MSMechanical SciencesMSMech. Sci.2191-916XCopernicus GmbHGöttingen, Germany10.5194/ms-6-109-2015Flexibility oriented design of a horizontal wrapping machineGibertiH.hermes.giberti@polimi.ithttps://orcid.org/0000-0001-8840-8497PaganiA.Politecnico Di Milano, Dipartimento di Meccanica, Campus Bovisa Sud, via La Masa 1, 20156, Milano, ItalyFpz S.p.a., Via Fratelli Cervi, 18, 20049 Concorezzo (MB), ItalyH. Giberti (hermes.giberti@polimi.it)24July20156210911817March201519June20156July2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://ms.copernicus.org/articles/6/109/2015/ms-6-109-2015.htmlThe full text article is available as a PDF file from https://ms.copernicus.org/articles/6/109/2015/ms-6-109-2015.pdf
Flexibility and high production volumes are very important requirements in
modern production lines. In most industrial processes, in order to reach high
production volumes, the items are rarely stopped into a production line and
all the machining processes are executed by synchronising the tools to the
moving material web. “Flying saw” and “cross cutter” are techniques
widely used in these contexts to increase productivity but usually they are
studied from a control point of view.
This work highlights the kinematic and dynamic synthesis of the general
framework of a flying machining device with the emphasis on the driving
system chosen and the design parameter definition, in order to guarantee the
required performance in terms of flexibility and high production volumes. The
paper develops and applies a flexibility oriented design to an horizontal
wrapping machine.
Introduction
In modern production systems it is increasingly important to increase
productivity and at the same time ensure high flexibility levels with respect
to the change of product or the size thereof. These requirements are by
definition antithetical . It
is difficult for high production machines to elaborate a range of highly
diversified goods. On the other hand it is difficult for flexible machines to
reach high production levels.
In most industrial processes, in order to reach high production volumes, the
items pass through the production line in a continuous way. Thus the items or
process are rarely stopped and all the machining processes are executed with
the items in movement. Therefore the tools have to be synchronised to the
moving material web and after the machining process, those tools have to be
positioned at the starting point for the next cycle.
Processes such as welding, embossing, printing, cutting, sealing, gripping,
etc., normally found in a production line, are by their very nature not
continuous. In these cases the manufacturing processes have to be executed
when the item is stopped. Thus the production line works in an intermittently
way. To eliminate the wasting of time in stopping and restarting the line it
is necessary that the tools follow the items.
Regardless of the industrial field, when the tool moves along a rectilinear
trajectory, the application is generally called “flying saws”
and the tool is mounted on a slide that moves together with
the piece to be worked. After the machining process has been completed, the
tool returns to its original position ready for the next work cycle.
Alternatively if the tool moves along a closed trajectory, usually a circular
one, the flying tool is referred to as a cross cutter . These
kind of manufacturing processes are generally referred to as “flying
machining” and several devices have been developed to perform these in
various industrial fields.
Regardless of the industrial sector and the flying machining solution chosen,
the design set of problems and the methods of controlling the system are the
same. As shown in in fact flying saw and cross cutter systems
could been parametrized and studied in an analogous way. Obviously technical
solutions developed to move the tools are different but the methodology to
synthesise the system could be considered similar.
It is possible to find several papers that have been published regarding
flying machining but none of these deals with the problem in general: each
one regards specific cases. Most of them are about the control problem. In
, for example, a new digital control system has been
designed and implemented in order to replace the existing obsolete one in a
cutting system into a production line of STAHL-37 steel tubes. In this case
the existing hardware of the cutting system (motor, drive, mechanical
equipment) has been maintained. A similar approach is presented in
, but in this case the authors suggest substituting the drive
and control systems in order to improve the performance of the cross cuter in
the paper or board production line. For these purposes a close examination of
the characteristics and requirements of basic subsystems of the paper-board
cross cutter from the control system perspective is done.
The control system is studied in depth in . In that work the
authors propose a control architecture based on ARM and FPGA to reach
high-speed, high-precision, high dynamic, high rigidity performance in a
flyng shear cutting system. In view of the increase in demand in the face of
the increasing of wrapper machine request for wrapping machines, particularly
in the Chinese market , the authors of the paper
show a synchronizing servo motion and an iterative learning control useful
for horizontal flow wrapper. Also in this case the focus of the work is on
the control system and on the architecture whereby one can obtain good
cutting accuracy and eliminate the repeatable position error. The control
problems have been widely studied since the second half of the last century
. With the spread of new electronic devices the control
approach changed shifting from analog solutions to digital ones
up to the more modern approaches mentioned above.
These studies address the control system in reaching the required performance
and no analysis is addressed on the layout of the cutting tool. In
an optimal control system is considered in order to minimize the
driving torque. In this case kinematic and dynamic are taken into account but
without a detailed study on the effects that the design parameters have in
terms of attainable productivity. A proposal for the revision of the cross
cutter system layout is presented in . The authors suggest
operating the cutter by separately controlled servo drives but, also in this
case the focus remains on how to control the cutter position.
This work highlights the kinematic and dynamic synthesis of a general flying
machining device. Particular attention is paid to the choose of the driving
system and the design parameters, so as to guarantee the required performance
in terms of flexibility and high production volumes. By virtue of the
generalisation set up in the design method is refers to the
cross cutter solution which is widespread in food packaging systems.
The focus of this study is on a flexibility oriented design procedure which
takes into account the input parameters necessary to avoid limitations and
constraints to the potential of the machine. A general framework is provided,
allowing the designer to assess different possible motor-reducer solutions
and design parameter combinations, taking into account the various advantages
or limitations in term of flexibility. This new approach satisfies two
requirements. The first one can verify, theoretically the cutting flexibility
in an existing cutting machine. The second can design a new cutting machine
capable of reaching a much higher production flexibility level.
This work is organized as follows. In Sect. , the flying
cutting machine is described. In Sect. the motion laws adopted
to perform the cutting operation are set out and analysed while their effects
on the dynamic loads are set out in Sect. . In Sect.
case study simulations and results are presented. In
conclusion in Sect. the final considerations are summarized.
Flow-pack systems: horizontal wrapping machine
A particularly lively industry in which the flying machining is used is the
packaging field. A packaging machine is a system used to cover wholly or
partially single items or collected group of them with a flexible material.
Wrapping machine is a kind of packaging machine that is used to wrap small
items with paper or plastic film. The first noted wrapping machine was
developed by William and Henry Rose, in England at the end of the nineteenth
century .
The typical layout of a flow-pack machine is depicted in Fig. . A specific wrapping machine is taken as an example in
order to support the theoretical background with a numeric example. It is
worth noting that the following considerations are general and not related to
a specific flying cutting technology application. The purpose of this kind of
machine is to weld and cut the double plastic film that will form the
package, while the product is already between them. The plastic film is
unreel by the film feed roller and passes through the forming
box that folds it in the final configuration. It is important to note that
the product arrives on a conveyor-belt and the plastic film is bent around
it. The product moves forward to the unit that package it. A couple of
rotating heads are used to execute these operations.
Usually, they are synchronous, having the same motor and control unit, even
if some attempts to adopt an asynchronous control strategy have been made
. On their external circumferences, n tools are
mounted with the double purpose to weld and cut the packages. In fact, each
tool is constituted by a central saw profile to cut each package, whose ends
are simultaneously welded by heat-seals units fitted on the side of the saw
profile.
Wrapping machine.
Design framework
Each package is composed by three parts as sketched in Fig. 2a:
two welded terminals (LT/2+LT/2) and the central part where the
object to package lies (LP,a). It is important to highlight that the
expression “product length” LP used in this work refers to the total
length of the packaged unit and not only to the length of the object to be
packaged (La).
Thus, the dimensional parameters LT and LP are the starting dimensions
to design the machine.
Characteristic dimensions.
Rotating heads.
Motion law superposition.
The more suitable working condition is to have a constant angular speed in
order to have negligible dynamic loads and thus this is the nominal working
condition. It correspond to an established product length defined as “base”
or “design” length L0. In every other cases, if the product length is
different from the design one, acceleration or deceleration are required in
order to account for the imposed target product length. Typically, the
base length L0 is provided by the costumer because it represents
the most common length and thus the target of the designer is to set up a
machine which shows the best performance in this configuration.
Motion sequence of the sealing process (LPL0).
Thus, the radius Rt of the rotating head (Fig. 2b) is
defined in order to obtain a circumference which length is proportional to
the design length itself:
2πRt=NL0
The integer ratio N=2πRt/L0 corresponds to the number of cutting
tools to be installed onto the rotating head. The dimension of the rotating
head Rt is usually bounded by the layout configuration of the machine
(Fig. ).
Laws of motion
One of the main characteristics of an automated machine is its productivity:
it represents the starting point to define the kinematic link between each
part of the whole mechanism. To satisfy the assigned productivity P of a
product with a length LP, the conveyor-belt has to maintain a constant
velocity v equal to:
v=Lp⋅P60P is usually expressed in pieces min-1, the cycle time is equal to
T=60/P. The total time T is defined as the sum of the duration of two
phases:
T=Tt+Ta
the cutting phase Tt. It is the part of the cycle dedicated to weld and cut
the packaging of the product,
the approaching phase between two cuts. It corresponds to the time Ta from
the finish of a cut and the beginning of the following one.
Cutting phase
During the cutting phase the angular velocity of the rotating head is
kept constant to cut and weld the packaging properly. The tangential velocity
of the rotating head has to be equal to the one of the conveyor-belt v,
resulting in a null relative velocity between them. Thus, the conveyor-belt
velocity v can be also defined as:
v=LtTt
because during the cutting phase Tt the conveyor-belt shift of a
distance equal to Lt. This condition allows to define the angular velocity
ωt of the rotating head during the cutting phase:
ωt=vRt=LtRtTt
Usually the length of the welded part of the packaging is defined a-priori
and does not depend to the product length LP. Thus, the length Lt is
not a design parameter for the law of motion because it is imposed by the
dimension of the cutting tools and it is typically defined by the costumer.
Approaching phase
As mentioned above, if the product length is equal to the design one (LP=L0) the rotating head maintains during the approaching phase a
constant angular velocity ωa equal to the one of the cutting
phase (ωt). If the product length is greater or smaller than the
design one, the angular velocity of the rotating head during the
approaching phase must decrease or increase to properly repositioning
the tool for the next cutting phase. A smart approach to generalize
the problem is to describe the angular velocity ω as the sum of two
contributes:
ωt: the constant angular velocity that allows to cut the L0
length,
ωa=ωt+Δω where Δω the variation of angular velocity
needed to get the tools in the correct position to execute the next cut.
The variation of the angular speed Δω depends on the product
length and the design length. It is null only if the product length is equal
to the design one. In the other cases to define its value it can be
convenient to consider the equivalent linear path of the tool as a function
of time. Using this different point of view it is possible to define the law
of motion of the tool as the superimposition of the path corresponding to the
constant angular speed and of the “Δ” path needed to reach at the
correct position and time the package to process (Fig. ),
considering that its duration is equal to the one of the approaching
phase one and it correspond to a linear distance equal to ha=L0-Lt.
Two conditions can be reached:
LP<L0. The approaching length ha is greater than the required one:
h=LP-Lt. The rotating heads must accelerate to recover this additional length.
LP>L0. The approaching length ha is smaller than the required one:
the rotating heads must decelerate. In extreme cases, it must rest or reverse the rotation direction.
A motion law with a total lift equal to h=LP-Lt and a
duration time equal to Ta=T-Tt is adopted to perform the
modulation of the rotating heads velocity. In Fig.
both the cases above described are shown. The dotted line represents the feed
of the conveyor-belt. Being its speed constant, as a function of time, it has
a linear trend, starting from zero and ending at the processed length LP.
During the cutting phase, the feed of the rotating heads is the same
of the one of the conveyor-belt, being null the relative velocity between
them. If the product length is longer than the design one, the rotating head
have to slow down (Fig. a). If it is smaller than the
design one, the rotating head must increase its angular velocity in order to
recover the length deficit as reported in Fig. b.
Dimension-less design of motion laws
Named y(t) the path of the rotating head during the approaching
phase, it is important to note that its “shape” is not defined a priori. In
fact, some different laws of motion, even if they result in very similar
behavior in the positioning, differ in relevant ways if the corresponding
accelerations are analyzed as shown for three different motion laws
in Fig. .
Each law of motion can be expressed using a dimension-less space and time
parameters:
ζ=y(t)hξ=tTa
The results is that the law of motion is totally describable using the
corresponding ζ=ζ(ξ) function, with 0≤ζ≤1 and
0≤ξ≤1. The velocity and the acceleration are obtainable using the
following differential relations:
y˙=dydt=d(hζ)d(Taξ)=ζ′hTay¨=dy˙dt=hTadζ′dt=hTa∂ζ′∂ξdξdt=ζ′′hTa2
being ζ′ and ζ′′ the dimensionless expressions of velocity and
acceleration, respectively.
Every law of motion must satisfy null speed both at the starting and at the
ending time instants (ζ′(ξ=0)=ζ′(ξ=1)=0), while it must provide
the correct lift starting from ζ(ξ=0)=0 reaching ζ(ξ=1)=1 at
the end. As a consequence, it can be demonstrated that the only constrains on
the dimensionless acceleration ζ′′ are:
∫01ζ′′(ξ)dξ=0∫01ζ′′(ξ)ζdξ=-1
Comparison between different motion laws.
Backward cut increasing the product length.
β as a function of product length and productivity.
Using the dimensionless form to describe the laws of motion, some
coefficients can be defined to capture several of their notable properties.
Thus, it is possible to define the dimension-less speed coefficients Cv,
that is useful to take into account the peak value of the speed, defined as:
Cv=y˙maxhta
Furthermore, dealing with acceleration, it is possible to define the
dimension-less acceleration coefficient Ca and the dimension-less root
mean square (r.m.s.) acceleration coefficient Ca,rms defined
respectively as:
Ca=y¨maxhta2Ca,rms=y¨rmshta2
A comparative collection of Ca, Ca,rms and Cv is provided
(Table ) in order to highlight their effectiveness in describing
and comparing the properties of different laws of motion.
Dimension-less r.m.s. acceleration and speed coefficients.
The advantage of using the dimension-less form to deal with the different
laws of motion is that they are quickly comparable referring to the
coefficients that summarize their performance. As an example, using the
dimensional-less coefficients Ca,rms, it is possible to highlight the
role of the adopted law of motion on the root-mean-square value of the
angular acceleration of the rotating heads:
β as a function of product length.
β surface as a function of tools number.
β as a function of input parameters.
ω˙L,rms=armsRT=Ca,rmsRThTa2TaT
being arms the tangential acceleration of the rotating head, calculated
on the whole duration time T while the dimensionless coefficient refers
only to the approaching phase Ta.
Dynamics analysis
The sizing of the motor-reducer unit is performed under the hypothesis of
pure inertial load considering that during the cutting phases,
both the friction and the cutting forces are negligible. With this
assumption, the only load that the motor have to face with is the rotating
heads own inertial load.
α-β method
To properly size the motor-reducer unit, the α-β method is
adopted . This method has the advantage of
highlighting and separate the terms of the power balance that regards the
motor unit and the reducer. This method allows both to avoid an iterative
design procedure and to define, for each motor unit considered, the
corresponding range of transmission ratios that are suitable for the analyzed
application. The motor performance is described by a key-factor called
accelerating factor α, defined as the ratio between the square
of the nominal torque of the motor Cm and its own rotational inertial
momentum Jm:
α=Cm2Jm
The accelerating factor derives from the rated motor torque condition
Cm,rms<=Cm used to check the motor thermal equilibrium in which the
value Cm,rms is the root mean square of the torque required by the motor
to carry out the task. This is calculated by:
Cm,rms=∫0ta1taτCr+Jmω˙rτ2dt
where ta is the cycle time, Jm the rotor inertia, τ the
transmission ratio and Cr and ω˙r the load torque and the
load angular acceleration respectively. Substituting the square of
Cm,rms into the rated motor torque condition it is possible to solve the
inequality with respect to the accelerating factor term defined beforehand.
A more refined definition of the accelerating factor is the
specific accelerating factor that is described in , but
for the aims of this work the simpler one presented above has been considered
sufficiently accurate. The load factor β contains the
information regarding the root mean square load during a cycle and
thus it allows to summarize in one single parameter the load the motor is
subject to (using a thermal design criterion):
β=2ω˙r,qCr,q*+ω˙rCr*‾
where ω˙r,q and Cr,q* are, respectively, the root
mean square of the angular acceleration and the resistant torque while
ω˙rCr*‾ is the mean value of their product. Having
defined both α and β, the condition for the correct sizing of
motor-reducer unit can be re-written () as:
α≥β+fτ
being τ the transmission ratio defined as:
τ=ωrωm.
The load factor β is directly linked to the flexibility of the machine.
It is equal to zero only if the product length LP is equal to the design
length L0, while, as shown in Sect. , it grows if the
rotating head needs to be accelerated or decelerated to process a greater or
a product length smaller than the base one.
Load factor
As a consequence of pure inertial load assumption, the load factor
β defined in Eq. () becomes:
β=4JLω˙r,rms2
being JL the momentum of inertia of the couple of rotating heads
(JLRt=2JTRt). It is important to highlight
that the best operative condition corresponds to β equal to zero, that
implies no inertial loads, obtainable only with a null
ω˙r,rms.
Combining Eqs. () and (), it is possible
to highlight the design terms:
β=4JLCa,rmsRThta2taT2=4JLCa,rmsRTLP2πRtN-LPLP-LTP6022
This Eq. () is particularly important because it allows
to describe the load factor as a function of the input parameters.
Gearbox
The change in transmission ratio range, defined as Δτ=τmax-τmin, can also be expressed as a function of the input parameters:
Δτ=Jmα±α-4Jrω˙r,rms2Jrω˙r,rms=τoptαβ±αβ-1
being the ratio Jm/Jr the optimal transmission ratio
τopt. It is worth noting that this equation is function only of the
load factor and not of the single input parameters of which it is
function. Thus it represents a general result for every input parameters
combinations which produces the same value of β.
Finally, the last check on the available τ serves the purpose of
ensuring that the maximum angular velocity required by the law of motion can
be provided. Using the introduced formulation:
where Cv is the dimension-less velocity coefficient depending to the
specific law of motion (Table ) adopted and referring only
to the approaching phase.
β surface as a function of tools number – bottom view.
τ as a function of load factor β for four different motors.
Numerical analysis and results
In the previous section, the load factor β and the admissible range for
the transmission ratio Δτ=τmax-τmin were expressed
as a function of the input parameters. Numerical results are obtained in this
section for a real wrapping machine with the parameters shown in Table .
It is worth underling that the acceleration and the deceleration of the
driving law of motion are equal and constant (motion law labeled “Acc
const symm” in Table ). No refinements have been made on
the law of motion because the aim of this work is to investigate its role on
the flexibility of the machine and not comparing different adoptable
solutions. Nonetheless, it is important to highlight that in some cases the
selected law of motion is not able to perform the desired operation. In fact,
due to a product length larger than the design one, an erroneous cut could be
done if the tool happens to move backward too much as reported in Fig. .
This fact results in a maximum product length
processable using the adopted law of motion. This constraint can be avoided
using a different law of motion that implies the block of the tool. In the
presented results this condition was reached in order to avoid introducing a
complication not useful to the aim of the present work.
As an example, Fig. a reports the surface that
graphically describes the load factor as a function of both the variation in
the productivity P and the product length LP. For sake of clarity,
Fig. reports the top view of the 3-D surface.
It could be seen that if the product length is equal to the design one the
load factor is still equal to zero irrespective of the assigned
productivity. It is worth noting that the growing of the load factor
as a consequence of the change of the product length is not symmetrical. In
Fig. , is shown that β is more sensitive to a
decrease of the product size instead of its increase.
Finally, the load factor is more sensitive to a growth in productivity than
in a change of product length. Furthermore, the productivity of high-speed
automated lines is defined as the one of the so called bottleneck
workstation that is the station with the lowest nominal production rate
. As a consequence, the effect of the product length
on the productivity not only affect the single machine but involves the whole
automated line productivity and should be carefully taken into account by
designers.
A refinement of the analysis consists in considering the effect of the number
of cutting tools N. The results is a group of surfaces (Fig. ) that represent the functions:
β=f(LP,P,N)
with different values of input parameters. A top view is reported in Fig. .
This kind of comparative plot can be used to properly design the machine
using the a simple procedure:
identify the number of tools N in order to obtain the smallest load factor to package
with a certain length and with an assigned productivity (Fig. ).
design the most flexible flying-cutting machine minimizing the curvature of the surface
corresponding to a certain number of tools. In the presented application, the smoothest surface
is obtained with N equal to 4 tools. The solution corresponding to N equal to 3 shows unsuitable
high value corresponding to the combination of high productivity and short product length.
define the maximum productivity allowed with a prescribed set of input parameters. The load
factor grows as the third power of P and, as a consequence, high values of β could be quickly
reached. Changing the number of tools allows to obtain a larger productivity than the one reachable without changing the rotating heads setup.
Finally, a collection of β-τ plots is presented in Fig. .
It is important to underline that this kind of plot depends
only on the selected motor unit (α) and on the load factor
(β) but not to the single input parameters resulting in a more general
point of view of the problem. This last plot gives two advices to the
designer. The first is that, the bigger the load factor becomes, the
smaller the range of admissible transmission ratio Δτ is. In the
worst condition, corresponding to α=β, the only useful
transmission ratio is the optimum one (τopt). It also allows to
identify the maximum load factor the motor can withstand.
Conclusions
This paper deals with the flexibility-oriented design of a flying-cutting
machine. A general framework is provided, allowing the designer to assess
different possible motor-reducer solutions and design parameter combinations,
taking into account the various advantages or limitations in terms of
flexibility. This new approach satisfies two requirements. The first one can
verify, theoretically the cutting flexibility in an existing cutting machine.
The second can design a new cutting machine capable of reaching a much higher
production flexibility level.
A specific wrapping machine is used as example to describe the methodology
but this choice does not limit the extendibility of the method to other
flying machine layouts.
By means of the α-β sizing motor method it has been
possible to obtain an expression that highlights the influence on the motor
load factor with respect to the machine parameters such as the number
of cutting tools installed, the motion law adopted and the size of the
product required to be wrapped. Thus it is possible to compare motor-reducer
solutions and to select one so as to ensure, on the one hand, larger
productivity and, on the other hand, a larger range of product
size.
References
Bebic, M., Rasic, N., Statkic, S., Ristic, L., Jevtic, D., Mihailovic, I.,
and Jeftenic, B.: Drives and control system for paper-board cross cutter,
15th International Power Electronics and Motion Control Conference and
Exposition, EPE-PEMC 2012 ECCE Europe, art. no. 6397495,
LS6c.31–LS6c.38, 2012.
Diekmann, A. and Luchtefeld, K.: Drive Solutions, Mechatronics for Production
and Logistics, in: Intermittent drives for cross cutters
and flying saws, edited by: Kiel, E., 378–389, Springer-Verlag, Berlin, Heidelberg,
2008.
Giberti, H., Cinquemani, S., and Legnani, G.: A practical approach to the
selection of the motor-reducer unit in electric drive system,
Mech. Based Des. Struc., 39,
303–319, 2011.
Giberti, H., Cinquemani, S., and Legnani, G.:
Effects of Transmission Mechanical Characteristics on the Choice of a
Motor-Reducer, Mechatronics, 20,
604–610, 2010.
Giberti, H., Clerici, A., and Cinquemani, S.:
Specific Accelerating Factor: One More Tool in Motor Sizing Projects,
Mechatronics, 24, 898–905,
2014.
Hansen, D., Holtz, J., and Kennel, R.: Cutter distance sensors for an adaptive
position/torque control in cross cutters, IEEE Ind. Appl. Mag.,
9, 33–39, 2003.
Hooper, J. H.: Confectionery Packaging Equipment, Springer, Gaithersburg,
Maryland,
1999.
Liberopoulos, G. and Tsarouhas, P.: Reliability analysis of an automated pizza
production line, J. Food Eng., 69,
79–96, 2005.
Matthews, J., Singh, B., Mullineux, G., and Medland, T.: Constraint-based
approach to investigate the process flexibility of food processing
equipment, Comput. Ind. Eng., 51,
809–820, 2006.
Peric, N. and Petrovic, I.: Flying Shear Control System,
IEEE T. Ind. Appl., 26, 1049–1056, 1990.
Sethi, A. K. and Sethi, S. P.: Flexibility in manufacturing a survey,
Int. J. Flex. manuf. Sys.,
2, 289–328, 1990.Shao, W., Chi, R., and Yu, L.: Synchronizing servo motion and iterative
learning control for automatic high speed horizontal flow wrapper,
Proceedings of the 2012 24th Chinese Control and Decision Conference,
CCDC, art. no. 6244470, 2994–2998, 2012.
Shepherd, R.: A Computer-Controlled Flying Shear, Students'
Quarterly Journal, 34, 143–148, 10.1049/sqj.1964.0006, 1964.
Shewchuk, J. P. and Moodie, C. L.: Definition and classification of
manufacturing flexibility types and measure, Int. J. Flex. manuf. Sys., 10, 325–349,
1998.
Strada, R., Zappa, B., and Giberti, H.: An unified design procedure for flying
machining operations, ASME 2012 11th Biennial Conference on
Engineering Systems Design and Analysis, ESDA 2012, 2,
333–342, 2012.
Varvatsoulakis, M. N.: Design and implementation issues of a control
system for rotary saw cutting, Control Eng. Pract., 17, 198–202, 2009.Visvambharan, B. B.: On-line digital control system for a flying saw cutting
machine in tube mills, Industrial Electronics Society, IECON '88.
Proceedings, 14 Annual Conference of IEEE Industrial Electronics, vol. 2,
385–390, 10.1109/IECON.1988.665170, 1988.
Wu, H., Wang, C., and Zhang, C.: Design of Servo Controller for
Flying Shear Machine Based on ARM and FPGA, J. Netw., =
9, 3038–3045, 2014.
Wu, Y.: China Packaging Machinery Industry is Facing Tremendous
Challenges, China Food Industry, 183, 6 pp., 2010.