*Yang Xu,
Zhijun Sun,
Shuang Huang,
Xiaowei Sheng,
Xinfu Chi
Dynamic Characteristic Analysis
of the Needle Multi-linkage Mechanism in
a Carpet Tufting Machine’s Driving System
DOI: 10.5604/12303666.1196619
School of Mechanical Engineering,
Donghua University,
Shanghai, P. R. China
*E-mail: xuyang@dhu.edu.cn
Abstract
In a typical carpet tufting machine, kinematic and dynamic characteristics of the needle
multi-linkage mechanism are the important factors affecting the quality of the tufting carpet. For providing a rational basis for mechanism design and vibration characteristic analysis, a mathematical model of the needle multi-linkage mechanism is constructed using the
complex vector analysis method. On the basis of the model, kinematic characteristic curves
and dynamic characteristic curves of the needle multi-linkage mechanism are analysed
by simulation methods. Finally experimental validation of the alternating load dynamic
characteristics is performed on the needle multi-linkage mechanism in a typical carpet tufting machine. The results prove the theoretical analysis validity of the needle multi-linkage
mechanism.
Key words: carpet tufting machine, needle multi-linkage mechanism, kinematic characteristics, dynamic characteristics.
nIntroduction
Carpet tufting technology originated in
America. Due to low cost and easy-to-develop new varieties, tufted carpet quickly
occupied the market from the 1840s,
whose production accounted for 80% of
the total amount of all kinds of carpets
[1 - 3].
The carpet tufting machine is very complex modern textile equipment that can
be used to weave all kinds of tufted carpet products. The multi-linkage mechanism is one of the most important parts
of the carpet tufting machine’s driving
system [4 - 9]. Its motion trajectory, displacement, velocity and acceleration determine the quality of the tufting carpet,
and the inertial force and inertial torque
produced by the multi-linkage mechanisms, which are both an alternating load,
will react on the main shaft and cause it
to vibrate. Therefore knowing the motion law and alternating load characteristics of the multi-linkage mechanism is
very important. Not only can it provide
an instruction for the mechanism design
of a carpet tufting machine, but also it
is the basis for vibration characteristic
analysis of the whole mechanical system.
Focusing on a typical tufting machine,
its driving system is introduced in this
paper. Then the needle multi-linkage
mechanism in a carpet tufting machine’s
driving system is described. A mathematical model of the needle multi-linkage mechanism is constructed using the
complex vector analysis method. Kinematic and dynamic characteristics of the
needle multi-linkage mechanism are analysed. Motion curves and force curves
of the needle multi-linkage mechanism
are obtained by simulation methods. Finally the alternating load dynamic characteristics of the needle multi-linkage
mechanism were verified by experiment.
The results prove the theoretical analysis validity for the needle multi-linkage
mechanism.
The tufting carpet machine’s
driving system
Figure 1 shows a schematic diagram of
the typical tufting carpet machine’s driving system. In general, the driving system
of a typical tufted carpet machine con-
sists of the main shaft, the driven shaft
of the needle multi-linkage mechanism,
the driven shaft of the hook multi-linkage
mechanism, multiple sets of the needle
multi-linkage mechanism and multiple
sets of the hook multi-linkage mechanism. The needle multi-linkage mechanism and hook multi-linkage mechanism
are made up of the driving link and driven link, respectively.
The basic working principle of carpet
tufting is shown as follows. Thousands
of tufting needles are driven by the main
shaft in the carpet tufting machine’s driving system to move up and down together. At the same time, the looper hooks
the yarn and makes it form a loop on
the rear of the backing, coordinating with
the tufting needle movement precisely.
By controlling the yarn-feeding, different
loop heights can be obtained [10, 11].
driven link of needle
multi-linkage mechanism
driven link of needle
multi-linkage mechanism
driven shaft of needle
multi-linkage mechanism
driving link of needle
multi-linkage mechanism
main shaft
hook shaft
driven link of hook
multi-linkage mechanism
Figure 1. Schematic diagram of a typical tufting carpet machine’s driving system.
Xu Y, Sun Z, Huang S, Sheng X, Chi X. Dynamics Characteristic Analysis of the Needle Multi-linkage Mechanism in a Carpet Tufting Machine’s Driving System.
FIBRES & TEXTILES in Eastern Europe 2016; 24, 3(117): 103-109. DOI: 10.5604/12303666.1196619
103
Dynamic model of needle
multi-linkage mechanism
Needle multi-linkage mechanism
structure
A schematic diagram of the needle multilinkage mechanism is shown in Figure 2,
in which the driving link of the needle
multi-linkage mechanism is a crank
rocker mechanism containing rod l1, rod
l2, rod l3 and a rack, and the driven link
of needle multi-linkage mechanism is
an offset rocker slider mechanism containing rod l4, rod l5 and slider l6. Rod l3
and rod l4 are fixedly connected at joint
C and the rod l4 follows the reciprocating swing of rod l3. The tufting needle N1
and N2 fixedly connected with slider l6
at point F, and the tufting needle move
up and down together with the slider.
The role of the needle multi-linkage
mechanism is to transform the rotary motion of the main shaft into the vertical reciprocating motion of the tufting needles.
Kinematic model
The basic task of the kinematic mathematical model is to determine the angular
displacement θi, angular velocity wi and
angular acceleration ai of rod li (i = 1, 2,
..., 6) in the needle multi-linkage mechanism.
The graphical and complex vector methods are commonly used in kinematic
modeling. The graphical method is visualised, but the accuracy is limited, being suitable for analysing the motion of
a simple mechanism. The complex vector
method has high accuracy and is suitable
for analysing the motion of a complex
mechanism [12, 13]. In this paper, a kinematic model of the needle multi-linkage
mechanism is constructed using the complex vector method. Kinematic models of
the crank rocker mechanism and offset
rocker slider mechanism in the needle
multi-linkage mechanism are respectively constructed as follows:
l4
l3
B
l1
O
H1
l6
A
x x1
y
l2
w1 l
1
(2)
2
2
lOC
H1 + x1
O
C =
(3)
−1
O
θ1
φ4 =
104
2
(5)
− φ1 − θ1
According to cosine theorem,
expressed as:
l3
l4
C
D
(6)
φ
3
can be
θ5
θ4
b1
l5
E
y
l6
F′
Figure 3. Schematic diagram of the crank rocker mechanism.
π
2
2
l AC
= l12 + lOC
− 2 ⋅ l1 ⋅ lOC ⋅ cos φ4
θ3
H1
F
O′′
O′
x1
(4)
Here, φ4 and l AC can be obtained by:
The equation above is nonlinear and is
very difficult to solve. The geometric
method is applied for solving the equation. According to the geometric characteristics of triangle DOCO’, φ1 and lOC
can be expressed as:
O′
1
 l

=
φ2 sin −1  1 ⋅ sin φ4 
 l AC

(1)
O
x1
1
According to the geometric characteristics of triangle DAOC , φ2 can be expressed as:
0
l1 cos θ1 + l2 cos θ 2 + l3 cos(θ3 − π ) − x1 =

l
sin
θ
l
sin
θ
l
sin(
θ
π
)
H
0
+
+
−
−
=
1
2
2
3
3
1
1
A
N2
φ = tg ( x / H )
1
H1
φ4
F
Figure 2. Schematic diagram of needle
multi-linkage mechanism.
According to the closed graph
OABCO’O, the real and imaginary
parts of the complex vector equation of
the crank rocker mechanism are directly
listed as Equation 1:
θ2
x2
N1
C
φ3
φ2
E
y l2
Kinematic model of the crank rocker
mechanism
Figure 3 shows a schematic diagram of
the crank rocker mechanism. In Figure 3,
li represents the rod length, θi the angular
displacement of rod li, x1 the line distance of OO’, and H1 is the line distance
of O’C. Here, i = 1, 2, 3.
φ1
l5
C
B
θ3
l3
D
x2
x
Figure 4. Schematic diagram of the offset rocker slider mechanism.
FIBRES & TEXTILES in Eastern Europe 2016, Vol. 24, 3(117)
FR _ l
a)
b)
2 _ l1 _ y
( xA , y A )
(x
s1 , ys1
FR _ O _ l _ y
)
1
( xo , yo ) O
1
s1
ml g
M b1
FR _ l
Fl
2 _ l1 _ x
A
Fl _ y
( xB , yB ) B
(x
s2 , ys2
Fl _ x
1
FR _ l
1
2 _ l1 _ x
FR _ O _ l _ x
FR _ l
1
2 _ l1 _ y
) s2
3
2_ y
FR _ C _ l _ y
c)
3
2_ y
FR _ l _ l
Fl _ y
x ,y 
 s3 s3  s3


2_x
( xB , yB )
FR _ l _ l
3
2_x
3
Mr
3
Fl
2
FR _ C _ l _ x
( xC , yC ) C
3 2_x
ml g
A ( xA , y A )
FR _ l _ l
Fl _ x
ml g
B
3
3
FR _ l _ l
3
2_ y
Figure 5. Force analysis diagram for the crank rocker mechanism; a) force analysis diagram for rod l1, b) force analysis diagram for rod
l2, c) force analysis diagram for rod l3.
 l2 + l2 − l2 
φ3 cos −1  AC 3 2  − φ2
=
 2 ⋅ l AC ⋅ l3 
(7)
Therefore, the rotary angle θ3 of rod l3
can be derived as follows:
θ3 =
3π
− φ1 − φ3
2
(8)
From Equation 1, the rotary angle θ 2 of
rod l2 can be expressed as:
 l3 sin θ3 − l1 sin θ1 + H1 
 (9)
l2


θ 2 = sin −1 
Taking the first derivative of Equation 1,
the angular velocities w2 and w3 of rods
l2 and l3 can be obtained as follows, respectively.
l1w1 sin (θ1 − θ3 )
l2 sin (θ 2 − θ3 )
(10)
l1w1 sin (θ1 − θ 2 )
l3 sin (θ3 − θ 2 )
(11)
w2 = −
w3 =
Taking the second derivative of Equation 1, the angular accelerations a2 and
a3 of rod l2 and rod l3 can be derived as
follows, respectively.
a2 =
l3w32 − l1w12 cos (θ1 − θ3 ) − l2w22 cos (θ 2 − θ3 )
l2 sin (θ 2 − θ3 )
a3 =
l2w + l w cos (θ1 − θ 2 ) − l3w cos (θ3 − θ 2 )
l3 sin (θ3 − θ 2 )
2
2
2
1 1
(12)
2
3
slider mechanism can be obtained as folaCF ′ =
−(l4 a4 cos θ 4 − l4w42 sin θ 4 + l5 a5 cos θ5 − l5w52 sin θ5 )
(19)
lows:
aCF ′ =
−(l4 a4 cos θ 4 − l4w42 sin θ 4 + l5 a5 cos θ5 − l5w52 sin θ5 )

−1  x2 − l4 cos θ 4 
θ5 = cos 

l5
(14) Dynamic model



l =
The basis task of dynamic analysis is
 CF ′ l6 − l4 sin θ 4 − l5 sin θ5
to analyse the inertial force and inertial
According to the intersection angle b1 of torque produced by the needle multirods and l4 , the angle θ 4 of rod l4 can linkage mechanism. In this section,
be expressed as follows:
dynamic models of the crank rocker
(15) and offset rocker slider mechanisms in
θ 4 = θ3 + b1 − 2π
the needle multi-linkage mechanism are
Because rods l3 and rod l3 are fixedly respectively constructed as follows.
connected at joint C, the angular velocities and angular acceleration of rods l3
Dynamic model of the crank rocker
and l4 should be equal, and thus, w4 = w3 , mechanism
a4 = a3 . Taking the first derivative of Figure 5 shows a force analysis diagram
Equation 14, the angular velocity w5 of for the crank rocker mechanism. In Figure 5, xsi and ysi represent the horizonrod l5 and linear velocity vCF ′ of slider l6
tal
ordinate and the vertical coordinate of
can be derived as follows, respectively.
rod centroid si . xz respectively, and y z
l w sin θ 4
(16) the horizontal ordinate and vertical coorw5 = − 4 4
l5 sin θ5
dinate of joint z (z = O, A, B, C). mli is the
vCF ′ = −l4w4 cos θ 4 − −l5w5 cos θ5 (17) mass of rod li . Fli _ x and Fli _ y represent
the X direction inertial forces and those of
Taking the second derivative of Equa- the Y directions of rod li . M i represents
tion 14, the angular acceleration a5 of the inertial torque of rod li . FR _ z _ li _ x and
FR _ z _ li _ y represent the X direction’s rerod l5 and linear acceleration aCF ′ of
action force and Y direction’s reaction
slider l6 can be derived as follows, reforce, respectively, which joint z gives
spectively.
to rod . FR _ li _ l j _ x and FR _ li _ l j _ y represent the X direction’s reaction force and
(l4 a4 sin θ 4 + l4w42 cos θ 4 + l5w52 cos θ5 )
(18)
a5 = −
the Y direction’s reaction force, respecl5 sin θ5
(13)
Kinematic model of the offset rocker
slider mechanism
Figure 4 shows a schematic diagram of
the offset rocker slider mechanism. In
Figure 4, li and θi represent the same
as those of the crank rocker mechanism.
Here, i = 4, 5. x2 is the line distance of
O′O′′ .
According to the closed graph CDEFC,
the real and imaginary parts of the complex vector equation of the offset rocker
FIBRES & TEXTILES in Eastern Europe 2016, Vol. 24, 3(117)
 FR _ l2 _ l1 _ x + FR _ O _ l1 _ x =
− Fl1 _ x

(22)
− Fl1 _ y
 FR _ l2 _ l1 _ y + FR _ O _ l1 _ y − ml1 g =

−M1 =
0
 M b + FR _ O _ l1 _ x ( ys1 − yo ) + FR _ l2 _ l1 _ y ( x A − xs1 ) − FR _ l2 _ l1 _ x ( y A − ys1 ) − FR _ O _ l1 _ y ( xs1 − xo ) =
 FR _ l3 _ l2 _ x − FR _ l2 _ l1 _ x =
− Fl2 _ x

(25)
− Fl2 _ y
 FR _ l3 _ l2 _ y − FR _ l2 _ l1 _ y − ml2 g =

−M 2
 FR _ l3 _ l2 _ x ( ys 2 − yB ) + FR _ l3 _ l2 _ y ( xB − xs 2 ) + FR _ l2 _ l1 _ x ( y A − ys 2 ) + FR _ l2 _ l1 _ y ( xs 2 − x A ) =
Equations 22 & 25.
105
 FR _ C _ l3 _ x − FR _ l3 _ l2 _ x =
− Fl3 _ x

(28)
− Fl3 _ y
 FR _ C _ l3 _ y − FR _ l3 _ l2 _ y − ml3 g =

−M 3
 M r + FR _ C _ l3 _ y ( xC − xs 3 ) + FR _ l3 _ l2 _ y ( xs 3 − xB ) − FR _ C _ l3 _ x ( yC − ys 3 ) − FR _ l3 _ l2 _ x ( ys 3 − yB ) =
1
0
1
0
0
0
0


0
1
0
1
0
0
0

 −( y A − ys1 ) ( x A − xs1 ) ( ys1 − yo ) −( xs1 − xo )
0
0
0

−1
0
0
0
1
0
0

0
0
0
0
1
0
=
A 
−1

0
0
( ys 2 − yB ) ( xB − xs 2 )
0
 ( y A − ys 2 ) ( xs 2 − x A )

0
0
0
0
−1
0
1

0
0
0
0
0
−1
0


0
0
0
0
−( ys 3 − yB ) ( xs 3 − xB ) −( yC − ys 3 ) ( xC

FR1 =  FR _ l2 _ l1 _ x
 Fl1 _ x
B =−
FR _ l2 _ l1 _ y
FR _ O _ l1 _ x
− Fl1 _ y + ml1 g 0 − Fl2 _ x
FR _ O _ l1 _ y
− Fl2 _ y + ml2 g
FR _ l3 _ l2 _ x
−M 2
− Fl3 _ x
FR _ l3 _ l2 _ y
FR _ C _ l3 _ x
− Fl3 _ y + ml3 g
(23)
 Fl2 _ x = −ml2 as 2 x

(24)
 Fl2 _ y = −ml2 as 2 y

 M 2 = − J s 2 a2
Equation 25 (see page 105)
0
0
0 
0
1

0
0
0
0

0
0

0
0

1
0
− xs 3 ) 0 
0
l

− 3 (w32 cos θ3 + a3 sin θ3 )
as 3 x =
2
(26)

l3 2
a =
− (w3 sin θ3 − a3 cos θ3 )
 s 3 y
2
(30)
FR _ C _ l3 _ y
− M 3 − M r 
l
l

−l1w12 cos θ1 − 2 w22 cos θ 2 − 2 a2 sin θ 2
as 2 x =
2
2

l2 2
l2
2
a =
−l1w1 sin θ1 − w2 sin θ 2 + a2 cos θ 2
 s 2 y
2
2
M b1 
T
 Fl3 _ x = −ml3 as 3 x

 Fl3 _ y = −ml3 as 3 y

 M 3 = − J s 3 a3
(31)
(32)
T
 FR _ l5 _ l4 _ x + FR _ C _ l4 _ x =
− Fl4 _ x
(35)

− Fl4 _ y
 FR _ l5 _ l4 _ y + FR _ C _ l4 _ y − ml4 g =

−M 4
 M r + FR _ l5 _ l4 _ x ( yD − ys 4 ) + FR _ C _ l4 _ y ( xs 4 − xC ) − FR _ l5 _ l4 _ y ( xD − xs 4 ) − FR _ C _ l4 _ x ( ys 4 − yC ) =
(27)
Combining Equation 20 with Equation 28, a matrix equation can be obtained as follows:
(29)
AFR1 = B
 FR _ l6 _ l5 _ x − FR _ l5 _ l4 _ x =
− Fl5 _ x

(38)
− Fl5 _ y
 FR _ l6 _ l5 _ y − FR _ l5 _ l4 _ y − ml5 g =

−M 5
 FR _ l6 _ l5 _ x ( ys 5 − yE ) + FR _ l6 _ l5 _ y ( xE − xs 5 ) + FR _ l5 _ l4 _ x ( yD − ys 5 ) + FR _ l5 _ l4 _ y ( xs 5 − xD ) =
Equations 28, 30, 31, 32, 35 & 38.
tively, which rod li gives to rod l j . M r
and M b1 are, respectively, the resistance
torque and balancing torque of the crank
From Figure 5.a, the inertial force and
inertial moment of rod l1 can be determined as:
 Fl1 _ x = −ml1 as1x

 Fl1 _ y = −ml1 as1 y

 M 1 = − J s1a1
rocker mechanism. Here, i = 1, 2, 3.
Based on the complex vector method,
the acceleration of centroid s1 can be expressed as follows:
l1 2

as1x = − 2 w1 cos θ1

a = − l1 w 2 sin θ
1
1
 s1 y
2
(20)
Fl
4
FR _ C _ l
4_ y
( xC , yC ) C
s4
s4
Fl
4
Mr
FR _ C _ l _ x
4
FR _ l
( xD , yD ) D
_y
(x , y ) s
ml g
Similarly the force balance equations of
l2 and l3 can be obtained as follows according to Figures 5.b and 5.c.
5 _ l4 _ x
5 4_ y
a)
The force balance equation of rod l1 can
be expressed as Equation 22 (see page
105).
FR _ l
FR _ l _ l
(
D xD , yD
5 _ l4 _ y
(x
FR _ l _ l
5
(21)
s5 , ys5
4_x
)s
5
b)
According to Figures 6.a and 6.b,
the force balance equations of l4 and l5
can be respectively expressed as follows.
l
l

− 4 w4 cos θ 4 − 4 a4 sin θ 4
as 4 x =
2
2

l4
l4
a =
− w4 sin θ 4 + a4 cos θ 4
 s 4 y
2
2
FR _ l
6 _ l5 _ x
5_ y
( xE , yE ) E
6_ y
5_x
FR _ E _ l
5_ y
FR _ E _ l
5_x
E ( xE , yE )
6 _ l5 _ y
Fl
Fl
(33)
FR _ l
c)
Fl
5
4
Dynamic model of the offset rocker
slider mechanism
Figure 6 shows a force analysis diagram
for the offset rocker slider mechanism. In
Figure 6, Fr is the friction force of slider
l6 when the tufting needle stabs into the
backing. Other symbols are of the same
meaning as for the crank rocker mechanism. Here, i = 4, 5, 6.
)
ml g
4_x
Here, A is the coefficient of the matrix,
FR1 the unknown force matrix of the
crank rocker mechanism, and B is the
known force matrix of the crank rocker
mechanism.
s6
ml g
Fr
Fl
6_x
6
( xF , yF ) F
FR _ F _ l
6_x
Figure 6. Force analysis diagram for the offset rocker slider mechanism; a) Force analysis diagram for rod l4, b) Force analysis diagram
for rod l5, c) Force analysis diagram for slider l6 when the tufting needle moves down.
106
FIBRES & TEXTILES in Eastern Europe 2016, Vol. 24, 3(117)
 Fl4 _ x = −ml4 as 4 x

 Fl4 _ y = −ml4 as 4 y

 M 4 = − J s 4 a4
(34)
l
l

−l4w42 cos θ 4 − l4 a4 sin θ 4 − 5 w52 cos θ5 − 5 a5 sin θ5
as 5 x =
2
2

l5 2
l5
2
a =
−l4w4 sin θ 4 + l4 a4 cos θ 4 − w5 sin θ5 + a5 cos θ5
 s 5 y
2
2
(36)
 Fl5 _ x = −ml5 as 5 x

 Fl5 _ y = −ml5 as 5 y

 M 5 = − J s 5 a5
1
0
1
0
0
0


0
1
0
1
0
0

 −( ys 4 − yC ) ( xs 4 − xC ) ( yD − ys 4 ) −( xD − xs 4 )
0
0

−1
0
0
0
1
0
C=

−1
0
0
0
0
1

0
0
( yD − ys 5 ) −( xD − xs 5 ) ( ys 5 − yE ) −( xs 5 − xE )


−1
0
0
0
0
0

−1
0
0
0
0
0

(37)
FR 2 =  FR _ C _ l4 _ x
According to Figure 6c), the force balance equations of slider l6 when the tufting needle moves down can be given by:
− Fl6 _ x
 FR _ l6 _ l5 _ x − FR _ F _ l6 =

Fl6 _ y
ml6 g − Fr + FR _ l6 _ l5 _ y =
(39)
When the tufting needle moves up, Fr in
the equation above is the reverse. Other
parameters remain unchanged.
FR _ C _ l4 _ y
FR _ l5 _ l4 _ x
FR _ l5 _ l4 _ y
FR _ l6 _ l5 _ x
FR _ l6 _ l5 _ y
FR _ F _ l6 _ x
 Fl4 _ x − Fl4 _ y + ml1 g − M 4 − Fl5 _ x − Fl5 _ y + ml5 g − M 5 0 − Fl6 _ y − Fr + ml6 g 
D =−
T
0 0
0 0 
0 1

0 0
0 0

0 0
1 0

0 0 
(41)
M r 
T
(42)
(43)
Equations 41, 42 & 43.
Table 1. Main parameters of the needle multi-linkage mechanism.
Length, mm
Mass, kg
Moment of inertia, × 10-3 kg·m2
l1
15
3.07
4.34
Combining Equation 33 with Equation 39, a matrix equation can be obtained as follows:
l2
138
3.79
26.99
(40)
Where, C is the coefficient of the matrix. FR 2 the unknown force matrix of
the offset slider mechanism, and D is
the known force matrix of the offset slider
mechanism (see Equations 41, 42 & 43).
120
120
240
crank
angle
/(°)
crank
angle
θ θ
, 1deg
360
1
6.69
l5
120
0.36
0.91
l6
440
1.47
19.15
—
—
70
x1
—
100
H1
155
10
5
w2
w3
w4
w5
0
-5
-10
0
b)
120
240
crank angle
angle θ1θ/(°,) deg
crank
1
360
-0.39
-0.4
-0.41
0
120
240
crankangle
angle θθ1/(,°)deg
crank
1
360
e)
1
0
-1
-2
0
120
240
crank angle
angle θθ1/(, °deg
)
crank
1
600
α2
α3
α4
α5
400
200
0
-200
-400
-600
0
c)
2
-0.38
-0.42
10.77
1.74
x2
slider's velocity,
velocity/(m
Slider’s
rads
⋅s -1-1)
Slider’s
displacement,
slider's displacement
/(m) m
a)
0
2.96
Rod’s
angle
rads
the
rod's
angleacceleration,
acceleration /(rad
)
⋅s -2-2
360
-120
d)
θ2
θ3
θ4
θ5
115
125
cast steel
l4
360
-2
slider's acceleration,
acceleration /(m
⋅s -2)
Slider’s
rads
the
rod'sangle,
angle /(
°)
Rod’s
deg
600
Material
l3
Rod’s
velocity,
rads
the
rod'sangle
angle velocity
/(rad
⋅s -1)-1
CFR 2 = D
Link parameter
120
240
crankangle
angle θθ1/(,°)deg
crank
1
360
100
50
0
-50
-100
0
f)
120
240
crank angle
angle θθ11,/(deg
°)
crank
360
Figure 7. Motion curves of needle multi-linkage mechanism; a) rod’s angle displacement curves, b) rod’s angle velocity curves, c) rod’s
angle acceleration curves, d) slider’s linear displacement curve, e) slider’s linear velocity curve, f) slider’s linear acceleration curve.
FIBRES & TEXTILES in Eastern Europe 2016, Vol. 24, 3(117)
107
-1000
022
108
194
287
crank
angleθθ1,1/(
°)
crank angle
deg
0
-2000
360
Reaction
force
/(N) N
Reaction
force,
Reaction
/(N)
Reactionforce
force,
N
1000
500
0
FR C l3 x
FR C l3 y
22
108
194
287
crankangle
angle θθ1,/(deg
°)
crank
360
500
0
-500
-1000
-1500
22
108
194
287
crank
angle
/(°)
crank
angle
θ θ,1deg
360
1
g) FR _ l _ l _ x and FR _ l _ l _ y
6
5
6
5
1500
1000
1000
-1000
FR C l4 x
FR C l4 y
22
108
194
287
crank
angleθ θ,1deg
/(°)
crank
angle
1
300
FR F l6 x
200
100
0
-100
-200
-300
22
108
194
287
crank
angle
/(°)
crank
angle
θ θ,1deg
108
194
287
360
crank
angleθ θ,1deg
/(°)
crank
angle
1
360
1
h) FR _ F _ l _ x
6
FR l5 l4 x
FR l5 l4 y
500
0
-500
-1000
-1500
360
22
108 194
287 360
crank
angle
/(°)
crank
angle
θ1θ
, 1deg
f) FR _ l5 _ l4 _ x and FR _ l5 _ l4 _ y
e) FR _ C _ l4 _ x and FR _ C _ l4 _ y
Reactionforce
force,
Reaction
/(N)N
Reaction
/(N)
Reactionforce
force,
N
FR l6 l5 x
FR l6 l5 y
1500
-500
22
c) FR _ l3 _ l2 _ x and FR _ l3 _ l2 _ y
0
1
1000
-2000
360
500
d) FR _ C _ l _ x and FR _ C _ l _ y
3
3
1500
108
194
287
crank angle
angle θθ1,/(deg
°)
crank
FR l3 l2 x
FR l3 l2 y
-1000
b) FR _ l2 _ l1 _ x and FR _ l2 _ l1 _ y
1500
-1000
22
0
1
a) FR _ O _ l4 _ x and FR _ O _ l _ y ,
4
-500
FR l3 l2 x
FR l3 l2 y
-1000
1000
Reaction
/(N)
Reactionforce
force,
N
-2000
Reaction force,
force/(N)
Reaction
N
0
1000
150
Inertial
/(N.m)
Inertialtorque
torque,
N.m
1000
2000
2000
FR O l1 x
FR O l1 y
Reaction force/(N)
Reaction
force, N
Reaction
Reactionforce
force,/(N)
N
2000
100
50
0
-50
-100
-150
0 22
108
194
287
crank angle
angle θθ1/(,°deg
)
crank
1
360
i) M r
Inertial
torque, N.m
Inertial torque/(N.m)
20
15
10
5
0
-5
022
108
194
287
crank
angleθ θ,1/(
°)
crank
angle
deg
j) M b1
360
1
Dynamic characteristic analysis
Focusing on tufting carpet machine type
DHGN801D-400, the dynamic characteristics of the needle multi-linkage mechanism is simulated using the model above.
The main parameters of the needle multilinkage mechanism are shown in Table 1
(see page 107). Assume the friction force
Fr = 1000 N when the tufting needle moves on the backing and friction
force Fr = 1000 N when it moves under
the backing. Here, b1 = 168°. The motion and force curves of the needle
108
Figure 8. Force curves of needle multi-linkage mechanism.
multi-linkage mechanism are shown in
Figure 7 (see page 107) and Figure 8,
respectively.
Analysing Figure 7, it is noted that
the range of rotation angle θ 2 is from
101.7° to 114.3° when the main shaft
rotates one circle. The tufting needle
stroke is about 33 mm. The range of
θ3 , θ 4 and θ5 is, respectively, within
184.3° - 199.4°, -7.89° - 7.38° and 257.9°
- 258.5°. From , it is clear that the motion curves of the needle multi-linkage
mechanism are smooth and have only
a little shock on the whole mechanism.
These data are consistent with the actual
running ones of tufting carpet machine
type DHGN801D-400.
Analysing Figure 8, it is noted that
the inertial forces and inertial torque
produced by the needle multi-linkage
mechanism are an alternating load. When
the rotation angle of the main shaft is
about 22 degrees, the tufting needle just
moves downward to stab the backing.
FIBRES & TEXTILES in Eastern Europe 2016, Vol. 24, 3(117)
20
15
Torque
(N.m)
Torque,
N.m
When the main shaft rotates 108 degrees,
the tufting needle arrives at the lowest point. Starting from 109 degrees,
the tufting needle moves upwards. When
the rotation angle of the main shaft is
about 194 degrees, the tufting needle
just moves upward to stab the backing.
The tufting needle arrives at the highest
point until the rotation angle of the main
shaft is 287 degrees. Then the tufting
needles will continue to move up and
down together and repeat this process.
From Figure 9, it is clear that the torque
that the driven shaft of the needle multilinkage mechanism suffered is far greater
than that on the main shaft. Therefore it
is more important to study the effect of
alternating loading on the driven shaft of
the needle multi-linkage mechanism than
thaton the main shaft.
10
5
0
14.02
14.11
14.2
14.3
time(s)
time,
s
14.375
Figure 9. Experimental result of balancing torque.
nExperiment
To demonstrate the correctness of the theoretical analysis of the needle multi-linkage mechanism, experimentally validation was performed on a tufting carpet
machine type DHGN801D-400. Wireless
torque sensor DH5905 was applied for
measuring the balancing torque of needle
the multi-linkage mechanism. The sampling frequency was set to 500 Hz and
the rotation speed of the main shaft was
160 r.p.m. Here, the main shaft rotating
one circle takes 0.375 seconds. The balancing torque of the needle multi-linkage
mechanism can be obtained as shown in
Figure 9.
Analysing Figure 9, it is noted that
the tufting needle just moves downward
to stab the backing when the main shaft
rotates to 22 degrees (14.02 s). When the
main shaft rotates to 108 degrees (14.11 s),
the tufting needle arrives at the lowest
point. The tufting needle moves up to
stab the backing when the main shaft rotates to 194 degrees (14.20 s). The tufting
needle arrives at the highest point until
the main shaft rotates to 287 degrees
(14.30 s). When the main shaft rotates
to 360 degrees (14.375 s), one cycle is
over. Compared with Figure 8.j and Figure 9, it is noted that the experimental
result of the balancing torque coincides
with simulation results in the previous
section. In the process of simulation, due
to the friction force Fr chosen according
to experience, the experimental result of
the balancing torque is not able to totally
identically equal to simulation results.
FIBRES & TEXTILES in Eastern Europe 2016, Vol. 24, 3(117)
nConclusions
In this work, it was found that the inertia
forces and inertia torque acting on needle
driven shaft are much greater than that
acting on the main shaft. It is more important to study the effect of alternating
loading on the driven shaft of the needle
multi-linkage mechanism than to study
that on the main shaft.
7. Price HB. Tufting machine-has each
needle holder between and selectively
connectable to limbs of yoke on pushed
rod, U.S. Patent: US 4815402. 1989.
8. Beasley M. Tufting machine needle bar
connecting rod drive cam-comprises upper and lower halves securable about
drive shaft, U.S. Patent: US 5320053.
1993.
9. Roy TC, Rodney EH. Needle bar foot
Acknowledgements
This paper was supported by the National
Natural Science Foundation of China (Grant
No. 51175075).
construction for multiple needle skipstitch tufting machine, U.S. Patent:
US3978800. 1976.
10.Meng Zhuo, Sun Jingjing, Zhou Tingze,
et al. Research on the infuluence that
stop position of carpet tufting machine to
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Received 05.08.2014
Reviewed 07.07.2015
109