Published: 26 September 2017

A dynamic analysis of six-bar mechanical press

Assel Mukasheva1
Saduakhas Japayev2
Gulnara Abdraimova3
Batyrkhan Kyrykbaev4
Kuatbek Kozhamberdiyev5
Bagdat Uskembayeva6
Algazy Zhauyt7
1Institute of Mechanics and Mechanical Engineering named after Academician U. A. Joldasbekov, Almaty, 050013, Kazakhstan
2, 3, 4, 7, 1Kazakh National Research Technical University named after K. I. Satpayev, Almaty, 050013, Kazakhstan
5, 6Almaty University of Power Engineering and Telecommunication, Almaty, 050013, Kazakhstan
Corresponding Author:
Algazy Zhauyt
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Abstract

This paper analyzes the dynamical behavior of a six-bar linkage used in mechanical presses for metal forming such as deep drawing. Raising the technical level of machines requires an expansion of technological capabilities of the equipment and devices of the existing structures, as well as their equipping with fundamentally new mechanisms. In this regard, the task of developing methods for the dynamic of complex flat lever mechanisms with the desired laws of motion of the input and output elements allowing automatizing the implementation of all design phases with the use of computer is quite relevant. The simulation results obtained with a Maple program are validated by comparing the theoretical values of the input moment with the ones obtained from the conservation of energy law. Content of the article is distinguished by serious problem statement, interesting theoretical study and its practical test. This article provides new scientific results that have theoretical and applied significance.

1. Introduction

The work is carried out using various techniques, as well as techniques and their computer programming of kinematic analysis [1]. The more complicated device of the lever transmission, the analysis and synthesis of such mechanisms will be difficult [2]. Therefore, a two-part structural group will be used for practice [3]. Leverage consists of the main mechanism consisting of four parts of the structural group; their application in technology will not be [5, 6]. The reason is, the difficulty of distributing the practice of design engineers in the field of investigation of the mechanism from the structural group of four parts [7-9]. Automation and automatic press is carried out by means of processing of the two-lever mechanism of the structural group functionality [10-12]. In this regard, based on the structural group of four parts, mechanisms and planning machines, the synthesis of dynamic planning, processing of a numerical algorithm is a versatile issue, consisting of a structural group of four parts [13, 14].

2. Materials and methods

Dynamical equations on the first degree of freedom of the mechanism can be calculated from the basis of the algorithmic system without resorting to the cumbersome approach of solving the reduced force and mass [1]. The approach excludes the process of differentiating cumbersome expressions and allows us to construct an explicit dynamic equation with fairly good approximations [2]. The executive mechanism of the exhaust press machine is a flat crank-and-rod mechanism of the fourth class, represented in Fig. 1.

In a variant of the dynamic equation on the first degree of the mechanism is presented:

1
Jqq¨+0,5J'qq˙2=QD-QCq,q˙,t,

where q – accumulated coordinates, Jq, the reduced moment of inertia and its production from the accumulated coordinates, QD, QC The forces accumulated in motion and accordingly resistance forces [3-4]. In this algorithm Eq. (1) the d’Alembert-Lagrange equations are applied:

2
QD+i=1NPCi+FirOiq+MOiPC+MOiFφq=0.

Fig. 1Kinematic model of six-bar mechanical press

Kinematic model of six-bar mechanical press

On the basis of Eq. (2) from Eq. (1), by means of variation, it is possible to obtain discrete values of the inertia moment and its derivative, as well as the reduced moment of the resistance force mechanism [5-7]. The digital calculated algorithm of the mechanism includes the following main values: the equations of motion of a strictly secured press machine are indicated below [8-10]. Positioning function: φ2=φ2φ1, φ3=φ3φ1, φ4=φ4φ1, xF=xFφ1. Is determined by the formula:

3
xF=l32-l42-Ax2-Ay2+Bx2+By22Ax-Bx or xF=±l32-Ay2-Ax,
4
tgφ3=AyxF+Ax, tgφ4=ByxF+Bx.

φ2 and we use the following equation to determine the quantitative structure of the mechanism:

5
[l32-Ay2-l42+By2-(Ax-Bx)2]2=4(Ax-Bx)2l42-By2,

where:

6
Ax=a-l2cosφ2-l1cosφ1, Ay=-l2sinφ2-l1sinφ1,
7
Bx=-l2'cosφ2-α-l1cosφ1, By=-l2'sinφ2-α-l1sinφ1.

The mechanism connects the center of the mass coordinates using the following formula:

8
xS2=l1cosφ1+r2cosφ2+α2,yS2=l1sinφ1+r2sinφ2+α2,
9
xS3=l1cosφ1+l2cosφ2+r3cosφ3+α3,yS3=l1sinφ1+l2sinφ2+r3sinφ3+α3,
10
xS4=l1cosφ1+l'2cosφ2-α+r4cosφ4+α4,yS4=l1sinφ1+l'2sinφ2-α+r4sinφ4+α4.

Than we determine by the formula of analogue velocity:

11
u51=dxFdφ1=1cosφ3-Acosφ4-l1sinφ1cosφ3-Acosφ4+l1cosφ1(sinφ3+Asinφ4),

cosφ3-Acosφ40 by agreement.

where:

12
A=l2sin(φ3-φ2)l2'sin(φ4-φ2+α),

and so:

13
u21=dφ2dφ1=lγsin(γ-φ3)l2sin(φ3-φ2),
14
u31=dφ3dφ1=lγsin(φ2-γ)l3sin(φ3-φ2),
15
u41=dφ4dφ1=lγsin(φ2-α-γ)l4sin(φ4-φ2+α).

sin(φ3-φ2)0, sin(φ4-φ2+α)0 by agreement:

16
lγ=(u51+l1sinφ1)2+l12cos2φ1, tgγ=u51+l1sinφ1l1cosφ1, cosφ10.

Accordingly, we define the velocity analogue with the following formula:

17
u21'=d2φ2dφ12=Δ2Δ, u31'=d2φ3dφ12=Δ3Δ, u51'=-l1u21'sinφ2+l3u31'sinφ3+B1,

where:

18
Δ=a11a22a33-a13a22a31-a21a12a330,
Δ2=B1-B3a22a33-a31a22B4-a12a33B2,
Δ3=-(B1-B3)a21a33+(a11a33-a13a31)B2+a21a13B4Δ4
=-B1-B3a22a31+a11a22-a21a12B4+a12a31B2,

and more:

19
a11=-l2sinφ2+l2'sinφ2-α, a12=-l3sinφ3, a13=l4sinφ4,
a21=l2cosφ2, a22=l3cosφ3, a23=0, a31=l2'cosφ2-α,
a32=0, a33=l4cosφ4, B1=l1cosφ1+l2u212cosφ2+l3u312cosφ3,
B2=l1sinφ1+l2u212sinφ2+l3u312sinφ3,
B4=l1cosφ1+l2'u212cosφ2-α+l4u412cosφ4,
B4=l1sinφ1+l2'u212sinφ2-α+l4u412sinφ4.

In general the angular velocity ωk, k=2,3,...,4 and acceleration εk, k=2,3,...,4. Speed and acceleration of the 5 (F) wet by the speed and acceleration of the engine joints 1 generation [11, 12], with the following formula:

20
ωk=uk1ω1, εk=uk1'ω12+uk1ε1, VF=u51ω1, WF=u51'ω12+u51ε1,

where ω1, ε1 angular velocity and angular acceleration of the drivers joints [13].

The complex movement of the mechanism ω1=const, ε1=0 accepted for permanently movement:

21
ωkP=uk1ω1, VFP=u51ω1, εkP=uk1'ω12, WFP=u'51ω12,

and ω1=0 in the initial movement:

22
εkΗ=uk1ε1, WFΗ=u51ε1.

We determine the velocity and accelerations of the center of gravitation of the link [14] accordingly Eq. (8-10) on the basis of Eq. (20):

23
x˙S2=-ω1l1sinφ1+r2u21sinφ2+α2y˙S2=ω1l1cosφ1+r2u21cosφ2+α2,,
x¨S2=-ε1l1sinφ1+r2u21sinφ2+α2 -ω12l1cosφ1+r2u212cosφ2+α2+r2u21'sinφ2+α2,y¨S2=ε1l1cosφ1+r2u21cosφ2+α2 -ω12l1sinφ1+r2u212sinφ2+α2-r2u21'cosφ2+α2,
x˙s2=us2xω1, y˙s2=us2yω1, x¨s2=x¨s2P+x¨s2Η=us2x'ω12+us2xε1,
y¨s2=y¨s2P+y¨s2Η=us2y'ω12+us2yε1,

where:

24
uS2x=-l1sinφ1+r2u21sinφ2+α2,uS2y=l1cosφ1+r2u21cosφ2+α2,
25
u'S2x=-l1cosφ1+r2u212cosφ2+α2+r2u21'sinφ2+α2,u'S2y=-l1sinφ1+r2u212sinφ2+α2-r2u21'cosφ2+α2.

3. Results and discussion

According to the 3D Maple program, you can see the enlarged internal structure of the planned new type of automatic press of the hammer-stamping mechanism, considering the scheme, during the work of the links the main role of the parts; we see that each force is affected by different forces, thereby losing its workforce. And also, relying on the path of analytics and kinematics, we do not the effect to the link mechanism, but the values that we do not take into account have a significant effect on the mechanism, and so that all the values have been taken into account we come to the aid of the Maple program (see Fig. 2-8).

Fig. 2Six bar linkage motion simulation in Maple

Six bar linkage motion simulation in Maple

Fig. 3Computed plot of the crank angular velocity

Computed plot of the crank angular velocity

Fig. 4Computed plot of the pressure

Computed plot of the pressure

Fig. 5Computed plot of the moments of driving forces and resistance forces

Computed plot of the moments  of driving forces and resistance forces

Fig. 6Computed plot of the power on the internal combustion engine shaft

Computed plot of the power  on the internal combustion engine shaft

Fig. 7Computed plot of the dynamic characteristics of the engine

Computed plot of the dynamic  characteristics of the engine

Fig. 8Computed plot of the angular velocity of rotor and motor moment

Computed plot of the angular velocity  of rotor and motor moment

4. Conclusions

In the current study, the dynamic analysis of a six-bar linkage of a mechanical press for deep drawing has been investigated developing a Maple program. Raising the technical level of machines requires an expansion of technological capabilities of the equipment and devices of the existing structures, as well as their equipping with fundamentally new mechanisms. Creation and implementation of new structures of industrial robots, equipment for light industry, mining, and oil and gas industry requires the use of mechanisms with a complicated motion of actuating devices. In this regard, the task of developing methods for the kinematic and dynamic of complex flat lever mechanisms with the desired laws of motion of the input and output elements allowing automatizing the implementation of all design phases with the use of computer is quite relevant.

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Cited by

Mechanism Design for Robotics
Claudio Villegas | Mathias Hüsing | Burkhard Corves
(2021)

About this article

Received
12 July 2017
Accepted
23 July 2017
Published
26 September 2017
SUBJECTS
Mathematical models in engineering
Keywords
press automation
six-bar linkage
computed plot
numerical algorithm
dynamic analysis