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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. [email protected]. 2 Corresponding Author. [email protected]
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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