, the kinetic energy in the damping can be used in different ways compared to the friction energy. In Fig. 4 a comparison of the power loss is given for an assumed sine-wave motion. The friction losses of the primary part and the JDC carriage are displayed against the frequency. In this case, the friction losses are very different, since a linear direct drive stimulates the machine frame differently depending on the frequency. Hence, the applied energy is varying. The results show that the new concept of the relative guidance causes clearly smaller energy dissipations in all frequency ranges. An average energy conservation in the energy losses of 50.9% is reached with this configuration in the examined frequency band. 4. Energy-optimal dimensioning of the coupling elements
Fig. 2. Comparison of energy flow with and without jerk-decoupling.
The change of the energy loss in the synchronous motor can be neglected by using a jerk-decoupling (refer to chapter 2). In this chapter an energy optimization of the coupling elements on the basis of the system simulation and the energy observer is accomplished. The object is to gain experience for the energy optimization of feed axes of the three mechanical couple parameters
B. Denkena et al. / CIRP Annals - Manufacturing Technology 58 (2009) 339–342
341
Fig. 4. Comparison of the power loss of both guiding concepts (P = primary part, JDC = jerk-decoupling carriage). Fig. 5. Influence of the couple parameters on the compliance-frequency responses of the frame.
of the JDC in comparison to [11]. In the following the dimensioning of the coupling elements from the control engineering view is regarded, i.e. the mass of the JDC carriage mJDC, the spring stiffness cJDC and the damping constant dJDC. The motion profile is the same as it is already depicted in chapter 2. Before the optimization of the coupling parameters, the optimization of the moved masses is the focus of the investigation. Thus the parameters, which are adjusted in the control of the linear motor, have their validity related to the relative motion between
the two bodies. In the following a stopped linear direct drive is regarded, whose primary part is to be accelerated with a constant jerk. The accruing starting-jerk-efficiency at the time t = 0 depends on the mass ratio of the two motor components. If the mass of the JDC carriage mJDC corresponds to the mass of the primary part mP, the efficiency amounts hStJ = 0.5. At constant mP, the efficiency improves with an increasing mass of the JDC carriage. But this
Fig. 6. Energy-optimal dimensioning of the JDC.
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B. Denkena et al. / CIRP Annals - Manufacturing Technology 58 (2009) 339–342
5. Verification of the simulations
Fig. 7. Position step response of the linear direct drive (P = primary part, JDC = jerkdecoupling carriage).
Finally the results of the simulations are verified at the test bed. A translatory feed axis with a maximum traverse path of 1150 mm and a maximum feed force of 7920 N has been build up. This test bed includes the new relative guiding concept for the JDC and adjustable coupling elements. In Fig. 7, a position step of 100 mm of the linear motor is regarded. It is to be recognized that the JDC carriage achieves a clearly greater balancing motion with an implemented JDC, than with a rigid attachment of the JDC carriage to the machine frame. However, this movement has no influence on the positioning accuracy of the linear motor. In Fig. 8 the oscillation velocity of the machine frame during a force step is represented. Here a clearly reduced oscillation stimulation is shown by using the JDC. It has been pointed out that it is possible to economically operate JDC systems in high-dynamic axes with the help of the new developed relative guidance [12]. 6. Summary In this contribution the relative guidance for jerk-decoupled feed axes is presented. A huge advantage can be seen in the clearly smaller friction energy losses of this guiding system in relation to separate guidances. Moreover, the proceeding for a controltechnical and energetic dimensioning of jerk-decoupled feed axes is presented. Frequency responses are considered in order to be able to absorb the resonances of the machine frame optimally. Also system simulations were performed in order to monitor the energy losses. With the help of this energy-optimal dimensioning the energy losses, which are related to the JDC, can be minimized by up to 50%. In the last step the results of the simulations are verified by means of a realised test bed using the patented relative guiding concept. This presented proceeding for an energy-optimal design of a jerk-decoupled translatory feed axis can be applied to other linear direct driven feed axes, for instance of machine tools, to improve the dynamic behaviour and to decrease the energy consumption.
Fig. 8. Oscillation velocity of the machine frame.
relation is valid only for the starting point of movement. For a detailed examination of the optimization of the mass ratio in dependence of the expected maximum dynamic values (acceleration amax and jerk jmax) refer to [12]. In the following view the optimization of the spring-damperelements is presented, at first from the control engineering view. For a better illustration of the optimization, the appropriate frequency responses are depicted in Fig. 5. For an optimum design the machine frame frequency response is important. Two parameters have to be optimized: The compliance in the first resonance point must be as small as possible and the frequency of the resonance point has to be as high as possible. If the frequency response of the JDC carriage is stable, the optimization from the control engineering view is completed. Moreover, an optimization of the spring-damper-elements in view of the losses can be accomplished, as previously described in chapter 2. With the consideration of these two criteria, it can now be examined for an optimum of the couple parameters within a ‘‘meaningful’’ range. This meaningful range contains the boundary condition of the possible design in respect to existing couple elements on the market. If both views are standardized, the diagrams in Fig. 6 can be obtained [12]. On the basis of this example it is to be recognized that the interpretation from the view of control engineering takes an optimal state. With a view to the energy loss, it can still be optimized. In this case, an enlargement of the spring stiffness cJDC would slightly raise the maximum point of compliance, but would minimize on the other hand the energy loss by up to 50%.
Acknowledgment The authors thank the European Commission for founding the Integrated Project ‘‘Next Generation Production Systems’’.
References [1] Van Brussel H, Van den Braembussche P (1998) Robust Control of Feed Drives with Linear Motors. Annals of CIRP 47:325–328. [2] Bubak, A., Soucek, P., Zeleny, J., August 3-7 2003, New Principles for Design of Highly Dynamic Machine Tools, Proceedings of the international conference ICPR-17, Blacksburg, Virginia, USA. [3] Erkorkmaz K, Altintas Y (2001) High Speed CNC System Design: Part I—Jerk Limited Trajectory Generation and Quintic Spline Interpolation. International Journal of Machine Tools and Manufacture 41(9):1323–1345. [4] Weck M, Kru¨ger P, Brecher C (2001) Limits for Controller Settings with Electric Linear Drives. International Journal of Machine Tools & Manufacture 41:65–88. [5] Berkemer J, Altenburger R, Koch T, Lehner W-D (2004) Effektive Nutzung des Leistungspotenzials von Direktantrieben. wt Werkstattstechnik Online 94(5):233–241. [6] Weck M, Ostermann T (2003) Lineardirektantriebe mit Impulsentkopplung. Antriebstechnik 42(11):61–64. [7] Denkena B, Hesse P (2005) Wirtschaftlichkeitsbetrachtung von Trapezprofilen. wt Werkstattstechnik Online 95(5). [8] Denkena B, Mo¨hring H-C, Hesse P (2006) Energiebetrachtung ruckentkoppelter Vorschubachsen – Simulative Untersuchungen des Energieflusses ruckentkoppelter Vorschubachsen. wt Werkstattstechnik Online 95(5). [9] Denkena B, Mo¨hring H-C, Hesse P (2007) Energy-Flow in Jerk-Decoupled Translatory Feed-Axes. Journal of Mechanical Engineering—Part C 221/1:89–98. [10] Patent Application Publication DE 102006046974 B3: Ruckentkoppelte Antriebsachse, Filing Date 04.10.2006, Publication Date 24.04.2008, Leibniz Universita¨t Hannover. [11] Neugebauer R, Riedel M, Drossel W-G (2004) Modellbasierte Auslegung von Koppelelementen. Antriebstechnik 43(11):70–74. [12] Hesse, P., 2008, Energieeffizientes Relativfu¨hrungskonzept fu¨r ruckentkoppelte Vorschubachsen, PhD Thesis, Leibniz Universita¨t Hannover, PZH–Verlag.
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology journal homepage: http://ees.elsevier.com/cirp/default.asp
Energy optimized jerk-decoupling technology for translatory feed axes B. Denkena (1), P. Hesse, O. Gu¨mmer * Institute of Production Engineering and Machine Tools (IFW), Leibniz Universita¨t Hannover, 30823 Garbsen, Germany
A R T I C L E I N F O
A B S T R A C T
Keywords: Machine tool Adaptronic Jerk-decoupling
Dynamic feed axes for machine tools are usually optimized for high jerk rates. This, however, might lead to excitations of the machine frame due to reaction forces of the linear motor. This paper describes the development of a jerk-decoupled feed axis with an innovative guidance system and energy-optimized spring-damper-elements. An accomplished system simulation is based on an energy observer applied to accomplish the energy-optimal design of an example jerk-decoupled feed axis. The simulatory results are verified at a test bed using adjustable adaptronic components. A concluding verification proves the positive effects of this technology without negative effect on the accuracy. ß 2009 CIRP.
1. Introduction
2. System simulation
High-dynamic feed axes are usually equipped with linear direct drives instead of ball screw drives. The quoted advantages are higher accuracy, reliability and attainable dynamics. One drawback concerning a robust control at load variations is described in [1]. Another disadvantage is the jerk dependent reaction force on the secondary part of the linear motor, which will act in the opposite direction and with the same magnitude as the active force on the primary part [2]. As a result, the maximum accelerations and jerks have to be limited due to dynamic reactions of the machine frame [3,4]. To decouple these reaction forces in critical frequency ranges from the machine frame, without substantially limiting the dynamics of the primary part at the same time, jerk-decoupling technologies [5,6] have been developed. The principle of jerkdecoupling is shown in Fig. 1. The jerk-decoupling technology is based on a linear motor’s secondary part which is not bolted to the machine frame, but mounted on a separate slide which again is linked to the machine frame with spring-damper-elements. As a result, a mechanical filtering of the dynamic forces is possible. Critical oscillations may clearly be reduced. The major disadvantage of known jerk-decoupling systems is the additional secondary part slide. For a complete feed axis, a minimum of four guideways is required, two for the table with primary part and two for the secondary part slide. Both have to be of high stiffness because they have to transmit the high normal forces of the linear motor. This requirement makes jerk-decoupling systems expensive, particularly when long feed strokes are necessary. On top, high pretension of the secondary part guideways and passive spring-dampersystems reduces the energy efficiency of the feed axes. The research described in this paper addresses these disadvantages and proposes a new solution design.
The basis of a system simulation with an energy observer is given by different models of the mechanics, the drive technology, respectively electro-technology and the control engineering. A simulation for different basic structures using jerk-decoupling (JDC) makes sense with regard to the expected costs of appropriate system realizations. A model of the linear motor and the control circuits has been developed. In order to get the best approximation of the linear synchronous motor, a model of a rotating main machine is applied. By way of control, a field orientated control is used. This control provides a smooth motion at low speeds as well as an efficient operation at high speeds. Moreover, it is used to control linear motors, especially in machine tools. The models of control engineering employed are described in more detail in [7] and the mechanics, as well as the drive technology, are given in [8]. The system simulation considers mechanical elements like the friction in all runner blocks and the energy losses in the damping elements. The friction in the runner blocks is illustrated with three effects of the Coulomb’s and viscous friction as well as the Stribeck-effect. Based on this simulation environment considering the primary and secondary part of the jerk-decoupled axis and the use of a model of a synchronous linear direct drive, an energy observer has been developed. This observer monitors the energies in the individual elements. The focus is here on the ‘‘energy sinks’’, as for example the friction effects or the damping losses. Hence this system simulation enables the comparison of different guiding systems and concepts. More details regarding different simulations of energy losses can be derived from [9]. The basis of the following analysis represents an assumed jerk-limited trapezoidal motion profile at the desired value of the simulation. This was published in [7] and contains the algorithm for the determination of the allocated times and the behaviour of the feed axis in the motion profile. For the following view the delimitation parameters were set to a maximum acceleration of 1 g, a maximum jerk of 500 m/s3 and to a maximum speed of 120 m/min.
* Corresponding author. E-mail address: [email protected] (O. Gu¨mmer). 0007-8506/$ – see front matter ß 2009 CIRP. doi:10.1016/j.cirp.2009.03.043
B. Denkena et al. / CIRP Annals - Manufacturing Technology 58 (2009) 339–342
340
Fig. 1. Principle of jerk-decoupling. Fig. 3. Classical separate guidance (top) versus new relative guidance (bottom).
At the top of Fig. 2 the prior mentioned motion profile of the primary part in horizontal feed direction is depicted. During this motion profile, an energy of 68 J is converted within the guidance of the primary part (Prim.). An energy loss of 63 J is added, which is converted in the linear motor (LM). In the lower third of Fig. 2 a supplemental diagram of the energies of the drive system with JDC is represented. In addition an energy loss of 27 J in the friction of the JDC carriage and 44.5 J in the damping occurs. It is to be recognized that more work is converted in the mechanics, which must be applied by the linear motor. However, the losses in the linear motor remain constant. This is justified in the allocation of the work in force and velocity. In JDC systems the applied force is the same as in classical drive systems. However, the velocity is larger, because an additional movable body has been integrated. Since the force is proportional to the current and the velocity is proportional to the voltage, a higher voltage is necessary to float the same current. So the energy losses in the synchronous motor remain approximately the same, since the energy losses are proportional to the square of the currents. Only the magnet wheel voltage and thereby the terminal voltage increase. 3. Relative guidance concept Previous constructions of jerk-decoupled feed axes have been designed using separated guiding system concepts (Fig. 3). In this case, the primary part and the secondary part are guided separately to the machine frame. Compared to this, a new relative guiding system has been developed. This new concept provides a serial first
guidance, the exterior, which guides the primary part relative to the machine frame. A serial second guidance, the interior, guides the secondary part relative to the primary part. A connection from the secondary part to the machine frame does not exist in this new design. A technical comparison of the prior mentioned guiding concepts shows an advancement of the relative guidance concerning the force path and the vibration behaviour. The attraction force of the linear motor is carried only by the interior guidance, so that the exterior precision guidance is not affected. Due to this comparison, in the following work the relative guidance concept is analyzed in more detail. Since in the course of the following verification described here, the developed relative guiding system presents itself as favourable and economically advantageous in comparison to the separate guidance, a patent by the Leibniz University of Hanover is pending [10]. On the basis of the system simulation in chapter 2, an energy observation of the relative guiding system has been performed. Therefore, two different system simulations were developed. On one hand the separate guiding system, which is characterised by the independence of the guidance frictions and on the other hand the relative guidance, which is characterized by the coupled guiding behaviour. Regarding a point-to-point motion of 100 mm (refer to Fig. 2), it is to be recognized that the friction of the relative guidance in both guidances, the primary part and the jerkdecoupling carriage, decreased. Here the energy loss converted by friction decreases in the primary guidance from 18.9 to 13.3 J, which equals 29.6%. At the same time the friction energy of the secondary guidance decreases from 8.0 to 3.1 J, thus around 61.3%. Because of the ‘‘shorter’’ force flow, the high attraction force of the linear motor is carried only by the second guidance. The primary guidance assumes the precision function in this new arrangement. Parallel to the reduction of the friction energy the energy loss in the damping of the JDC rises. This is justified by the fact that a smaller friction in the system permits more movement of the JDC carriage and thus more kinetic energy in the damping is converted. However, the kinetic energy in the damping can be used in different ways compared to the friction energy. In Fig. 4 a comparison of the power loss is given for an assumed sine-wave motion. The friction losses of the primary part and the JDC carriage are displayed against the frequency. In this case, the friction losses are very different, since a linear direct drive stimulates the machine frame differently depending on the frequency. Hence, the applied energy is varying. The results show that the new concept of the relative guidance causes clearly smaller energy dissipations in all frequency ranges. An average energy conservation in the energy losses of 50.9% is reached with this configuration in the examined frequency band. 4. Energy-optimal dimensioning of the coupling elements
Fig. 2. Comparison of energy flow with and without jerk-decoupling.
The change of the energy loss in the synchronous motor can be neglected by using a jerk-decoupling (refer to chapter 2). In this chapter an energy optimization of the coupling elements on the basis of the system simulation and the energy observer is accomplished. The object is to gain experience for the energy optimization of feed axes of the three mechanical couple parameters
B. Denkena et al. / CIRP Annals - Manufacturing Technology 58 (2009) 339–342
341
Fig. 4. Comparison of the power loss of both guiding concepts (P = primary part, JDC = jerk-decoupling carriage). Fig. 5. Influence of the couple parameters on the compliance-frequency responses of the frame.
of the JDC in comparison to [11]. In the following the dimensioning of the coupling elements from the control engineering view is regarded, i.e. the mass of the JDC carriage mJDC, the spring stiffness cJDC and the damping constant dJDC. The motion profile is the same as it is already depicted in chapter 2. Before the optimization of the coupling parameters, the optimization of the moved masses is the focus of the investigation. Thus the parameters, which are adjusted in the control of the linear motor, have their validity related to the relative motion between
the two bodies. In the following a stopped linear direct drive is regarded, whose primary part is to be accelerated with a constant jerk. The accruing starting-jerk-efficiency at the time t = 0 depends on the mass ratio of the two motor components. If the mass of the JDC carriage mJDC corresponds to the mass of the primary part mP, the efficiency amounts hStJ = 0.5. At constant mP, the efficiency improves with an increasing mass of the JDC carriage. But this
Fig. 6. Energy-optimal dimensioning of the JDC.
342
B. Denkena et al. / CIRP Annals - Manufacturing Technology 58 (2009) 339–342
5. Verification of the simulations
Fig. 7. Position step response of the linear direct drive (P = primary part, JDC = jerkdecoupling carriage).
Finally the results of the simulations are verified at the test bed. A translatory feed axis with a maximum traverse path of 1150 mm and a maximum feed force of 7920 N has been build up. This test bed includes the new relative guiding concept for the JDC and adjustable coupling elements. In Fig. 7, a position step of 100 mm of the linear motor is regarded. It is to be recognized that the JDC carriage achieves a clearly greater balancing motion with an implemented JDC, than with a rigid attachment of the JDC carriage to the machine frame. However, this movement has no influence on the positioning accuracy of the linear motor. In Fig. 8 the oscillation velocity of the machine frame during a force step is represented. Here a clearly reduced oscillation stimulation is shown by using the JDC. It has been pointed out that it is possible to economically operate JDC systems in high-dynamic axes with the help of the new developed relative guidance [12]. 6. Summary In this contribution the relative guidance for jerk-decoupled feed axes is presented. A huge advantage can be seen in the clearly smaller friction energy losses of this guiding system in relation to separate guidances. Moreover, the proceeding for a controltechnical and energetic dimensioning of jerk-decoupled feed axes is presented. Frequency responses are considered in order to be able to absorb the resonances of the machine frame optimally. Also system simulations were performed in order to monitor the energy losses. With the help of this energy-optimal dimensioning the energy losses, which are related to the JDC, can be minimized by up to 50%. In the last step the results of the simulations are verified by means of a realised test bed using the patented relative guiding concept. This presented proceeding for an energy-optimal design of a jerk-decoupled translatory feed axis can be applied to other linear direct driven feed axes, for instance of machine tools, to improve the dynamic behaviour and to decrease the energy consumption.
Fig. 8. Oscillation velocity of the machine frame.
relation is valid only for the starting point of movement. For a detailed examination of the optimization of the mass ratio in dependence of the expected maximum dynamic values (acceleration amax and jerk jmax) refer to [12]. In the following view the optimization of the spring-damperelements is presented, at first from the control engineering view. For a better illustration of the optimization, the appropriate frequency responses are depicted in Fig. 5. For an optimum design the machine frame frequency response is important. Two parameters have to be optimized: The compliance in the first resonance point must be as small as possible and the frequency of the resonance point has to be as high as possible. If the frequency response of the JDC carriage is stable, the optimization from the control engineering view is completed. Moreover, an optimization of the spring-damper-elements in view of the losses can be accomplished, as previously described in chapter 2. With the consideration of these two criteria, it can now be examined for an optimum of the couple parameters within a ‘‘meaningful’’ range. This meaningful range contains the boundary condition of the possible design in respect to existing couple elements on the market. If both views are standardized, the diagrams in Fig. 6 can be obtained [12]. On the basis of this example it is to be recognized that the interpretation from the view of control engineering takes an optimal state. With a view to the energy loss, it can still be optimized. In this case, an enlargement of the spring stiffness cJDC would slightly raise the maximum point of compliance, but would minimize on the other hand the energy loss by up to 50%.
Acknowledgment The authors thank the European Commission for founding the Integrated Project ‘‘Next Generation Production Systems’’.
References [1] Van Brussel H, Van den Braembussche P (1998) Robust Control of Feed Drives with Linear Motors. Annals of CIRP 47:325–328. [2] Bubak, A., Soucek, P., Zeleny, J., August 3-7 2003, New Principles for Design of Highly Dynamic Machine Tools, Proceedings of the international conference ICPR-17, Blacksburg, Virginia, USA. [3] Erkorkmaz K, Altintas Y (2001) High Speed CNC System Design: Part I—Jerk Limited Trajectory Generation and Quintic Spline Interpolation. International Journal of Machine Tools and Manufacture 41(9):1323–1345. [4] Weck M, Kru¨ger P, Brecher C (2001) Limits for Controller Settings with Electric Linear Drives. International Journal of Machine Tools & Manufacture 41:65–88. [5] Berkemer J, Altenburger R, Koch T, Lehner W-D (2004) Effektive Nutzung des Leistungspotenzials von Direktantrieben. wt Werkstattstechnik Online 94(5):233–241. [6] Weck M, Ostermann T (2003) Lineardirektantriebe mit Impulsentkopplung. Antriebstechnik 42(11):61–64. [7] Denkena B, Hesse P (2005) Wirtschaftlichkeitsbetrachtung von Trapezprofilen. wt Werkstattstechnik Online 95(5). [8] Denkena B, Mo¨hring H-C, Hesse P (2006) Energiebetrachtung ruckentkoppelter Vorschubachsen – Simulative Untersuchungen des Energieflusses ruckentkoppelter Vorschubachsen. wt Werkstattstechnik Online 95(5). [9] Denkena B, Mo¨hring H-C, Hesse P (2007) Energy-Flow in Jerk-Decoupled Translatory Feed-Axes. Journal of Mechanical Engineering—Part C 221/1:89–98. [10] Patent Application Publication DE 102006046974 B3: Ruckentkoppelte Antriebsachse, Filing Date 04.10.2006, Publication Date 24.04.2008, Leibniz Universita¨t Hannover. [11] Neugebauer R, Riedel M, Drossel W-G (2004) Modellbasierte Auslegung von Koppelelementen. Antriebstechnik 43(11):70–74. [12] Hesse, P., 2008, Energieeffizientes Relativfu¨hrungskonzept fu¨r ruckentkoppelte Vorschubachsen, PhD Thesis, Leibniz Universita¨t Hannover, PZH–Verlag.