FR3103046A1 - PROCESS FOR DETERMINING A CHAIN OF DIMENSIONAL TOLERANCES - Google Patents

Abstract

The invention proposes a system and a method for the rapid and robust determination of a chain of dimensional tolerances representing a good compromise between a pessimistic approach of worst-case type assemblies and an optimistic approach of pure statistical type while presenting very simple calculations. to achieve and implement. Said system comprises a processor (5) configured to: define a first assembly tolerance (WC (Y)), said to be of the “worst case” type as a function of the tolerance magnitudes of a set of links corresponding to said set of links. elements, -defining a second assembly tolerance (RSS (Y)), said to be of the “pure statistical” type as a function of said tolerance quantities, -determining a disproportion indicator (D) of said tolerance quantities as a function of said first tolerance assembly, and-determining an optimal assembly tolerance (ASCR (Y)) by correcting said second assembly tolerance by means of said disproportion indicator. Fig. 1

Description

PROCESS FOR DETERMINING A CHAIN OF DIMENSIONAL TOLERANCES

The present invention relates to the general field of the assembly of sub-assemblies of a vehicle and more particularly, to the determination of a chain of dimensional tolerances for the assembly of a set of elements corresponding to at least one part of an aircraft.

It finds an application in the aeronautical, space, automobile, railway or nautical industry in which it is necessary to know the chain of tolerances of sub-assemblies in order to ensure that these sub-assemblies can be assembled together successfully.

State of the prior art

When designing a vehicle, we seek to define the dimensions of the various elements to be assembled as well as the acceptable tolerances guaranteeing a precise assembly between these elements. Tolerances are usually defined before the start of the production phases.

A first method of calculating tolerances called "worst case" type is based on the condition of maintaining the required output tolerance for any combination of the actual dimensions of the elements. In this case, this method calculates the sum of tolerances of the different elements to be assembled to predict the worst case.

“Worst case” type calculations guarantee high accuracy, but have very high production costs. This kind of tolerance calculation is highly conservative, especially when the chains are made up of many links. Indeed, the "worst case" method is pessimistic and unrealistic because it is very unlikely that the dimensions of all the elements to be assembled will vary simultaneously in a minimum or maximum way and therefore there is little chance that the assembly of the elements either equal to the sum of the minima or to the sum of the maxima.

There is a second method using statistical calculations of the "RSS" type (Root of the sum of the squares), often used with a fixed correction coefficient. This second method is based on the assumption that extreme values of dimensional deviation of individual elements is very unlikely. More particularly, the RSS-type assembly tolerance implies very severe assumptions on the input data and assumes that the various elements are produced with a level of precision of the order of . This greater dimensional tolerance on the elements of the assembly implies a reduction in production costs. However, the approach presents a very optimistic view and does not provide a sufficiently precise prediction. In particular, statistical calculations of the RSS type with a fixed coefficient do not take into account the topology (disproportion) of the coast chain and give results exceeding the "worst case" when there are few links or a large link crushes the others.

The object of the present invention is therefore to remedy the aforementioned drawbacks by proposing a method for determining a chain of dimensional tolerances representing a good compromise between the pessimistic approach of worst-case type assemblies and the optimistic approach of RSS type while presenting calculations that are very simple to perform and implement.

Presentation of the invention

The present invention is defined by a method for determining a chain of dimensional tolerances for the assembly of a set of elements, comprising the following steps:
-definition of a first assembly tolerance WC(Y), called "worst case" type according to the tolerance magnitudes of a set of links corresponding to said set of elements,
-definition of a second assembly tolerance RSS(Y), called "pure statistical" type according to the tolerance magnitudes of said set of links,
-determination of a disproportion indicator D of the tolerance magnitudes of said set of links as a function of said first assembly tolerance,
-determination of an optimal assembly tolerance ASCR(Y) by correcting said second assembly tolerance by means of said disproportion indicator, said optimal assembly tolerance representing a compromise between a pessimistic approach to assembly of the worst case type and an optimistic approach of the pure statistical type, and
-validate the dimensioning of said set of elements for an assembly according to said optimum assembly tolerance.

This method for determining tolerance chains is simple, robust, and economically advantageous compared to an approach of the worst case type, while ensuring a fairly accurate prediction.

This process allows either to evaluate the tolerance to be defined at the level of the assembly result or to define the tolerances of the elements participating in it in a robust and economically advantageous way.

In addition, the method according to the invention makes it possible to guard against non-compliance with the assumption of distributions of the elements participating in the tolerance chain and, within a certain limit, from disturbances which may modify the result of the assembly such as the effects of gravity forces on the structure.

Moreover, by freeing oneself from production hypotheses, it suffices to give oneself a tolerance interval independently of production and it is therefore not necessary to make measurements on the elements produced.

Advantageously, the disproportion indicator D of the tolerance quantities indicates the state of distribution of the links as a function of the first assembly tolerance, of the tolerance quantities, and of the number of links, said disproportion indicator D being defined from the following way:

Or represents the first assembly tolerance, is an influence coefficient of geometric origin, represents the tolerance quantity of the ith link and represents the number of links.

This indicator is based on the disparity of the chain to predict the deformation of the distribution of the assembly tolerance and thus makes it possible to correct the optimistic assembly tolerance.

Advantageously, the optimum assembly tolerance is determined by applying a form factor f to the second assembly tolerance, said form factor f being determined by a linear regression between said disproportion indicator D and a value recorded for the quantiles Q( Y).

Advantageously, the optimum assembly tolerance is equal to the minimum between, on the one hand, said second assembly tolerance multiplied by said form factor and, on the other hand, said first assembly tolerance.

According to a feature of the present invention, the first assembly tolerance is a linear combination of the tolerance magnitudes of said set of links defined as follows:

According to another feature, the second assembly tolerance is the root of the sum of the squares of the tolerance magnitudes of said set of links, each being affected by the corresponding influence coefficient, the second assembly tolerance being defined as next :

According to an embodiment of the present invention, the determination of the chain of tolerances consists in determining the optimal assembly tolerance according to predetermined tolerance magnitudes of said set of links.

According to a variant, the determination of the chain of tolerances consists in determining the magnitudes of tolerance of said set of links according to a predetermined assembly tolerance.

Advantageously, the elements of the tolerance chain can be defined in a one-dimensional, two-dimensional or three-dimensional way.

Advantageously, said set of elements corresponds to at least part of an aircraft.

Advantageously, said set of elements can be a set of elementary parts or a set of objects from among the following objects: sections of fuselages, fins, wings, passenger doors, cargo doors, engines, nacelles, reactor masts, horizontal and vertical planes , landing gear, cabin components or other parts of the aircraft.

The invention also relates to a method for assembling a set of elements, comprising the steps of the method for determining a chain of dimensional tolerances according to the characteristics above and further comprising the following steps:
-adapt the dimensioning and the geometry of said set of elements according to the optimum assembly tolerance, and
-assembling said set of elements according to positioning devices associated with said elements.

Advantageously, the assembly is carried out using assembly tools comprising at least one of the following tools: fixed tools, robots, drilling grids, hole-to-hole assembly mechanisms with or without interference, and mounting mechanisms. assembly with or without deformations.

The invention also relates to a system for determining a chain of dimensional tolerances for the assembly of a set of elements, said system comprising a processor configured for:
-defining a first assembly tolerance (WC(Y)), called "worst case" type according to the tolerance magnitudes of a set of links corresponding to said set of elements,
-defining a second assembly tolerance (RSS(Y)), called "pure statistical" type according to the tolerance magnitudes of said set of links,
-determining a disproportion indicator (D) of the tolerance magnitudes of said set of links as a function of said first assembly tolerance,
-determining an optimal assembly tolerance (ASCR(Y)) by correcting said second assembly tolerance by means of said disproportion indicator, said optimal assembly tolerance representing a compromise between a pessimistic approach to assembly of the worst case type and an optimistic approach of the pure statistical type, and
-validate the dimensioning of said set of elements for an assembly according to said optimum assembly tolerance.

Other advantages and characteristics of the invention will appear in the non-limiting detailed description below.

Brief description of figures

A description will now be given, by way of non-limiting examples, of embodiments of the invention, with reference to the appended drawings, in which:

schematically illustrates a system for determining a chain of dimensional tolerances, according to one embodiment of the invention;

is a flowchart schematically illustrating the steps of a method for determining a chain of dimensional tolerances, according to one embodiment of the invention;

is a simple example of a one-dimensional tolerance chain illustrating assembly tolerance calculations;

illustrates different types of distributions of the output requirement ranging from a uniform distribution D1 to a Gaussian distribution D4, according to the invention; And

represents the result obtained, once the linear regression is applied to a representative set of tolerance chains.

The concept underlying the invention is to substitute the input data of a tolerance chain considered unreliable, by a more conservative distribution.

Fig. 1 schematically illustrates a system for determining a chain of dimensional tolerances, according to one embodiment of the invention.

This system 1 comprises input interfaces 3, a data processing processor 5, memories 7, and output interfaces 9.

In accordance with the invention, the system 1 is configured to determine a chain of dimensional tolerances for the assembly of a set of elements e1-e4. By way of example, the elements e1-e4 represented correspond to at least a part of an aircraft and more particularly, to fuselage and wing sections of an aircraft.

By “set of elements” is meant a set of partial components each of which may be a subset of more elementary elements. For example, an aircraft can be considered to be composed of several elements comprising, in a non-exhaustive manner: an airframe, a powertrain, flight controls, on-board services, an avionics system, and internal or external loads. Each of these elements is itself a subset composed of the more elementary elements. For example, the cell comprises a fuselage, a wing, empennages and a landing gear. Furthermore, each element of the subset is in turn composed of other elements and so on. For example, the wing has two wings, ailerons, and tails. Also, the internal structure of each wing includes spars and ribs, etc.

Thus, the assembly of a set of elements requires the determination of the chain of dimensional tolerances corresponding to this set. The tolerance chain is generally expressed by a formula defining an output requirement Y according to the input data Xi.

A chain of tolerance, in its simplest, linear version, links output requirement Y to input data Xi through the following formula:

The output requirement Y is associated with the tolerance, result of an assembly either to be determined or to be checked, the Xi representing the tolerances of the elements e1-e4 to be assembled together, being a linear influence coefficient of geometric origin and N being the number of elements e1-e4 in the assembly line. Note that the coefficient influence of an element's tolerance on the Y output, can be equal to +1 or -1 in the context of a so-called one-dimensional 1D tolerance chain, and can be equal to any value in the case of a 2D or 3D tolerance chain.

In the following, the tolerance interval of the output requirement Y and that of the input tolerances Xi of the elements e1-e4 to be assembled will be denoted IT(Xi) and IT(Y) respectively.

Fig. 2 is a flowchart schematically illustrating the steps of a method for determining a chain of dimensional tolerances, according to one embodiment of the invention.

Initially, at step E0, the input data and initialization data collected via the input interfaces 3 are recorded in the memories 7 of the system 1.

At step E1, the processor 5 is configured to define a first assembly tolerance according to the input data representative of the tolerance quantities of a set of links corresponding to the set of elements to be assembled. It will be noted that the elements e1-e4 of the tolerance chain can be defined in a one-dimensional, two-dimensional or three-dimensional way.

For example, the first assembly tolerance is of the "worst case" type WC (Worst Case) and is defined as a simple linear combination of the tolerance quantities of the set of links as follows:

Or represents the first assembly tolerance, being the influence coefficient, representing the tolerance quantity of the ith link and representing the number of links. More precisely, is a variable that represents the tolerance and is the tolerance interval defined on this variable. Besides, each link is represented by the tolerance quantity affected by its weighting coefficient (i.e. influence coefficient) corresponding.

At step E2, the processor 5 is configured to define a second statistical type assembly tolerance as a function of the tolerance magnitudes of the set of links.

By way of example, the second assembly tolerance is of the "pure statistical" type corresponding to the root of the sum of the squares RSS (Root Square Sum) of the tolerance magnitudes of the set of links, each being affected by the coefficient of influence corresponding. Thus, the second assembly tolerance RSS(Y) is defined as follows:

Fig. 3 is a simple example of a one-dimensional tolerance chain illustrating assembly tolerance calculations.

According to this example, the tolerance chain has five (N=5) links corresponding to five elements e1-e5, each Xi value being equal to ±1mm and each influence coefficient being equal to 1mm.

Thus, the first assembly tolerance WC(Y) is equal to:

The second assembly tolerance RSS(Y) is equal to:

The second assembly tolerance RSS(Y) implies that the data follows a centered normal distribution. More specifically, the second assembly tolerance RSS(Y) assumes that the different elements are produced according to a Gaussian with a level of precision of the order of (Or being the standard deviation). This assumption can make the estimate of the tolerance of assembly very optimistic and difficult to carry out industrially especially in the case of an approach of initial design.

Thus, considering that the input data of a tolerance chain may be unreliable, the present invention proposes replacing them with a more conservative distribution such as a uniform distribution. The result of this substitution can make the distribution of the output requirement Y any.

Indeed, Fig.4 illustrates different types of D1-D4 distributions of the output requirement Y ranging from a uniform distribution D1 (i.e. unbalanced) to a Gaussian distribution D4 (i.e. balanced). The four distributions D1-D4 are represented according to input data with different tolerances Xi. Furthermore, each distribution is included in a tolerance interval IT(Y). Note that an unbalanced distribution means that there is a tolerance input data Xi much larger than all the others.

It will be noted that according to the distribution of the links of the chain and the number of links, the result approaches, at its two extremes, either a uniform distribution D1, or a Gaussian distribution D4. In the case of a uniform distribution D1, the output requirement Y follows any statistical law.

For a given distribution of links, the key parameter to control is the 99.73% quantile, which classically corresponds to the notion of . In its variants, the method can be applied to any required quantile.

Thus, in order to predict the deformation of the distribution and to correct the optimistic assembly tolerance, the present invention proposes to construct a disproportion indicator based on the disparity of the chain.

Indeed, in step E3, the processor 5 is configured to determine a disproportion indicator D of the tolerance magnitudes IT(Xi) of a set of N links as a function of the first assembly tolerance WC(Y). The disproportion indicator D then indicates the state of distribution of the links of the chain according to the first assembly tolerance WC(Y), the tolerance quantities IT(Xi), and the number N of links: D= F(N, IT(Xi), WC(Y)).

Advantageously, the disproportion indicator D can be defined as follows:

Thus, the indicator D reveals the disproportion of certain links over the others, which would indicate an output Y tending to be "unbalanced" as shown on the distributions D1 and D2 of the diagram of Fig. 4.

Note that the disproportion indicator D can vary from 0 to 100%, 0 being the unbalanced state and 100 being the total preponderance of the largest link in the chain (i.e. the case with a single link).

In addition, at step E4, the processor 5 is configured to determine a safe result coefficient “Safety Coefficient Result ASCR”, known as optimal assembly tolerance ASCR(Y) by correcting the second assembly tolerance RSS(Y) by means of the disproportion indicator D. This optimal assembly tolerance represents a compromise between a pessimistic approach to assembly of the type worst case WC and an optimistic approach of the pure statistical type RSS.

According to an embodiment of the present invention, the optimal assembly tolerance ASCR(Y) is determined by applying a parameter called form factor f(Y) to the second assembly tolerance RSS(Y). This shape factor f(Y) can be determined by a linear regression between the disproportion indicator D and a recorded value of the quantiles Q(Y) at 99.73% using, for example, a classic statistical method of the Monte-Carlo type or by a convolution product.

For standardization reasons, we introduce the form factor corresponding to the value of the quantiles Q(Y) divided by an inflation factor of a normal to the uniform (i.e. 1.73.RSS). According to the Central Limit Theorem, the inflation factor represents the expected result if the tolerance chain was perfectly balanced with an infinity of links.

Fig. 5 represents the result obtained, once the linear regression is applied to a representative set of tolerance chains.

The abscissa of the graph corresponds to the values of the indicator D and the ordinate corresponds to the values of the quantiles Q(Y) divided by the inflation factor (i.e. Q(Y)/1.73RSS(Y)). This plot shows a strong linear correlation which is sufficient for tolerance estimation purposes. Thus, one can use a coefficient based on these results and depending on the disproportion indicator D in order to determine the shape factor f(Y). In this case, the form factor f(Y) can be described by a straight line having for example, the following expression:

As variants, other affine expressions as a function of the disproportion indicator D can be envisaged.

The evaluation of the form factor f(Y) for a given disproportion indicator D can then be multiplied by the result of the second assembly tolerance RSS(Y) to determine the optimal assembly tolerance ASCR(Y), from the following way:

Advantageously, if the optimal assembly tolerance ASCR(Y) is greater than the worst case WC, the worst case value should be retained. In this case, the optimal assembly tolerance can be expressed as the minimum between on the one hand the second assembly tolerance RSS(Y) multiplied by the form factor f(Y) and on the other hand, the first tolerance assembly WC(Y), as follows:

Thus, the system and method of the present invention uses an indicator of disproportion of the links in order to correct a classic statistical result with a view to more robustly estimating the results of a tolerance chain.

Applying this method to the example of Fig. 3, we find an optimal assembly tolerance ASCR(Y) of the order of ±3.73mm which is a good compromise between the value WC(Y)=±5mm of the first assembly tolerance WC and the value RSS (Y)=±2.24mm of the second RSS assembly tolerance.

The optimal assembly tolerance ASCR(Y) according to the present invention represents the best estimate of the tolerances to be defined on an output requirement Y knowing the values of the input data Xi in a robust design approach. Of course, if the value of Y is fixed, the formula for the optimal assembly tolerance ASCR(Y) also makes it possible to determine the most favorable combination of tolerances on the Xi data allowing the requirement to be met on Y.

Thus, according to an embodiment of the present invention, the determination of the chain of tolerances may consist in determining the optimal assembly tolerance according to predetermined tolerance magnitudes of the set of links.

As a variant, the determination of the chain of tolerances can consist in determining the tolerance quantities of the set of links according to a predetermined assembly tolerance. In other words, the method of the present invention makes it possible either to evaluate the tolerance to be defined at the level of the assembly result or to define the tolerances of the elements.

At step E5, we validates the sizing of the set of elements to produce an assembly according to the optimal assembly tolerance. Furthermore, the numerical results, curves, statistical distributions, etc. can be displayed for example on a screen of the output interfaces 3.

This process thus makes it possible to calculate a chain of dimensions very quickly, and therefore to give an immediate result on an assembly output without the need for special digital processing tools. Note that you can easily add a link, or modify one to see the impact on the output in real time. This process thus provides effective decision support when defining tolerances before assembly.

The invention also relates to a method for assembling a set of elements. This method uses the steps for determining a chain of dimensional tolerances according to Fig. 2.

Indeed, once the result of the optimal assembly tolerance is obtained, the dimensioning and the geometry of the set of elements are adapted according to this result.

In addition, in a manner known to those skilled in the art, the set of elements is assembled by being guided for example by positioning devices associated with the elements.

Advantageously, the assembly is carried out using assembly tools comprising at least one of the following tools: fixed tools, robots, drilling grids, hole-to-hole assembly mechanisms with or without interference, and assembly with or without deformations.

The system or method of the present invention can be applied to all the stages of construction of an aircraft (aeroplane, helicopter, satellite, etc.) comprising in particular the assembly of sub-assemblies such as sections of fuselages, fins, wings , passenger, cargo or other doors, systems, engines, nacelles, reactor masts, horizontal and vertical planes, landing gear or cabin elements, but also elementary parts.

The assembly can be carried out using any type of assembly tools including, for example, fixed tools, robots, drilling grids, hole-to-hole assembly mechanisms with or without interference, assembly with or without deformations, etc.

In addition, the system or method of the present invention can be applied to different sources of tolerance chains, whether they are so-called 1D chains and processed manually or so-called 2D or 3D chains and processed with tolerance simulation software such as 3DCS, MECAMASTER or others.

Advantageously, the present invention can be applied to the entire chain of suppliers participating in the production of an aeronautical program.

Thus, the present invention has many advantages over the prior art.

It makes it possible to estimate in a robust way the results of dispersion of a chain of tolerance, presupposing a risk of not controlling the distribution of the individual tolerances of the chain. It precisely covers assemblies where the proportion of links would be unbalanced.

Furthermore, the method of the present invention is faster than conventional means and only takes into account a few elementary parameters of the chain. It can be calculated manually or with simple computer means such as spreadsheets.

In addition, the method of the present invention gives a good approximation (less than 5% deviation from conventional means) for similar starting calculation assumptions.

It should also be noted that the application of the optimal assembly tolerance formula ASCR(Y) does not presuppose any particular knowledge of statistics and can be exchanged with suppliers in order to standardize the tolerance results provided.

Claims (14)

Method for determining a chain of dimensional tolerances for the assembly of a set of elements, characterized in that it comprises the following steps:
-definition of a first assembly tolerance (WC(Y)), called "worst case" type according to the tolerance magnitudes of a set of links corresponding to said set of elements,
-definition of a second assembly tolerance (RSS(Y)), called "pure statistical" type according to the tolerance magnitudes of said set of links,
- determination of a disproportion indicator (D) of the tolerance magnitudes of said set of links as a function of said first assembly tolerance,
-determination of an optimal assembly tolerance (ASCR(Y)) by correcting said second assembly tolerance by means of said disproportion indicator, said optimal assembly tolerance representing a compromise between a pessimistic approach to assembly of the type worst case and an optimistic approach of the pure statistical type, and
-validate the dimensioning of said set of elements for an assembly according to said optimum assembly tolerance. Method according to Claim 1, characterized in that the disproportion indicator (D) of the tolerance quantities indicates the state of distribution of the links as a function of the first assembly tolerance, of the tolerance quantities, and of the number of links , said disproportion indicator (D) being defined as follows:
Or represents the first assembly tolerance, is an influence coefficient of geometric origin, represents the tolerance quantity of the ith link and represents the number of links. Method according to Claim 1 or 2, characterized in that the optimum assembly tolerance is determined by applying a form factor (f) to the second assembly tolerance, the said form factor (f) being determined by a linear regression between said disproportion indicator (D) and a noted value of the quantiles (Q(Y)). Method according to any one of the preceding claims, characterized in that the optimum assembly tolerance is equal to the minimum between on the one hand said second assembly tolerance multiplied by said form factor and on the other hand said first tolerance assembly. Method according to any one of the preceding claims, characterized in that the first assembly tolerance is a linear combination of the tolerance magnitudes of said set of links defined as follows:
Method according to any one of the preceding claims, characterized in that the second assembly tolerance is the root of the sum of the squares of the tolerance magnitudes of said set of links, each being affected by the corresponding influence coefficient, the second assembly tolerance being defined as follows: Method according to any one of the preceding claims, characterized in that the determination of the chain of tolerances consists in determining the optimum assembly tolerance as a function of predetermined tolerance magnitudes of said set of links. Method according to any one of Claims 1 to 6, characterized in that the determination of the chain of tolerances consists in determining the magnitudes of tolerance of said set of links as a function of a predetermined assembly tolerance. Method according to any one of the preceding claims, characterized in that the elements of the tolerance chain can be defined in a one-dimensional, two-dimensional or three-dimensional manner. Method according to any one of the preceding claims, characterized in that the said set of elements corresponds to at least a part of an aircraft. Method according to claim 10, characterized in that said set of elements can be a set of elementary parts or a set of objects among the following objects: sections of fuselages, fins, wings, passenger doors, cargo doors, engines, nacelles , engine masts, horizontal and vertical planes, landing gear, cabin elements or other parts of the aircraft. Method for assembling a set of elements, characterized in that it comprises the steps of the method for determining a chain of dimensional tolerances according to any one of the preceding claims and in that it further comprises the following steps:
-adapting the sizing of said set of elements according to the optimum assembly tolerance, and
-assembling said set of elements according to positioning devices associated with said elements. Method according to Claim 12, characterized in that the assembly is carried out using assembly tools comprising at least one of the following tools: fixed tools, robots, drilling grids, hole-to-hole assembly mechanisms with or without interference, and assembly mechanisms with or without deformations. System for determining a chain of dimensional tolerances for the assembly of a set of elements (e1-e4), characterized in that it comprises a processor (5) configured for:
-defining a first assembly tolerance (WC(Y)), called "worst case" type according to the tolerance magnitudes of a set of links corresponding to said set of elements,
-defining a second assembly tolerance (RSS(Y)), called "pure statistical" type according to the tolerance magnitudes of said set of links,
-determining a disproportion indicator (D) of the tolerance magnitudes of said set of links as a function of said first assembly tolerance,
-determining an optimal assembly tolerance (ASCR(Y)) by correcting said second assembly tolerance by means of said disproportion indicator, said optimal assembly tolerance representing a compromise between a pessimistic approach to assembly of the worst case type and an optimistic approach of the pure statistical type, and
-validate the dimensioning of said set of elements for an assembly according to said optimum assembly tolerance.