In order to improve the reliability of the mechanical movement of the rotary electronic dobby, the kinematics analysis of the heald selection mechanism is carried out and the simulation is carried out with Matlab. Firstly, the operation mechanism of the heald selection mechanism is analyzed in detail. The conjugate cam is mapped. The cam profile curve is fitted with cubic spline interpolation. Secondly, based on the overall analysis method and the complex vector method, the kinematics analysis of the key components after the high pair low generation is performed, and the angular displacement and angular velocity of each component are calculated with the rotation of the active cam. Finally, the movement curve diagram is drawn with Matlab, which lays the foundation for the dynamic analysis and in-depth study of the selection mechanism in the future.
As the most advanced high-speed shedding device [
The rotary dobby is composed of heald selection mechanism, heddle lifting mechanism, electronic control equipment module, etc. The heald selection mechanism is the core control mechanism of the dobby [
At present, for the heddle selection mechanism of the dobby machine, Shen Yi et al. [
As the society has higher and higher requirements for production efficiency, the speed, accuracy and reliability of the rotary dobby have been continuously improved. As the key control mechanism of the dobby, the heddle selection mechanism is of great significance to accurately establish the motion model of the rotary dobby and conduct in-depth kinematics analysis on it.
For this reason, this article uses the high pair low generation method [
The selection system includes a selection cam and a selection control mechanism, consisting of a conjugate cam 5, a roller 6, an auxiliary swing arm 7, a main swing arm 8, an iron suction swing lever 10, a right signal swing arm 12, and a left signal swing arm 13. The composition is shown in
arm, the release and pull-in of the electromagnet determines whether the iron-absorbing swing rod is in contact with the right signal swing arm 12 and the left signal swing arm 13, and the iron-absorbing swing rod contacts the signal swing arm. The shaft rotates, and under the action of the clutch pawl 4, the driving disc 2 and the heald lifting disc 3 become a whole, thereby completing the selection of the heald frame. In order to realize the precise control of the heald frame by the heald selection system and avoid the mechanical collision between the heald selection system and the heald lifting system, a safe corner must exist.
Since the movement of the right signal swing arm and the left signal swing arm are similar, the left signal swing arm is selected for kinematic analysis, and the instantaneous state of the mechanism is simplified. The mechanism selects the kinematics of the comprehensive system according to the method of high pair and low generation of the mechanism. The model is simplified into a plane link mechanism model, the mechanism’s high and low degrees of freedom, instantaneous speed, and instantaneous acceleration remain unchanged.
Measure the actual profile of the conjugate cam, use a three-coordinate measuring instrument to map the cam, as shown in
After the cam high pair low is replaced, the cubic spline interpolation method
is used to solve the curvature radius of the plane cam whose cam profile is discrete points, as shown in
Calculation formula of radius of curvature
ρ = [ ( x ′ ) 2 + ( y ′ ) 2 ] 3 / 2 x ′ y ″ − x ″ y ′ (1)
where x ′ , y ′ , x ″ , y ″ can be obtained by cubic spline interpolation, the coordinates of the center of curvature A j
{ x A j = x B j − ρ B cos α B j y A j = x B j − ρ B j sin α B j (2)
The rod length of the members O A j , B j A j is l O A j , l B j A j is
l O A j = ( x A j − x O ) 2 + ( y A j − y O ) 2 (3)
l B j A j = ( x A j − x B j ) 2 + ( y A j − y B j ) 2 (4)
Kinematics analysis of crank rocker mechanism and swing guide rod mechanism respectively, and the vector equation is obtained from the kinematic model
O A + A B = O C + C B (5)
E C + C D = E D (6)
Write Formula (5) in plural form
l O A e i θ 1 + l A B e i θ 2 = l O C e i β + l C B e i θ 3 (7)
The real and imaginary parts of Formula (7) are respectively equal to obtain
l O A cos θ 1 + l A B cos θ 2 = l O C cos β + l C B cos θ 3 (8)
l O A sin θ 1 + l A B sin θ 2 = l O C sin β + l C B sin θ 3 (9)
And then get
l A B 2 = ( l O C cos β + l C B cos θ 3 − l O A cos θ 1 ) 2 + ( l O C sin β + l C B sin θ 3 − l O A sin θ 1 ) 2 (10)
To facilitate the solution of θ 3 , Formula (10) can be rewritten as the following equation
A sin θ 3 + B cos θ 3 + C = 0 (11)
where: A = 2 l C B l O C sin β − 2 l O A l C B sin θ 1 ; B = 2 l C B l O C cos β − 2 l O A l C B cos θ 1 ;
C = l O C 2 + l C B 2 + l O A 2 − l A B 2 − 2 l O A l O C ( cos θ 1 cos β + sin θ 1 sin β )
θ 3 = 2 arctan A ± A 2 + B 2 − C 2 B − C (12)
θ 2 = arctan l O C sin β + l C B sin θ 3 − l O A sin θ 1 l O C cos β + l C B cos θ 3 − l O A cos θ 1 (13)
In the formula, write Formula (6) in plural form
l E C e i α + l C D e i θ 4 = l E D e i θ 5 (14)
The real part and imaginary part of Formula (14) are respectively equal to obtain
l E C cos α + l C D cos θ 4 = l E D cos θ 5 (15)
l E C sin α + l C D sin θ 4 = l E D sin θ 5 (16)
The same can be obtained
θ 5 = arctan l E C sin α + l C D sin θ 4 l E C cos α + l C D cos θ 4 (17)
In triangular CDE, from the law of cosines
l E D = l E C 2 + l C D 2 − 2 l E C l C D cos ( θ 4 − α ) (18)
Can be obtained from the assembly relationship
θ 4 = θ 3 − γ (19)
So far, the change rule of the position of each rod of the selection mechanism with the rotation angle θ 1 of the conjugate cam can be obtained.
Deriving Formula (7) with respect to time can be obtained
l O A ω 1 e i ( θ 1 + π 2 ) + l A B ω 2 e i ( θ 2 + π 2 ) = l C B ω 3 e i ( θ 3 + π 2 ) (20)
The real part and imaginary part of Formula (20) are respectively equal to obtain
− l O A ω 1 sin θ 1 − l A B ω 2 sin θ 2 = − l C B ω 3 sin θ 3 (21)
l O A ω 1 cos θ 1 + l A B ω 2 cos θ 2 = l C B ω 3 cos θ 3 (22)
It can be solved by Formulas (21) and (22)
ω 2 = − l O A sin ( θ 1 − θ 3 ) l A B sin ( θ 2 − θ 3 ) ⋅ ω 1 (23)
ω 4 = ω 3 = l O A sin ( θ 1 − θ 2 ) l C B sin ( θ 3 − θ 2 ) ⋅ ω 1 (24)
Derivative Formula (14) with respect to time can be obtained.
l C D ω 4 e i ( θ 4 + π 2 ) = l E D ω 5 e i ( θ 5 + π 2 ) + v r e i θ 5 (25)
The relative velocity of component 5 is v r .
The real part and imaginary part of Formula (25) are respectively equal to obtain
− l C D ω 4 sin θ 4 = − l E D ω 5 sin θ 5 + v r cos θ 5 (26)
l C D ω 4 cos θ 4 = l E D ω 5 cos θ 5 + v r sin θ 5 (27)
Rotate the xEy coordinate system around pointE by angle θ5 Then by Formulas (26), (27) we can get
ω 5 = l C D ω 4 cos ( θ 4 − θ 5 ) l E D (28)
v r = − l C D ω 4 sin ( θ 4 − θ 5 ) (29)
Derivation of Formula (20) with respect to time can be obtained
l O A ω 1 2 e i ( θ 1 + π ) + l A B ω 2 2 e i ( θ 2 + π ) + l A B α 2 e i ( θ 2 + π 2 ) = l C B ω 3 2 e i ( θ 3 + π ) + l C B α 3 e i ( θ 3 + π 2 ) (30)
The real and imaginary parts of Formula (30) are respectively equal to obtain
l O A ω 1 2 cos θ 1 + l A B ω 2 2 cos θ 2 + l A B α 2 sin θ 2 = l C B ω 3 2 cos θ 3 + l C B α 3 sin θ 3 (31)
− l O A ω 1 2 sin θ 1 − l A B ω 2 2 sin θ 2 + l A B α 2 cos θ 2 = − l C B ω 3 2 sin θ 3 + l C B α 3 cos θ 3 (32)
By Formula (31), (32) can be solved
α 3 = l O A ω 1 2 cos θ 1 − θ 2 + l A B ω 2 2 − l C B ω 3 2 cos ( θ 3 − θ 2 ) l C B sin ( θ 3 − θ 2 ) (33)
α 2 = l O A ω 1 2 cos θ 1 − θ 2 + l A B ω 2 2 cos ( θ 3 − θ 2 ) − l C B ω 3 2 l A B sin ( θ 3 − θ 2 ) (34)
Derivation of Formula (25) with respect to time can be obtained
l C D ω 4 2 e i ( θ 4 + π ) = 2 v r ω 5 e i ( θ 5 + π 2 ) + l E D ω 5 2 e i ( θ 5 + π ) + l E D α 5 e i ( θ 5 + π 2 ) + a r e i θ 5 (35)
The same can be obtained
a r = l E D ω 5 2 − l C D ω 4 2 cos ( θ 4 − θ 5 ) (36)
α 5 = − [ 2 v r ω 5 + l C D ω 4 2 sin ( θ 4 − θ 5 ) ] / l E D (37)
The geometric symbols and physical parameters of the heddle selection mechanism of a certain type of rotary dobby machine are shown in
Through Matlab software programming calculation, the angular displacement, angular velocity and angular acceleration curves of the iron-absorbing pendulum are obtained, as shown in Figures 5-7.
It can be seen from Figures 5-7 that the angular displacement of the iron-absorbing pendulum is within the safe corner 15˚, the angular velocity and angular acceleration meet the requirements of the motion characteristics, and the angular acceleration curve is smoother.
| Structural parameters | Description |
|---|---|
| i | Component number |
| θi | The included angle between the i component and the positive x-axis |
| LBC/mm | 137.9 |
| LCD/mm | 137.9 |
| LOC/mm | 204.1 |
| LEC/mm | 185.8 |
| α/(˚) | 31.2 |
| β/(˚) | 69.7 |
| γ/(˚) | 20.3 |
The operating principle of the rotary dobby machine selection mechanism is analyzed deeply. Build a kinematic model, and use the three-coordinate instrument to measure the contour of the conjugate cam to obtain discrete points. The kinematics analysis of the heald selection mechanism is carried out and the simulation is carried out with Matlab. Determine the law of change of the angular displacement and angular velocity of every component accurately, locate the motion trajectory of every component accurately, and avoid interference between the selection mechanism and the lifting mechanism, providing a theoretical basis for whether the speed and acceleration meet the requirements, and providing a basis for future kinetic analysis.
The authors declare no conflicts of interest regarding the publication of this paper.
Yu, H.B., Zhao, X.P., Yin, H.H. and Shao, H.Y. (2021) The Kinematics Analysis of Heald Selecting Mechanism of Rotary Electronic Dobby. Open Journal of Applied Sciences, 11, 93-102. https://doi.org/10.4236/ojapps.2021.111007