Gap volume prediction for aircraft wing assembly

In this work, two methods for predictive shimming based on laser scan technology and point cloud processing software have been presented. The first one is direct measurement method in PolyWorks, and the second one is feature-based modelling method in SolidWorks. Firstly, both component-level and assembly-level scans are collected by a laser scanner. Then, the point clouds are post-processed and registered in PolyWorks. Thirdly, gap information (shape and thickness) is obtained either in PolyWorks or in SolidWorks. Results show that the proposed methods can obtain gap information successfully based on current hardware and software.


Introduction
Variations inevitably occur during manufacturing and assembly processes.Variations will propagate and accumulate through production chain which could lead to difficulties (nonconformance to design) in downstream processes.This is especially true in aircraft production in which millions of components need be assembled together to a high precision.One particular challenge currently faced by aerospace manufactures is how to efficiently and effectively fill in the non-conformed gaps between joining components of aircraft assembly in order to ensure the structure integrity.
To eliminate or control gaps within tolerances, shimming process is required.In a conventional shimming process, the parts will be pre-assembled initially [1].A worker may use a measurement equipment, such as feeler gauges, to manually measure the thickness of a gap that is divided into thousands of small areas and draw a thickness map.Then a shim will be produced based on this map and inserted into the gap.After that, the filled gap will be measured again to see if it is within tolerance.If not, the same work will be repeated.The shimming process is a trial-and-error process and consumes much time, material and labor cost.Research shows that nearly 30% of the cycle time is consumed by measuring and shimming during one wing assembly process [2].Therefore, it is necessary to find a way to accelerate this process.
The concept 'Measurement assisted assembly (MAA)' was proposed by Muelaner et al. [3,4].An important part of MAA is predictive process, including predictive shimming and fettling.Predictive shimming is defined as to measure parts to estimate shim geometry before parts being assembled by using advanced technology, e.g.laser scan technology [5].During the past two decades, ideas for predictive shimming have been proposed in many patents [6][7][8].Jamshidi et al. [9] reviewed metrology-enabled activities in aircraft manufacturing and assembly process, in which predictive shimming is identified as one of the great challenges to be addressed.
There are two kinds of methods for predictive shimming in the literature.The first method is using machine learning technology to predict new shims based on historical data [10], Available online at www.sciencedirect.com

Introduction
Variations inevitably occur during manufacturing and assembly processes.Variations will propagate and accumulate through production chain which could lead to difficulties (nonconformance to design) in downstream processes.This is especially true in aircraft production in which millions of components need be assembled together to a high precision.One particular challenge currently faced by aerospace manufactures is how to efficiently and effectively fill in the non-conformed gaps between joining components of aircraft assembly in order to ensure the structure integrity.
To eliminate or control gaps within tolerances, shimming process is required.In a conventional shimming process, the parts will be pre-assembled initially [1].A worker may use a measurement equipment, such as feeler gauges, to manually measure the thickness of a gap that is divided into thousands of small areas and draw a thickness map.Then a shim will be produced based on this map and inserted into the gap.After that, the filled gap will be measured again to see if it is within tolerance.If not, the same work will be repeated.The shimming process is a trial-and-error process and consumes much time, material and labor cost.Research shows that nearly 30% of the cycle time is consumed by measuring and shimming during one wing assembly process [2].Therefore, it is necessary to find a way to accelerate this process.
The concept 'Measurement assisted assembly (MAA)' was proposed by Muelaner et al. [3,4].An important part of MAA is predictive process, including predictive shimming and fettling.Predictive shimming is defined as to measure parts to estimate shim geometry before parts being assembled by using advanced technology, e.g.laser scan technology [5].During the past two decades, ideas for predictive shimming have been proposed in many patents [6][7][8].Jamshidi et al. [9] reviewed metrology-enabled activities in aircraft manufacturing and assembly process, in which predictive shimming is identified as one of the great challenges to be addressed.
There are two kinds of methods for predictive shimming in the literature.The first method is using machine learning technology to predict new shims based on historical data [10], Available online at www.sciencedirect.com

Introduction
Variations inevitably occur during manufacturing and assembly processes.Variations will propagate and accumulate through production chain which could lead to difficulties (nonconformance to design) in downstream processes.This is especially true in aircraft production in which millions of components need be assembled together to a high precision.One particular challenge currently faced by aerospace manufactures is how to efficiently and effectively fill in the non-conformed gaps between joining components of aircraft assembly in order to ensure the structure integrity.
To eliminate or control gaps within tolerances, shimming process is required.In a conventional shimming process, the parts will be pre-assembled initially [1].A worker may use a measurement equipment, such as feeler gauges, to manually measure the thickness of a gap that is divided into thousands of small areas and draw a thickness map.Then a shim will be produced based on this map and inserted into the gap.After that, the filled gap will be measured again to see if it is within tolerance.If not, the same work will be repeated.The shimming process is a trial-and-error process and consumes much time, material and labor cost.Research shows that nearly 30% of the cycle time is consumed by measuring and shimming during one wing assembly process [2].Therefore, it is necessary to find a way to accelerate this process.
The concept 'Measurement assisted assembly (MAA)' was proposed by Muelaner et al. [3,4].An important part of MAA is predictive process, including predictive shimming and fettling.Predictive shimming is defined as to measure parts to estimate shim geometry before parts being assembled by using advanced technology, e.g.laser scan technology [5].During the past two decades, ideas for predictive shimming have been proposed in many patents [6][7][8].Jamshidi et al. [9] reviewed metrology-enabled activities in aircraft manufacturing and assembly process, in which predictive shimming is identified as one of the great challenges to be addressed.
There are two kinds of methods for predictive shimming in the literature.The first method is using machine learning technology to predict new shims based on historical data [10], while the second one is using point cloud algorithms and computational software to process data.Manohar et al. [10] proposed a method that combines sparse sensor optimization with robust feature extraction.The method can predict shims by using historical Boeing production data of a representative aircraft.
For the second method, researchers develop computational algorithms, e.g.K-nearest Neighbor Search [11,12], and use computational software to process scanned data.Schimick et al. [12] proposed an algorithm to generate solid shim volume models by using Visual Studio.Point cloud data are obtained from a laser scanner and divided into printable subparts.A greedy surface triangulation method is used to create meshes of surface clouds to enclose the volume between two mating surfaces.Then, the meshes are repaired until no more connected edges can be found.Finally, the meshes are exported to a 3D printer to produce shims.In 2017, Ehmke et al. [1] proposed an extension of this algorithm, which includes obtaining two point clouds by scanning the two joining surfaces, downsizing the point clouds, moving the point clouds to their assembly position, dividing the gap or point clouds into a predefined number of sections, calculating the average gap height (centroid z-values), and deciding to use solid or liquid shim based on the gap height.In this study, the surfaces used were planes in rectangular shapes, and the point cloud data was in componentlevel.Assembly-level data were not used, and the possible deformation and mismatching during assembly processes were not considered.
Wang et al. [11] proposed an algorithm for hybrid shimming design, which includes gap calculation, local gap region segmentation and shimming constraint parameter determination (shim specification, gap value, and hole margin), validated through finite element modelling (FEM).Comparing the scanned data with nominal CAD model to find the deviations in PolyWorks, Ospina-Aldana et al. [5] used FEM to calculate the deformed shape of the skin based on deviations from nominal geometry.The deformed surfaces can be used to build 3D gap model.However, in these methods proposed by Wang et al. and Ospina-Aldana et al., the accuracy of the method remains unclear, and only component-level data have been considered.The assembly contact conditions are simulated in software, which means the part positions may not be the same as those in reality, and may lead to inaccuracy in final results.Therefore, this paper aims to develop a predictive shimming methodology that considers assembly-level scans and avoids using simulated contact conditions.
In this paper, two gap volume prediction methods for aircraft wing assembly are proposed, i.e. direct measurement method in PolyWorks and feature-based modelling method in SolidWorks.These methods consider scans both in assemblylevel and component-level, and develop a relatively simple way for obtaining profile and gap information for predictive shimming in aircraft wing spar-and-skin assembly.Accuracy and possible variation sources of the proposed methods are also investigated.To the best knowledge of the authors, this is the first paper disclosing these methods of building gap model with PolyWorks and CAD software.The approach has advantages in reserving relative component position information, avoiding complex algorithms and simulation of contact boundary conditions, which provides a simple and intuitive solution to predictive shimming.

Problem statements and strategies
Take a spar-and-skin assembly as an example, a gap appearing between joining interfaces is shown as Fig. 1a.To mimic the aircraft assembly, dummy assemblies of a small scale is used to demonstrate the methods, as shown in Fig. 1b.The objective is to find the gap shape and size between the two mating surfaces.
A laser-line scanner on a Romer Absolute Arm (7325SEI) is used to obtain point cloud data of the assembly and individual parts.The point cloud data will be transferred to geometrical software PolyWorks.In virtual computational environment, the problem is converted to obtain thickness of the gap.To do this, it is necessary to find the two mating surfaces of which the gap is composed.In this study, they are spar mating surface and skin mating surface.When the assembly is scanned, the skin and spar mating surfaces cannot be directly scanned.Therefore, individual skin and spar should be firstly scanned, and registration can be carried out to register individual part point clouds to the assembly point clouds.The mating surfaces of assembly can then be replaced by those of individual parts.After registration, polygonal model can be generated and gap measurement can be conducted.The first approach is to measure the gap directly in PolyWorks, while the second approach is to build gap model in SolidWorks.To simplify the question and show the validation of the overall methodology, it is assumed that all parts are rigid and the surfaces are flat planes in the experiments, so that it is viable to extract surfaces as plane features using least-square algorithm.The detailed approaches are described in next section.

Methods
Fig. 2 shows the proposed methods which consists of three stages, i.e. data collection, data processing, and gap measurement.

Stage 1: Data collection
Firstly, the spar and skin are scanned individually.Then, the two parts are assembled, and the assembly is scanned with the laser scanner as well.The outputs of this stage are three point clouds.

Stage 2: Data processing
The goal of this stage is to use individual part scanned data to accurately replace its corresponding component in the scanned assembly data.This is called registration, which is usually done by transformation of coordinates with rigid coordinate transformation matrices.In this study, it is assumed there is no part compliance during assembly process in order to simplify the problem, and show the validity of proposed approaches.Therefore, rigid registration can be conducted.
The Stage 2, which is implemented in PolyWorks, consists of three sub-processes, i.e. point cloud post-processing, prealignment, and rigid registration.Raw point clouds usually contain millions of points, as well as noise data.Therefore, post-processing is necessary to simplify them and remove unwanted data.Typical methods include filtering, subsampling, and outlier removal, etc.After cleaning, point clouds are pre-aligned with matching point pairs.Those point pairs are selected from both the assembly scanned data (Fig. 3a) and individual spar/skin scanned data (Fig. 3b).This step helps the software gain a coarse rigid transformation matrix, and avoid computing results falling into a local optimal solution.In PolyWorks, at least three matching point pairs between the two point clouds should be selected for posture registration by best-fit data alignment.After registration, individual part scanned data should be in the same coordinate system as assembly scanned data, as shown in Fig. 3c.After registration, polygonal models can be generated from registered point clouds.

Stage 3: Gap measurement
As shown in Fig. 2, two methods have been proposed for gap measurement in this study, which are direct measurement method in PolyWorks, and feature-based modelling method in SolidWorks.

Direct measurement method in PolyWorks
In PolyWorks, the gap between two mating surfaces of the skin and spar can be measured, and a colormap can be created by the function 'clearance measurement colormap'.All of the measurement in this paper are in millimeters.
Fig. 4 shows the fundamental theory for distance measurement between two polygonal data objects.P (red dot) is one of the triangle vertices on the spar mating surface of spar polygon mesh, which is taken as the basis object to calculate gap thickness in PolyWorks.Q is a matching point of P on the skin mating surface of skin polygon mesh along the triangle vertex normal vector n1.The gap thickness at P is defined as the distance between P and Q, |PQ|.Let n2 represent the surface normal vector at Q.The angle between n1 and n2 is denoted as α.The maximum range of |PQ| and α, which correspond to 'max distance' and 'max angle' settings in PolyWorks, are defined by the user.
The direct measurement method are as follows.Firstly, a reference data should be chosen.In our case study, the spar polygonal model was recognized as basis object (corresponding to 'master object' in PolyWorks).This means the gap is always calculated using the normal of the triangle vertices of the spar polygonal model.
Secondly, the user defines the upper boundary of the thickness of the gap.This is done by setting relative large initial values of 'max distance' and 'max angle' in PolyWorks, followed by adjustments.For example, initially 2.5mm and 45 degree were set in the case study.The software calculates colormaps based on these settings, which gives maximum and minimum thickness of the gap each time.The minimum thickness setting will not change with 'max distance', while the maximum thickness will.
It was found that 'max distance' and 'max angle' parameters will influence the continuation of colormap.Different settings result in different calculated area on the surfaces, therefore resulting in different maximum and minimum average clearances.One way to determine the max distance setting is to ensure that the colormap is large enough to cover the whole mating surfaces.We investigated how much effects they will bring to colormap continuation, and found that 'max angle' has less influences than 'max distance'.When the 'angle' was decreased from 45 degree to 10 degree, the mean thickness was from 1.479 to 1.474mm.However, when the angle was below 10 degree, the continuation was found to be influenced hugely.Besides, when the max distance was set too low, the colormap will be discontinuous.Therefore, the user should find the most suitable values for them through this process, and this is socalled parameter settings and adjustments in Fig. 2.
Finally, the gap thickness colormap can be generated in PolyWorks, as shown in Fig. 9 (section 4).

Feature-based modelling method in SolidWorks
In SolidWorks, mating surfaces can be reconstructed, and therefore a 3D gap model can be built up.
The first step of this method is to find mating surfaces of spar and skin in PolyWorks.After polygonal model generation, the user should identify which surfaces are for feature extraction.
Then, the skin and spar surfaces surrounding the gap are extracted from polygonal models using least-square algorithm.The extracted surfaces are exported to SolidWorks for surface reconstruction and gap modelling.
In the surface reconstruction step, the skin mating surface is extended until it is large enough to cover the spar mating surface.In the next gap modelling step, the spar surface is thickened, and is then trimmed by the envelope of the skin mating surface, thus the final gap model is obtained.
Finally, in SolidWorks, the thickness of the gap model can be evaluated.
Based on the colormaps generated by the above two methods, the user can pick and get the gap thickness in a single point.In this way, the existing manual method currently used in industry can be replaced by our digital measurement method, provided enough accuracy can be achieved.

Method validation
To validate the proposed methods, two case studies are conducted.The first one is to validate the two approaches.The second one is to compare the results of digital measurement in PolyWorks with manual measurement using feeler gauges.The software, equipment and experiment materials used in this study are as follows:  Romer Absolute Arm 7325 SEI (Accuracy stated by manufacturer: ±0.084mm),  Two composite skin samples (The first one is a composite skin in a similar size of the spar web, denoted as skin_a, see Fig. 5a.The second one is a large skin made by medium-density fiberboard, denoted as skin_b, see Fig. 5b)  One composite spar sample (Fig. 1b)

Case study 1
In the first case study, two groups of scan data were collected, including the skin_a and spar, and the skin_b and spar.The laser scanner was used to scan individual parts firstly.Then, skin and spar were assembled with a shim added between the spar and skin along the bolts to enlarge the gap.Point cloud data (Fig. 6) was generated from scanner and transferred to PolyWorks.
In PolyWorks, point cloud registration was carried out, and polygonal meshes were generated from point clouds.The mating surfaces of spar and skin were extracted, as shown in Fig. 7. Then the 3D gap model was built, as shown in Fig. 8.
In PolyWorks, the max distance was set to 2.2mm and the max angle set to 10 degree.When the max distance was set to equivalent or above 2.2mm, nearly all triangle vertices on the spar mating surfaces can be found to match with compatible points on skin mating surfaces, i.e. the gap colormap is continuous with the minimum value of max distance to be 2.2mm.Fig. 9 show the gap colormaps in PolyWorks (Fig. 9a, b) and the thickness evaluation of gap models in SolidWorks (Fig. 9c,  d).It can be seen that the results from the two methods are similar.The differences between gap model thickness map and PolyWorks colormap are mainly because of the variations in the measurement and data processing, as well as the assumption regarding the planar mating surfaces in this study.This case study shows both approaches are viable to measure the gap successfully.The colormap in PolyWorks is more easily to be obtained and closer to real results due to the avoidance of surface reconstruction.However, the gap model in SolidWorks is more continuous.

Case study 2
In this case study, the gap between spar and skin_a were measured both by feeler gauges and PolyWorks.As shown in    11 is standard deviation of gap measurement results in PolyWorks, which is ±0.254mm.The mean value of deviations between two groups of data is 0.107mm, and the max and min deviations are 0.264 and 0.010mm, respectively.Fig. 11 shows that manual measurements are smaller than the corresponding value of digital measurements, and digital measurement results can reflect manual measurement results within error limits.

Conclusion
This paper proposed two methods for predicting gap volume based on laser scan technologydirect measurement method and feature-based modelling method.Two case studies were conducted to validate the approaches.The proposed methods can help achieve predictive shimming in many industries, e.g.aerospace, ship and automobile.To ensure higher accuracy, this method still needs to be improved.
There are several possible error sources in the whole process.Firstly, the laser scanner accuracy was not adequate for shimming small gaps (usually the gap dimension is between 0.2mm-1.3mm).Secondly, registration of different point cloud data can be one of the major sources of uncertainty.Therefore, the registration accuracy improvement could be a key step for improving the accuracy of final gap model.Thirdly, the effects of parameter settings in PolyWorks on final results may not be negligible.
Although currently it has several limitations and much work is yet to be done, it has been confirmed that the development of the predictive shimmingas a vital step for automationwas the step in the right direction.
Future work will involve looking into applications to largescale part and assemblies considering part compliance.Improvement of accuracy will also be investigated by utilizing metrology equipment in higher precision and developing error mitigation approaches in datum setting and calibration/ measurement processes.

Fig. 2 .
Fig. 2. Flow chart of the overall methods