Elastic vibrations of the peg during part alignment

Since 1961, when the first industrial robot was introduced in GM (General Motors) Ternstedt plant in Trenton, NJ (New Jersey), annual demand on robot systems continuously increases and consisted of 166028 units in 2011. The main consumers of robotic systems remains automotive, electronics, chemical/rubber/plastic industries, where robots used in various parts assembly, welding, painting pick-and-place tasks [1]. To ensure product quality and reduce production costs the use of robotic systems is effective but expensive solution. More over robots/manipulators requires periodical maintenance and replacement of wear and tear parts to ensure high performance accuracy which is very important in automated assembly. However wearing parts not the only source of the assembly errors. Tolerances of assembled parts, positioning errors, vibrations in manufacturing area reduces robots ability for successful task performance and simple peg-to-hole assembly operation might be impossible. Here are number of inventions that help to increase accuracy and efficiency of robots or manipulators. Device with remote center of compliance (RCC) introduced by D. E. Whitney in 1981 is probably the best known invention helping to accomplish assembly and engaging tasks [2]. Different modifications of RCC devices are still used now days. It is very effective mechanical tool with no requirement of auxiliary energy source or sophisticated software and acting on forces that rises in a contact point between mating parts. However drawback of this device is that it can be used only for the chamfered parts. Active compliant devices are systems mainly with position, force/momentum sensors feedback or vision based systems. Position corrections of the mating parts mainly done by robot/manipulator servo actuators in correspond to error signal from the feedback sensors [3-5]. It is advanced but expensive systems requiring additional computing power for feedback signal processing. And not always possible to get correct signal from the sensors or because of the wrong view angle machine vision systems fails. Vibrational part alignment classifies as passive compliant method. Whilst auxiliary energy source is used to generate vibrations were is no feedback from the sensors and no position correction signals formed to the robot/manipulator actuators. Kaunas University of Technology is one of the leading institutions in vibratory technologies as well as in vibratory alignment research. Their scientists have introduced alignment method when RCC device is used together with axial vibrations of one of the mating parts (peg or bushing) [6, 7]. System excitation and compliant device stiffness parameters were defined for steady and stable performance. This method prevents key insertion problem jamming and wedging. Mating part alignment on a vibratory plane is described in paper [8]. In this case chamferless parts can be used since every point of interwinding helix path is checked in a search field. But this is more complex system then previous described as bushing is movable based on a plane vibrating in a two perpendicular directions. Also forces of dry friction between plane-bushing and bushingpeg have to be taken to account when setting parameters for stable and reliable performance. All vibratory methods mentioned above uses low frequency vibrations (tenth to hundreds of Herz). Paper [9] describes alignment method when one of the mating parts (particular peg) is excited with the high frequency vibrations thus creating elastic deformations in it. In a mean time bushing is movable based on a plane. The alignment goes due friction forces when the peg is in a contact with bushing. It was experimentally set what influence of excitation frequency and amplitude, initial peg-bushing pressing force has to the alignment time. It was also showed the ability to use this method for mutual part alignment made from different materials and with different geometrical shape. However there is still lack of research data on a vibration character of the peg while in a contact with bushing. The aim of this paper is to explain nature of the peg’s tip vibrations when it’s in contact with bushing. As well as to answer how bushing is pointed to the correct alignment direction.


Introduction
Since 1961, when the first industrial robot was introduced in GM (General Motors) Ternstedt plant in Trenton, NJ (New Jersey), annual demand on robot systems continuously increases and consisted of 166028 units in 2011.The main consumers of robotic systems remains automotive, electronics, chemical/rubber/plastic industries, where robots used in various parts assembly, welding, painting pick-and-place tasks [1].
To ensure product quality and reduce production costs the use of robotic systems is effective but expensive solution.More over robots/manipulators requires periodical maintenance and replacement of wear and tear parts to ensure high performance accuracy which is very important in automated assembly.However wearing parts not the only source of the assembly errors.Tolerances of assembled parts, positioning errors, vibrations in manufacturing area reduces robots ability for successful task performance and simple peg-to-hole assembly operation might be impossible.
Here are number of inventions that help to increase accuracy and efficiency of robots or manipulators.Device with remote center of compliance (RCC) introduced by D. E. Whitney in 1981 is probably the best known invention helping to accomplish assembly and engaging tasks [2].Different modifications of RCC devices are still used now days.It is very effective mechanical tool with no requirement of auxiliary energy source or sophisticated software and acting on forces that rises in a contact point between mating parts.However drawback of this device is that it can be used only for the chamfered parts.
Active compliant devices are systems mainly with position, force/momentum sensors feedback or vision based systems.Position corrections of the mating parts mainly done by robot/manipulator servo actuators in correspond to error signal from the feedback sensors [3][4][5].It is advanced but expensive systems requiring additional computing power for feedback signal processing.And not always possible to get correct signal from the sensors or because of the wrong view angle machine vision systems fails.
Vibrational part alignment classifies as passive compliant method.Whilst auxiliary energy source is used to generate vibrations were is no feedback from the sensors and no position correction signals formed to the robot/manipulator actuators.
Kaunas University of Technology is one of the leading institutions in vibratory technologies as well as in vibratory alignment research.Their scientists have introduced alignment method when RCC device is used togeth-er with axial vibrations of one of the mating parts (peg or bushing) [6,7].System excitation and compliant device stiffness parameters were defined for steady and stable performance.This method prevents key insertion problem jamming and wedging.
Mating part alignment on a vibratory plane is described in paper [8].In this case chamferless parts can be used since every point of interwinding helix path is checked in a search field.But this is more complex system then previous described as bushing is movable based on a plane vibrating in a two perpendicular directions.Also forces of dry friction between plane-bushing and bushingpeg have to be taken to account when setting parameters for stable and reliable performance.
All vibratory methods mentioned above uses low frequency vibrations (tenth to hundreds of Herz).Paper [9] describes alignment method when one of the mating parts (particular peg) is excited with the high frequency vibrations thus creating elastic deformations in it.In a mean time bushing is movable based on a plane.The alignment goes due friction forces when the peg is in a contact with bushing.It was experimentally set what influence of excitation frequency and amplitude, initial peg-bushing pressing force has to the alignment time.It was also showed the ability to use this method for mutual part alignment made from different materials and with different geometrical shape.However there is still lack of research data on a vibration character of the peg while in a contact with bushing.
The aim of this paper is to explain nature of the peg's tip vibrations when it's in contact with bushing.As well as to answer how bushing is pointed to the correct alignment direction.

Experimental setup for vibratory part investigation
To investigate peg's vibrations while it's in a contact with bushing the following experimental equipment has been used (Fig. 1).Peg 4 is fixed in a middle crosssection in a gripper 1. Piezoelectric vibrator 2 is pressed to the upper end of the peg with pressing force F1 and excites peg in axial direction.Excitation signal to the vibrator provided by signal generator 3. The lower end of the peg is pressed to the bushing 5 with initial pressing force F2 while axis misalignment Δ.
To register peg's vibrations, one axis laser dopler vibrometer (LDV) is used.The interferometer head OFV512 measures vibrations and controller OFV5000 coverts signal from interferometer to the voltage signal corresponded to vibration amplitude.Further signal captured with oscilloscope PicoScope 4424 and displayed on a computer screen.In order to find movement trajectory of the peg's end tip, measurements of two perpendicular axes (X-Y, Z-Y, Z-X) were taken.Synchronization signal related to the excitation signal was used to synchronize measurement process.As long as vibrations are periodic and steady, vibrations magnitude (x i , y i , z i ) of each axis is defined at the same periodic time τ i according to the synchronization signal (Fig. 2).Plotting those values in a Cartesian coordinate system peg's path in all three planes found.
Time interval between two vibration signals at the same instantaneous phase gives us phase difference ε between those signals.Amplitude, V 132

Results of experiments
Influence of forces F1 and F2 to vibration amplitude was investigated on peg No. III.Pressing force of piezoelectric vibrator to the peg was gradually increased every 14 N and corresponding measurements of vibration magnitudes on all three axes were taken.The results are shown in Fig. 3. Force F1 and excitation frequency has no impact on vibration magnitude along axis OY.Vibration amplitude in OX axis direction gradually increases when pressing force reaches 49 N and later stabilizes at 115 N. Meanwhile overall OX vibration magnitude decreases as excitation frequency increases.Amplitude of longitudinal vibrations increases more rapidly after F1 exceeds 90 N until that growth relatively small.Such character of amplitude increment related with contact area changes between peg and piezoelectric vibrator.More force is applied bigger micro deformations between peg and vibrator thus bigger contact area and more excitation energy transferred to the peg.Since excitation of the peg is done with high frequency and small amplitudes contact area between peg and vibrator plays vital role.This could be seen from graph 1 and 2, as excitation frequency increases pressing force F2 also has to be increased to keep same longitudinal vibration amplitude.It was also experimentally set that mutual part alignment starts when force F2 exceeds 90 N, until that process of part alignment is not stable or it doesn't work at all.

Fig. 4 Vibration amplitude versus force F2
If force F1 had no impact on vibrations in OY axis, totally different impact had force F2.As the peg is pressed to the bushing with axis misalignment Δ = +1.5 mm, vibration amplitude gradually increases as force F2 increases.The same tendency is kept even if excitation frequency changes in range from 6523 to 6723 Hz (Fig. 4).In our case part alignment is most rapid when peg is excited at 6623 Hz frequency and vibrations in OY axis is the biggest.
Experiment results mentioned above in generally shows what influence for the vibrations amplitude has mounting conditions of the peg, and also that excited peg vibrates in three directions perpendicular each other.But there still no answer why bushing is slides toward coordinate axes centre.To find out what factors in charge of this effect, motion trajectory and direction of peg's tip was determined.
After excitation frequency for stable and steady part alignment was experimentally set to all pegs (Table 1), motion trajectory of the tip was taken in all three coordinate planes.Excitation frequency mainly depends from the peg's natural frequency, design of the gripper and force F2.Thus for the grippers with different design or made from different material excitation frequency for steady and stable part alignment will be different.In our case excitation frequency for stable and steady part alignment have lied between second and third natural bending mode of the peg.When the peg is pressed to the bushing with the force F2 = 2.2 N and axis misalignment Δ = -1.5 mm, lateral vibrations on OY axis increases significant and peg's end moves in elliptical shape trajectory in all three coordinate planes(Fig.6).Black dots on the path indicate its direction.For the different pegs, direction of rotation is different and that depends from excitation frequency and natural mode gripper-peg system vibrates.
In order the alignment of the parts could occur, bushing has to slide along positive OY direction.There are two ways how bushing is aligned.First is so called direct alignment (Peg II and III).In this case peg's tip moves counter-clockwise in ZOY plane (Peg II and III, c), thus direction of the normal force in the contact point lies on the positive OY direction and bushing is directly pushed toward coordinate axes center.Vibrations along OX axis has little effect since their amplitude smaller than OY, and overall vibrations are more polarized along OY axis (Peg II and III, a).Normal peg to bushing pressing force is bigger when longitudinal vibrations amplitude is negative.Thus propellant force is bigger when peg vibrates along positive OY axis rather than negative.
Second way of part alignment is indirect alignment (Peg I).Here peg's motion is clockwise in ZOY plane (Peg I, c) and bushing is pushed from the coordinate axes center.But because of the peg's tip elliptical movement in YOX plane (Peg I, a), bushing is turned by the angle so the alignment trajectory lie on the major axis of the ellipse and then pushed towards coordinate axes center.Results of peg's tip trajectory while Δ = +1.5 mm presented in Fig. 7.As contact conditions between peg and bushing has changed (contact area crescent now faced to opposite side), phases between vibrations also changed.In this case for the bushing to align with the peg, bushing has to slide along negative OY direction.Peg's I and II tip moves clockwise in a ZOY plane (Peg I and II, c) thus direct alignment is going.
Bushing with the Peg III is aligned during indirect alignment.The bush is propelled along negative OY direction, but because of rotation effect in YOX plane (Peg III, a) bushing is turned and pointed to the coordinate axes center.
It's clear that during direct alignment peg's motion in ZOY plane plays key role, meanwhile during indirect alignment there is combination of peg's movement in ZOY and YOX planes.It is necessary that the entire rear surface of the peg is in contact with piezoelectric vibrator, so the maximum vibration energy passes from vibrator to peg.However there is a limit of maximum vibrator to peg pressing force and further increase of F1 has no effect to magnitude of lateral vibrations.
2. Under proper excitation frequency peg has longitudinal and lateral OX vibrations while lateral OY vibrations are negligible.Excitation frequency depends on peg's natural frequency, mechanical design of the gripper and pressing force F1.
3. Lateral OY vibrations increases when the peg to bushing pressing force increases.
4. When initial relative position between peg and bush changes, contact area crescent between parts also changes its orientation.That leads to the phase changes between vibrations and direction of propellant force.
5. If propellant force directed to the coordinate axes center, direct part alignment is going.If propellant force directed from the coordinate axes center, indirect part alignment is going.In this paper experimentaly analyzed elastic vibrations of the peg while in a contact with bushing in automated assembly.Experimental setup and methodology of investigation are explained.Influence of excitation frequency and mounting conditions of the peg to the peg' tip lateral and longitudinal vibrations amplitude was determined.Peg's tip movement trajectory in three perpendicular planes were concluded while contact position between peg and bush is different.Analysis of experimental data explaines reasons why bushing always slides toward coordinate axes center despite its original position.

Fig. 1
Fig. 1 Experimental setup: ameasurement scheme: 1gripper; 2piezoelectric vibrator; 3excitation signal generator Г3-56/1; 4peg; 5bushing; 6fiber interferometer OFV512; 7vibrometer controller OFV5000; 8oscilloscope PicoScope4424; 9personal computer PC; bmeasurement equipment Vibrometer measurements were taken in a three directions X, Y, Z.Where X, Y corresponds to lateral vibrations in a two perpendicular directions and Z are longitudinal vibrations.Axial misalignment of the parts -Δ and +Δ lies on OY axis.Thus mutual part alignment occurs when bushing center coincides with coordinate axes center.Peg's tip vibration magnitude was investigated under different pressing forces F1 (vibrator to the peg) and F2 (peg to the bushing) when excitation frequency ν varies from 6523 to 6723 Hz, and tip movement trajectory was defined in relation with misalignment position Δ.

Fig. 5 Fig. 5
Fig. 5 Path trajectory of unloaded peg: ain YOX plane; bin ZOY plane Longitudinal vibrations are dominant in all cases and are twice as high as transverse ones.While in YOX plane they are polarized in OX direction since peg's vibra-

Fig. 7
Fig. 7 Path trajectory of loaded peg when Δ = +1.5 mm: ain YOX plane; bin ZOX plane; cin ZOY plane 4. Conclusions 1.It is necessary that the entire rear surface of the peg is in contact with piezoelectric vibrator, so the maximum vibration energy passes from vibrator to peg.However there is a limit of maximum vibrator to peg pressing force and further increase of F1 has no effect to magnitude of lateral vibrations.2.Under proper excitation frequency peg has longitudinal and lateral OX vibrations while lateral OY vibrations are negligible.Excitation frequency depends on peg's natural frequency, mechanical design of the gripper and pressing force F1.3.Lateral OY vibrations increases when the peg to bushing pressing force increases.4.When initial relative position between peg and bush changes, contact area crescent between parts also changes its orientation.That leads to the phase changes between vibrations and direction of propellant force.5.If propellant force directed to the coordinate axes center, direct part alignment is going.If propellant force directed from the coordinate axes center, indirect part alignment is going.

Table 1 .Table 1
Characteristics of excitation signal and aligned parts 2 ft     where fvibration frequency; Δttime interval between two signals.Excitation parameters and objects of experiments presented in