Patent Grant
10838411
The field of the invention is that of mechanical part production. The invention relates more specifically to a step for assembling parts together which may require a prior machining operation, for example grinding, to make good any production defects which might make it difficult or even impossible to assemble them. It finds application in particular in the assembly of aerospace parts, for example the assembly of a blade and its leading-edge reinforcement.
The assembly of a blade made of a composite material with its titanium leading-edge reinforcement is a time-consuming step. There may be difficulties of varying degree associated with assembling a blade and its leading-edge reinforcement, depending on their respective shapes. Sometimes assembly is only possible after manual grinding of the blade. Such grinding operations are time-consuming steps to be avoided wherever possible, since they can adversely affect the mechanical performance levels of the finished part. Sometimes even grinding is insufficient to fully make up for production anomalies and render assembly possible.
One objective of the invention is to obtain a high-quality assembly whilst minimising the risk of having to perform a machining operation in order to allow two mechanical parts to be assembled together, such as, for example, a grinding operation with the aim of allowing a blade and a leading-edge reinforcement to be assembled together.
In order to achieve this it proposes a method of assembling parts chosen from a plurality of first parts and a plurality of second parts. The method comprises the following steps.
For each first part and each second part from the plurality of first parts and the plurality of second parts, a step for estimating a defectiveness indicator for assembly of the first part with the second part.
For a batch of N assemblies to be made, a step for assigning N first parts from the plurality of first parts to N second parts from the plurality of second parts, in order to form N pairs of a first part and of a second part. Said assignment is performed in such a way that said N pairs minimise a total defectiveness which corresponds to the sum of the defectiveness indicators for assembly of each of the N pairs.
Some preferred, but not restrictive, aspects of this method are as follows:
The invention also relates to a system and a computer program product capable of implementing this method.
Other aspects, aims, advantages and characteristics of the invention will become more apparent on reading the following detailed description of its preferred embodiments, given as non-restrictive examples, and undertaken with reference to the appended drawings, wherein
The invention relates to a method for assembling parts chosen from a plurality of first parts and a plurality of second parts. One embodiment example which will be described in detail hereafter relates to the assembly of a blade (first part) and of a leading-edge reinforcement (second part).
This assembly method comprises a first step consisting of selecting two parts to be assembled by means of a relevant logic process. During a second step these two parts are assembled without adhesive in order to verify that they are a good geometric match. In a third step, if necessary, grinding is performed in order to remove surplus material identified on one of the parts. In a fourth step, a verification of whether sufficient grinding has been performed is carried out. If the verification is positive, bonding of the two elements is carried out in a fifth step. The first step is therefore a determining step for the subsequent steps and the duration of the operation and the quality of the final assembly are dependent upon it.
The method according to the invention is used to optimise the choice of parts to be assembled by specifying parts to be assembled which will maximise the quality of the assembly.
In the field of optimisation, reference is generally made to minimisation of a cost-function, where this minimisation may include, in the context of the invention, the following technical objectives:
An assembly station is considered where, at different moments in time, a batch of N assemblies must be made using the parts available for assembly. By way of an illustrative example, the aim may be to make one batch of 8 assemblies per day from 16 blades and from 40 leading-edge reinforcements available.
The first plurality of parts and the second plurality of parts are not restricted to the parts available for assembly, but may include parts already present in the facility but not within the assembly station because, for example, they are undergoing inspection operations. By way of an example, 80 leading-edge reinforcements are delivered to the facility each week, but only enter the assembly station in batches of 8 to replace the available reinforcements in the assembly station which have been used each day to make the batch of 8 assemblies.
With reference to
In one embodiment example the defectiveness indicator of a pair formed by a first part and a second part may be made up of two elements:
By seeking to minimise such a defectiveness indicator (comparable to an assembly cost), it is thus sought to minimise the quantity of material removed by grinding and to form pairs which are as close as possible to the nominal. This defectiveness indicator for assembly of a first part j and of a second part I can be expressed as Cij=Gij+∥Pij−P0∥, where Gij represents the quantity of grinded material and ∥Pij−P0∥ represents a relative position of the parts in relation to a nominal position.
The defectiveness indicator for assembly of a first part and a second part may be estimated from geometric characteristics of said parts measured, for example, using tracer probes.
In one embodiment, simple geometric characteristics of the parts and a predictive model capable of learning are used to predict a probability that the assembly can be made without grinding. The greater the probability then the smaller the defectiveness indicator for the assembly of the parts is. This model is the result of a learning process using experience acquired on a certain number of pairs for which assembly has already been attempted.
By way of an example relating to the assembly of a blade and of a leading-edge reinforcement, a target distance go between the apex of the blade and the leading-edge reinforcement may be calculated using measured geometric characteristics from a simple formula: target distance=nominal distance+measured geometric characteristics.
In parallel the measured geometric characteristics are also used to predict a distance gp between the apex of the blade and the leading-edge reinforcement using a predictive model where the learning process uses pairs for which assembly has already been attempted.
The distance gp may in particular be expressed as a linear function of certain geometric characteristics of the blade and of the leading-edge. The parameters of the linear function are learned using linear regression from data obtained on pairs for which assembly has already been attempted.
The target distance go and the predicted distance gp are then compared. The closer they are, the greater the possibility that the pair can be assembled without grinding. On the other hand, if the difference between these distances exceeds a threshold it may be considered that the pair cannot be assembled.
Knowing go−go, the probability p that the pair can be assembled without grinding is calculated. This probability p is in effect a function of go−gp and this function may have been learned using pairs for which assembly has already been attempted.
When the pair can be assembled (|go−gp|≤glim), its defectiveness indicator may be expressed as |gp−gnominal|+(1−p)*Coûtponçage, where gnominal corresponds to the nominal distance, p is the probability that the pair can be assembled without grinding and Coûtponçage corresponds to the cost of grinding (i.e. the amount of material grinded) when |go gp|=glim.
In another embodiment, point clouds which represent the 3D surfaces of the first and of the second parts are used. An attempt to align these point clouds is used to predict the areas which are to be grinded (in the case where grinding must be performed) and therefore the amount of material to be removed. This alignment may be performed according to the techniques described in the thesis by Simon Flory entitled “Constrained Matching of Point Clouds and Surfaces”, 2009. In this embodiment, the grinding cost is estimated more precisely, since the amount of material that will have to be removed can be estimated.
The matrix of defectiveness indicators is continuously calculated, that is, it is updated each time the geometry of a new part is known. It is also updated each time a part becomes unavailable (for example because the part has been assembled or scrapped): the line or column corresponding to the part that has become unavailable is then removed from the matrix.
It is moreover possible to take into account the fact that the geometry of certain parts is sometimes known long before the latter become available to be assembled. By way of an example, the leading-edge reinforcements are produced in a facility other than the facility where the station for assembly with the blades is located. The geometry of the leading-edge reinforcements may be measured in the original production facility and therefore known before these reinforcements are delivered to the facility where assembly is carried out. This makes a good overview of “future” reinforcements and therefore, as will be described in more detail below, improves prediction of the consequences of the choice of pairs made at a time t on choices which must be made at a later time.
With reference to
This assignment step may be performed whenever necessary when an operator wishes to know which pairs must be assembled. This step is typically implemented every day in order to identify the N pairs which have to be made during the day.
This assignment step implements the solution of a linear assignment problem, that of determining N pairs which meet the quantitative objective of minimisation of the total defectiveness whilst maintaining the production rate (i.e. making N assemblies, for example making 8 assemblies per day) in order not to slow down production.
A linear assignment problem is a problem in which resources must be assigned to tasks. A cost is associated with each resource-task pair, and the pairs must be chosen so as to minimise the overall cost of the assignment. This problem can be written in the form argminx
where ci,j is the cost of assignment of the resource i to the task j, and xi,j decision variables where xi,j=1 if the resource i is assigned to the task j, and 0 otherwise;
and under constraints according to which:
This assignment problem may be solved using the Hungarian algorithm or in accordance with linear optimisation techniques (simplex algorithm or interior point algorithm, for example).
The assignment problem may take the constraint of compliance with production rates into account in the form of a cost referred to as R which corresponds to the inability to make one of the N assemblies required (there are not enough “assemblable” parts). Thus if a first part and a second part cannot be assembled, their defectiveness indicator is R. A prohibitive indicator may be regarded as making parts incapable of being assembled, and any indicator estimated as being greater than a threshold is set to R.
The assignment problem may take other constraints into account such as, for example, giving priority to the oldest parts available for assembly. A surface treatment applied to leading-edge reinforcements to improve bond quality means that these reinforcements cannot remain at the assembly station for too long a period. If they remain there more than ΔtlimB days, for example 50 days, they must be scrapped and are therefore no longer available for assembly. The cost of such scrapping is referred to as SB. On the other hand, in order to help monitor production it is preferable that the order of production for the blades is maintained for as long as possible at assembly. Thus a cost is associated with keeping a blade available for assembly (i.e. assembly takes place too late) for a time greater than ΔtlimA, for example greater than 5 days, which is referred to as DA.
This set of costs may be summarised in an objective function to be optimised. Between t=0 and t=T:
where:
Once the N pairs are formed after the assignment step, the operator assembles these pairs at the assembly station, thus producing the batch of N assemblies. The actual defectiveness for assembly of these N pairs is recorded. In particular the amount of material grinded and the deviation from the nominal are recorded.
This information on actual assembly defectiveness (or real pairing costs) may be used continuously and automatically in the event of the operator becoming aware that a pair that has been formed cannot in fact be assembled. In this case the parts remain at the assembly station and a record is made in memory that they cannot, in fact, be assembled, so as to prevent them being proposed once again. In order for this to occur, the estimated defectiveness indicator for this pair is corrected in order to associate the cost R with it.
This information about the real pairing costs may also be used discontinuously and non-automatically to re-calibrate the defectiveness indicator prediction model. The estimated indicators predicted by this model are compared with the real costs and this comparison is used to detect any deviation of the prediction model and to re-calibrate it if necessary by repeating the learning process using new gathered data.
Still with reference to
The step CRT for correction of the defectiveness indicators reduces an estimated defectiveness indicator for a first part and for a second part in order to favour the selection of this assembly during the assignment step. It provides a matrix of corrected indicators
The aim of this reduction is, for example, to favour assembly of parts which have been available for assembly for the longest time.
Thus a reduction in the estimated defectiveness indicator of a first part with a second part can be performed when the first part has been available for assembly for a time which is greater than a first threshold. Thus a time for which a blade has been present in the assembly station for too long may be anticipated, for example of more than 3 days. The corrected indicator for this blade j, for any reinforcement which can be assembled with the blade j, is stated as =Cij−DA. In other terms, if this blade does not undergo assembly at a time t, then this will cost DA since this blade will be considered to be subject to a delay during the days to come.
Alternatively, and/or in a complementary manner, a reduction is made in the estimated defectiveness indicator for assembly of a first part with a second part when the second part has been available for assembly for a period which is greater than a second threshold. Scrapping of a leading-edge reinforcement may be anticipated when it has been available for assembly for more than, for example, 43 days. The corrected indicator for this reinforcement i, for any blade j which can be assembled with the reinforcement i, is stated as =Cij−SB. In other terms, if this reinforcement does not undergo assembly at a time t, then this will cost SB since this reinforcement will be scrapped during the days to come.
According to other strategies for reducing the estimated defectiveness indicator, knowledge of future parts coming to the assembly station is used to favour assembly of parts which are difficult to assemble in comparison with easy-to-assemble parts.
For example, a reduction of the estimated defectiveness indicator for the assembly of a first part with a second part is carried out where said reduction is weighted by a factor which represents a probability that no first part, which becomes available for assembly during availability of the second part for assembly, can be assembled with the second part (i.e. the estimated defectiveness indicator for assembly of the second part with each of the future first parts is equal to R). The greater the possibility of not finding, in future first parts, a first part which can be assembled with the second part, then the greater the reduction.
Considering a leading-edge reinforcement i available for assembly from agei(t) at time t, there are Nit blades which will be available for assembly before the reinforcement i is scrapped. These are blades which would enter the assembly station during the next Δt−agei(t) days. The term pi is the probability that this reinforcement i can be assembled with a blade (this probability may be estimated on the basis of the ability of this reinforcement to be assembled with blades which have previously been available for assembly).
The probability that no blade, which will become available for assembly during the availability of the reinforcement i for assembly, can be assembled with the reinforcement i is Pit=(1−pi)N=Cij−SB×Pit. This reduction may be accompanied by the reduction favouring the oldest blades as described above.
According to another example of strategy for reducing the estimated defectiveness indicator which makes use of knowledge of future parts coming to the assembly station, the estimated defectiveness indicator for assembly of a first part with a second part is reduced when no second part, which is available for assembly with the first part during the availability of the first part for assembly, can be assembled with the first part (i.e. the estimated defectiveness indicator for the first part with each of the future second parts is equal to R). This other example may be implemented jointly with the above example including the probability Pit.
Considering a blade j available for assembly from agej(t) at time t, there is a set of reinforcements jt which will become available for assembly with the blade j before the blade j is considered to be too old (i.e. within the next Δt
−agej(t) days). If, in the set
jt, no reinforcement can be assembled with the blade j, the defectiveness indicator for any reinforcement i that can be assembled with the blade j is corrected according to
=Cij−DA. Otherwise no correction is made.
The following description relates to the step SUB for selecting a sub-set of parts in order to form a sub-matrix of indicators
For example, each time that a batch of N assemblies is to be made, the smallest sub-assembly of blades which can be used to make N assemblies with the set of reinforcements is selected. This selection is made by including the blades in the sub-set depending on the length of time they have been in the assembly station. The resulting sub-set is referred to as (t).
This selection requires knowledge of the maximum number of possible assemblies starting from a given set of blades and a given set of reinforcements. This is possible by representing the sets of blades and of reinforcements in a binary bipartite graph linking the set of blades to the set of reinforcements with an edge i,j if the pair i,j can assembled. An algorithm for maximum cardinality matching in a bipartite graph, such as, for example, the Ford-Fulkerson algorithm, is used to determine the number of possible assemblies.
The step SUB for selecting a sub-set of parts may also involve forming a sub-set of said plurality of second parts made up of the oldest second parts available for assembly. During the assignment step AFF, the N second parts assigned to the N first parts then belong to said sub-set of said plurality of second parts.
For example once the sub-set of blades (t) is selected, the smallest sub-set, referred to as
(t), of reinforcements which can be used to make the N assemblies with the blades of sub-set
(t) is selected. This selection is made by including the reinforcements in the sub-set
(t) depending on the length of time they have been in the assembly station.
Alternatively, the formation of a sub-set ′(t) of said plurality of second parts is performed in such a way that the second parts of said sub-set
′(t) are used, with the first parts of said sub-set
(t) of first parts, to make M assemblies without machining, where M corresponds to the number of assemblies without machining which can be made with the second parts of said plurality of second parts and the first parts of said sub-set
(t) of said plurality of first parts. During the assignment step AFF, the N second parts assigned to the N first parts then belong to said sub-set
′(t) of said plurality of second parts.
In this alternative, once the sub-set of blades (t) is selected, the smallest sub-set
′(t) of reinforcements which can be used to make N assemblies with the blades of sub-set
(t) and to make M assemblies without grinding is selected. M corresponds to the number of assemblies without grinding that it is possible to make with the blades of the sub-set
(t) and the set of reinforcements. In such a manner the assignment is carried out with the oldest reinforcements without adversely affecting the number of assemblies that can be made without grinding.
In one practical application of the algorithm, the number M is not in actual fact precisely known, since it is simply possible to estimate a probability that a pair can be made without grinding or not. Thus there is not a number M of assembles that can be made without grinding, but an estimate m of the expected value of the number of assemblies that can be made without grinding if the pairs are made with the blades of the sub-set (t) and the set of reinforcements. Thus the sub-set of reinforcements
′(t) is chosen which can be used to make N assemblies with the blades of the sub-set
(t) and give an expected value m′ of the number of assemblies that can be made without grinding (from amongst the N chosen pairs) which is close to the expected value: Thus m−m′<∈ is sought where ∈ is a threshold defined depending on the applications.
With reference to
The invention also relates to a non-transitory medium which can be read by a computer which stores program code instructions for executing the estimation and assignment steps of the method when said instructions are executed on the computer.
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| Number | Date | Country | |
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| 20180196412 A1 | Jul 2018 | US |
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| 62434087 | Dec 2016 | US |
