Keywords: P&O-guided; F/T-driven; Compliance assembly; Large components alignment
1. Introduction
In recent years, with the rapid development of the assembly technology toward being digital, flexible and intelligent, Germany and the United States as the representative of the world's leading industrial countries are moving towards a new round of industrial revolution which uses intelligent equipment and information communication. Various information sensing technologies and data collection methods are the premises of industrial automation and information technology integration in the intelligent assembly. Measurement Aided Assembly (MAA) [1]-[2] is one of its forms of implementation, also is the inevitable trend of large component intelligent assembly technology development. The large components such as airframes, satellites and rockets typically have similar characteristics i.e., large size, easily deformed, complex coordination relationship, etc. In the conventional assembly process, large scale fixtures, which consist of large steel structures configured for a special component or structure, are used to position the components,
with manual operation to realize the geometrical relationships and constraints between components, and to ensure their variation within acceptable tolerances. With such an assembly process it is difficult to accurately adjust the position and orientation (P&O). Moreover, it needs a large work space and a lot of manpower. So, the conventional low accuracy and inefficient assembling process cannot meet the demand of advanced, flexible, accurate and high-efficient large components assembly [3]-[4].
The development of large scale metrology technologies, which are based on the high-precision and efficient digital measurement systems, have become the key technologies during assembly for process control and quality assurance. To improve the efficiency and precision of assembly, a novel assembly system based on MAA is proposed by manufacturers and researchers which has been employed in level docking system in large component assembly of spacecraft [5], digital alignment system for large component assembly of aircraft [6]-[7], vertical docking system in large component assembly of satellite[8], etc.
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The MAA technology uses the digital measurement system (such as electronic theodolite, laser tracker, indoor GPS, camera systems) to measure the P&O of components and assist the adjustment of P&O [9]-[10]. However, the electronic theodolite and laser tracker are by-point measurement way. Indoor GPS can be used in a fixed space, and be susceptible to signal interference. Camera systems are more sources of error. With the improvement of the manufacturing accuracy, the accuracy of the measurement system will be lower than that of assembly design, which will fails the assembly. In robotic assembly applications (such as peg-in-hole, surface grinding), when the assembly objects are in contact during assembling, the compliant control methods that make the interaction forces as a constraint condition are used to recognize and change the contact state, and finish the assembly [11]. These methods provide a new assembly idea for the MAA technology. The force measurement and control technology will depend on two important parts: sensors and force control.
Six-dimensional F/T sensors: The isotropic configuration of the six-dimensional F/T sensor based on SP, the task-oriented design method of the six-dimensional F/T sensor and a six-dimensional F/T sensor to complete peg-in-hole assembly task have been introduced in [12]-[13]. A six-beam sensor based on SP and an idea of “joint less” structure and beam sensors to improve the precision and sensitivity in measuring a small F/T have been proposed in [14]. A six-dimensional heavy F/T sensor with high stiffness and good linearity based on SP has been presented in [15]. Experimental results verified the feasibility and validity of the sensor by the established calibration platform [15].
Force control techniques. A shape recognition algorithm based on a six-dimensional F/T sensor and a hole detection algorithm have been reported in [16]. The six-dimensional F/T sensor to estimate the contact phases and designed the assembling strategy to achieve the force-guided robotic assembling in [17]-[19]. The admittance characteristics for a force-guided robotic assembly have been studied and analytical derivations for different contact states are presented in [20]. A modified control scheme for SP with compensation for interaction force control and positional error recovery is introduced in [21].A novel strategy of the high-precision chamferless peg-hole insertion with a six-dimensional F/T sensor is introduced in [22].
The MAA technology for large component assembly so far presented only considers the geometrical characteristics and doesn't give any attention to the physical characteristics. Focusing on the geometric and physical characteristics of large components, this paper proposes a two-stage alignment framework for large components based on P&O and F/T. This paper is organized as follows: Section 1 introduces the development and application of MAA technology, highlights the measurement of interaction force and its significance in assembling. Section 2 provides the two-stage alignment framework of large components based on P&O and F/T in detail, Section 3 provides the P&O-guided alignment based on model. Section 4 provides the F/T-driven alignment based on six-dimensional F/T feedback. A practical alignment system is designed to verify the effectiveness of the proposed framework,
and the obtained results are discussed in section 5. Section 6 concludes the paper and assesses the presented framework.
2. Framework of large components two-stage alignment based on P&O and F/T
As shown in Fig. 1, the two-stage alignment framework of large components based on P&O and F/T can be divided into two sections:
(1)The base environment for aligning large components: The software and hardware that are used to support the two-stage alignment of large components based on P&O and F/T are shown in Fig. 1. The software system includes Product Data Management (PDM) system, database, integrated control platform, etc. The hardware system includes a digital measurement system, force sensors, P&O adjustment platform, fixed platform, control cabinet, assembly fixtures, etc. The software and hardware will communicate with each other.
Fig. 1. The two-stage alignment framework of large components based on P&O and F/T
(2)The enabling technologies for aligning large component: The alignment based on P&O and F/T has two stages as illustrated in Fig.1. The P&O-guided alignment. The measurement process model is integrated with the assembly planning to instruct the deployment and planning of digital measurement systems, enabling automation. Through processing and analyzing measurement data in the alignment process, the geometrical information of components viz., P&O, dimension, variation and others are calculated and compared with the design requirements. Then, the feedback from the analysis is used to adjust the P&O adjustment platform. The F/T-driven alignment. The compliant assembly model is integrated with the assembly planning to follow the six-dimensional F/T feedback, enabling automation. Through processing and analyzing measurement data in the alignment process, the interaction force between the components is calculated. Then, the feedback from the
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analysis is used to adjust the P&O adjustment platform. The two-stage alignment of large component based on P&O and F/T in this paper can be described by the flowchart shown in Fig 2.
Fig. 2. The two-stage alignment of large component
3. P&O-guided alignment based on model
3.1. Mathematical model of P&O
Schematic diagram of the P&O adjustment platform is shown in Fig. 3. It consists of a moving platform and a stationary platform, which are connected using six stretchable limbs through spherical joints. Such arrangement offers 6-Degrees-Of-Freedom (DOF) motion due to the movements of six limbs as a whole. The cartesian coordinate system o0-x0y0z0 is located in the center of the top surface of the stationary platform and the cartesian coordinate system o1-x1y1z1 is located in the center of the bottom surface of the moving platform. The centers of the spherical joints are denoted as Ai and Bi (i=1,…,6).
Fig. 3. Schematic diagram of the P&O adjustment platform Fig. 4. The relationship between P&Os
The P&O of the moving platform with respect to o0-x0y0z0 can be expressed using a six-dimensional variable T1-0= {x,y,z, , , }, which includes the amount of rotation and displacement of o1-x1y1z1 with respect to o0-x0y0z0. Where , , are the rotational angles of each axis of o1-x1y1z1; x,y,z are the displacements of the original point of o1-x1y1z1.
Ai is one of the points on the moving platform and the position of Ai in o0-x0y0z0 and o1-x1y1z1 can be expressed in the form of vectors as Pi0 = [Ai0,1]T, Pi1 = [Ai1,1]T. Where Ai0 = (xi0,yi0,zi0) is the coordinate in o0-x0y0z0. Ai1 = (xi1,yi1,zi1) is the coordinate in o1-x1y1z1. The two vectors are different descriptions of the same point; hence they can be related using a linear transformation as follows:
3 3 3 11 0 1 0 1 0
1 3
, [ ]0 1i i
R MT P P T (1)
where R3 3 is called the rotation matrix, and M3 1 is called the displacement vector. If Pi1 is known, and Pi0 is obtained though measurement, according to (1), the x,y,z, , , can be calculated by measuring the coordinates of at least three points which are mutually non-collinear.
3.2. Assembly relationship model of P&O
The position of Ai in o2-x2y2z2 can be expressed in the form of a vector as Pi2=[Ai2,1]T, where Ai2=(xi2,yi2,zi2) is the coordinate in o2-x2y2z2. As shown in Fig. 4, the P&O of the moving platform with respect to o0-x0y0z0 can be expressed by T1-0, the P&O of the digital measurement equipment in relation to o0-x0y0z0 can be expressed by T2-0 and the P&O of the moving platform with respect to o2-x2y2z2 of measurement coordinate system is expressed by T1-2.
T1-0, T2-0 and T1-2 are related as T1-0 Pi1 = Pi0, T2-0 Pi2 =Pi0, T1-2 Pi1 =Pi2. The relationship between these P&Os is as follows: T1-0= T2-0 T1-2. When there are multiple P&Os in the alignment process, their relationship can express the final assembly relationship and determine the assembly parameters. The relationship between P&Os can be obtained following the method so far discussed.
4. F/T-driven alignment based on six-dimensional F/T feedback
4.1. Analytical algorithm of six-dimensional F/T
According to screw theory, the external load [Fs Ms]T on the moving platform in o1-x1y1z1 as shown in Fig. 3, can be calculated by applying the force equilibrium equation as follows.
[ ]F G f (2)
where F=[Fs Ms]T=[Fx Fy Fz Mx My Mz]T, f=[f1 f2 f3 f4 f5 f6]T.
6 61 11 2 3 4 5 6
1 1 6 601 02 03 04 05 06
1 1 6 6
A BA BA B A BA S A S
S S S S S SG
S S S S S S
(3)
where Ai and Bi are coordinates in o1-x1y1z1. fi is the measured force of limbs. Hence, the external load [Fs Ms]T can be calculated using (2).
4.2. Geometric and mechanical models of components
The components which are studied in this paper have certain rigidity, and their P&Os are adjusted for alignment at low speeds. Therefore, the alignment process for the large component can be described as a typical peg-in-hole assembly.
The contact state of three points on the upper circle surrounding the hole is determined by the P&O-guided alignment process, which is the beginning of the F/T-driven alignment process. The geometric and mechanical models of components are analysed as shown in Fig.5. In (b), F and M are calculated by using the analytical algorithm. f1 and f2 are
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the supporting forces and is the friction coefficient. Following equations can be established.
When the three contact points on the upper circle surrounds the hole, the P&O of peg should be adjusted. Say, Fh and Mx are applied (as in fig.6).
Fig. 6. Mechanics analysis of P&O adjustment process
1 1 2 2
1 1 2 2
1 1 2 2
cos sin cos sinsin cos sin cos
/ 2 / 2 ( )
yh yh
zh zh
xp xp
F f f f f maF f f f f ma
M f L f d s f d f L l I
(6)
When the peg is in uniform motion and ayh=0, azh=0, xp=0, f1> 0, f2> 0, then
cos sincos sin
yh
zh
FF
(7)
22
2
22
2
sin cos2 2
cos1
sin cos2 2
sin1
xp
h
d dL L d s l s lMF
d d s l L L d s l
(8)
The P&O of peg can be adjusted until the next contact state satisfying the above relationship. The same analytical method is used for adjusting other contact states as well. From the change of contact state, F/T-driven alignment process is described in Fig. 7.
Fig. 7. F/T-driven alignment process from the change of contact state
5. Experimental results and Discussion
As shown in Fig. 8 and Fig.9, the designed experimental system includes laser tracker, force sensors, P&O adjustment platform, fixed platform, control cabinet, assembly fixtures and an integrated control platform. As shown in Fig. 10 and Fig.11, the GUI for integrated control platform includes functional areas, navigation tree, a graphical display for status monitoring and functional dialogs. Experimental process is divided into two stages:
Fig.8. Experimental environment of P&O-guided alignment process
Fig. 9. Experimental environment of F/T-driven alignment process
(1) P&O-guided alignment process: Firstly, measurement plan is carried out that includes laser tracker configuration and station planning, P&O measurement characteristics planning (planning results as in Fig. 8) etc. Then, the measurement field is constructed. Secondly, Laser tracker automatically measures the P&O measurement characteristics to fit the P&O of components. Then the assembly coordination is determined. The automatic measurement dialog and the assembly
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coordination dialog are shown in Fig. 10. Thirdly, the calculation results are used to adjust the P&O adjustment
platform. These steps are repeated until the P&O adjustment platform reaches the target P&O.
Fig. 10. GUI of Integrate control platform for P&O-guided alignment process
Fig. 11. GUI of Integrate control platform for F/T-driven alignment process
(2) F/T-driven alignment process. Firstly, the experimental setup has six force sensors which are placed in each limb of
P&O adjustment platform to measure the forces on each limbs and then the six-dimensional F/T is calculated based on the
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analytical algorithm (as shown in Fig. 9). Secondly, the gravity of the moving platform, assembly fixtures and components are compensated. The gravity compensation dialog in GUI of integrated control platform is shown in Fig. 11. Thirdly, the compliance assembly is started (as in Fig. 11). The calculation results are used to adjust the P&O adjustment platform. The F/T-driven alignment process is repeated until the interaction force meets the threshold value.
In the above experiments, the alignment process is completed successfully. The precision of the system varies in different stages. In the P&O-guided alignment process, the precision of the system depends on the precision of digital measurement system and the positioning accuracy of P&O adjustment platform. In the F/T-driven alignment process, the precision of the system depends on the precision of force sensors. The precision analysis is out of scope of this paper as this document is drafted to introduce the idea.
6. Conclusions
Considering the geometry and physical characteristics of the alignment of large component, a two-stage alignment framework for large components based on P&O and F/T methods is presented in this paper. It can evaluate the target alignment quickly from the geometry and mechanical parameters. Two stages of framework are presented, which are the P&O-guided stage and the F/T-driven stage. The measurement process model and the compliance assembly model are presented to design an intelligent alignment process.
The implemented framework contains functionality that supports planning and automatic measurements, P&O fitting, MAA automation, six-dimensional F/T measurement and compliance assembly automation. The alignment experiment was performed on the self-designed alignment system using aerospace products and the relevant experimental results proved that the proposed two-stage alignment framework for large components is effective. Future research will focus on the accuracy analysis of six-dimensional F/T measurement and more applications of artificial intelligence technology in the F/T-driven stage.
The proposed alignment approach can be applied to the sleeve connection of large components, just like peg-in-hole assembly. It can also be applied to the alignment of surface and plurality of holes for large components. But the large components should have enough rigidity.
Acknowledgements
This work is under the support of National Defense Basic Scientific Research (No. A2120132007) and Fund of National Engineering and Research Center for Commercial Air-craft Manufacturing (No. SAMC14-JS-15-055).
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