KINEMATICS OF MECHANISM WITH ROTATING CAM AND FLAT FACE OSCILLATING FOLLOWER . PART II : NUMERICAL AND EXPERIMENTAL METHODS

The first part of the work studied the rotating circular cam mechanism with flat face follower using analytical methods. The second part analyses the mechanism from kinematical point of view employing numerical methods and experimental techniques. There is a perfect agreement between numerical and analytical results, but the experimental results are more difficult to evaluate and compare as they are influenced by numerous error sources. The paper presents these inaccuracy sources and the ways to diminish their effects.


INTRODUCTION
The first part of the paper was dedicated to the analytical kinematics of rotating circular cam mechanism with flat face follower and the expressions for displacement, angular velocity and angular acceleration were obtained.
The same parameters must be used in validating the theoretical results via other methods.First, a numerical analysis is proposed using CATIA DASSAULT software; secondly, experimental tests are made using equipment designed and assembled in the laboratory.The comparison of the results proves a perfect concordance between the tree types of results.

NUMERICAL MODELING OF MECHANISM'S KINEMATICS
The numerical modeling of the mechanism's kinematics is accomplished, based on both classical and recent knowledge, and using the DMU-KINEMATICS module of CATIA DASSAULT software [1][2].For obtaining the aimed results, it is required that previous steps are made, namely designing the elements of the mechanism using the PART DESIGN component of the same software.
The parts of the mechanism are afterwards assembled using the ASSEMBLY DESIGN component [1].The mechanism and the constructive data are presented in Figure 1.As further will be shown, the accomplishment of kinematical modeling of the mechanism depends on the correctness of imposed constraints.

EXPERIMENTAL KINEMATICAL ANALYSIS OF THE MECHANISM
The virtual mechanism presented in Figure 1 was actually constructed and a d.c.motor with reduction gearbox is the driving element.In order to measure the accelerations, on the follower it was mounted an acceleration sensor with the possibility of measurements of three orthogonal acceleration components.The sensor axes were oriented, thus the Ox axis should be directed along the contact line and the axis Oy, normal to this and as consequence, the Oz axis is normal to the plane of motion, Figure 2. In this coordinate system, the normal acceleration is oriented along Ox axis, the line from the centre of follower's joint to the sensor, and the tangential acceleration, t a r    is oriented along Oy axis.The signal generated by the acceleration sensor is transmitted to an acquisition board processed, and afterwards processed using the LABVIEW software [3][4].
For acceptable experimental results, two dynamical conditions must be fulfilled [5]: a. Constant rotation velocity of the driving motor; b.System's vibrations should not affect considerably the experimental results.
In order to verify the first condition, on the frontal surface of the cam was placed a paper disc, with the centre on the rotation axis of the motor, having angular gradations.For a set value of motor voltage, the motion of the cam was video captured with a high speed camera, (420 frames/sec), and afterwards the image was decomposed into frames with a specialized software.Thus, the time dependency for the position angle of the cam was obtained.It can be noticed that the signals from all the axes are affected by the noise produced by the system's vibrations [6][7].As a first cause estimated to be responsible of noise generation was the presence of sensor's wires.To respond to this question, the sensor was assembled on an aluminum cantilever beam, let to vibrate free.The obtained signal is smooth enough and thus one can abandon the wires' influence.So, the sources generating vibrations remain the driving motor and the relative motions from the mechanism's pairs.To verify this hypothesis, the connection between the motor shaft and cam's shaft was uncoupled.In this case, also, the signal is smooth enough as to drop the hypothesis that the vibrations are generated in one of the mechanism's pairs.With the driving motor mechanically uncoupled, at start, the plots from Figure 4 are obtained, thus attesting that the vibration source id the motor.To limit the effect or perturbation vibrations, two options come into view: either replacement of driving motor by a more noiseless one or changing the rigid coupling between the driving motor and the cam with a toothed belt.The motor vibrations effects can be limited by motion transmission from motor to cam's shaft using a toothed belt instead of a rigid clutch.

CONCLUSIONS
The paper presents a comparison between the results of kinematical analyses for rotating cam mechanism with oscillating flat face follower, obtained via two analytical methods, a numerical method and an experimental one.The experimental results were obtained using a test rig specially designed for the research.The experimental data were acquired using a three-axes acceleration sensor, assembled on the mechanism's follower.As it can be seen from Figure 5.a, there is no difference between analytical and numerical results.From the experimental results, Figure 5.b, compared to Figure 5.a, it is difficult to draw a conclusion.This fact is caused mainly by the vibrations generated by the driving motor and by the time increment limitation of the acceleration sensor.Even with all these difficulties, by proper filtration of experimental data and restraining the domain, the plots from Figure 5.b are obtained.It must be emphasized that special attention must be paid when experimental data are processed [8].From this figure, it can be seen a good qualitative concordance between analytical or numerical results and the experimental ones.The main conclusion emerging from the above aspects is that experimental analysis is a thornier task than numerical or theoretical analysis.However experimental analysis is the only way to validate or not a certain hypothesis for most of the times.For the present case, if the cam's profile were a random and not a circular one, applying the numerical or analytical method requires finding, previously, the coordinates of the points from the profile of the cam, which is also an experimental operation.After all experimental data are acquired, the second step follows, consisting in interpretation and processing the data.It is needed knowledge to identify the error sources and to remove or at least to limit their influence.In the present case, the main source of errors consists in the vibrations of the driving motor from the test-rig.As future works, it is required first, redesigning the coupling between the cam's shaft and the motor's shaft and replacing it with a toothed belt transmission.Secondly, the agreement between theoretical and experimental results has to be verified and if a suitable concordance exists, the device can be used in the analysis of mechanisms with complex cam profiles.
and control", Contract No. 671/09.04.2015,Sectoral Operational Program for Increase of the Economic Competitiveness co-funded from the European Regional Development Fund.

Fig. 1 .
Fig.1.The virtual mechanism (a) and the variation diagrams for the angle of position (b), angular velocity (c) and angular acceleration (d) of the follower.

Figure 3 .
Figure3.a.presents the experimental points for the position of cam's angle and the interpolation line.Though from the plot, it seems that the variation of cam's rotation angle depends linearly on time, fact that should indicate a constant rotation velocity of the cam, the numerical calculus and the plot of instantaneous angular velocity, Figure3.b,proves a harmonic variation of this.A plausible cause of the graph's aspect, Figure3.b, could be the eccentric assembly of the cam on the motor shaft.More explicit, the cam's own weight has a momentum that during the rise phase of the follower is a resistive one while during the descending phase is an active one.This effect is accentuated by the momentum of the cam-follower reaction force.Concerning the

Fig. 4 .
Fig. 4. Signal acquired from the acceleration sensor and processed using the LABVIEW software.