Design and Simulation of a Flexible Cutting Machine for Roll Forming Product.
Park, Hong Seok ; Dang, Duc Viet ; Lee, Gyu Bong 等
Design and Simulation of a Flexible Cutting Machine for Roll Forming Product.
1. Introduction
Roll forming parts are frequently applied to many kinds of industry
and automobile sector. Along with straight roll forming product, some of
roll forming products require a cured path (usually in arc form). In
this case, the cut-off process is more difficult than that of straight
products. The roll forming process requires the cutting operation to
separate a long formed strip to a desired length. The cutting devices
for straight roll forming parts are developed at a high level as
illustrated in Fig. 1. However, the cutting device for curved products
is still underdeveloped. Consequently, design a flexible and
multi-functional cutting devices that can cut different cross section
and product with arc or curvature in the longitudinal direction of roll
forming product is a significant research. In order to develop a new
product, the physical prototype can no longer suitable due to the time
-consuming and cost-intensive manufacturing and testing to detect weak
spots and optimize design [1]. Fortunately, literature reviews have
performed that approaches based upon virtual prototype simulation, using
well-defined material properties, numerical models, and controllers, can
be considered as an intelligent solution to obtain reliable results.
With the support of the virtual prototype, the designer can analysis and
optimize the mechanical design or the control design to achieve a
perfect system, therefore it saves time and cost and reduces the risk of
device damage caused by the conflict between both systems. There has
been a considerable amount of research in the virtual prototype
simulation which demonstrated the advantages of this method, such as
Catalin et al. [2] simulated the windshield wiper system with the
support of the virtual prototyping platform. Zouhaier [3] has built the
crank slider mechanism to illustrate the behavior of the whole
mechatronic system under different control strategies. Hajicek [4]
presented a methodology for establishing virtual CNC machine tool.
Moreover, the virtual prototypes of industrial equipment have been
proposed to investigate dynamic behaviour in the initial stage [5] [6].
The results of the aforementioned efforts indicated that virtual
prototyping techniques could be considered as a powerful approach to
simulation and optimization the physical prototype of the new product.
Therefore, this works attempted to develop a flexible cutting machine
with the virtual prototype simulation.
This paper is organized as follows: the research methodology is
described briefly in section 2. The concept of the flexible cutting
machine is performed in section 3 and the multi-body system model is
shown in section 4. Section 5 will be explained the virtual controller.
The results of co-simulation are showed section 6 and the conclusions
are presented in this section 7.
2. Research methodology
The virtual prototype simulation platform includes CAD-Computer
aided design, MBS-Multibody systems, FEA-Finite element analysis and
DFC-Design for control programs [2], as depicted in Fig. 2. The CAD
environment is used to create the geometric model of the system from the
concept of the manufacturer, which contains information about the mass
and inertia properties of the rigid parts. The MBS software, which
represents the central component of the virtual prototyping platform, is
used for analyzing, optimizing and simulating the kinematic and dynamic
behavior of the mechanical system. The FEA software is used for modeling
flexible components. DFC is a software product which is used to design
the control system. This software exchange information with the MBS
software. The exchange process creates a closed loop in which the
outputs of the MBS model are the inputs for the control system and
conversely. The combination between the MB S and the DFC system will be
implemented the virtual prototype.
The virtual prototype simulation of the flexible cutting machine is
established by the combination ADAMS software and MATLAB/Simulink
software as described in Fig. 3. With the concept of the machine, the
modeling will be established in SOLIDWORKS and then exported to ADAMS
software to create the multi-body system, with the possibility of
virtual measurement of any parameters of any components in the virtual
model. The controller will be designed in MATLAB environments which is
well-known for designing a control system. The co-simulation model of
both softwares will generate the virtual prototype which is performed
the real behavior of the machine.
3. The concept of the flexible cutting machine
Based on the straight forming machine, we attempt to develop the
flexible cutting machine. This machine is used to manufacture the
products require a cured path (usually in arc form), as shown in Fig. 4.
To satisfy the design requirements of the flexible cutting machine,
two conceptual designs were proposed. The cutting machine using three
degrees of freedoms and cutting saw was shown in Fig. 5, which includes
two translations (longitudinal and traverse axis) and a rotational axis.
The cutting movements are conducted based a combination of the machine
bed and rotary table.
The conceptual machine using two degrees of freedoms is presented
in Fig. 6. During forming process, the machine moves on two concentric
circular rails. We can change the radius of the moving path by adjusting
the position of the upper table. The cutting angle can be adjusted by
means of a rotational pivot.
Based on the combination of the two proposed concepts, a concept
design of the flexible cutting machine was proposed using five axes. The
specifications and the construction of the roll cutting machine are
shown in Fig. 7. During forming process, the base, turn, up-down, slide,
and head unit are fixed. The head unit moves in the specific curved
paths that is similar to the product profiles. The cutting movement at
the end point of the contour is conducted by shearing die with the
support of hydraulic cylinder.
The developed forming machine is a kind of moving cutting mechanism
one. The cutting mechanism that not only generates the curved parts, but
also cut off into accurate distance. The advantages of the flexible
cutting machine are as follows compared to the conventional one:
--The machine can cut any kind of roll forming product regardless
of straight or curve profile.
--Cutting distance is accurate because the mechanism is driven by
servo motor.
--Hydraulic shearing mechanism with low noise.
4. Multi-body system for the flexible cutting machine
4.1. Analytical modeling of a constrained multi-body mechanical
system
In this work, the flexible cutting machine was investigated as a
multi-body mechanical system including of several rigid bodies. In the
multi-body system [7], the generalized coordinates associated with rigid
body i is denoted in what follows by
[mathematical expression not reproducible] (1)
with [p.sub.i],[[epsilon].sub.i] is the position and the
orientation of a rigid body, respectively. For the system model
containing nb bodies, the vector q is represented to describe the
position and orientation of each body at a given time in the system.
q = [[[q.sup.T.sub.1] [q.sup.T.sub.2] ... [q.sup.T.sub.nb]].sup.T]
(2)
Joints are regarded as constraints in the multi-body system which
generally are obtained as
[PHI] = [PHI](q, t) = 0 (3)
The entire constraint equations imposed by the joints are showed as
[mathematical expression not reproducible] (4)
where, nj is the number of joints in the system. By taking one time
derivative of the position kinematic constraint equation (4), the
velocity kinematic constraint equations are expressed as follows
[[PHI].sub.g](q, t)[??] = -[[PHI].sub.t](q, t) (5)
By taking one time derivative of the kinematic constraint equations
Eqn (5), the acceleration kinematic constraint equations are obtained as
[mathematical expression not reproducible] (6)
The Lagrange multipliers form of the constraints acting on the
multi body system can be written as
M[??] + [[PHI].sup.T.sub.q][lambda] = F (7)
where, M is the generalized mass matrix that equates diag[[M.sub.1]
[M.sub.2] ... [M.sub.n]]; F is the system force vector; and 1 is the
array of Lagrange multipliers. Combining Eqns (6) and (7), the complete
set of constrained equations of motion can be written as follows
[mathematical expression not reproducible] (8)
Theories of multi-body systems are embedded to modelling and
analysis using computational method. It allows the designer to observe
how the mechanism functions without having to build an expensive real
world model and doing labour intensive measurements.
4.2. Multi-body system model
In order to generate the multi-body system of the flexible cutting
machine, all components or elements which have the shape and dimensions
of the physical model are modeled as 3D solid by SOLIDWORKS. The
geometry was transferred to ADAMS environment using the standard file
parasolid. The modeling process is constructed as the following sequence
for an easy modification in the design phase. Firstly, the geometrical
parameters of the parts such as material properties must be defined,
then mass and inertial matrices are generated automatically with main
parameters in Table 1. The flexible cutting machine model in ADAMS takes
several aspects into account, such as gravity, contact constraints,
joints, friction, motion and reference markers. All these definitions
and setting must be defined properly for good approximation of real
machine behavior in the virtual environment. The multi-bosy system of
the flexible cutting machine in ADAMS software is depicted as Fig. 8.
The simulation results of the position and velocity of the head
unit in ADAMS software as shown in Fig. 9 and Fig. 10 The trajectory of
the head unit in X-axis and Y-axis are reflected correctly the shape of
the product. Moreover, the velocity of the head unit is 200mm/s in the
moving process and 300mm/s in the return process as the specifications
of the machine when design. Therefore, the multi body simulation model
can be used to imitate the characteristics of the flexible cutting
machine.
5. Development of a control system for the flexible cutting machine
5.1. The interaction between the multi-body system and the control
system
The principle of the connection between ADAMS and MATLAB/Simulink
is depicted as Fig. 11. The input signal is a torque of the main servo
motor and the output signals are the measured parameters of the position
of the head unit. Subsequently, this model is exported to
MATLAB/Simulink which have a *.m file and an adams_sys are created as
shown in Fig. 12. It is also generates a command file (*.cmd) and a
dataset file (*.adm), which will be used during the simulation process.
The adams_sys block is created based on the information from the *.m
file. With these file, the control system block will be created in
MATLAB/Simulink.
5.2. Controller design
The PID control method can be applied easily and is widely known in
many control applications because of its simplicity and effectiveness.
However, this method is insensitive to parameter changes as proportional
gain [K.sub.P], integral gain [K.sub.I], derivative gain [K.sub.D] and
only suitable for the linear system. Luckily, there has been extensive
interest in self-tuning these three controller gains. For examples, the
PID self-tuning methods based on the relay feedback technique were
presented for a class of systems [8]. An adaptive PID control tuning was
proposed to cope with the control problem for a class of uncertain
chaotic systems with external disturbance [9]. Moreover, sliding mode
control (SMC) is one of the popular strategies to deal with uncertain
control systems [10], [11]. The main feature of SMC is the robustness
against parameter variations and external disturbances. Consequently,
the adaptive PID with SMC control system (ASMP) can be updated online
the PID gains with an adequate adaptation mechanism that is adapted with
variations of system parameters and external disturbances. In this work,
the ASMP is proposed to control the rolling process of machine. Fig. 13.
shows the block diagram of the adaptive SMC with PID control system for
the flexible cutting machine.
The flexible cutting machine is considered as a system with a
single-input and multi-output. The state-space equation which expresses
the head unit position can be expressed as follows:
[mathematical expression not reproducible] (9)
where, X = ([x.sub.1], [x.sub.2], [x.sub.3], [x.sub.4]) is a state
variable vector that represents the position and velocity of the head
unit in the X-axis and Y-axis, respectively. The [f.sub.1](X),
[b.sub.1](X), [f.sub.2](X) and [b.sub.2](X) are the nonlinear functions.
The [d.sub.1](t) and [d.sub.2](t) are presented for the bounded lumped
disturbances which include the system parameter variations and external
disturbances. The [u.sub.x] and [u.sub.y] are the control input to
control the position of the head unit in X-axis and Y-axis,
respectively.
From (9), the mechanical model has two subsystems: the position of
the head unit in X-axis and Y-axis. Therefore, the sliding surfaces of
the two subsystems are defined as:
[s.sub.x] = [[??].sub.x] + [[lambda].sub.x][e.sub.x] (10)
[s.sub.y] = [[??].sub.y] + [[lambda].sub.y][e.sub.y] (11)
In this paper, a control input u were designed to control
simultaneously the position of the head unit in X-axis and Y-axis. The
design methods for these two controllers are similar, therefore, we will
show the algorithm to drive the head unit's position in X-axis.
With the equation (10), where [e.sub.x]= [x.sub.d] - x; [x.sub.d]:
desired position; x: measured position; and [[lambda].sub.x]: positive
constant.
Derivative (10) and substituting [mathematical expression not
reproducible]
[mathematical expression not reproducible] (12)
The control input of PID controller is designed based on (12):
[mathematical expression not reproducible] (13)
where, A = [[K.sub.P][K.sub.I][K.sub.D]] is the vector of the gain
of PID controller and B = [[s [integral] s [ds/dt]].sup.T] is a basic
vector of PID controller; [epsilon] is an appropriate error. The control
signal [u.sub.x] of the controller is determined as:
[u.sub.x] = [u.sub.PID] + [u.sub.h] = [??]B + [u.sub.h] (14)
where, [mathematical expression not reproducible] is estimated
value of vector A; [u.sub.h]: control signal of the auxiliary
controller.
Substituting (14) into (12) yields
[mathematical expression not reproducible] (15)
where A = A - [??] is estimation error. In order to prove the
stability, the Lyapuvov function can be used.
V = [1/2][s.sup.2.sub.x] + [1/2[gamma]][A.sup.2] (16)
Derivative (16) yields:
[mathematical expression not reproducible] (17)
From (17), we have ([s.sub.x][b.sub.1]B + [1/[gamma]][??]) = 0
Hence, [mathematical expression not reproducible]
The three PID gains ([K.sub.P], [K.sub.I], and [K.sub.d]) are
on-line updated by the following adaptive laws:
[mathematical expression not reproducible] (18)
Considering (17) [??] = [s.sub.x][b.sub.1][epsilon] -
[b.sub.1][u.sub.h][s.sub.x] [less than or equal to] 0
With the auxiliary controller : [u.sub.h] = [eta]sgn(s); the sign
function
[mathematical expression not reproducible] (19)
We have:
[mathematical expression not reproducible], (20)
Equation (17) proves that the sliding surface is stability. The
control input for controlling the flexible cutting machine is composed
of the position control input [u.sub.x] and [u.sub.y] as:
u=[u.sub.x] + [u.sub.y] (21)
6. Simulation results
In this section, the co-simulation is implemented between the
multi-body system and the ASMP controller. First of all, the proposed
ASMP is applied for tracking control of the head unit of the roll
forming machine, and the comparisons with PID control are presented in
Fig. 14. From this figure, we can see that both PID and ASMP have the
overshoot and settling time is nearly zero, and the steady state error
has satisfied the stable control criteria, and disturbances are
perfectly eliminated very fast responses to overcome the initial error
conditions. However, the proposed ASMP control obtained much better
tracking performance than PID control, indeed, the error tracking of
ASMP control is smaller than PID control in the X-direction and
Y-direction. Consequently, the ASMP controller approach is suitable for
the roll forming machine which robust regardless of the system parameter
and disturbance variations strategy.
Furthermore, the simulation results of the virtual prototype
machine were conducted to derive the important parameters to optimize
the machine prototype. Fig. 15 shows the dynamic simulation of the head
unit, it was verified accurately with the specification of machine.
Moreover, the value force and torque of the ball-screw and the head unit
is shown in Fig. 16. The force of the ball screw impact to the head unit
to implemented the rolling process is maximum to 750N, as illustrated in
Fig. 16a. To make the head unit moving followed the curved part of the
product, the largest contact force is 130N, as presented in Fig. 16b.
Fig. 16c demonstrated the maximum torque to the ball screw is nearly
2000 N-mm. Therefore, these results were considered to support design
engineers to decide the best parameters for the machine.
7. Conclusion
In this paper, the flexible cutting machine for roll forming
product was designed and simulated, based on a multibody system and the
implementation of modern control technology. The mechanical model of the
flexible cutting machine is established with the concept ideas to
response the cutting requirements of roll forming product. Subsequently,
the modelling of machine was transferred to ADAMS environment for
analysis the dynamic behavior and the ASMP controller was designed for
controlling the nonlinear process movement of the machine in
MATLAB/Simulink. The virtual prototype simulation has already performed
that the ASMP controller robustly against disturbance, increased
productivity by reducing downtime, the virtual mechanical model could
precisely described the dynamic behavior of the flexible cutting
machine. Significantly, the approach can support the designers to modify
the mechanical and control designs to eliminate errors and increase the
accuracy. Therefore, this work is expected as a contribution to
improving the prototype's performance of the flexible cutting
machine.
In spite of the simulation models are useful, physical experiments
to verify the simulation and optimization results are indispensable.
Fig. 17 shows the physical prototype is established in the company. The
verification of the proposed ASMP method will be implemented in this
test and the results of the experimental study will be presented in a
future paper.
DOI: 10.2507/27th.daaam.proceedings.092
8. References
[1] C. Brecher, M. Week, S. Witt Y. Altintas. (2005). Virtual
Machine Tool CIRP Annals--Manufacturing Technology, vol. 54, no. 2, pp.
115-138
[2] Catalin Alexandra, Claudiu Pozna. (2009), Dynamic Modeling and
Control of the Windshield Wiper Mechanisms, Wseas transactions on
systems, vol. 8, no. 7
[3] Zouhaier Affi, Lotfi Romdhane. (2005), ADAMS/Simulink interface
for Dynamic Modeling and Control of Closed Loop Mechanisms, Proceedings
of the 7th WSEAS international conference on Automatic control, modeling
and simulation, USA, ISBN:960-8457-12-2, pp. 353-356
[4] Zdenek Hajicek. (2015), Simulation of virtual machine tool
during the development phase, Proceedings of the 26th DAAAM
International Symposium, ISSN 1726-9679, ISBN 978-3-902734-07-5, pp.
0948-0954
[5] Park Hong Seok & Le Ngoc Tran. (2011), A 3d simulation
system for mobile harbourcrane based on virtual prototyping technology,
Proceedings of the 22nd International DAAAM Symposium, ISSN 1726-9679,
ISBN 978-3-901509-83-4, pp. 0035-0036
[6] Zoran Pandilov, Andrzej Milecki, Amadeusz Nowak, Filip Gorski,
Damian Grajewski Damir Ciglar, Tihomir Mulc & Miho Klaic. (2016),
Virtual Modelling and Simulation of a CNC Machine Feed Drive System,
Transaction of FAMENA, vol. 39, no. 4, pp. 37-54
[7] Dan Negrut, Brett Harris. (2001), ADAMS Theory in a Nutshell
[8] A. Leva. (1993), PID autotuning algorithm based on relay
feedback, IEE Porc-Control Theory Appl., vol. 140, pp. 328-337
[9] W. D. Chang & J.J. Yan. (2005), Adaptive robust PID
controller design based on a sliding mode for uncertain chaotic systems,
Chaos Solitions & Fractals, vol. 26, pp. 167-175
[10] K. D. Young, V. I. Utkin & U. Ozguner. (1999), A control
engineer's guide to sliding mode control, IEEE Trans. Control Sys.
Tech, vol. 7, pp. 328-342
[11] A. S.I. Zinober. (1994), Variable Structure and Lyapnuov
Control, Berlin: Springer-Verlag, 1994
This Publication has to be referred as: Park, H[ong] S[eok]; Dang,
D[uc] V[iet]; Lee, G[yu] B[ong] & Veza, I[vica] (2016). Design and
Simulation of a Flexible Cutting Machine for Roll Forming Product,
Proceedings of the 27th DAAAM International Symposium, pp.0633-0644, B.
Katalinic (Ed.), Published by DAAAM International, ISBN
978-3-902734-08-2, ISSN 1726-9679, Vienna, Austria
Caption: Fig. 1 The cutting devices for straight product
Caption: Fig. 2. The virtual prototyping platform
Caption: Fig. 3. The strategy for design and simulation of the
flexible cutting machine.
Caption: Fig. 4. The main types of work piece will be manufactured
by the developed flexible cutting machine
Caption: Fig. 5. The cutting machine with three degrees of freedom
Caption: Fig. 6. The cutting machine with two degrees of freedom
Caption: Fig. 8. The multi-body system model of the flexible
cutting machine in ADAMS. MSC
Caption: Fig. 9. The simulation results in the moving process
Caption: Fig. 10. The simulation results in the return process
Caption: Fig. 11. The principle of the connection between ADAMS and
MATLAB/Simulink
Caption: Fig. 12. The adams_sub block
Caption: Fig. 13. Proposed ASMP control system scheme.
Caption: Fig. 14. Tracking the performance of the head unit of roll
forming machine
Caption: Fig. 15. The dynamic behavior of the head unit
Caption: Fig. 16. The force of main components in the roll forming
machine
Caption: Fig. 17. Physical prototype of the flexible cutting
machine for roll forming product.
Table 1. Characteristics of main components of the flexible
cutting machine in ADAMS
Body name Material Mass (kg) [I.sub.xx]
(kg.[m.sup.2])
Base Unit Cast steel 1424.6 1063.65
Turn Up and Down Unit Cast steel 421.34 78.44
Slide Unit Cast steel 280.76 42.24
Head Unit Cast steel 172.69 857.78
Shearing Die Die steel 38.01 188.19
Body name [I.sub.yy] [I.sub.zz]
(kg.[m.sup.2]) (kg.[m.sup.2])
Base Unit 796.51 278.63
Turn Up and Down Unit 52.62 43.95
Slide Unit 35.73 13.38
Head Unit 699.35 1175.74
Shearing Die 154.14 258.99
Fig. 7. The specifications and functionality of
the flexible cutting machine
Roll cutting machine specifications
SPECIFICATIONS VALUE UNIT
SHEARING POWER 1.5 TON
SHEARING SPEED 0.3 mm/s
MOVING SPEED 12 m/min
RETURN SPEED 18 m/min
SERVO MOTOR 3 kW
POWER
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