Dynamics Research of rigid-flexible model of crank-rocker mechanism with Multi Clearance

This paper takes the crank-rocker mechanism as the research object purposed for the simulation of the motion pair with clearance utilizing the contact force model and the coulomb friction model, we build the virtual prototype of four-bar mechanism with clearance joints in the ADAMS. The article mainly contrasts the influence dynamics characteristics towards the mechanism multi-joint clearance between the rigid rocker and the flexible rocker . Considering the jointed arm' s flexibility, the four,five and six order modal of the rocker , generated by ANSYS as a neutral document , were imported into ADAMS for simulation.The result shows that Mechanism with four joint clearance increased the impact on the speed and the acceleration appeared greater fluctuation,the flexible rod has a buffer effect to the contact-impact forces,and the dynamic characteristics of fluctuations are improved.


Introduction
With the high speed, overloading, the rapid development of precision mechanical and aerospace engineering, accurate prediction of mechanism motion demand is higher and higher.
In most of the mechanical system, the mechanism of artifacts usually by kinematic pair connection.
Due to error in the process of manufacture,   The expression of the Impact function is as follows [5]: K is stiffness coefficient, the fomula is as follows:    The simulation results and analysis.Figure 5         of the collision of pin shaft and shaft sleeve, the mechanism motion more tend to be ideal.

1 .
assembly and mechanism motion produced by friction, wear, and the influence of such factors as movement exists between vice clearance.And the existence of the gap destroyed an ideal organization model, cause the collision of kinematic pair, cause the violent vibration of institutions, led to the decrease of the mechanical system stability and precision, and thus the efficiency and service life.In recent years, for mechanism with clearance, and there were many research of flexible components [1], but for considering four kinematic pair clearance and flexible connecting rod four-bar linkage study also is less.In this paper, based on two state model using coulomb friction model and collision model [2-4], and consider the connecting rod for the flexible body, including four crank rocker mechanism with clearance joints and soft model for the study of dynamics.As the existence of the joint clearance, the center distance between the shaft pin and sleeve is no longer zero, and resulted collision and friction of shaft pin and sleeve.There are three kinds states of shaft pin: free state, collision, Continuous contact.Center distance is e, When e<r, shaft pin is in a free state.When e>r, the shaft pin and sleeve generate collision.When the shaft pin and the sleeve in collision, the contact force decompose into the normal collision force N F and the tangential friction T F .In order to describe the rule of the collision between two objects, ADAMS software use the IMPACT function to solve the force of two objects at the time of the collision, and the motion rule of the two objects in the before collision and after collision.The function of the collision between two objects is equivalent to a nonlinear spring-damper model.As shown in Fig.2.

Fig 1 .
Fig 1.Normal and tangential contact force when the shaft pin and sleeve is in a collision.
ratio and contact radius of the object.δ is the collision depth.Collision index n can reflect the level of material nonlinearity, normal metal materials takes the number of 1.5.In ADAMS, transient damping coefficient is the step function of collision depth, the value of c is determined by the Step function.Generally speaking, damping coefficient value take 0.1 ~ 1% of stiffness coefficient K[6], recommend max d value is 0.01mm.Generally, friction coefficient data obtained from experiments, normal dynamic friction coefficient take 0.1, static friction coefficient take 0.3.

Figure4.
Figure4.Four,five and six modal of flexible rocker.

and figure 6
figure 6 respectively a handle for the rigid and flexible connecting rod and rocker speed curve.Agencies began to work, two kinds of condition occurred on the connecting rod and a handle speed curve of a certain fluctuation, but the joystick is flexible, the speed is less volatile.At a later time,

Figure 7
Figure 7 and figure 8 respectively a handle for the rigid and flexible connecting rod and rocker speed curve.Rigid for analysis, rocker, connecting rod and rocker acceleration to the existence of the gap significantly in unstable state, shaft and shaft sleeve is in a state of collision and separation.When rocker for the flexible connecting rod and a handle fluctuates significantly decreases, and the acceleration amplitude greatly reduced, curve fluctuations more smoothly, also shows that the collision of flexible factor counter shaft and shaft sleeve have buffer action.

Figure 9 Figure5.
Figure 9 and 10 respectively a handle for the rigid and flexible component pin shaft and shaft sleeve contact between the collision force curve.Diagram curve clearly shows flexible joystick and shaft sleeve absorbs the shock, the collision has obvious cushioning, flexible factors to contain much clearance between the crank rocker mechanism motion state is very good, make body more close to ideal state, reduce the rigid adverse impacts on the state of motion artifacts.

Figure6.
Figure6.Rocker X-axis speed in the case of the rigid and flexible rocker.

Figure7.
Figure7.Link X-axis acceleration in the case of the rigid and flexible rocker.

Figure8.
Figure8.Rocker X-axis acceleration in the case of the rigid and flexible rocker.

Figure9.
Figure9.X-axis contact force between shaft and sleeve of link and rocker in the case of the rigid and flexible rocker.

Figure10. 4 Conclusions
Figure10.X-axis contact force between shaft and sleeve of rocker and rack in the case of the rigid and flexible rocker.