Variation Sensitivity Study for an Aerospace Wing Spar Assembly

McKenna, V., Jin, Y., Murphy, A., Morgan, M., Fu, R., McClory, C., Higgins, C., Collins, R., & Qin, X. (2018).Variation Sensitivity Study for an Aerospace Wing Spar Assembly. In P. Thorvald, & K. Case (Eds.), Advances inManufacturing Technology XXXII: Proceedings of the 16th International Conference on Manufacturing Research,incorporating the 33rd National Conference on Manufacturing Research, September 11–13, 2018, University ofSkövde, Sweden (pp. 171-176). (Advances in Transdisciplinary Engineering; Vol. 8). IOS Press.https://doi.org/10.3233/978-1-61499-902-7-171Published in:Advances in Manufacturing Technology XXXII: Proceedings of the 16th International Conference onManufacturing Research, incorporating the 33rd National Conference on Manufacturing Research, September11–13, 2018, University of Skövde, Sweden

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Download date:03. Oct. 2020

Variation Sensitivity Study for an

Aerospace Wing Spar Assembly

Vincent MCKENNAa,1, Yan JIN a,2, Adrian MURPHY a, Michael MORGAN a,

Rao FU a, Caroline MCCLORY

a, Colm HIGGINS a, Rory COLLINS and Xuda QIN

b a Queen’s University Belfast, Northern Ireland

bTianjin University, China

Abstract. Despite manufacturing sub-components to a high precision, large

overconstrained assemblies are often impossible to assemble to tolerance limits when variations are present. This necessitates expensive and time consuming

variation management processes at assembly, such as shimming. Existing research

has not established a methodology to model the variation propagation mechanisms that results in this assembly variation. This paper presents such a methodology,

which has the ability to quantify the assembly variation of overconstrained

assemblies at the planning stage, providing useful data for determining the most appropriate combination of fabrication and assembly processes to use for a given

case. The methodology is validated using an aerospace wing spar assembly, and a

sensitivity study completed to rank the key variation drivers in the overconstrained assembly.

Keywords. Variation propagation, overconstrained assemblies, sensitivity study.

1. Introduction

The management of accumulated variation in overconstrained assemblies, which are

common in the aerospace industry, is a challenging task for production planners. This is

because the achievement of each assembly Key Characteristic [1] (KC) is not

independent, therefore improving one KC can degrade another KC. Despite designers

assigning tight tolerance requirements to sub-component manufacture, variation

propagates and accumulates during manufacture and assembly, often making it

impossible to achieve all assembly KCs within tolerance simultaneously. As a result,

additional variation management processes such as shimming and fettling are required

at the assembly stage, which are expensive and time consuming [2].

In order to quantify the cost implications of managing this excess variation at the

planning stage, the variation must be characterised, and its magnitude estimated.

However, the variation propagation mechanism for overconstrained assemblies is not

currently well understood. Assembly variation modelling has been the subject of a large

amount of research [3], which has established methods for modelling connective

assemblies [4][5], and has facilitated the analysis of assemblies where parts are

assembled through part-to-part mating surfaces [6][7][8]. To date, most assembly

variation models have focused on the connective assembly relationships between parts.

Overconstrained assemblies, however, present a unique challenge, as part relationships

1 Corresponding Author. vmckenna02@qub.ac.uk. 2 Corresponding Author. y.jin@qub.ac.uk

can be spatial instead of connective. This means that the final variation at assembly is

not simply equal to sub-component fabrication tolerances, as assembly variation is also

affected by many other variation sources, such as fixture variation, fit-up errors and the

alignment and orientation of parts in relation to each other in the assembly fixture. A

method dealing with these potential variation sources has not been fully established in

current variation models for overconstrained assemblies, creating a barrier to

understanding the key variation drivers. This paper therefore presents a methodology to

analyse and model variation propagation in overconstrained assemblies, and illustrates

how key variation drivers can be identified using a sensitivity study.

2. Aerospace Case Study

To illustrate the challenge of overconstrained assemblies, an aerospace case study is

presented. The case study consists of a section of an aircraft wing, consisting of a

structural spar and four hinge brackets from an aircraft wing [2], as shown in Figure 1.

Figure 1. Spar and hinge bracket assembly.

The assembly is overconstrained, as the two mating feet per hinge bracket result in

the spar being mounted at eight places along its span, which is five more than is required

for location of the spar. There are three KCs which must be achieved in this assembly,

highlighted in Figure 1. The first KC is the alignment of the four hinge brackets to each

other along the hinge bracket datum hole x-axis. This is to ensure the correct operation

of the aircraft control surfaces, which are mounted to the hinge brackets. The second KC

that must be satisfied is the alignment of each of the four hinge brackets to the spar

surface along the y-axis. This is to make certain that the assembly fits within the wing’s

airfoil profile. Finally, the third KC that must be achieved is the mating of the hinge

bracket feet to the spar surface, without gaps or clashes occurring. This is to ensure the

structural integrity of the overall assembly.

The case study is assembled using a fixture which spatially locates the spar and hinge

bracket from each other. However, it has been found that all three KCs cannot be

Hinge Bracket

Wing Spar

Clashes Assembly KC3

No gaps or clashes between spar

and hinge brackets

Assembly KC1 Alignment of hinge bracket

datum holes along x-axis

Z

Y

X

Assembly KC2 Alignment of each hinge

bracket to the spar along y-axis

Gaps

achieved simultaneously even when tight tolerances are assigned to the hinge bracket

and spar fabrication processes. This is because the final assembly variation is a function

of both variations induced at sub-component manufacture and variations induced during

assembly itself. This results in expensive processes needing to be added to the production

chain to manage the excess variation and bring the assembly within tolerance.

A study is therefore presented to analyse the major variation sources in the assembly,

and subsequently derive the variation propagation mechanism. Determining where

assembly variation occurs and at what magnitude is the novel deliverable of this research,

and will aid production planners manage variation in overconstrained assemblies.

3. Variation Source Analysis and Variation Modelling

Variations can come from a wide range of sources [5] including but not limited to,

individual component variations, variations due to small kinematic adjustments, fixture

and assembly process variation and variations due to measurement errors are also

possible [5]. Table 1 collates the variation sources considered in this paper. The typical

magnitude of variation for machining processes [9], and the tolerance of CFRP processes

[10] were used to define the likely manufacturing variation magnitude. Variation in

fixture features and assembly positioning errors were estimated to be an order of

magnitude smaller than manufacturing variations.

Table 1. Hinge bracket fabrication due to fabrication processes

Variation I.D. Variation Source Magnitude (mm)

Variation A – δA Roughing and finishing machining cuts on aluminium ±0.1250

Variation B – δB Drilling of datum hole in aluminium ±0.1900

Variation C – δC Prepreg CFRP manufacturing process variations ±0.6000 Variation D – δD Drilling of datum holes in CFRP ±0.2000

Variation E – δE Fixture errors ±0.0100

Variation F – δF Assembly positioning errors ±0.0100

The spar, hinge bracket and assembly feature were represented as coordinate frames,

related to one another using homogeneous transformation matrices [11], and to the global

datum, G. The part and feature naming convention used in this paper is as follows:

Pi : the ith part i = 1, 2, 3, 4 …

MFeij : the jth mating feature of the ith part j = a, b, c, d …

DFeij : the jth datum feature of the ith part j = a, b, c, d …

Fiij : the jth fixture feature of the ith fixture j = a, b, c, d …

The key part features and their variation sources are shown in Figure 2.

Figure 2. Key features of the hinge bracket and spar.

Y

Z

X

4 hinge bracket parts, PHi

2 hinge bracket mating features, MFeij (YδA)

Datum surface,

DFeib (ZδA)

Locating pin

datum hole,

DFeia (yδB, ZδB)

G

X G

King pin

datum hole,

DFe1a

(xδD, ZδD)

Queen pin datum hole, DFe1b (xδD, ZδD)

1 spar part, PS 4 alignment datums,

DFe1k (zδC)

8 spar mating features, MFe1j (yδC)

X

Y

Z

X

Y Z

Different KC delivery chains will result in different magnitudes of assembly

variation occurring at different locations in the assembly. Therefore, in order to model

variation propagation in overconstrained assemblies, the order in which KCs will be

achieved during assembly must be determined prior to modelling. The spar and hinge

bracket case is described in Figure 3.

Figure 3. Assembly technique, including the achievement of KC1 and KC2.

The KC delivery chain is a consequence of the assembly technique. In assembly step

1, KC1 is achieved. At the next assembly step, KC2 is then achieved, without

diminishing KC1. However, although KC1 and KC2 can be achieved simultaneously, it

has been found that KC3 cannot be achieved as gaps or clashes between the spar and the

hinge bracket feet are resulted, Variation at the KC3 mating interface is due to both

manufacturing variation induced during spar or hinge bracket fabrication, and assembly

variation due to fixture variation of the spar and hinge bracket locators. For example,

variation changes when the hinge bracket is rotated to contact the index in order to satisfy

KC2. The inability to achieve KC3 is shown in Figure 4, along with the fixture and

assembly variation sources.

Figure 4. Assembly variation between spar and hinge bracket at KC3.

Whereas manufacturing variation can be readily measured during inspection, and

controlled through tolerance allocation, the variation induced during assembly is not as

intuitive to understand, and requires a mathematical model to quantify at the planning

stage. A variation propagation model was therefore developed and is shown in Figure 5.

Assembly Step 1 Assembly Step 2

KC1 achieved The assembly fixture locates the hinge bracket by its datum hole feature. KC1 is satisfied as the

fixture locates all hinge brackets along the same

axis, provided fixture variation is small.

KC2 achieved Next, the spar is loaded onto the fixture, and an

index blade (yellow) is moved to contact with the spar. The hinge bracket is then rotated to

contact the index, thus achieving KC2.

G G X

Y

Z

X

Y

Z

KC3 not achieved Gaps or clashes are present

between spar and hinge brackets

due to accumulated and

propagated variation.

Gaps/clashes

present

X

Y

Z

Spar king hole fixture feature,

Fi1a (δE, δF)

Spar queen hole fixture feature,

Fi1b (δE, δF)

Assembly fixture, Fi

G

4 Phi hole

fixture features,

Fi1g-j

(δE, δF)

4 index fixture features,

Fi1k (δE, δF)

Figure 5. Variation propagation model flowchart.

4. Sensitivity Analysis and Results Discussion

The sensitivity study completed for this case study consists of the worst case

variation being applied individually to each feature in the assembly, corresponding to the

manufacturing operation used to create the feature. For example, to calculate the effect

of the hinge bracket hole feature on the assembly variation level, the typical maximum

and minimum variation of a drilling process is used, with all other features in the

assembly were set to have zero variation. Each feature had the representative variation

magnitude applied in both the X, Y and Z directions separately. The effect of

manufacturing variation, plus any variation propagation at the assembly stage can then

be calculated. The study was then repeated for the next feature, until all features that

affect variation were tested. The key variation drivers are thus the features in the

assembly that cause the largest variation of the assembly KCs from nominal. With no

variation present, there is a perfect contact between the spar and each hinge bracket.

Variation induced at any given feature is propagated through the assembly and leads to

assembly variation at the KC features in the form of either a gap or a clash between the

spar and hinge bracket. The sensitivity study allowed the effect of the manufacturing

variation sources to be considered, to determine which creates the largest gap or clash at

KC3. Table 2 shows the variation that was inputted into the variation model of the spar

and hinge bracket assembly. From the sensitivity study, it can be seen that largest

variation driver is variation due to the spar prepreg manufacturing process, which also

had the largest magnitude of variation input.

Start Spar king hole 𝐓GDFe1a

Spar queen hole 𝐓GDFe1b

Define spar datum features 𝐓GDFe1k

(k = c, d, e, f)

Define spar mating features

𝐓GMFeia and 𝐓G

MFe1j

(j = a, b, …, h)

Find index position

𝐓GFik

(k = c, d, e, f) Hinge bracket datum

hole

𝐓GDFeia

(i = 2, 3, 4, 5)

Find contact point between the index and hinge bracket datum

surface

Find the maximum gaps between the mating features along the y-axis

Max {หδKC3jห (j= a, b, …, h) where:

ȁδKC3aȁ = ห 𝐓MFe2aMFe1a ห, ȁδKC3bȁ = ห 𝐓MFe2b

MFe1b ห, ȁδKC3cȁ = ห 𝐓MFe3aMFe1c ห, ȁδKC3dȁ = ห 𝐓MFe3b

MFe1d ห,

ȁδKC3eȁ = ห 𝐓MFe4aMFe1e ห, ȁδKC3fȁ = ห 𝐓MFe4b

MFe1f ห, หδKC3gห = ห 𝐓MFe5aMFe1g

ห, ȁδKC3hȁ = ห 𝐓MFe5bMFe1h ห

Define the mating features of hinge brackets, 𝐓GMFeia and 𝐓G

MFeib

(i = 2, 3, 4, 5)

Define hinge bracket posture

Table 2. Sensitivity study inputs and results

Variation

Source

Magnitude of part

variation inputs (mm)

Magnitude of largest calculated

gap or clash in assembly (mm)

Rank of

variation effect

Variation A +0.1250, -0.1250 0.1348 4

Variation B +0.1900, -0.1900 0.2048 3 Variation C +0.6000, -0.1900 0.6468 1

Variation D +0.2000, -0.2000 0.2156 2

Variation E +0.0100, -0.0100 0.0108 5

Variation F +0.0100, -0.0100 0.0108 5

It can be seen that the variations experienced at the KC3 interfaces are larger than

the manufacturing variation alone for each variation source, despite only one variation

being tested at a time. The sensitivity analysis give the variation scale and the rank of the

variation effects, so as to provide target directions to control the variation source.

5. Conclusion

Due to the ambiguous KC delivery chains of overconstrained assemblies, quantifying the

final assembly variation presents an extra challenge compared to connective assemblies.

This paper highlighted the importance of modelling variations induced by the assembly

process, in addition to sub-component manufacturing variation, when dealing with

overconstrained assemblies, in order to more accurately estimate the gaps and clashes

that will occur at assembly. Variation sources were analysed and modelled for a

representative industrial case study, consisting of an aircraft wing spar and hinge

brackets. A variation propagation model was tested, and a sensitivity study carried out

to identify the most significant variation drivers in the assembly.

Acknowledgements

The funding support from EPSRC project EP/P025447/1 is acknowledged. The funding

support from EU H2020 RISE 2016 - ECSASDPE 734272 project is also acknowledged.

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