Research paperMechatronics modeling and vibration analysis of a 2-DOF parallel manipulator in a 5-DOF hybrid machine tool
Introduction
High speed and high accuracy have become the most important performance requirements of modern machine tools [1], [2], [3]. Compared with the traditional machine tool, the parallel kinematic machine/hybrid machine tool has conceptual potential in better motion dynamics, lower mass/inertia property and higher structural rigidity [4], [5]. Thus, parallel manipulators are of great interest in both industry and academic, and many kinds of parallel kinematic machines have been proposed, such as the Ecospeed, Tricept and Exechon [6]. To fulfill the performance requirements, the machine tool is to employ small-mass and high-stiffness structural components, as well as high adjustable controller parameters. However, this leads to interactions between the mechanical structure and the control system, which may cause unexpected vibrations or even instability [7]. This limits further development of the machine tool.
Many research institutions and enterprises have begun to study the interactions between the control subsystem and the mechanical subsystem of CNC machine tools [8], [9]. Weck and Brecher et al. conducted a series of research on coupling of multi-body models with control loops [12], [13]. Witt discussed the FRFs of the tool center point at different controller settings [14]. These research focused on the influence of the control system on dynamic characteristics of the mechanical structure, but ignored the influence of the structure on the controller performance. Da Silva addressed the integrated design of structural and control parameters of serial machines [10]. Siemens [11] developed “Mechatronics Support” technology that can realize the dynamic simulation, performance optimization and structural design considering the electromechanical coupling effects. In spite of the numerous studies on mechatronics system, there are still many problems as pointed out by Bradley in his paper “Mechatronics-More questions than answers” [15].
Mechatronics modeling is the first and significant stage to investigate the interactions between the control subsystem and the mechanical subsystem. The traditional mechatronics modeling methods can mainly be classified as replacing model method and co-simulation approach [16]. The replacing model method utilizes either analogue models of mechanical structure for simulation of control loops or analogue models of control loops for FEA-model of the structure [12], [17]. Some scholars have done a great deal of research based on the former. However, this method pays attention to the controller performance and simplifies the structural flexibility too much. The co-simulation approach [7], [13] connects several independent simulation environments via interfaces during the simulation, such as a structural model in Finite element model and a control model in Matlab/Simulink. The velocity/displacement of the measurement system and the forces of the controllers are exchanged with the aid of interfaces between the multi-body simulation environment and the control design environment. The co-simulation method may be very precise, which depends on the selected integration scheme. However, the trade-off needs to be overcome between calculation efficiency and accuracy. Another challenge in the design of a mechatronics system is to generate a computer model that contains mixed energy domains and can derive uniform algebraic relations among state variables.
Some scholars have begun to establish mechatronics models based on bond graph theory proposed by H. M. Paynter from MIT. The bond graph represents all types of physical systems by considering the power exchange between its unified basic elements [18], [19], [20]. Thus bond graph modeling provides convenience for studying the interaction between subsystems. However, there are few literatures on the bond graph modeling of parallel manipulators [21], [22], [23]. Due to the nonlinear characteristics and flexible components of parallel manipulators, it is a challenging task to achieve the mechatronics model of a parallel manipulator.
In this paper, the mechatronics model of a 2-DOF parallel manipulator in a 5-DOF hybrid machine tool is established based on bond graph, and the coupled interactions between the mechanical subsystem and the control subsystem is investigated. The forced vibrations induced by motion command input and cutting forces are investigated. This paper is organized as follows. Section 2 gives the structure description and kinematic analysis of the 2-DOF parallel manipulator. Section 3 establishes the bond graph model for each component of the parallel mechanism. Section 4 addresses the integrated mechatronics model and the interactions between the mechanical subsystem and the control subsystem. Sections 5 and 6 deal with the CFRs of control loops with consideration of mechanical structure and the FRF of the moving platform considering control loops, respectively. Section 7 gives the conclusions of the paper.
Section snippets
Structure description
A 5-DOF hybrid machine tool is designed to mill huge blades and guide vanes for hydraulic turbines. As shown in Fig. 1, it is composed of a 2-DOF translational parallel manipulator, a 2-DOF rotational milling head and a feed worktable. It is usually used to carry out 5-face milling. The 2-DOF parallel manipulator consists of a gantry frame, a moving platform, two active sliders and two kinematic chains. Each chain is built as a parallelogram.
Kinematic analysis
The kinematic model of the parallel manipulator is
bond graph model of flexible links
Considering that the control subsystem influences the mechanical dynamics mainly in the parallelogram plane, the 2-DOF parallel manipulator is simplified as a 2D model to investigate the interactions between the control subsystem and the mechanical subsystem. The deformation normal to the parallelogram plane is neglected. Compared with the sliders and moving platform, the long thin links have large elastic deformation. The flexible links can make a significant effect on the dynamic performance
Coupling analysis of mechanical subsystem and control subsystem
Both the feed axes of the parallel manipulator are driven by the permanent magnet synchronous motors (PMSM). The voltage, torque constant, torque equations and back electric motive constant are the same as those of the DC motor, so the PMSM can be approximated as the DC motor to construct the bond graph model. Like most feed drives, the cascaded control structure is used which consists of a current loop, velocity loop and position loop. Due to the fast response speed of the current, the current
CFR of control loops considering mechanical structure
It is better to use the frequency response of the moving platform to study the forced vibration caused by the motion command input. However, it is difficult to measure the terminal movement of the moving platform due to the semi-closed loop control of the manipulator. In this section, the CFRs of the position and velocity loops with consideration of mechanical structure are utilized for the analysis of the forced vibration caused by the motion command input, as well as for the estimation of the
FRF of moving platform considering the control loops
The FRF of the moving platform with consideration of control loops is used to study the forced vibration caused by the cutting forces, as well as to estimate the influence of the control system on the mechanical structure. The servo motors are enabled and the initial position of the parallel manipulator is given as the motion command input. Thus, the whole mechatronic system of the parallel manipulator can be simulated.
The FRFs of the moving platform in the X-axis direction at different
Conclusions
This paper derives a mechatronics model of a 2-DOF parallel manipulator based on bond graph, and proposes an approach to investigate the interactions between the mechanical subsystem and the control subsystem. From this investigation, the following conclusions can be drawn:
(1) As a modeling tool, bond graph technique is effective to design and analyze a mechatronics system from scratch. The bandwidth of the velocity loop is coupled with low-order natural frequency of the mechanical structure.
Acknowledgment
This work is supported by the National Natural Science Foundation of China (Grant nos. 51622505 and 51575307), the Science and Technology Major Project-Advanced NC Machine Tools & Basic Manufacturing Equipments (2016ZX04004004), and Top-Notch Young Talents Program of China.
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