MECHATRONIC WORKSTATION FOR ADAPTIVE ASSEMBLY TASKS

МЕХАТРОННАЯ СТАНЦИЯ АДАПТИВНОЙ СБОРКИ

Prof. Dr.Sc. Georgiev K., Prof. Dr. Maga D., Bulgarian Academy of Science – Institute of Mechanics,

University of Trencin ,Slovakia, Abstract This work presents some aspects of mechatronic workstation for adaptive assembly tasks, modelling and 3D simulation of the workstation . Some problems of so called intelligent mechatronic devices ( sockets ) are presented and practical results of study are discussed. KEY WORDS: WORKSTATION,SOCKETS,MECHATRONIC ACTUATORS 1.Introduction The greatest difficulty for robotic systems is the assembly of low clearance parts because the assembly clearance is smaller than the positioning errors of assembly systems. In general the process of adaptive assembly is a discrete state consisting of several phases demanding appropriate control through internal and external sensors.As a whole the process of assembly must be safe, fast and stable in time. According to the specifics of assembly tasks and operations the whole process can be divided to three phases: transporting movement with velocity, micro motions with low velocity and mating of details with method of local dynamic compliance . In this paper a methodology for adaptive assembly tasks of rotational and prizmatic

details,without chamfers is presented ,based on using of new innovative solutions and complex simulations of mechatronic workstation .[1,2,3].Commercialy available robotic manipulators are neither accurate,responsive ,nor well suited to interact with their environment .Lack of accuracy is caused primarily by unmeasured deflection of the robot structures or drives and low actuator/servo resolution. Interaction with the environment is hampered by the inability to accurately modulate the end-point impedance of the robots. The correction of small end point errors generally requires movement of several,if not all of the manipulator,s actuators.The developed workstation used for adaptive assembly tasks of rotary and non-rotary details incorporates the advantages or 3R assembly robots.

2. Modeling and computer simulation of robot links and contact stages The object of interest is a generalized structure (R⊥R⎥⎟R) of an anthropomorphic industrial robot with three degrees of freedom (three regional macro motions) and corresponding generalized coordinates:

332211 ;; ϕϕϕ === qqq , assuming that the links are rigid bodies and the joints are frictionless and non-compliant. a) The dimensions of the links are given in advance

(lengths ) and their mass 3,2,1; =ili 3,2,1; =imi are computable as well as the corresponding axial and centroidal moments of inertia from the individual tensors of inertia . )(i

skJ

b) Link 1 rotates with , link 2 realizes spherical

motion with angular velocity 1q&

22112 kqkqq &&& += ; link 3 does a complex movement represented by a translation along with the centroid and a spherical movement around it: 332113 )( kqqkqq &&&& ++= .

Using Lagrangian dynamics we can derive the dynamic equations of assembly robots with joints, which have n freedom and n+1 links:.

The full dynamic model is presented in [2] and in this paper we shortly note that , the models derived, based on the Lagrange’s equations have the advantage that they are in closed form concerning the geometrical,inertial and functional parameters of the mechanical system. The joint reactions are excluded and considering the immense computational power of today’s computers one can successfully explore various aspects of the dynamic modeling of the robotized system. This enables us to carry out dynamic synthesis of the technological movements and to build a strategy for dynamic behavior when performing adaptive assembly operations. Using MATLAB and Solid Works environments, we can derive effective solutions for the corresponding parameters as well as get results applicable in the practice in order to achieve higher velocities and minimal duration of the technological assembly tasks with adaptation. ( Fig. 1a) and 1b)).

iskiii Jhlm ,,,

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Fig.1 a) Matlab simulation of robotic regional structure ,designed for workstation

Fig.1b) Solid works simulation of mass/inertia properties of robot links

Fig.2 a) Contact interaction of details – simulation blocks

Fig.2 b) Simulink modeling of contact stages ,during adaptive assembly tasks Using the idea of designing the system from modular structures with 3R active joints and adaptive sockets (accommodating the concept of local dynamic compliance), we are able to combine higher speed, thus obtaining solutions to the extremely difficult assembly tasks of prismatic details without chamfers.After the virtual 3D model is built( using Solid Works environment) it is possible to conduct various simulations. This enables us to research the model, carry out different scenarios to see what will be the behavior of the real adaptive assembly cell. The results from the kinematic simulations are presented further in the paper. However the question of the validity of the model is always open. Even in the user’s guide of the simulation product is written that one shouldn’t rely solely on the obtained results. That is why it was necessary to validate the results. For this purpose a mathematical kinematic computer model was built and researched using Matlab v6 combined with the specialized software toolbox Robotics Toolbox. The kinematic model was introduced using Denavit- Hartenberg convention. The direct and inverse kinematics was solved and the results were exported to the 3D robot model .Based on respective simulations we obtain the following results : at lower values of angular velocity of driving shaft and higher spring stiffness the driving robot torques are extremely low and the influence of initial contact between the assembled details is minimal . This fact is confirming at the investigation of robot joint reactions at the computer simulations . ( fig.3)

Fig.3 Modelling of Robot driving torques at the adaptive assembly tasks

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3. Principles of operation of adaptive sockets An adaptive assembly device using scanning vibration of the base details compensates the corresponding linear and angular inaccuracies. To achieve this the double-sided shaft with the offset weights is actuated by the motor with angular velocity, determined by the control system and realized by the system for coordination and fixation.The platform of the adaptive assembly device oscillates depending on the setting of the dynamic system with controlled amplitude and frequency. The base detail oscillates too, thus realizing vibration motion and the corresponding seeking curves or surfaces with the other detail as well as compensating for the linear and angular three dimensional inaccuracies and accomplishing the assembly process. From both scientific and practical point of view, robotized assembly of non-rotational details remains extremely difficult task characterized by:High level of uncertainty of contact situations between the assembled details, having in mind that using three dimensional mesh for positioning and orientation, the possible contact situations are 1060. Even if ideal conditions and sensors are given there exist great difficulties determining the contact situations and the corresponding point of static balance. The author’s concept for local micro motion using dynamic compliance essentially improves the parameters of the mechatronic assembly system incorporating simplified and low-cost control system through industrial PD controllers.The dynamic compliance concept used in the research, consists of: Self-adjusting (self-correcting) function of the adaptive devices using level feedback through sensor blocks -Self-correction of frequency micro motion (oscillations) and assembling force of the robot.

Fig.4 .3D simulations of mechatronic workstation – positioning table with sockets The three dimensional model of the device is built using Solid Works 2005 environment ( fig.4) assuming

that all main dimensions of the real model are exactly reproduced. All cinematic connections and degrees of freedom are kept in accordance with the original, as well as all mass and inertia characteristics.The correct construction and mating of all the details in the assembly allows us to create a virtual assembled model of the adaptive assembly cell. Further more the problem of straight line trajectory movement was solved and also exported. Using the mathematical results obtained the 3D model of the robot was driven to various location and its position and orientation was measured. The results coincided completely with the calculated ones. Further more a simulation of the adaptive assembly socket was conducted and the results again coincided completely with the experimental data obtained from a working real prototype The next step in the development is to calculate most precisely the drive parameters of feeding (positioning ) table in order to simulate the whole mechatronic system in 3D aspect and to create virtual product solutions (mechatronic product development ).

4. Virtual Work Method for mechatronic actuator Analysis and design Electrical drive systems and motors are the most frequently used kind of drives in mechatronic machines. Computer simulation of operation of the device under design is one of the most important tool use to support design process. The hightorque stepper with 2 stators and a rotor in form of a ring have been designed and optimized. The magnetic field analysis ,based on finite elements has been realized for model of actuator supplied with rated current,single and double phase supply. Basic actuator parts have been taken into account so the field has been analyzed in both air gaps in stator and rotor teeth and in pole shoes.The basic mathematical bakgrounds almost identical with bases of Coenergy Method. The difference is only in process of definition of moving parts of the machine. The solution is obtained by „virtual“ works evaluation – this means that no real rotor movement is generated and no real works are produced. Only one FE solution is required, valid for given rotor position. Increased demands are laid on mesh quality, since all nodes must have a defined factor of virtual movement possibility u:

• nodes with possible movement or rotation (rotor): u = 1

• nodes in rotor neighborhood: 0 ≤ u ≤1 • other nodes: u = 0

The Finite Element system evaluates several air layers in the air gap and eliminates the local errors and inaccuracies. Classical rotary machinery with one stator and one rotor can be successfully solved with this method; however, when using special geometries, especially with extremely thin air gap, even the model building should lead to impassable problems. The criteria of torque evaluation methods differ according to the author of publication or required results. In our case, the accuracy is understood as relative to the maximal possible static torque.

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Since the Megatorque actuator has a very complicated geometry, a simple rotary model with three Finite Element meshes of different mesh density have been constructed and solved :

• coarse mesh, 1400 elements 1400 nodes, • medium mesh, 4800 elements, 5000 nodes, • fine mesh, 10000 elements, more than 12000

nodes. Comparison of obtained results, where 100% have been defined as maximal value of torque obtained with fine mesh by Maxwell Stresses. Typical torque characteristics for Megatorque actuator can be seen in Fig. 5.

0

20

40

60

80

100

30 35 40 45 50 55 60 65 70 75

rotor possition (°)

Torq

ue (%

)

coarse

medium

fine

Fig. 5 – Typical Torque Dependences

The obtained results have been verified on model of Megatorque actuator. Because of the complicated geometry, only position of maximal torque has been solved and analyzed. According to the symmetry conditions, described above, three meshes of different quality have been used:

• standard mesh, 8574 elements, 7635 nodes, • fine mesh, 32460 elements, 37570 nodes, • extra fine mesh, 93432 elements, 116978 nodes.

Obtained results (in %) can be seen in Tab. 2.

Table – Torque Accuracy Implemented on Megatorque Actuator

Maxwell Arkkio Coenergy Standard

mesh 103,8 % 119,0 % 95,4 %

Fine mesh 101,8 % 107,0 % 112,5 % Extra fine mesh 100,0 % 102,6 % 96,7 % The analysis of current supply influence on actuator torque is based of fact, that three phase machine will be supplied with maximum two phases at the same time. The supply of third phase will not lead to adequate torque increase. So the analyzed supply cases have been as follows:

A, double phase supply, both phases supplied with rated current, same polarity,

B, double phase supply, both phases supplied with rated current, opposite polarity,

C, double phase supply, one phase with rated current, second with half size current, same polarity,

D, single phase supply. Typical comparison of static torque courses, obtained be all three used methods, can be seen in Fig. 5 (valid for supply case A). Similar analysis has been done for circle shaped slot.

-7000-6000-5000-4000-3000-2000-1000

01000

0.8 1.0 1.2 1.4 1.6 1.8 2.0Rotor Position (°)

Torq

ue (N

m/m

)

Maxwell StressesArkkio's MethodCoenergy Method

Fig. 6 – Typical Torque Distribution in Megatorque Actuator 5. Conclusions

Based on the investigation , a methodology for creation and investigation of such kind of mechatronic workstations was developed for the purposes of innovative assembly technology. Real experimens on adaptive assembly tasks – tests have been performed with workpieces with clearance less than 0,014 mm and full insertion was possible up to linear errors of 0,7-0,9 mm and angular errors of about 2 0. The time of seeking and assembly is less than 1,8 sec. Real adaptive sockets (modules) have been designed and tested successfully for the needs of assembly automation .Problem solutions very commonly relies on decomposition into smaller more easily understood solutions,ie the braking down of a problem into soluble parts.The whole process of investigation and creation mechatronc workstation can be represented in the form of splitting ,efectivly component solutions and integration after that via electronical (information) means

6 .References 1. Georgiev K., Kamenov V., Multifunctional robotic cell for adaptive assembly operations, Varna 2004, Proceedings of International Baltic-Bulgarian conferenceMechatronics, 06.2004. 2. Georgiev Kr.,.Robotic systems for adaptive assembly operations , D.Sc,Thesis ,2004, 278p., 3. Georgiev Kr., Development and investigation of adaptive device for robotized assembly,Journal of Engineering Mechanics ,Brno , 1994,(5-6 ) , 250-273 4. Maga D.,.et all , Finite element based analysis of special mechatronic actuators, Journal of Theoretical and applied mechanics ,BAS,Sofia,2006 (6) ,in print . 5.MATLAB 6.0 User.s guide ,2001 6.Solid works 2005 User,s guide ,2005 7.Georgiev Kr.,Kamenov V.,Computer simulation of intelligent mechatronic systems, June 2006., Tu Sliven Conference (Proceedings),p .164-168,2006,Journal of Mechanical engineering ,Issue 1 ,Varna.

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