wishbone shaped damper of a helicopter rotor. An alternative approach consists in rotating the mandrel. (on z-axis) and using a delivery machine moving along ...
FILAMENT WINDING: AN INTEGRATED SIMULATION ENVIRONMENT FOR AUTOMATED CELL PROGRAMMING Alfredo Anglani, Francesco Nucci, Alessandro Spagnolo Department of Innovation Engineering, University of Lecce, Italy KEYWORDS: Filament winding, Automated process, Computer simulation. ABSTRACT. Filament winding is a process in which tensioned resin-impregnated continuous fibers are placed on a specified path on a mandrel. Automated systems have been adopted to deliver the fiber with a fixed level of accuracy. Process simulation is a very important question in automated applications. Moreover, the necessity to process complex shape objects leads to consider different alternatives to deliver the fiber along the model. In this paper, we developed a methodology to obtain simulation models in an integrated software environment. The proposed solution, on the one hand, focuses on the exploitation of the degrees of freedom in the cell, on the other, it considers the part program generation when a rotating mandrel is adopted. A test case has been realized in order to check the feasibility of our approach. Two different filament winding cell models have been developed by following the proposed approach and an in-depth analysis is carried out in order to investigate on both solutions.
1
INTRODUCTION
Filament winding is an effective method to manufacture composite objects. In this process, composite layers are continuously wound on a mandrel. Previous studies suggested that product quality highly depends on process parameters. Since in such a kind of technology a wide range of variables is involved, it is very difficult to tune the system when a new product shape has to be manufactured. Simulation plays an important role in this context, hence innovative methodologies are continuously issued in order to produce high quality simulation models. A filament winding cell can consist in several components. Basically, the main ones are fiber supply spools, a resin impregnator (if needed), fiber delivery or delivery eye unit, and a mandrel. The delivery eye places fibers on a specified path on the mandrel. The strands can either be pre-impregnated with polymeric resin or impregnated during the process. Once the winding is completed, the resin is cured and, then, the mandrel is removed. Since the winding is performed under tension, depending on the surface geometry, fibers can slip from the chosen position. Hence, a stable winding path has to be carefully designed in order to avoid the slipping. Major efforts have been made in the introduction of a robotic manipulator to perform the fiber placement activity. Indeed, in terms of shape, the high variability of such objects implies enormous difficulties in the design of automated machines. Existing flexible filament winding cells deal only with simple shape objects. Moreover, when machines work with complex geometry pieces, a low grade of flexibility is available. Therefore, only particular classes of pieces can be wound by using such machines. Recently, different filament winding cells have been designed in order to solve such a problem. Highly flexible cells have been issued and different complex shape objects have been obtained by filament winding technology. Depending on the manipulator workspace, using redundant degrees of freedom of a manipu-
lator, it is possible to choose among multiple movement strategies in order to optimize several factors. Nevertheless, such robotic based filament winding cells entail several drawbacks: robots do not allow high production rates; different robot degrees of freedom are not exploited; the winding of particularly complex shape objects can lead robots to assume critical configurations. Different studies have been made on this issue, [1][2][3][4]. Various theories suggest the way of obtaining the manipulator delivery eye point sequence once the path winding on the model is assigned, [5][6]. Recently, the determination of the corresponding robot part program has been investigated [7]. Additional studies have been made on this topic in order to find the solution of the manipulator inverse kinematic problem using a numerical algorithm, [8] [9] [4]. Other studies have investigated the possibility of evaluating, in qualitative and quantitative terms, the results of these inverse kinematic algorithms, [10] [11]. In this paper we have dealt with the evaluation of automated filament winding cells in which degrees of freedom are distributed between the mandrel and the delivery mechanism. The main advantage consists in the possibility of using - for a specific family of pieces – an overall number of degrees of freedom lower than the ones required by adopting a robotic cell with a fixed mandrel. Moreover, both high speed winding and low stress may be obtained in cell mechanisms. In the following section, the generation of the cell part program is presented. Then a methodology based on a simulation model for the study of such a cell is described. Finally, a test case is presented in order to show the potential of such a methodology and simulation results are reported.
2
DEGREES OF FREEDOM IN AN AUTOMATED CELL
Several approaches have been used to investigate on the possibility of adopting general-purpose machines for filament winding. Particularly, most of the studies focused on the application of anthropomorphic robots. The limited skill of such a kind of manipulator and the particular nature of the filament winding do not suggest the use of such a solution for a variety of products. The problem is of major importance for the complex shape objects. It is very important to note that a careful distribution – between delivery machine and mandrel – of the available degrees of freedom in such a cell, increases in the variety of obtainable pieces. An innovative approach to the classical robotic cell consists in the possibility of (1) moving the mandrel – in order to facilitate the machine work – and (2) using a simpler delivery machine (in terms of number of degrees of freedom). In this way, the main advantage consists in using a less complex delivery device and reducing stress factors during the working phase. It is important to note that the movement complexity reduction implies taking into account questions concerning automation science, such as minimization of joint wearing, working range for each joint and movement inversions. The main drawback consists in the need of controlling, simultaneously, different mobile systems. It is important to note that the distribution of available degrees of freedom can lead to the reduction of their overall number. For example a six-axes robot can be used to perform a winding operation for the pieces reported in FIGURE 1 – final piece (a) and mandrel (b) are represented. The piece is a wishbone shaped damper of a helicopter rotor. An alternative approach consists in rotating the mandrel (on z-axis) and using a delivery machine moving along a vertical plane. The combination of such movements leads to obtaining a feasible winding operation by using only 3 degrees of freedom. In order to guarantee a proper stress distribution and a right winding on the mandrel, the configuration has to take into account the fiber tension force. Indeed, the delivery eye point sequence is generated in order to maintain a particular mutual condition between mandrel and fiber – fiber has to be tangential to the mandrel in the delivery point. Such a condition must be ensured after the movements have been divided between mandrel and delivery device. In TABLE 1 different feasible alternatives are reported.
(a)
(b)
FIGURE 1. Wishbone shaped damper of a helicopter rotor TABLE 1. Division of degrees of freedom for a winding operation
Degrees of freedom Delivery device Mandrel 6 0
3
Total 6
2
1
3
3
0
3
0
3
3
Description Six axes robot, difficulty to realize a part of complex shape objects Efficiency in the division of movements. Wide range of complex shape objects can be obtained. Robot with not enough skill to realize a complex shape object. System having a fixed delivery device. It is difficult to control both tension and fiber delivering.
PART PROGRAM GENERATION
Part program generation basically consists in the determination of the exact list of movements for each component in time. Such an activity is very complex when the number of degrees of freedom is high. Indeed, the availability of different solutions to execute a particular movement leads to consider various alternatives. In such a context, complicated inverse kinematic algorithms have to be adopted. When the number of degrees of freedom is limited, this module can be significantly simplified by focusing on the particular division of movements. Once the point sequence – the delivery eye has to pass through – is determined, the methodology we adopted consists in expressing the coordinates in a way linked to the available degrees of freedom. In such a context, a coordinate transformation has to be performed in order to get the final variables. The above solution allows finding a solution to the problem expeditiously, with regard to the part program determination of the cell described in the previous section. The Cartesian coordinates (x,y,z) in the three-dimensional space are transformed in a cylindrical form (r,α,z), see FIGURE 2..
P(x,y,z) z x
α
z
y
Variable Association r horizontal movement of the delivery device z vertical movement of the delivery device rotational movement of the mandrel α
r
FIGURE 2. Cylindrical coordinate system
Both coordinate systems have the same origin – i.e. in the mandrel rotation axis, on the bottom part. The correspondence between coordinate variables and cell movements is described in FIGURE 2. Supposing the piece is fixed, the point sequence the delivery eye has to pass through – to lay the fiber on FIGURE 1a path – can be obtained, [6]. Since the delivery device has two degrees of freedom, it can lay down the fiber only on a YZ parallel plane. Such a plane is named reachable plane (RP from this point on) having a geometrical expression of x=x0. Consequently, the piece has to be rotated so that the corresponding delivery eye point belongs to RP. Hence, a coordinate transformation is performed each time Referring to FIGURE 3a, {O1, X1, Y1, Z1} is a referring frame rotated at angle α, with respect to {O, X, Y, Z}. Transformation formulas are reported in (1). (1) x = x1 cosα − y1 sinα , y = x1 sinα + y1 cosα, z = z1 Z = Z1
Y = Y1
P
x0 O = O1
α
x0 α
Y Y1
P1 r!
1
X1 X
(a)
α
P θ1 r! X = X1 θ O = O1 (b)
(c)
FIGURE 3. Rotation of the referring frame (a), geometrical description of the mandrel rotation (b) and reachable plane representation (c)
Supposing {O, X, Y, Z} referring frame is fixed and {O1, X1, Y1, Z1} rotates along with the mandrel. Delivery eye coordinate values are known in the {O1, X1, Y1, Z1} because this referring frame is integral with the mandrel. Referring to the XY plane view, P1 is the position of the delivery eye assuming piece is fixed, whereas P is the corresponding point on RP where delivery has to be actually carried out, by rotating the piece of α (see FIGURE 3b and FIGURE 3c). In order to determine α, the difference between θ e θ1 has to be calculated, where θ (θ1) is the angle between OP (OP1) and X-axis. Since the winding path is available, it is possible to determine θ1 by using (2). Supposing that ρ=|OP|= |OP1|= [(x1)2+(y1)2] ½ and cos(θ)=x0/ρ, it is possible to obtain θ by using (3). In this way, the angle α – the mandrel has to rotate in order to bring P1 on RP – is equal to (θ−θ1). Once a rotation has been performed, the delivery eye can reach the final point and the next point in the sequence has to be considered – so a new rotation is made to bring it on the RP. Consequently, each point in the delivery-eye location list is subjected to consecutive coordinate transformations because of the repeated rotations. θ1 = atan (y1/x1) θ = acos (x0/ρ)
4
(2) (3)
MODEL BUILDING
The proposed methodology enables the designing of a simulation model for an automated filament winding cell. A proper template has been produced for the selected software architecture, which is Visual Nastran 6.2 enhanced with Visual Basic 6 features under MS Windows O.S. The main advantage of the solution proposed consists in the possibility of straightforwardly producing a winding cell model once
the main characteristics of the process are available. Indeed, the Windows-based interface and Visual Nastran features enable the simulation modeler to easily import cell components and describe how the whole system works. In order for this software package to be capable to meet the filament winding needs, Visual Basic integration has been developed. This makes it possible to read of a filament winding part point sequence – in terms of delivery eye locations and mandrel points – and reproducing it on the designed model. An additional advantage consists in the possibility of varying the process parameters during the simulation running. Indeed for actuators, it is possible to vary the following parameters: velocity, acceleration, force. Whereas for motors, the following quantities can be changed: angular velocity, angular acceleration, torque. For this reason, it is very simple to develop a proper Visual Basic module capable of controlling, over time, the value of such parameters in order to obtain a particular motion law [12]. Finally, it is possible to develop a generation part program module based on the characteristics of the designed model; in this context the availability of a programming language – such as Visual Basic – permits to reach an high level of flexibility and efficiency. Once the part program computation algorithm issues the list of movements required to lay the fiber down, the Visual Basic module sends the parameters - such as position, velocity, acceleration - to simulate the expected movement for actuators and motors modeled in Visual Nastran. Moreover, it is possible to reproduce the fiber tension – Visual Basic module can vary the module and the direction of such a parameter depending on the delivering path.
5
TEST CASE
In order to demonstrate the possibility of our approach to study a generic filament winding cell for the processing of complex shape objects, we designed two simple cells to lay down the fiber on the mandrel showed in FIGURE 1b. Simulation models have been compared in terms of performances by using features available in the developed template. Cell configurations are represented in FIGURE 4. Z
Z
L
ω
L1 R
L1
D2
L3
θ
L6 L2
D
a
L4
L2
a0 t
Tool Z Tool Y
L3
Tool Z
D1 B
Y
L5
-a0 tL/2
Tool Y
tL
Y
(a)
(b)
(c)
FIGURE 4. First (a) and second (b) robotic cell. Motion law(c)
Once the delivery device is considered, it is important to analyze the stress the delivery eye is subject to. The designed model provides force and torque data for each model component. In particular, reaction forces are very significant for the evaluation of each joint stress. The realized template allows running different simulations by using different limits for the simulation parameters (i.e. acceleration or torque) in order to study the system performances depending on such factors. For example, a constant acceleration motion law can be used to control both actuators and motors (FIGURE 4c). The winding path is sampled so that a point sequence is issued. The delivery device passes from one point to the next one by using the motion law. For each active element in the model, a maximum acceleration value and a specific motion
length are available. First, the actuator/motor completing for last the own motion is detected – this element, at a given time tL, completes the action by using the maximum available acceleration. The others can adopt an acceleration value lower than the maximum obtainable in order to complete the activity at the same time tL. An interesting study can be performed by analyzing the connection between such acceleration limits and system performance, in terms of process completion time. Fiber tension is assumed constant. Two files provide the coordinates of the set point for delivery eye and the corresponding one on the mandrel. In the first model, an actuator is used for the delivery eye vertical movements. Whereas, in the second, a motor – controlling a connecting rod and a crank –– is applied. In both models a motor controls the mandrel rotation and an actuator moves the delivery eye horizontally.
6
RESULTS
Several simulation runs have been performed in order to study the winding process by using the two models considered. For each actuator/motor, different values of maximum acceleration have been established. In other words, simulation runs use different values for aMAX in order to determine which part of the model needs of performance improving. Threshold values are reported in TABLE 2 and refer to FIGURE 4a cell model. In the FIGURE 4b cell model mandrel and horizontal actuator thresholds are the same, whereas crank motor acceleration limit is calculated so that completion time is equal for both models. TABLE 2. Maximum acceleration for the active elements in the two models
Simulation run 1 2 3 4
Mandrel [rad s-2] 25 50 25 25
Maximum acceleration Horizontal Actuator Vertical Actuator [cm s-2] [cm s-2] 25 25 25 25 50 25 25 50
The first model analysis – concerning the mandrel motion – shows the selected threshold value is excessive for the kind of movement to be performed; hence processing time is not affected by mandrel rotation. Moving concerning the other active elements are crucial in both models. Indeed, completion time greatly depends on such movement parameters. Maximum value for the actual mandrel acceleration is reported in TABLE 3 – row 1. As it is possible to note no variation is detected when aMAX changes. The maximum value of mandrel acceleration is 17 (upper bounds are reported in TABLE 2). Consequently, there is no need to improve performance in such a motor when aMAX is greater than 17. For the first model, the maximum of delivery eye acceleration along the two directions is reported in TABLE 3 – row 3 and 4. When aMAX is doubled (simulation run 3 and 4) it is possible to note that the actual acceleration maximum changes. It is possible to observe the decreasing of the processing time (see TABLE 3 – row 5) along with the different simulation runs. Passing from the simulation run 1 to 4, saved time is equal to 16.76%. Threshold acceleration values greatly affects reactions performed by the actuators and motors. In TABLE 3 – row 6 and 7 – these aspects are showed, differences in the two models are due to the unlike mass distribution in the models. It is important to note when horizontal (vertical) actuator acceleration increases, horizontal (vertical) constrain reaction gets higher; see TABLE 3 – row 6 (TABLE 3 – row 7).
TABLE 3. First model simulation results
Row 1 2 3 4 5 6 7
Simulation run Mandrel Max Angular Acceleration [rad/ s2] Mandrel Max Torque [Ncm] Max Ay [cm/s2] Max Az [cm/s2] Processing time [s] Max horizontal actuator reaction [N] Max vertical actuator reaction [N]
1 17.0 4.0 22.4 24.1 70.4 2.6 177.4
2 17.0 4.0 22.4 24.1 70.4 2.6 177.4
3 17.0 4.0 47.3 24.1 65.2 5.6 177.4
4 17.0 4.0 22.4 49.2 58.6 2.6 181.9
On the basis of the results obtained, the second model behavior is quite similar to the other one in terms of mandrel rotation motor and horizontal movements. Instead, differences can be detected for the constraint reactions because of the variation in the mass distribution. Since different ways to obtain the vertical movements are, simulation results are significantly altered for such a question. In the first model, an actuator directly controls vertical movement accelerations. In the second model, the complexity of the relation standing between rotation motor and vertical displacement makes difficult the controlling of the vertical acceleration. The comparison of the maximum values for the vertical movements acceleration in both models is reported in TABLE 4 – rows 1-4. As it is possible to note in the second model, acceleration is greater than the one on the first. This behavior greatly affects the force values on the two models. Negative acceleration values are related to downward movements. Moreover, data reported in TABLE 4 – rows 5-8 – makes it easy to observe the second model is more stressed in the z-axis verse. TABLE 4. Simulation result comparison
Row 1 2 3 4 5 6 7 8
Model 1 2 1 2 1 2 1 2
Simulation run Parameter Min vertical acceleration [cms-2] Min vertical acceleration [cms-2] Max vertical acceleration [cms-2] Max vertical acceleration [cms-2] Min vertical force on delivery arm [N] Min vertical force on delivery arm [N] Max vertical force on delivery arm [N] Max vertical force on delivery arm [N]
1
2
3
4
-24.1 -51.4 24.1 54.6 112.6 109.4 118.3 121.9
-24.1 -51.4 24.1 54.6 112.6 109.4 118.3 121.9
-24.1 -51.4 24.1 54.6 112.6 109.5 118.3 121.9
-49.2 -115.6 49.2 79.3 109.7 101.8 121.3 124.8
The second model is subjected to wider variability. This is particularly clear in simulation run 4 – difference between maximum and minimum values is 22.9 N whereas in the first it is just 11.3 N. The analysis on the forces and torques in the other constraints leads to the conclusion that differences exist due to the distinct geometry. In TABLE 5 variations of the crank gear angular acceleration and motor torque are shown. In particular, maximum values are reported. It is possible to note peak values increase from the first to the last simulation run, except for the second – only the mandrel motor acceleration is altered. TABLE 5. Second model simulation results
Row Simulation run 1 Max crank gear angular acceleration [rads-2] 2 Max crank gear motor torque [Nm]
1 7.0 28.6
2 7.0 28.6
3 12.4 28.6
4 15.7 29.8
7
CONCLUSION
The proposed methodology permits to investigate on a given filament winding cell. In particular, the above mentioned analysis allows the selection of the appropriate winding parameters in order to maximize system performance taking into account the stress the different elements are subjected to. Moreover, the proposed approach exploits the possibility of using an integrated architecture to take advantage of the Visual Nastran and Visual Basic software packages. A theoretical approach is issued in order to manage the rotation of the mandrel and improve the utilization of the available degrees of freedom in a generic cell. The methodology enables the simulation model designer to quickly develop an accurate representation of a winding device. Moreover, a study is carried out in order to analyze in quantitative terms the results of such simulation models.
8
ACKNOWLEDGEMENTS
The work described in this paper has been funded by Project 488-92 "Sistema di produzione filament winding di manufatti a geometria complessa caratterizzati da alte prestazioni funzionali ed alta affidabilità", cluster C19, programma operativo del piano “Tecnologie Innovative per i Beni Strumentali”.
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