Content area
Purpose
>Aerospace assembly demands high drilling position accuracy for fastener holes. Hole position error correction is a key issue to meet the required hole position accuracy. This paper aims to propose a combined hole position error correction method to achieve high positioning accuracy.
Design/methodology/approach
>The bilinear interpolation surface function based on the shape of the aerospace structure is capable of dealing with position error of non-gravity deformation. A gravity deformation model is developed based on mechanics theory to efficiently correct deformation error caused by gravity. Moreover, three solution strategies of the average, least-squares and genetic optimization algorithms are used to solve the coefficients in the gravity deformation model to further improve position accuracy and efficiency.
Findings
>Experimental validation shows that the combined position error correction method proposed in this paper significantly reduces the position errors of fastener holes from 1.106 to 0.123 mm. The total position error is reduced by 43.49% compared with the traditional mechanics theory method.
Research limitations/implications
>The position error correlation method could reach an accuracy of millimeter or submillimeter scale, which may not satisfy higher precision.
Practical implications
>The proposed position error correction method has been integrated into the automatic drilling machine to ensure the drilling position accuracy.
Social implications
>The proposed position error method could promote the wide application of automatic drilling and riveting machining system in aerospace industry.
Originality/value
>A combined position error correction method and the complete roadmap for error compensation are proposed. The position accuracy of fastener holes is reduced stably below 0.2 mm, which can fulfill the requirements of aero-structural assembly.
1. Introduction
Transport planes, carrier rockets, missile launchers and other aerospace products are large-span thin-walled structures, which are constructed by crisscrossed girders and stringers as skeletons and covered by metal or carbon fiber-reinforced polymer (CFRP) panels as skins. Commonly, the skeletons and skins are mainly fastened by riveting joints; thus, the position accuracy of the fasteners is one of the main factors that affect the service life and safety of the products (Mei et al., 2015; Bi et al., 2013; Mei et al., 2018). Usually, the nominal positions of the fastener holes are directly obtained through the theoretical digital models of the products prescribed by designers (Robert, 2001). However, the actual fastener positions of the products are often deviated from the theoretical digital models due to assembly tolerances, gravity deformation errors, etc. (Bi et al., 2013; Bi and Liang, 2011). Once there are deviations between the nominal and actual positions of the fastener holes, the stress evenness around riveting fasteners is changed and the fatigue life of the aerospace products is reduced (Li et al., 2021). Hence, such position deviations or errors need to be eliminated to ensure the position accuracy of the fastener holes.
Generally, the skeletons and skins of aerospace products are first fixed on the assembly fixture to establish their relative position prior to connecting. Then, small reference holes are made to preassemble them together, followed by drilling and riveting operations (Zhang et al., 2018). More importantly, the reference holes are also used as geometric features to compare with theoretical digital models to correct for the deviations between them. That is, the positions of the reference holes in ready-to-assembly components are detected through the vision system; then, position deviations of the fastener holes are calculated by the position deviation of reference holes (Zhu et al., 2014; Tian et al., 2014). Based on the position deviation of the reference holes and the position relationship between the reference holes and the fastener holes, an error function is established, and the position errors of the fastener holes are compensated to improve the drilling accuracy (Zhao et al., 2017). Thus, correction results are significantly related to the selection of reference holes, and it could work better when products possess substantial stiffness to resist assembly deformation.
Practically, the aerospace products are thin-walled chambers with complex curved surface. They are assembled with manufacturing tolerance and clamping errors, which easily lead to deviations of hole positions between theoretical models and real components. From the perspective of the surface shape of the aerospace components, Zhu et al. (2013) constructed a bilinear error surface using the deviation vectors of the reference holes. The nominal positions of the fastener holes were compensated with linear interpolation, which greatly improved the drilling position accuracy of the assembly parts with sharp curvatures. To improve the drilling accuracy of aircraft cylindrical parts, Bi et al. (2015) proposed an interpolation Coons surface error correction method, which introduced normal vectors of the reference holes. To guarantee the hole margin, Wang et al. (2015) presented a correction method for hole positions based on hole margin constraints and Shepard interpolation to ensure the distance between the hole center and the boundary of trench in skeletons. As for hole perpendicularity, Zhang et al. (2012) proposed an algorithm based on the principal that four non-coplanar points could define a unique sphere tangent in spatial geometry. The normal vector of the curve surface of a workpiece at the drilling points was deduced by four displacement sensors installed on the end-effector in a flexible drilling system. Yan and Cheng (2015) presented a hole modification method, which could avoid the reliance on integral precision of the whole structures. The locations of holes along the line between two inspected preassembly holes could be calculated via the proposed spatial coordinate transformation matrix. Shi et al. (2020) exhibited a correction strategy based on Kriging interpolation through which the position deviations of the fastener holes could be predicted. The predicted hole position errors were highly dependent on the quantity and layout of reference holes. Based on the combination datum theory, an on-position measurement method was developed for position error compensation by Zeng et al. (2021), and the final coaxiality error of the gimbal was reduced to 0.022 mm. These hole position error correction methods which compensate position deviation in view of geometric features are suitable for automatic drilling and riveting system.
Since aerospace products are large-span structures with low stiffness, they are easily deformed or distorted under clamping force, machining force, gravity effects, etc., during assembly process. Thus, hole position error can be also compensated from the perspective of deformation. Cheng et al. (2011) presented a two-stage and eight-state hierarchical model of multi-state riveting process for thin-walled structures. Bases on this model as well as the “N-2-1” positioning principle, positioning error of each stage was analyzed according to manufacturing error, position accuracy and the mismatch error. Zhang et al. (2012) established a product deformation model for automatic carriers, in which the gravity deformation formula of the drilling point was constructed according to the spatial relationship between drilling points and the deformation curve of the beam. The iterative optimization method was used to compensate the hole position errors of product deformation. Lu and Islam (2013) developed a simplified method to compensate thermally induced volumetric error by modeling the positioning error as functions of ball-screw nut temperature and travel distance. The average absolute and relative errors were reduced by 30.44 μm and 77%, respectively. To improve local drilling precision and quality, Jie (2013) developed a simplified analytical model to clarify the interlayer gap formation mechanism as well as the effects of related factors for drilling stacked metal materials. It indicated that the interlayer gap size had a significant effect on interlayer burr size. Liu et al. (2020) established a mathematical model of interlayer gap with bidirectional clamping forces, based on which the optimization of the bidirectional clamping forces was performed to reduce the degree and non-uniformity of the deflections in stacked plates. Pogarskaia et al. (2020) proposed a new geodesic algorithm for the fastener pattern optimization in the A350 fuselage assembly process. The proposed algorithm was allowed to perform optimization 50 times faster than the local variations used before due to its non-iterative procedure.
In view of the advantages of the above two kinds of position compensation methods, the present research proposes a combined method aiming at the position error correction of fastener holes for large-span aerospace products. The gravity deformation error and the non-gravity deformation error are divided according to the features of position errors. The bilinear interpolation surface model is constructed to correct the non-gravity deformation error of the product. Meanwhile, the gravity deformation model based on the elasticity theory is established to correct the gravity deformation error. The average, the least square and the genetic optimization algorithms are used to optimize the gravity deformation model to furtherly improve the position accuracy of the drilling. The correctness of the combined methodology is verified by the simulation and experiment examples.
2. Establishment of position error correction model
2.1 Principle of position error correction
The large-span air vehicle launching container together with the self-developed drilling–riveting combined machining tool is illustrated in Figure 1 to elaborately present the position error correction method. The machining tool is composed of the machine tool guideway, the moveable machine tool platform, the multifunctional end effector, a vision system constructed by a Gocator 3210 industrial camera and two rotary fixtures. The moveable machine tool platform carries the multifunctional end effector and runs along the machine tool guideway, forming a five-axis machining tool. Two rotary fixtures carry the air vehicle launch container for drilling and riveting operation. The launch container is a rectangular box constructed by aluminum alloy skeletons and covered with thin skins. Each surface of the launch container is flat with a geometric dimension of about 7.0 m × 1.0 m. Since there are four flat surfaces in the launch container to be drilled, the pair of rotary fixtures are required to turn over the container to make each drilling surface faced with the multifunctional end effector. Thus, there are not only assembly errors and gravity deformation errors in the box but also systematic errors such as distortion deformation caused by asynchronous rotation of two rotary fixtures. The error composition is complex and needs to be skillfully compensated.
The error correction process of hole position for the launch container is elaborately illustrated in Figure 2. First, the hole position errors are divided into gravity deformation error and non-gravity deformation error, and the latter includes rotary tooling positioning error, assembly error, etc. Then the bilinear error surface model is built to compensate for the non-gravity deformation error. Comparatively, the position error distribution of gravity deformation is more complicated. It is necessary to analyze it in detail based on the mechanics’ theory and establish the simplified gravity deformation formula. Third, three algorithms are used to optimize the model to furtherly improve the position error correction accuracy. Finally, the hole position error is corrected by the proposed combined model.
2.2 Construction of non-gravity deformation error
Typical aerospace structures, such as fuselage panels and launch containers, appear to be smooth globally in the drilling region and flat locally in the vivacity of the drilling spot. The reference holes are usually defined at the four corners of the drilling region, as shown in Figure 3. Thus, the drilling region can be expressed in terms of a bi-parametric surface:
where parameters u and v are the spatial position of the drilling points relative to the corner control reference holes. If P00, P01, P11 and P10 are defined as four boundary control points of the bi-parametric surface, the points in the processing surface can be rewritten as:
According to equation (2), the nominal surface can be represented as S0(u, v). Similarly, the actual surface can be represented as S1(u, v), and a mapping relationship is established between nominal and actual surfaces:
where ΔP1, ΔP2, ΔP3 and ΔP4 are error vectors between nominal and actual corner reference holes. The required error correction vectors ΔS* between nominal and actual corner reference holes can be obtained once parameters (u*, v*) are substituted into the equation (3). Based on the above deduction, the bilinear error surface correction model established for non-gravity deformation errors is represented as follows:
2.3 Construction of gravity deformation error
2.3.1 Spatial posture analysis of components
As mentioned earlier, the launch container is a large-span structure. The gravity could cause beam bending, which is similar to a beam with simply supported ends. The surface switch on the rotary fixtures would distort the container in axial direction, which complicates the gravity deformation. As given in Figure 4, the local coordinate system O−XYZ and the workpiece coordinate system O1−X1Y1Z1 are defined, respectively, to compensate for the gravity deformation error of the launch container. In the local coordinate system, the X-axis is parallel to machine tool guideway, and the Y-axis is parallel to direction of gravity. The Z-axis can be determined by the right-hand rule. In the workpiece coordinate system, the reference points in the drilling surface are selected and measured using the vision system firstly. Then, a workpiece plane is constructed according to these measured points, and the normal direction of the plane is defined as the Y1-direction [Figure 4(b)]. The X1-axis coincides with the central axis of the workpiece plane. The Z1-axis is determined by the right-hand rule.
The gravity components of the launch container in the workpiece coordinate system are illustrated in Figure 4(c), which can be presented as:
where α and β are the deflection angles from Y- and X-axes, respectively.
To figure out parameters α and β, the reference points shown in Figure 4(b) are used to fit the workpiece plane using the least-squares function (Arun et al., 1987). Generally, the workpiece plane is defined by the following equation:
where a0, a1 and a2 are parameter that define the plane. The distance sum S between the reference points and the workpiece plane is can be calculated by:
High accuracy of workpiece plane could be obtained if equation (7) meets the following conditions:
which could be turned into equation group as follows:
Once the workpiece plane is obtained through above equations, the workpiece coordinate system and angles of α and β can be calculated.
2.3.2 Construction of gravity deformation formula
According to equation (5), the gravity components of the launch container in the workpiece coordinate system is defined as a gravity vector (Gx, Gy, Gz). Since the position error in X1-direction is not sensitive to the gravity effect, the deformation of the drilling points along the X1-direction can be ignored. Besides, the deformation of the drilling points along the Y1-direction in the launch container can be compensated by the axial feed of the end effector, so the deformation in Y1-direction can also be ignored. Thus, the main factor of the position deviation is induced by gravity in Z1-direction.
Considering that the launch container is a hollow rectangular large-span box with one end hinged and the other end rolled, it can be considered as a collection of many simply supported beams as illustrated in Figure 5. The self-gravity of the container is uniformly distributed in these beams, along which the distributed force of gravity is q. According to mechanics theory, the deformation curve of the simplified beam collection of the container in the Z1-direction can be calculated by:
where l is the length of the launch container beam; E is the elastic modulus of the container material; I is the moment of inertia of the cross-section; and h is the distance between the drilling point and the left hinged end.
Since the launch container is composed of skins and supporting structures such as stringers and skeletons, it is hard to determine the parameters in the equation (10) directly. Thus, the equation (10) is directly reflected by the following equation:
where a is the deformation coefficient. In this way, the position error model of gravity deformation can be denoted by:
2.3.3 Solution for deformation coefficient
The accurate establishment of gravity deformation equation (11) is significant to the compensation accuracy of the required error correction vectors in equation (3). The drilling workpiece surface of the launch container is illustrated in Figure 6, where the fastener holes and the reference holes are arranged trimly. The position errors ΔP of reference holes consist of the gravity deformation error ΔG and the non-gravity deformation errors ΔS.
To solve the gravity deformation coefficient a, the position errors need to be separated since the correction principles of the two kinds of position errors are different. It can be seen from Figure 6 that the reference holes (black points as given in Figure 6) at four corners of the workpiece surface are fixed in the conformal frames. The gravity deformation error in these local regions can be ignored. Therefore, a non-gravity bilinear interpolation error surface model ΔS (u, v) can be constructed to calculate the non-gravity position errors of the reference holes (red points as given in Figure 6). The theoretical errors ΔS(a) are calculated from the equation (11). The deformation coefficient can be determined by defining ΔG = ΔG(a), the solution process as shown in Figure 7.
However, there will be multiple deformation coefficient solutions since a large number of reference holes are arranged on the workpiece surface of the launch container. Thus, the average, least square and genetic optimization algorithms are used comparably to figure out the optimal deformation coefficient.
2.3.3.1 Average algorithms.
In average algorithms, the actual gravity deformation errors ΔGi (i = 1,2,…,n) and the theoretical gravity deformation errors ΔGi (a)(i = 1,2,…,n) of the reference holes are equal:
By applying the average method, the optimal deformation coefficient a is denoted as follows:
2.3.3.2 Least squares algorithms.
It is assumed that ΔGi (i = 1, 2, …, n) and ΔGi (a) (i = 1, 2, …, n) are equal; the equation (13) can be rewritten as:
Let y = ‖ΔG‖ and x = |−h(l3−2lh2 + h3)|; the equation (15) can be furtherly rewritten as:
The coefficient a can be obtained by linear fitting by the least-square method (Peng et al., 2016). It is supposed that:
The derivative is taken on both sides of equation (17). By setting the derivative to be zero, the deformation coefficient a can be obtained:
2.3.3.3 Genetic optimization algorithms.
The genetic optimization algorithm for solving the deformation coefficient is illustrated in Figure 8 (Cheng and Yang, 2012). Obviously, the deformation coefficient a is the design variables of the genetic optimization model. The optimal solution of a is randomly distributed around theoretical item q/24EI, so the range of a is set from 0 to q/12EI. According to the deformation coefficient solution strategy, the smaller the difference between ΔGi (i = 1, 2, …, n) and ΔGi (a)(i = 1, 2, …, n), the more accurate the deformation coefficient a. Therefore, the objective function is defined as:
In view of the fact that the calculation result may be stable in a locally optimal solution in a short time, a certain amount of calculation algebra Ni is chosen as the termination condition. Finally, the optimal deformation coefficient a0 is determined.
3. Validation for position error correction method
3.1 Position accuracy evaluation by simulation approach
During drilling process, the positions of the fastener holes change with the deformation of the drilling workpiece surface in the launch container, and their absolute positions could not be measured directly in assembly site. Since the deformation of the workpiece could be tracked effectively in simulation environment, the deformation of the launch container in drilling process is simulated in ABAQUS software platform to acquire the position error of fastener holes.
3.1.1 Simulation setup
The three-dimensional (3 D) finite element model of the launch container with a total geometric dimension of 7.0 m × 1.0 m × 1.0 m is presented in Figure 9. The container together with two conformal frames is simplified as a thin-walled large-span rectangular box and modeled by 3 D shell elements S4R. The edge length and thickness of the shell element is set to be about 0.1 m and 0. 05 m, respectively, by homogenization of skeletons and skins. The left and right ends of the launch container are hinged as illustrated in Figure 5. The gravity is loaded on all elements, and a slight rotational disturbance is exerted to the right end surface to simulate the discordant rotation of two rotary fixtures in Figure 1. The material properties of aluminum alloy are listed in Table 1. After the simulation, the deformation of the simplified launch container is presented in Figure 9(b), from which the deformed position data of the drilling points are abstracted with a row space of 0.4 m and a column space of 0.2 m to validate the position error correction model as constructed in Figure 2.
3.1.2 Position accuracy of error correction
The accuracy evaluation of the non-gravity deformation error correction is presented in Figure 10. When no correction is applied to the position of drilling points, both the gravity deformation and container distortion cause the deviation of drilling position. The curves of uncorrected errors exhibit the same increasing trend as the drilling points move father away from the starting point at the left end of the launch container. The maximum position error even reaches 40.0 mm. This is because the left end is hinged and there is no X-axis rotational degree of freedom, and the distortion of the container accumulates along the number increasing direction and becomes much bigger at the right end. Also, the position error of rows r1 and r4 is higher than rows r2 and r3. The reason is that rows r1 and r4 are on the edge of the processing surface where the drilling hole position is more sensitive to the torsion of the workpiece. As the position errors corrected with the non-gravity deformation model, actually the distortion deviations of the drilling points are compensated. As a result, the error curves approximately conform to the law of gravity deformation of the simplified launch container given in Figure 5, and the maximum position error is reduced to 5.0 mm, revealing that the non-gravity deformation errors are effectively corrected.
The accuracy evaluation of gravity deformation error correction is presented in Figure 11. Obviously, the position errors are greatly reduced compared with the uncorrected position errors, revealing that the proposed position error correction method is effective in compensating large-span aerospace assembly structures. The position accuracy of three used algorithms is listed in Table 2; the average position errors of corrected reference points are reduced to about 0.568 mm, 0.515 mm and 0.475 mm for the cases disposed with the average, the least-squares and the genetic optimization algorithms, respectively. This regulation indicates that the gravity deformation error correction method based on the genetic optimization algorithm achieves the best results in alleviating position error to a certain extent, which is attributed to its wide search range and the multiple search points. This ability benefits the genetic optimization algorithm to discover global optimum and avoids trapping in a locally optimal solution. Therefore, the position error correction method based on the genetic optimization algorithm is more suitable for solving the deformation coefficient.
3.2 Position accuracy evaluation by drilling experiment
3.2.1 Experimental setup
The experimental validation is carried out on the self-developed drilling–riveting combined machining tool as illustrated in Figure 1, and the real machining tool equipment is presented in Figure 12. During the drilling process, the actual positions of the reference holes in the launch container are firstly got by the vision measurement system. Then, the positions of the drilling holes are corrected by the proposed method. The measurement error of the vision system used in the present research is within 0.035 mm, which is an order of magnitude lower than the required hole position accuracy. In the vision measurement process, the template matching method is used to process the two-dimensional image information of the reference holes. As shown in Figure 13, T(m, n) is the template of the hole to be measured, and S(row, col) is the point cloud of the workpiece surface. The template T(m, n) overlays on the searched point cloud S(row, col) and translates throughout the cloud. The area where the template covers the searched point cloud is called the subgraph Sij(m, n), where (i, j) is the position number of the subgraph center in the searched point cloud. The position with the highest similarity between Sij(m, n) and the template T(m, n) is considered as the position of the hole. The error method is used to evaluate the similarity between T(m, n) and Sij(m, n) (Zou et al., 2019):
where the minimum value of E(i, j) is the position of the matched target hole. It is obvious that the smaller the template, the faster the matching speed. The matching rate K of template matching method is calculated by the following formula (Jeyasenthil and Choi, 2019):
where the higher the matching rate K, the higher the credibility of the matching process. The matching result of the hole to be measured is presented in Figure 13(b), where the matching rate K is 98.1057%.
3.2.2 Verification of drilling position accuracy
To validate the correction algorithm, a real launch container workpiece including aluminum alloy and CFRP panels is used for drilling test, and the drilling region is the part of the launch container surface. The drilling surface is divided into four areas, namely A, B, C and D zones, as shown in Figure 14. The holes in zone A is drilled with the proposed method to correct the two types of errors together. The holes in zone B is drilled without the position correction algorithm. The holes in the zone C drilled with non-gravity deformation error correction method, and the holes in the zone D is drilled with gravity deformation error correction method. The reference hole is defined every 0.5 m interval, and the nominal drilling hole space is 0.05 m. Since the absolute position of the actual drilling holes in the workpieces cannot be measured directly, the position accuracy of the drilling can be evaluated by relative position of holes, namely, column spacing and hole row spacing. The position error is defined by:
where s and r are theoretical value of hole column spacing and hole row spacing, respectively. s’ and r’ are their actual measured value.
The position accuracy of the drilled holes in aluminum alloy and CFRP workpieces is presented in Figures 15 and 16, respectively. It is easily observed that position errors of fastener holes for two kinds of material workpieces could reach ±1.3 and ±2.4 mm, respectively, when no correction method is applied to the drilling process. In comparison, the final hole position errors are reduced to ±0.7 mm when only gravity deformation is corrected, and they are within ±0.36 mm when only non-gravity deformation is corrected. It seems that the influence of gravity deformation on position error is not as significant as that of non-gravity. This is because the gravity deformation is limited locally within 0.5 m between two reference holes. By applying the position error correction method, hole position errors are reduced to ±0.2 and ±0.3 mm for two kinds of materials, which is acceptable for the large-span aerospace structures. The rest position errors that could not be compensated by the proposed method are calibration errors, measurement errors of reference holes, positioning errors of the machine tool and environmental factors.
The above experimental results show that the position precision obtained through one single error correction method is much lower than the proposed combined method, which can be explained by correction principles of the two methods illustrated in Figure 17. The bilinear interpolation method focuses on the correction of approximately linear errors, while the gravity deformation model mainly corrects the non-linear errors caused by gravity. Consequently, the error correction result is poor when the error and its compensation method are mismatched. It is also worth noting that four non-gravity deformation correction curves exhibit the slight “U” shape. The phenomenon can be attributed to the fact that the curve error is corrected using a straight line as illustrated in Figure 17(a). Meanwhile, the correction results using the gravity deformation model are irregular. As presented in Figure 17(b), the error correction is insufficient when the deformation coefficient is small, under which circumstance the over-correction would occur. By comparing the four curves, it is possible to conclude that dividing the errors into two categories and correcting them with different principle algorithms is completely effective.
In addition, both the traditional mechanics theory method and the proposed method are used to compensate the same set of hole position data, the correcting precision is shown in Figure 18. The position error of drilling holes with the traditional mechanics theory method could reach 0.606 mm, while the position error compensated by the proposed combined error correcting method in in the present research achieves an accuracy of 0.125 mm. In the assembly of the aerospace structures, the required position accuracy of the fastener holes is 0.5 mm. Thus, the accuracy of the proposed error correction method can fulfill the requirement in aircraft manufacturing.
4. Conclusions
In the present research, a combined method of position error correction for automatic drilling in aerospace manufacturing is proposed and validated on the large-span air vehicle launching container. The category and incentive of position errors in large-span aerospace structures during assembly is elaborately analyzed, and the errors are divided into non-gravity and gravity deformation errors. The non-gravity error is corrected by the proposed bilinear interpolation surface model based on the vision measurement data of reference holes set at intervals in the workpiece surface. The gravity deformation formula is established using the theory of elasticity, based on which the gravity deformation error model is further constructed and optimized by genetic optimization strategy to solve the problem of low accuracy of gravity deformation formula coefficients. By implementing the proposed error correction model in the drilling process of launch container, the position errors of fastener holes can be limited within 0.2 mm. Compared with the traditional mechanics theory method, the position error is reduced by 43.49%. Thus, the accuracy and effectiveness of the proposed error correction method is experimentally verified.
The research was supported by National Key Research and Development Program of China (Grant No. 2019YFB1310101), National Natural Science Foundation of China (Grant No. 52005259) and Youth Science and Technology Innovation Fund of Nanjing University of Aeronautics and Astronautics (Grant No. 1005-XAC2003).
The authors would also like to thank the editors and the anonymous referees for their insightful comments.
Air vehicle launch container and the corresponding drilling and riveting combined machine tool
Hole position error correction flowchart
Schematic diagram of hole position deviation
Schematic diagram of the local and workpiece coordinate systems
Simplification of the force analysis model of the launch container
Drilling workpiece surface of the launch container
Flowchart of deformation coefficient solution
Flowchart of genetic optimization algorithm for solving deformation coefficient
Boundary conditions and deformation of the simplified launch container
Accuracy of non-gravity deformation error correction in workpiece surface of launch container
Comparison of accuracy of the three used algorithms
Experimental platform of the drilling–riveting combined machining tool
Image matching process of hole position
Drilling surface and hole number of the launch container
Drilling position errors of the aluminum alloy workpiece in the launch container
Drilling position errors of the CFRP workpiece in the launch container
Schematic diagram of hole position correction principle
Correction accuracy comparison of drilling hole position error
Material properties of aluminum alloy used for the launch container
| Material parameters | E | µ | σb | ρ |
|---|---|---|---|---|
| Value | 68.9 Gpa | 0.33 | 228 Mpa | 2730kg/m3 |
Statistical results of three used algorithms for gravity deformation model
| Average position error/mm | r1 | r2 | r3 | r4 |
|---|---|---|---|---|
| Before correction | 20.738 | 13.800 | 13.271 | 19.528 |
| Average algorithm | 0.577 | 0.517 | 0.596 | 0.581 |
| Least square algorithm | 0.538 | 0.443 | 0.543 | 0.535 |
| Genetic optimization algorithm | 0.498 | 0.425 | 0.499 | 0.479 |
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