Proceedings of the 2006 American Control Conference WeA11.

4
Minneapolis, Minnesota, USA, June 14-16, 2006

A Numerical Model of the Weft Yarn Filling

Insertion Process in Rapier Looms

Fabio Previdi, Sergio M. Savaresi, Member, IEEE, and Corrado Volpi

 could often result in high tension peak values with a high

Abstract — This paper presents a mathematical model of the risk of yarn breakage. This is a particularly noxious event,
weft yarn filling insertion process in rapier looms. A finite because yarn breakages need direct human intervention and
length segment of yarn is spatially discretized. Each element a complete stop of the loom operations. In order to avoid
can interact only with the nearest neighbors by a viscoelastic
interaction. The elastic and damping constants have been
breaking events, active weft braking is currently under
estimated by using experimental data obtained with different development: by knowing the time and space profile of the
yarns. The resulting model has lumped parameters and it is tension into the yarn, it is possible to electronically regulate
completely described by a set of ordinary differential the brake force to control the tension in the weft yarn
equations. The model provides the time and spatial profile of avoiding or at least reducing breaking events. So, it is
the tension in the considered yarn segment as a response to strongly advisable to have a mathematical model which is
external forces applied to the weft yarn by the rapiers and the
weft brake. Also, interactions with guide-eyes and piezoelectric
able to give at any time the tension value in each point of the
feelers have been considered in the model. The simulation weft yarn. Unfortunately, to the best of the authors’
results confirm that the proposed model can be a useful tool in knowledge, software tools for simulation of the complete
predicting weft yarn breakage and in design of tension control filling insertion process in rapier or projectile looms are not
systems by weft braking action. available. In literature there is a fundamental lack of a
mathematical model of the filling insertion process.
I. INTRODUCTION However, some works about this subject, providing partial

P roduction of woven textile using rapier or projectile

looms is performed by alternate introduction of weft yarns
interesting results, are noteworthy. For instance, in [1] the
tip transfer process is analyzed and a prediction of the
velocity changes, which result in local high tension values,
between the shed in the warp yarns. Weft yarn insertion is is provided. In [2] a dynamical model of yarn in constrained
made by two rapiers each inserted approximately halfway conditions using linear differential algebraic equations is
through the shed. The yarn is picked up at the left side of the presented. In [3] a model of warp yarn tension is presented.
loom by the left-hand rapier (the “giver”) and strongly In [4] and [5] the tension variations determined by high
accelerated (up to 3000 m/s2) during the first half of his speed yarn unwinding from package are modeled. In [6] it is
trajectory. Then, the yarn is transferred to the right-hand provided a numerical model, validated by experimental
rapier (the “taker”), whose aim is to bring the yarn at the results, of the interaction of the lower warp sheet with
right side of the loom at a full stop. Finally, the weft yarn is objects moving in the loom. Although none of this works is
cut at the fabric left edge and the cycle is repeated (up to directly related to the subject of the present paper, they put
600 times per second in medium speed commercial looms). in evidence the high interest around the problem of
Weft brakes are placed at the left side of the loom to keep mathematical modeling of the operations of a rapier loom.
the yarn stretched during the filling insertion process. The In this paper, starting from the results described in [2] and
joint action of the high intensity insertion forces, applied by [7], a mathematical model of the filling insertion process in
the rapiers, and the braking force, applied by the weft brake, rapier weaving looms is presented. The model provides the
time and space profiles of the tension in the weft yarn
Manuscript received March 7, 2005. This work was supported by moving through the warp shed during the filling insertion
Promatech s.p.a., Italy. process. In order to develop such a model, different tools
F. Previdi is with the Department of Management and Information seemed to be feasible. First, partial differential equations
Technology, University of Bergamo, via Marconi 5, I-24044 Dalmine (BG),
Italy (corresponding author phone: +39.035.2052357; fax: could have been used. Unfortunately, they require a high
+39.035.2052377; e-mail: previdi@unibg.it). numerical effort. Moreover, it could be difficult to introduce
S.M. Savaresi is with the Department of Electronics and Computer in the equations the interactions between the loom elements
Science, Politecnico di Milano, p.zza Leonardo da Vinci 32, I-20133
Milano, Italy (e-mail: savaresi@elet.polimi.it).
and the yarn. As an alternative, also multibody simulation
C. Volpi is with Promatech s.p.a, via Divisione Tridentina 19/21, I- tools could have been used. These require specific skill and
24020, Villa di Serio (BG), Italy (e-mail: Corrado.Volpi@promatech.it).

1-4244-0210-7/06/$20.00 ©2006 IEEE 376

experience to define the model and the use of (usually very Yarn
FN Carrier
expensive) software tools. Also in this case the computation Feeler
Color selector
Brake rapier FR
time could be very long. The proposed model is made by a
set of ordinary differential equations with lumped 462 mm 220 mm 67 mm
parameters. The parameters have been estimated by
performing suitable experiments on the yarn to be used. The Fig. 2. Scheme of the weft yarn initial conditions.
model can be solved by easy-to-use computation software
tools with very small expense in term of computation time. The model describes the basic working cycle as follows:
In this work, Matlab® has been used. Moreover, the model x the left-hand rapier hooks up the yarn right tip and it is
allows the introduction, in a very simple and easy way, of accelerated in the right direction. In the meantime, the
the interactions of the loom elements with the yarn, which right-hand rapier moves towards the centre of the
are the main source of tension variations in the weft. The loom.
outline of the paper is the following. In Section II the x At about the centre of the loom, the right-hand rapier
proposed mathematical model is described. In Section III the takes the yarn tip from the left-hand rapier and it is
results of the experiments for parameter tuning are outlined. itself accelerated up to the extreme right end side of the
Finally, in Section IV, some results obtained by solving the loom, where it is completely stopped and the yarn is
proposed model are shown. released. In the meanwhile, the left-hand rapier moves
back to its initial position.
x The yarn is cut in correspondence of the initial position
of the left-hand rapier.
The proposed model describes the viscoelastic behavior
of the yarn during its motion through the loom. The yarn
interactions with the loom can be divided into two major
categories:
x active interactions, i.e. the forces applied by the
rapiers and the weft brake. These, from a control
theory point of view, are the system inputs, i.e. the
Fig. 1 Somet Alpha 1900 rapier weaving loom.
candidates for future control system development.
x Passive interactions, i.e. the internal forces
II. THE MODEL modifications induced by friction-like interaction with
passive elements of the loom, e.g., guide-eyes, feeler,
The proposed model considers a segment of weft yarn of
tension sensors, color selector, etc…
finite length L during the filling insertion process into the
The model is obtained by dividing the yarn segment into N
loom. The geometry used in the simulations has been
elements with length d, so that L Nd . The ith element has
derived with reference to an actual loom, i.e. the Somet
Alpha rapier loom developed by Promatech (Fig. 1). This an elementary mass m concentrated in the position xi. In the
loom performs up to 650 picks per minute and can process absence of external forces, the ith element interacts only with
natural, synthetic, artificial or blended yarns producing the nearest neighbors (the (i–1)th and the (i+1)th elements,
fabrics with specific weight ranging from 15 to 800 g/m2. respectively) by means of unidirectional viscoelastic
The geometry of the system in the initial conditions is interactions (see Fig. 3):
depicted in Fig. 2. The right tip of the yarn segment is ready mx1  Fe x 2  x1  d  Fv x 2  x1 0 (1.a)
to be hooked up by the left-hand (“giver”) rapier. The yarn mxi  Fe x i 1  x i  d  Fv x i 1  x i 
also moves through the color selector and a piezoelectric  Fe x i  x i 1  d  Fv x i  x i 1 0, i 2,  , N  1
feeler, whose aim is to detect breaking events in order to (1.b)
stop the loom. Also, the weft yarn is subject to the action of
mxN  Fe x N  x N 1  d  Fv x N  x N 1 0 (1.c)
the weft brake which applies a constant vertical force. The
remaining part of the considered segment is on the left side where:
of the brake and it is supposed not to be subject to any force ­ks per s ! 0
x Fe s ®
or other interactions with the loom. In Fig.2 the main forces ¯0 per s d 0
acting on the yarn are also depicted. These are, the rapier x Fv s cs
force FR and the braking force FN.
where k and c are the elastic and viscous coefficient,
respectively. Notice that the elastic force is defined so that
the yarn is subject only to tension stresses and it does not

377
react to compression. model, could enable the modeling of other phenomena like
i1 k i k i+1 k i+2 ballooning etc… Secondly, it must be noticed that the
proposed model formulation allows the introduction of as
many points of interaction with the loom as you like. As a
m c m c m c m
matter of example, two of them has been used for
d simulations (the feeler and the color selector), but this is not
xi-1 xi xi+1 xi+2 a limitation of the model. As a final instance, notice that also
Fig. 3. Yarn segmentation into a set of finite volume elements.
the models of the interactions can be easily modified in the
proposed model. As a matter of example, the linear weft
In order to take into account the passive and active brake can be modified by introducing a stick-slip friction
interactions with the loom some of the equations (1) must be model. Similarly, also the guide-like friction elements can be
modified. In particular, the last equation must be modified in modified and, for instance, made depending on the weft yarn
order to take into account the rapier forces FR: velocity.
mxN  Fe x N  x N 1  d  Fv x N  x N 1 FR t (1.d)
The weft brake effect can be modeled as follows: consider III. PARAMETER ESTIMATION
the element which, at a given time t, is at the position x j The model presented in Section II must be completed by
right behind the brake. The effect of the brake can be the estimates of the parameters k and c , which define the
considered by including in the jth equation the force FN mechanical viscoelastic properties of the considered yarn,
provided by the weft brake, in the direction opposite to the and by defining the input functions FN and FR t to be
yarn motion: provided to the model which characterize the loom during
mx j  Fe x j 1  x j  d  Fv x j 1  x j  its normal operating conditions. The values of P are
 Fe x j  x j 1  d  Fv x j  x j 1 PFN (1.e) available in literature (see for instance [9]). In order to
estimate k and c , a specific experiment has been done.
where P is the friction coefficient between the weft brake
Specifically, a piece of yarn of length L is placed in vertical
material and the considered yarn. Notice that, since the yarn position, hung at a tension sensor and with a small weight
is moving through the brake, the index j changes during (0.41 N) at the lower edge (see Fig. 4). The experiment is
time. Similarly, the equation of the element r, which at time performed as follows: starting from rest conditions the
t is right behind the piezoelectric feeler and the equation of weight is left free of falling with the yarn free of swinging.
the element s, which at time t is right behind the color
The tension T t is measured until the yarn is back in rest
selector, must be modified as follows:
mxi  Fe x i 1  x i  d  Fv x i 1  x i  position. An example of the measured tension T t is shown
in Fig. 5. The experiment has been carried with four
 Fe xi  xi 1  d  Fv xi  xi 1 (1  e PD )Ti , i r, s
different yarns that will be used later in the simulations.
(1.f)
where: Tension
x D is the deflection angle induced by the guide-eye or sensor
the feeler;
x P is the friction coefficient between the guide-eye or
Yarn
the feeler and the considered yarn. L
x Ti is the tension between the ith element and the (i+1)th.
This formulation for the interaction between the yarn and
guide-eye elements is based on the capstan theory, widely
used in textile engineering [8]. Finally, notice that, since the
yarn is moving through the brake, also the indexes r and s M
change during time. Finally, the following remarks about the
Mg
model can be done. First, the model is one-dimensional even
though the movement of the weft yarn has a three- Fig. 4. Scheme of the experimental set up used to estimate the viscoelastic
dimensional development. This can seem a fundamental parameters of the yarn.
limitation of this model. However, it must be considered that
the main product of the simulator is the time and space Notice that the total elastic constant K and the total
profile of tension, whose major effects are along the damping coefficient C are the parameters with physical
longitudinal axis of the yarn. Obviously, a two-dimensional meaning that will be provided by these experiments. These
parameters are in the following relation with the

378
corresponding parameters to be used in the discretized that drives the rapier movements. This mechanical drive is
model: k KN and c CN , as can be easily obtained by in rigid mechanic connection with the rapier ribbons and the
considering the expression of the total elastic constant of a absolute position of the rapiers can be computed. In Fig. 6,
set of identical springs in series and, similarly, for the the computed movements of the rapiers are shown. The left-
damping coefficient. The model has been modified to hand rapier starts from the left side of the loom, it moves at
describe the yarn in this specific setup: Eq. (1.a) has been the centre and then back. The right-hand rapier has a similar
changed in order to consider that the upper edge is movement starting from the right. The two trajectories are
constrained. The applied constant weight has been designed so that they overlap at the centre of the loom, so
introduced into Eq. (1.d) instead of the rapier force. Since that the tip transfer from the right-hand rapier to the left-
there are no other interactions with the loom, Eq. (1.b), (1.c) hand one can be done. Notice that it is a common practice in
have been used and Eq. (1.e), (1.f) have been eliminated. textile engineering to replace the time with the angular
The gravitational effect of the yarn has been neglected. position of the loom ribbon drive.
Using the measured tension during the experiment, the TABLE I
parameters can be estimated ESTIMATED PARAMETERS
^ `
Cˆ , Kˆ arg min J C , K
C ,K
(2) Material
Specific
K [N/m] C [Ns/m]
weight [g/m]
Heavy
1
M
2 19.7 · 10-3 97.90 0.3170
where J C, K ¦ T t  Tˆ t ; C , K (3) Cotton
M Light
t 1 9.8 · 10-3 89.25 0.2788
Cotton
being M the number of available samples and Tˆ t ; C , K is Linen 25.7 · 10-3 118.3 0.2077
the tension at time t provided by the model using the
current parameter values. In Fig. 5 it is shown an example of Wool 18.2 · 10-3 44.10 0.1600
the estimated tension for a cotton yarn with specific weight
60 Ne, corresponding to 9.8 ˜10 3 g/m. The considered 2500

sample length is 0.40 m. In Table I the estimated parameters

of four different yarns are shown. 2000
Absolute position [mm]

Tip transfer
(§185°)
1.6 Right-hand
1500
rapier
Cotton Ne 60
1.4 Measured tension
1000
1.2
500 Left-hand
1
Tension [N]

Estimated tension rapier

0.8 0
Grip position (§35°; –100 mm)
0.6
-500
0 50 100 150 200 250 300 350 400
0.4 Loom angle [degrees]

0.2 Fig. 6. Absolute position of the rapiers during their movements through the
warp shed.
0
1 2 3 4 5
Time [s] IV. SIMULATION RESULTS
Simulations have been carried out for a nominal speed of
Fig. 5. Estimated tension (dotted) and measured tension (solid) for a cotton 600 picks per minute, i.e. 0.1 s for each cycle (0°-360°).
yarn with specific weight of 9.8 ·10-3 g/m.
The output of a simulation is:
The force function FR t applied to the yarn by the x the position x i t of each element i 1,  , N during the
rapiers must be also defined. It is not feasible to directly integration time interval (0.1 s);
measure this function and, similarly, it is difficult to directly x the velocity x i t of each element i 1,  , N during the
trace the movement of the rapiers (whose mean speed is integration time interval (0.1 s).
about 20 m/s with peak values of 40 m/s). So, the position of From this output, it is easy to evaluate the tension T x i , t
the rapiers has been deduced by the position of the camshaft in each element i 1,  , N during the integration time

379
interval by simply evaluating the internal forces applied to 300°, 340° corresponding, respectively, to 7.2 ˜10 2 s,
each element. In the following, the considered yarn segment
8.3 ˜10 2 s, 9.4 ˜10 2 s. This simulation has been done with
length is L # 3.8 m , discretized using d 1 cm. Without
brake force FN 0.2 N . Again, a comparison is shown
loss of generality, the origin of the spatial variable has been
put in correspondence to the weft brake, so that all the between a rigid yarn (Fig. 8.b) and a more elastic one (Fig.
elements behind the weft have negative abscissa, while 8.a). Notice in Fig. 8.a, that a first hint of damped spatial
those in front of the brake have positive abscissa. In Fig. 7 waves is visible.
3.5
the time profile of the tension T xi * t , t in an element i *
Color selector Light
so that xi * 0  0 , i.e. initially behind the weft brake. This 3
cotton
260°
simulation has been done with brake force FN 0.2 N. In 2.5 Feeler

Tension [N]
Fig. 7, the passages of the yarn element through the weft 2

brake, the piezoelectric feeler and the color selector are

1.5 300°
evidenced. Also, tension discontinuity due to tip transfer Weft brake
between the rapiers is clearly shown. By observing these 1

plots, it is possible to put in evidence the clearly different 0.5 360°

dynamical behaviors of two different yarns. Specifically, in
0
Fig. 7.a cotton is used, which is a quite elastic yarn. In Fig.
7.b linen is used, which is a more rigid yarn (with respect to -0.5
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3
cotton). This last shows more damped tension profiles in Absolute position [m]
response of the application of external forces. (a)
3
3.5
Color selector Heavy Color selector Linen
2.5 cotton 3

Low Feeler 260°

2
damping
2.5 Feeler
Tension [N]

2
1.5
Tension [N]

1.5
Weft brake
1
Weft brake 300°
1
Tip
0.5
transfer
0.5
0
360°
0

-0.5
0 50 100 150 200 250 300 350 400 -0.5
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3
Loom angle [degrees] Absolute position [m]
(a) (b)
3
Color selector Linen
2.5
Fig. 8. Spatial profile of the tension T x i t , t at three different time

High
Feeler samples t : 260°, 300°, 340° corresponding, respectively, to 7.2 ˜10 2 s,
2
damping 8.3 ˜10 s, 9.4 ˜10 2 s. In Fig. 8.a the parameters relative to cotton are
2
Tension [N]

1.5 used, while in Fig. 8.b linen parameters are used.

Weft brake
1 In Fig. 9, it is shown the maximum tension
Tip TM t { max T x i t , t experienced by the yarn during the
0.5 transfer i 1,, N

0
insertion (maximum over all the elements at each time). This
is a crucial indicator to evaluate if the yarn could break
-0.5
0 50 100 150 200 250 300 350 400 during insertion. In fact, this plot immediately shows if the
Loom angle [degrees] yarn undergoes tension values above its ultimate strength. In
(b) Fig. 9, a simulation with braking force FN 0.2 N is
Fig. 7. Time profile of the tension T x * t , t in an element i * so that
i shown. The tension peaks due to the passage through the
xi* 0  0 , i.e. initially behind the weft brake. In Fig. 7.a the parameters weft brake and the color selector are clearly shown.
relative to cotton are used, while in Fig. 7.b linen parameters are used.
In Fig. 8 it is shown an example of spatial profile of the
tension T x i t , t at three different time samples t : 260°,

380
 3.5 The proposed model describes the process by means of
Peaks due to Heavy
Peaks due to nonlinear ordinary differential equations, which can be
3 color selection
braking cotton easily solved by means of standard commercial available
2.5 mathematical software tools. This formulation allows
Maximum Tension [N]

parameter estimation by performing simple experiments on

2 the selected yarns. The time and space profiles of the tension
are qualitatively similar to what usually measured on the
1.5
looms in normal operating conditions. Moreover, also the
1 peak tension values are in agreement with those normally
Tip experienced in weaving. The simulations also evidenced the
0.5 transfer different dynamical behavior of different yarns as a response
to velocity changes due to the interaction with the loom
0
elements.
-0.5
0 50 100 150 200 250 300 350 400
Loom angle [degrees] REFERENCES
Fig. 9. Maximum tension T M t { max T x i t , t experienced by the [1] R.M. Dawson, N. Georgiadis, A. Jelveh-Moghaddam and K.W.
i 1,, N
Songelaeli, “Filling velocity change at tip transfer on rapier looms: a
yarn during the insertion
simple analysis,” Textile Research Journal, vol. 66, n° 11, pp. 739-
746, 1996.
Finally, simulations have been performed, using different [2] C. Ngo Ngoc, P. Bruniaux and J.M. Castellain, “Constrained Dynamic
values of brake force FN ranging from 0.2 N to 1.0 N (see Yarn Modelling,” Textile Research Journal, vol. 72, n° 11, pp. 1002-
1008, 2002.
Fig. 10). Similarly as in Fig. 9, maximum tension values for [3] T. Osthus, E. De Weldige and B. Wulfhorst, “Reducing set-up times
cotton have been plotted as a function of time. Notice that, and optimizing processes by the automation of setting procedures on
looms,” Mechatronics, vol. 5, n° 2/3, pp. 147-163, 1995.
using a braking force of 1 N, the cotton yarn is very close to [4] J.D. Clark, W.B. Fraser and D.M. Stump, “Modelling of tension in
its ultimate strength (about 13 N). yarn package unwinding,” Jour. of Engineering Mathematics, vol. 40,
pp. 59-75, 2001.
14 [5] M.F. Yeung, A.H. Falkner and S. Gergely, “The control of tension in
Ultimate strength textile filament winding,” Mechatronics, vol. 5, n° 2/3, pp. 117-131,
12 1995.
Heavy [6] D. Vu Hung, J. Degriek, L. Van Langenhove and P. Kiekens,
1.0 N cotton “Numerical simulation of the yarn-object interaction,” Textile
Maximum Tension [N]

10
Research Journal, vol. 72, n° 8, pp. 657-662, 2002.
0.8 N [7] L. Vangheluwe, B. Sleeckx and P. Kiekens, “Numerical simulation
8 model for optimization of weft insertion on projectile and rapier
looms,” Mechatronics, vol. 5, n° 2/3, pp. 183-195, 1995
6 0.6 N [8] L. Vangheluwe and B.C. Goswami, “Strain rate in dynamic tensile
testing,” Textile Research Journal, vol. 68, n° 2, pp. 150-151, 1998.
4 [9] K. Slater, Textile Mechanics, The Textile Institute, London ,1977.
0.4 N
2
0.2 N
0

-2
0 50 100 150 200 250 300 350 400
Loom angle [degrees]
Fig. 10. Maximum tension experienced by the weft yarn during insertion at
increasing braking forces.

V. CONCLUDING REMARKS
A mathematical model of the filling insertion process in
rapier looms has been presented. This model allow a
complete description of the movement of the weft yarn
during insertion through the warp shed as a consequence of
the applied rapier forces and weft brake force. This is of
great interest for the development of active tension control
systems, since the weft is the best candidate as an actuator.

381