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Generation of manufacturing tolerancing with ISO standards
International Journal of Machine Tools & Manufacture 45 (2005) 1124–1131 www.elsevier.com/locate/ijmactool
Generation of manufacturing tolerancing with ISO standards Bernard Anselmetti*, Hassen Louati Laboratoire Universitaire de Recherche en Production Automatise´e, IUT de Cachan ENS Cachan, 61, avenue du Pre´sident Wilson, 94235 Cachan Cedex, France Received 19 November 2004; accepted 6 January 2005 Available online 22 February 2005
Abstract Current developments in tolerancing with ISO standards for the purpose of defining parts now call for new methods to analyze these threedimensional specifications and to generate manufacturing specifications with ISO standards. In this pursuit, the proposed method has been based on a graphical representation of part features, process plans and functional requirements defined with an ISO standard that includes datum reference frames. A simple iterative procedure determines the ISO specifications of each phase according to the workpiece set-up. This algorithm uses a vectorial representation of the tolerance zone that corresponds to degrees of freedom imposed by each set-up surface. The presentation is limited to the machining process alone. An application on a 3D milling machine will also be displayed. q 2005 Elsevier Ltd. All rights reserved. Keywords: Manufacturing specifications; Process deviations; ISO representation of dimensioning; Process planning; Small displacement torsor
1. Manufacturing tolerancing 1.1. Introduction In current industrial processes, definition drawing is imposed by the designer. The process planner selects the process plan according to the available machine tools and functional requirement values. Machined surfaces, partholders and set-up are all defined for each phase. Manufacturing drawings are generated in order to define both the shape of workpieces after each machining phase and the geometrical characteristics to be respected during production. New ISO tolerancing standards have yielded sizable improvements in the accuracy used to describe functional requirements with a three-dimensional approach. Location and orientation zones, datum reference frame, maximum material requirements are all new concepts. Metrology methods are now well adapted for identifying the compliance of machined workpieces with ISO
specifications. Today’s industrial planners are in need of tools for generating manufacturing specifications on the basis of functional requirements backed by ISO standards. This activity generally contains the three following steps: † Machining simulation: prediction of geometrical variations in the finished parts, according to both machining and set-up errors; † Workpiece geometry specifications: workpiece, in both its raw state and after each phase, using ISO language; † Optimization: adjustment of nominal dimensions and optimization of manufacturing tolerances, according to machining capabilities in order to reduce manufacturing costs. This paper’s contribution lies at the second step by virtue of offering a new method for determining manufacturing specifications with ISO standards. 1.2. Objectives
* Corresponding author. Address: Laboratoire Universitaire de Recherche en Production Automatise´e, IUT de Cachan ENS Cachan, 61, avenue du Pre´sident Wilson, 94235 Cachan Cedex, France. Tel.: C33 147 402 971; fax: C33 147 492 220. E-mail addresses: [email protected] (B. Anselmetti), [email protected] (H. Louati). 0890-6955/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2005.01.001
The manufacturing tolerancing objective is to control workpiece shapes and dimensions during the machining process. Manufacturing specifications must be derived from functional specifications for each machining phase.
B. Anselmetti, H. Louati / International Journal of Machine Tools & Manufacture 45 (2005) 1124–1131
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The machining adjuster must respect all manufacturing tolerances, regardless of preceding or following machining. Machining tolerance intervals must remain as broad as possible in order to facilitate operator work and reduce machining costs. 1.3. Three-dimensional approaches The unidirectional approach [1] has now become widespread within industry. A bi-directional approach [2] may be applied in Numerical Control machining yet does not take into account the effects of angular deviations in the workpiece set-up. The small displacement torsor (SDT), developed by Pierre Bourdet [3], is able to simulate the three-dimensional influence of fixturing and machining errors on the geometry of the finished part. Legoff [4] proposed an experimental approach to quantifying machining variations as torsors. Vignat and Villeneuve [5] detected the influential deviations of each phase using equations that yielded the sums of all geometrical deviations. This approach guides the planner in choosing manufacturing specifications. New constraints can then be added to the equation system to give relations between torsor components and the shape and dimension of the tolerance zone, in order to accurately obtain deviation on the finished part. Many other research approaches use the SDT for simulation, along with 3D modeling of the geometric defects of part surfaces: Tichadou [6] considered each manufacturing set-up as a mechanism and proposed a chart representation using industrial CAD–CAM system functionality. Benea [7] used virtual metrology to verify that the manufacturing process respected the ISO specifications of the definition drawing. Other mathematical tools (Jacobian matrix, transformation, projection, etc.) [8,9] have been proposed to analyze manufacturing tolerances. Kinematic models and robotic parameterization are applied to simulate either the possible motion of the tolerance zone or that allowed by MMC and LMC modifiers [10]. In the work presented herein, a simple algorithm will directly provide a complete set of manufacturing specifications in compliance with ISO standards, with the orientation and location specifications and datum reference frame. This approach uses a vectorial representation of the tolerance zone. The simulation methods mentioned above are applicable in calculating the resultant manufacturing specifications for each one of the functional requirements.
Fig. 1. Specification transfer with a datum reference frame.
functional requirements, defined in accordance with ISO tolerancing standards. Complementary requirements may also be imposed by the production process. Every functional and production requirement must be transferred into machining specifications. This transfer operation consists of sharing the tolerance of the studied requirement in order to allocate a manufacturing tolerance to each adjuster; in turn, this adjuster must control production, hence it is necessary that the specification lays out the relative position of machined surfaces with respect to set-up surfaces in the particular phase. The proposed set of transfer rules defines reference surfaces, toleranced surfaces and specifications for every manufacturing specification. In case of transfer, the rules impose the localization and orientation of manufactured surfaces in relation to a datum reference frame defined on the set-up surfaces. Anselmetti [11] introduced the transfer principle that will be detailed in Section 2.4 (Fig. 1). Three types of transfers can be differentiated: † The reference frame corresponding to the fixturing surfaces has been based on the initial requirement; the reference frame is duplicated in the manufacturing specification. † The reference has been generated by transferring onto the fixturing surfaces; a new reference frame is then built upon these surface set-ups. † The manufacturing surfaces lie between two surfaces machined within the phase; no reference is to be made in the corresponding specification. Thomas Raulin has been working in this direction and proposes a methodology with the support of a graph-based representation [12]. 2.2. Presentation of the transfer tables
2. Three-dimensional manufacturing transfer methods
This method requires three simulation tables (Fig. 2). The first table identifies the machined part geometry:
2.1. Transfer principle The definition drawing, process plan and the part-holder are known. The definition drawing of a part provides a set of
– Direction line: this line serves to define the main part directions: X, Y, Z and, if necessary, other directions (e.g. U, V)
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Table n˚ 1 Marks
Direction Fixturing surfaces Datums Surface mark
X
Y
H
Z
G C
1
2
I
D 3
4
B 5
6
7
8
9
A
10 11
12
13
14
F
15
16
17
18
19 20
Raw
Table n˚2 Process planning
Table n˚ 3 Transfer
Phase 10
3
2
Phase 20
3
2
Phase 30
3
2
N˚ symb
Dim
Spe
Dat
12
30 0.2
7
ABD
t1
4
FGH 30
Tol
Pha.
px
t2
19
A
20
t3
15
I
10
t4 t5
10 7
IG
3
3
px
1 1
rz 2
oz 1
2
px
1
rz
dx
oz
10
oz
1 oz
rz
IGH Raw
1
rz
oz 1 oz
1
oz
3
dx
2
1
oz
rz
dx
Fig. 2. Manufacturing transfer tables.
– Surface marks line: marks identifying all raw, machined and finished surfaces, including cylinder axes and median slot planes – Datum: name or reference surfaces used in the definition drawing – Fixturing surface line: marks ascribed to the fixturing surfaces. The second table describes the process plan, with one row devoted to the raw part and one to each machining phase. – In the raw part row, a cross identifies a surface of this raw workpiece. – In each machining phase row, a cross denotes manufactured surfaces within this phase. A point denotes a fixturing surface, adjacent to the preponderance order (1, 2, 3) to indicate the primary, secondary and tertiary fixturing surfaces, respectively. The third table depicts the transfer for every requirement. The first row describes the requirement and each subsequent row describes a manufacturing specification. The left side of the table contains the following columns: – Number (Nbr): indicates the mark of the studied requirement; – Symbol (symb): lists the specification symbol (location, parallelism, etc.); – Dimension (Dim): displays the nominal dimension corresponding to the specification; – Tolerance interval (tol): represents the tolerance interval of the requirement (or the mini/maxi for unilateral tolerance);
– Specified surface (Spe): toleranced surface mark of either the studied requirement or the manufacturing specification; – Datum (Dat): datum reference frame of either the studied requirement or the manufacturing specification, in order of primary, secondary, tertiary; – Phase (Pha) (not used if the studied requirement is a functional requirement): number of the phase that has imposed the production requirement (first row) or name of the phase for a particular manufacturing specification (subsequent rows). On the right side, the first row describes the studied requirement, as follows: – – – –
A toleranced surface is represented by an arrow; A datum surface is represented by a triangle; A datum axis is represented by a cross in a circle; The numbers 1, 2 and 3 indicate the preponderance order in the frame for the primary, secondary and tertiary ISO representation references of the studied requirement, respectively.
Under the studied requirement, manufacturing specifications are determined step by step using the algorithm presented in Section 2.3.2. – An arrow represents a toleranced surface; – A triangle represents the fixturing reference feature identical to the reference of the studied requirement; – A point represents a reference defined on this fixture surface within the phase, i.e. the target datum created directly on fixturing points or with the restricted zones
B. Anselmetti, H. Louati / International Journal of Machine Tools & Manufacture 45 (2005) 1124–1131
limited to those surfaces in contact with the machining fixture; – A white circle represents a fixture surface of the raw part; – Numbers 1, 2 and 3 indicate the preponderance order of the primary, secondary and tertiary datum, respectively, corresponding to the joint of the workpiece in the partholder (two associated surfaces in the common zone for defining a common datum are assigned the same number); – Under both toleranced surfaces and datum surfaces, a vectorial indicator characterizes the tolerance zone and reference function (Section 3.2). Similar tables have also been built for each one of the other studied requirements. 2.3. Vectorial indicator of tolerance zones 2.3.1. Definition Manufacturing specifications must be developed using the three-dimensional approach, which includes the form, orientation and position tolerances, in complement with datum reference frames and target datum. Along these lines, a vectorial representation of tolerance zones has been proposed in Fig. 3. The vector shows the direction of the tolerance zone, a letter indicates both the shape of the zone and the accepted number of degrees of freedom with respect to the corresponding nominal surface. The code p~u describes a tolerance zone defined between two parallel planes normal to the u~ direction. A plane, a cylinder axis or a point may lie in this zone. The code c~u describes a tolerance zone defined by a cylinder of direction u~ . A cylinder axis or point could be within this zone; ‘s’ defines a spherical zone for a given point. O~u imposes a plane or axis orientation around all directions normal to u~ , while r~u only imposes one orientation around u~ .
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Fig. 3 displays the corresponding graphic representation of the specification for each vectorial tolerance zone indicator. For example, the orientation of a plane around vector u~ , which belongs to this plane, by indicator r~u would require parallelism of this plane to a line D both belonging to this plane and normal to u~ . When placed near indicators, the arrows represent degrees of freedom (translation and rotation), which leave the tolerance zone invariant. For curved surfaces, the tolerance zone is defined by the envelope of a sphere whose diameter is equal to the tolerance exhibited at the nominal surface. This tolerance zone can be freely displaced in order to adjust it onto the real surface. The proposed indicator defines the available degrees of freedom. 2.3.2. Rules of vectorial indicator assignment on the studied requirement The studied requirement consists of either a position or orientation specification in relation to a datum reference frame. The toleranced feature is initially characterized directly by means of a vectorial indicator as in Fig. 3. Next, the function of every reference frame datum is characterized by a vectorial indicator. According to this approach, it is necessary to determine if a datum is able to locate or orientate the tolerance zone. A complex algorithm, based on geometrical tests, has been computerized; nonetheless, a convenient method is available for the process planner to establish these properties, as follows: † Delete useless tertiary datum of the reference frame, provided this datum is of no utility in defining the tolerance zone with respect to the datum reference frame. To the extent possible, delete useless tertiary and secondary datum.
Fig. 3. Vectorial representation of tolerance zones.
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Table 1 Surfaces of the studied requirement
Table 3 Surfaces after the second transfer
Set
E0
Set
E2
Surface number Phase number Indicator
7 Raw p~x
Surface number Phase number Indicator
7 Raw p~x
D(4) 30 p~x
B(10) 10 r~z
A(15) 10 o~z
† Place all usable theoretical dimensions between the toleranced feature and datum surfaces. These selected datum surfaces serve as positioning references in this direction or in many directions. † All other datum surfaces are orientating references. Two complementary rules must also be applied: † Whereas the preponderant datum orientates the reference system in two directions (o~u ), the complementary reference only orientates around one axis (generally r~u ). † In datum reference systems that include two parallel cylinders, both cylinders must be associated in order to yield one orientating datum. In the third table of Fig. 2, the vectorial indicator is placed near both the toleranced feature and useful datum surfaces of the studied requirement (Table 1). Useless datum must be deleted. This vectorial indicator has been defined according to the type of datum surface (plane, cylinder and point) and the reference function (position or orientation), by use of Fig. 3. 2.4. Transfer rules 2.4.1. Definition of active surfaces Within a given phase, machined surfaces and set-up surfaces are both considered active [13]. In this work, the active surfaces of a given phase are identified in the process plan (Table 2, Fig. 2) by either a cross or a point on the row corresponding to this phase. 2.4.2. Cases of direct specification If all surfaces of the requirement are active during the same phase, the manufacturing specification is then direct and identical to the requirement. The requirement is duplicated as a manufacturing specification within this phase. The tolerance value is not even known and may possibly be reduced as a result of tolerance optimization. Table 2 Surfaces after the first transfer Set
E1
Surface number Phase number Indicator
7 Raw p~x
B(10) 10 r~z
A(15) 10 o~z
H(1) Raw p~x
G(8) Raw r~z
F(19) 20 To ~z
B(10) 10 r~z
A(15) 10 o~z
H(1) Raw p~x
G(8) Raw r~z
2.4.3. Transfer rules The studied requirement is defined by a set of surfaces called E0 and has been represented on the first row of Table 3. For each surface of E0, it is necessary to determine both the vectorial indicator and number of the phase within which it had been completed. The determination of manufacturing specifications requires an iterative procedure, as follows: – Let i be the surface machined last during Phase n. Surface i must be localized or orientated in relation to the reference frame corresponding to the fixturing surfaces in this same phase. The vectorial indicator of surface i and Fig. 3 provide the symbol and shape of the tolerance zone. The datum reference frame must thus be reduced to just those truly useful surfaces for purposes of this specification. – This first machining specification can be represented on a new row placed under the studied requirement. An arrow marks the toleranced surface while points indicate the useful datum surfaces. – This specification can be represented on the machining drawing of Phase n. The symbol of the tolerance frame may be made more explicit depending on the relative position of both the toleranced feature and references (e.g. angularity, perpendicularity or parallelism). For a position specification, the theoretical dimension must be placed between the toleranced surface and the datum surfaces. – The vectorial indicator must be determined for every datum surface of this new manufacturing specification by applying the set of rules proposed in Section 2.3.2. – To obtain another manufacturing specification, the new set E1 is built starting from set E0, and then by removing the i machined surface and adding useful datum surfaces into the manufacturing specification along with their vectorial indicators. This iterative procedure gets repeatedly applied until all surfaces of set Ek are active within the same phase, thereby providing a direct specification. 2.4.4. Difference between target datum and a simple datum The functional requirements are defined in ISO tolerancing standards with a simple datum. Such a datum, for example, could be a plane tangent to the actual surface. In machining, the fixture surfaces in contact with the partholder are limited to one, two or three small surfaces; the corresponding reference constitutes a target datum.
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Fig. 4. Gap between various datum surfaces.
This type of datum may be different from a simple datum, in taking into account the flatness of the primary plane or the perpendicularity of a secondary plane. In Fig. 4 for example, the datum A used for this functional parallelism is very different from the datum C being displayed by the simple datum B and different from the datum E being displayed by the target datum D. A gap consequently exists between the simple datum of the studied requirement and the target datum used for fixturing. It then follows that there are two distinct levels of depth for applying transfer rules: – Both simple datum and target datum are considered to be identical, in neglecting form and orientation deviations; – Datum surfaces are considered to be different, which generates more complex transfers. The example from Section 3 neglects the deviation between datum.
3. Application example 3.1. Part and process planning definition The proposed procedure is applied to a jaw of a NC-lathe chunk machined on a three-axis milling machine. First of all, the top of Fig. 2 defines the geometry of workpieces,
including reference surfaces, and then the process plan encompasses both the surface marks and reference names (Fig. 5). Fig. 6 depicts the shapes of workpieces after each phase and set-up. 3.2. Determination of machining specifications The studied requirement is the localization of Plane 7 in relation to a datum reference frame composed of the primary datum A(15), the secondary datum B(10) and the tertiary datum D(4). The toleranced plane (7) must lie in a zone at a distance of 30 mm from D, the ~x -axis direction, defined by two planes 0.2 mm apart. The Plane 7 indicator is p~x . Datum A orients both the datum reference frame and the tolerance zone, in addition to eliminating rotations around ~x and ~y . We therefore assign it the vectorial indicator o~z . Datum B orients the tolerance zone around ~z and receives the indicator r~z . The tertiary reference D locates the zone in the axis direction and is assigned indicator p~x . These studied requirements then allow defining the initial table containing the first set of surfaces E0 (Table 1). All surfaces of this set E0 are not active within the same phase. The iterative transfer procedure must therefore be applied. In this set, Cylinder 4 is machined last (Phase 30), with indicator p~x . According to Fig. 3, this cylinder must be located in relation to the fixturing system of Phase 30 F G H. Datum H is used for inserting the theoretical dimension
Fig. 5. Definition drawing of a jaw.
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Fig. 6. Manufacturing drawings.
between H and Plane 7. The datum frame cannot be reduced. Vectorial indicators of these datum surfaces are defined using the set of rules described in Section 2.3. Manufacturing specification no. 1 can be represented both in Fig. 6 and in manufacturing drawing Fig. 6, Phase 30. In order to construct the set E1 presented in Table 2, Cylinder 4 has been extracted from E0 and the fixturing surfaces of Phase 30 F(19), G(8) and H(1) have been included. In this set E1, Plane 19 is machined last (Phase 20), with indicator ~z requiring, according to Fig. 3, an orientation specification in relation to the fixturing system of Phase 20 A G H. Datum surfaces H and G are not used for this specification; the datum frame is thus reduced to the primary fixturing reference A with vectorial indicator o~z . Manufacturing specification no. 2 can be represented both in Fig. 2 and in manufacturing drawing Fig. 6, Phase 20. To build set E2, Surface 19 is deleted; A(15) must be added, yet it already exists in set E1 with the same vectorial indicator o~z . According to Table 3, it is necessary to orientate Surfaces 10 and 15, machined in Phase 10, in relation to the fixturing system of Phase 20 I G H. Set E4 only contains surfaces of the raw workpiece (Table 4). This last table contains datum frame I G H of the preceding manufacturing specification in Phase 10. According to indicator p~x , Surface 7 must be located relative to this datum frame (manufacturing specification no. 5). The manufacturing specifications obtained for the studied requirement can be represented on manufacturing drawings (Fig. 6).
4. Distribution of tolerances The method presented herein yields manufacturing specifications for each functional or production requirement. In order to proceed with the synthesis of tolerances, a series of equations that provide the results of each tolerance chart with 3D influences must be written, as follows Ri Z
X
kij tij % Ci
where tij is the tolerance of a manufacturing specification, kij a coefficient of influence and Ci the limit of the studied requirement. The distribution of tolerances is optimized according to the capability of machine tools and processes. For this last step, the part fixture on a machine tool often induces the most significant source of uncertainty [14–16]. According to our approach, we estimate the influence of tool-holder deviations and dispersions for each manufacturing specification defined with ISO standards [17]. This error is calculated using an Excel solver by applying the concept Table 4 Surfaces of the raw workpiece Set
E4
Surface number Phase number Indicator
7 Raw p~x
I(20) Raw To ~z
H(1) Raw p~x
G(8) Raw r~z
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of small displacement torsor on the boundary points of the toleranced feature. The tolerance distribution can then be optimized by introducing manufacturing costs into the solver [18] Cost Z
X lij tij
where lij is the global machining dispersion for this machining specification.
5. Conclusion As a contribution to the future CAD/CAM system, this paper has proposed a graph that associates machine part definition, process plan representation, and functional and production requirements. A simple transfer procedure determines the 3D manufacturing specification defined with ISO tolerancing standards. The machined surfaces are either located or orientated with respect to a datum reference frame that must be reduced whenever possible. This method utilizes a vectorial representation of the tolerance zone that describes the surface set-up function within a phase. The range of potential uses for this approach appears to be very broad in assembly, for example. Proposed rules must be validated and completed for more complex examples and industrial parts. This algorithm must now be programmed within an Excel environment in VBA language and then coupled with CATIA V5, in order to import part geometry.
References [1] P. Bourdet, chaıˆnes de cotes de fabrication, l’inge´nieur et le technicien de l’enseignement technique (1973) 191. [2] B. Anselmetti, Simulation d’usinage bidimensionnelle sur un exemple en tournage en commande nume´rique, Me´canique Mate´riaux Electricite´ (1983) 398. [3] E. Ballot, P. Bourdet, A Computational Method for the Consequences of Geometrical Errors in Mechanisms, Proceeding of CIRP Computer Aided Tolerancing Fifth Seminar, Toronto, Canada (1997) pages 137 and 148.
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[4] O. Legoff, F. Villeneuve, F. Geiskopf, Three Dimensional Quantification of Machining Defects, Geometric Product Specification and Verification: Integration of Functionality, Kluwer Academic Publisher, Dordecht, 2003, pp. 185–196. [5] F. Vignat, F. Villeneuve, Application du torseur des petits de´placements a` l’e´tude 3D des tole´rances de fabrication: application au process de tournage 8e`me colloque national—AIP primeca (2003) pp. 238–258. [6] S. Tichadou, O. Legoff, J. Hascoe¨t, Process planning geometrical simulation: compared approaches between integrated CAD/CAM system and /Small Displacement Torsor[ model, Bath, UK, April 5–7, 2004 IDMME, 2004 [7] R. Benea, C. Fortin, C. Cloutier, Analyse de tole´rances en fabrication tenant compte des proce´de´s et des erreurs machines outils, Revue internationale de CFAO et d’informatique graphique, vol. 17, 2002, pp. 39–59. [8] L. Laperrie`re, W. Ghie, A. Desrochers, Projection of Torsors: a Necessary Step for Tolerance Analysis Using the Unified JacobianTorsor Model, Eighth CIRP International Seminar on Computer Aided Tolerancing, (2003) pp. 14–23. [9] F. Villeneuve, F. Vignat, 3D Synthesis of Manufacturing Tolerances Using a SDT Approach, Eighth CIRP International Seminar on Computer Aided Tolerancing (2003) pp. 279–290. [10] L. Pino, F. Bennis, C. Fortin, De´finition et calcul de la pie`ce virtuelle et re´sultante en assemblage, IDMME 2000, Montre´al, Canada, CD Rom. [11] B. Anselmetti, cotation de fabrication et me´trologie, Editions Herme`s Lavoisier, 2003. [12] T. Raulin, Formalisation d’une me´thodologie de spe´cification ge´ome´trique des e´tats interme´diaires des pie`ces fabrique´es, Bibliographie de DEA de Production Automatise´e, Ecole Normale Supe´rieure de Cachan, LURPA, 2002. [13] D. Duret, De´termination des intervalles de tole´rance en fabrication par une approche graphique, Actes se´minaire Tole´rancement et chaıˆnes de cotes, ENS Cachan, fe´v, 1995. [14] R. Ramesh, M.A. Mannan, A.N. Poo, Error compensation in machine tools—a review: part I: geometric, cutting-force induced and fixturedependent errors, International Journal of Machine Tools and Manufacture 40 (9) (2000) 1235–1256. [15] S.H. Huang, Q. Liu, Rigorous application of tolerance analysis in setup planning, The International Journal of Advanced Manufacturing Technology 2003; 196–207. [16] V. Bhat, E. De Meter, An analysis of the effect of datumestablishment methods on the geometric errors of machined features, International Journal of Machine Tools and Manufacture 40 (13) (2000) 1951–1975. [17] H. Louati, Elaboration et traitement de la cotation de fabrication en 3D en fraisage 3axes, me´moire de recherche, DEA Production Automatise´e, Ecole Normale Supe´rieure de Cachan, juillet, 2004. [18] B. Anselmetti, P. Bourdet, Optimization of a workpiece considering production requirements, Computers in Industry 21 (1993) 23–24.
Generation of manufacturing tolerancing with ISO standards Bernard Anselmetti*, Hassen Louati Laboratoire Universitaire de Recherche en Production Automatise´e, IUT de Cachan ENS Cachan, 61, avenue du Pre´sident Wilson, 94235 Cachan Cedex, France Received 19 November 2004; accepted 6 January 2005 Available online 22 February 2005
Abstract Current developments in tolerancing with ISO standards for the purpose of defining parts now call for new methods to analyze these threedimensional specifications and to generate manufacturing specifications with ISO standards. In this pursuit, the proposed method has been based on a graphical representation of part features, process plans and functional requirements defined with an ISO standard that includes datum reference frames. A simple iterative procedure determines the ISO specifications of each phase according to the workpiece set-up. This algorithm uses a vectorial representation of the tolerance zone that corresponds to degrees of freedom imposed by each set-up surface. The presentation is limited to the machining process alone. An application on a 3D milling machine will also be displayed. q 2005 Elsevier Ltd. All rights reserved. Keywords: Manufacturing specifications; Process deviations; ISO representation of dimensioning; Process planning; Small displacement torsor
1. Manufacturing tolerancing 1.1. Introduction In current industrial processes, definition drawing is imposed by the designer. The process planner selects the process plan according to the available machine tools and functional requirement values. Machined surfaces, partholders and set-up are all defined for each phase. Manufacturing drawings are generated in order to define both the shape of workpieces after each machining phase and the geometrical characteristics to be respected during production. New ISO tolerancing standards have yielded sizable improvements in the accuracy used to describe functional requirements with a three-dimensional approach. Location and orientation zones, datum reference frame, maximum material requirements are all new concepts. Metrology methods are now well adapted for identifying the compliance of machined workpieces with ISO
specifications. Today’s industrial planners are in need of tools for generating manufacturing specifications on the basis of functional requirements backed by ISO standards. This activity generally contains the three following steps: † Machining simulation: prediction of geometrical variations in the finished parts, according to both machining and set-up errors; † Workpiece geometry specifications: workpiece, in both its raw state and after each phase, using ISO language; † Optimization: adjustment of nominal dimensions and optimization of manufacturing tolerances, according to machining capabilities in order to reduce manufacturing costs. This paper’s contribution lies at the second step by virtue of offering a new method for determining manufacturing specifications with ISO standards. 1.2. Objectives
* Corresponding author. Address: Laboratoire Universitaire de Recherche en Production Automatise´e, IUT de Cachan ENS Cachan, 61, avenue du Pre´sident Wilson, 94235 Cachan Cedex, France. Tel.: C33 147 402 971; fax: C33 147 492 220. E-mail addresses: [email protected] (B. Anselmetti), [email protected] (H. Louati). 0890-6955/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2005.01.001
The manufacturing tolerancing objective is to control workpiece shapes and dimensions during the machining process. Manufacturing specifications must be derived from functional specifications for each machining phase.
B. Anselmetti, H. Louati / International Journal of Machine Tools & Manufacture 45 (2005) 1124–1131
1125
The machining adjuster must respect all manufacturing tolerances, regardless of preceding or following machining. Machining tolerance intervals must remain as broad as possible in order to facilitate operator work and reduce machining costs. 1.3. Three-dimensional approaches The unidirectional approach [1] has now become widespread within industry. A bi-directional approach [2] may be applied in Numerical Control machining yet does not take into account the effects of angular deviations in the workpiece set-up. The small displacement torsor (SDT), developed by Pierre Bourdet [3], is able to simulate the three-dimensional influence of fixturing and machining errors on the geometry of the finished part. Legoff [4] proposed an experimental approach to quantifying machining variations as torsors. Vignat and Villeneuve [5] detected the influential deviations of each phase using equations that yielded the sums of all geometrical deviations. This approach guides the planner in choosing manufacturing specifications. New constraints can then be added to the equation system to give relations between torsor components and the shape and dimension of the tolerance zone, in order to accurately obtain deviation on the finished part. Many other research approaches use the SDT for simulation, along with 3D modeling of the geometric defects of part surfaces: Tichadou [6] considered each manufacturing set-up as a mechanism and proposed a chart representation using industrial CAD–CAM system functionality. Benea [7] used virtual metrology to verify that the manufacturing process respected the ISO specifications of the definition drawing. Other mathematical tools (Jacobian matrix, transformation, projection, etc.) [8,9] have been proposed to analyze manufacturing tolerances. Kinematic models and robotic parameterization are applied to simulate either the possible motion of the tolerance zone or that allowed by MMC and LMC modifiers [10]. In the work presented herein, a simple algorithm will directly provide a complete set of manufacturing specifications in compliance with ISO standards, with the orientation and location specifications and datum reference frame. This approach uses a vectorial representation of the tolerance zone. The simulation methods mentioned above are applicable in calculating the resultant manufacturing specifications for each one of the functional requirements.
Fig. 1. Specification transfer with a datum reference frame.
functional requirements, defined in accordance with ISO tolerancing standards. Complementary requirements may also be imposed by the production process. Every functional and production requirement must be transferred into machining specifications. This transfer operation consists of sharing the tolerance of the studied requirement in order to allocate a manufacturing tolerance to each adjuster; in turn, this adjuster must control production, hence it is necessary that the specification lays out the relative position of machined surfaces with respect to set-up surfaces in the particular phase. The proposed set of transfer rules defines reference surfaces, toleranced surfaces and specifications for every manufacturing specification. In case of transfer, the rules impose the localization and orientation of manufactured surfaces in relation to a datum reference frame defined on the set-up surfaces. Anselmetti [11] introduced the transfer principle that will be detailed in Section 2.4 (Fig. 1). Three types of transfers can be differentiated: † The reference frame corresponding to the fixturing surfaces has been based on the initial requirement; the reference frame is duplicated in the manufacturing specification. † The reference has been generated by transferring onto the fixturing surfaces; a new reference frame is then built upon these surface set-ups. † The manufacturing surfaces lie between two surfaces machined within the phase; no reference is to be made in the corresponding specification. Thomas Raulin has been working in this direction and proposes a methodology with the support of a graph-based representation [12]. 2.2. Presentation of the transfer tables
2. Three-dimensional manufacturing transfer methods
This method requires three simulation tables (Fig. 2). The first table identifies the machined part geometry:
2.1. Transfer principle The definition drawing, process plan and the part-holder are known. The definition drawing of a part provides a set of
– Direction line: this line serves to define the main part directions: X, Y, Z and, if necessary, other directions (e.g. U, V)
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Table n˚ 1 Marks
Direction Fixturing surfaces Datums Surface mark
X
Y
H
Z
G C
1
2
I
D 3
4
B 5
6
7
8
9
A
10 11
12
13
14
F
15
16
17
18
19 20
Raw
Table n˚2 Process planning
Table n˚ 3 Transfer
Phase 10
3
2
Phase 20
3
2
Phase 30
3
2
N˚ symb
Dim
Spe
Dat
12
30 0.2
7
ABD
t1
4
FGH 30
Tol
Pha.
px
t2
19
A
20
t3
15
I
10
t4 t5
10 7
IG
3
3
px
1 1
rz 2
oz 1
2
px
1
rz
dx
oz
10
oz
1 oz
rz
IGH Raw
1
rz
oz 1 oz
1
oz
3
dx
2
1
oz
rz
dx
Fig. 2. Manufacturing transfer tables.
– Surface marks line: marks identifying all raw, machined and finished surfaces, including cylinder axes and median slot planes – Datum: name or reference surfaces used in the definition drawing – Fixturing surface line: marks ascribed to the fixturing surfaces. The second table describes the process plan, with one row devoted to the raw part and one to each machining phase. – In the raw part row, a cross identifies a surface of this raw workpiece. – In each machining phase row, a cross denotes manufactured surfaces within this phase. A point denotes a fixturing surface, adjacent to the preponderance order (1, 2, 3) to indicate the primary, secondary and tertiary fixturing surfaces, respectively. The third table depicts the transfer for every requirement. The first row describes the requirement and each subsequent row describes a manufacturing specification. The left side of the table contains the following columns: – Number (Nbr): indicates the mark of the studied requirement; – Symbol (symb): lists the specification symbol (location, parallelism, etc.); – Dimension (Dim): displays the nominal dimension corresponding to the specification; – Tolerance interval (tol): represents the tolerance interval of the requirement (or the mini/maxi for unilateral tolerance);
– Specified surface (Spe): toleranced surface mark of either the studied requirement or the manufacturing specification; – Datum (Dat): datum reference frame of either the studied requirement or the manufacturing specification, in order of primary, secondary, tertiary; – Phase (Pha) (not used if the studied requirement is a functional requirement): number of the phase that has imposed the production requirement (first row) or name of the phase for a particular manufacturing specification (subsequent rows). On the right side, the first row describes the studied requirement, as follows: – – – –
A toleranced surface is represented by an arrow; A datum surface is represented by a triangle; A datum axis is represented by a cross in a circle; The numbers 1, 2 and 3 indicate the preponderance order in the frame for the primary, secondary and tertiary ISO representation references of the studied requirement, respectively.
Under the studied requirement, manufacturing specifications are determined step by step using the algorithm presented in Section 2.3.2. – An arrow represents a toleranced surface; – A triangle represents the fixturing reference feature identical to the reference of the studied requirement; – A point represents a reference defined on this fixture surface within the phase, i.e. the target datum created directly on fixturing points or with the restricted zones
B. Anselmetti, H. Louati / International Journal of Machine Tools & Manufacture 45 (2005) 1124–1131
limited to those surfaces in contact with the machining fixture; – A white circle represents a fixture surface of the raw part; – Numbers 1, 2 and 3 indicate the preponderance order of the primary, secondary and tertiary datum, respectively, corresponding to the joint of the workpiece in the partholder (two associated surfaces in the common zone for defining a common datum are assigned the same number); – Under both toleranced surfaces and datum surfaces, a vectorial indicator characterizes the tolerance zone and reference function (Section 3.2). Similar tables have also been built for each one of the other studied requirements. 2.3. Vectorial indicator of tolerance zones 2.3.1. Definition Manufacturing specifications must be developed using the three-dimensional approach, which includes the form, orientation and position tolerances, in complement with datum reference frames and target datum. Along these lines, a vectorial representation of tolerance zones has been proposed in Fig. 3. The vector shows the direction of the tolerance zone, a letter indicates both the shape of the zone and the accepted number of degrees of freedom with respect to the corresponding nominal surface. The code p~u describes a tolerance zone defined between two parallel planes normal to the u~ direction. A plane, a cylinder axis or a point may lie in this zone. The code c~u describes a tolerance zone defined by a cylinder of direction u~ . A cylinder axis or point could be within this zone; ‘s’ defines a spherical zone for a given point. O~u imposes a plane or axis orientation around all directions normal to u~ , while r~u only imposes one orientation around u~ .
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Fig. 3 displays the corresponding graphic representation of the specification for each vectorial tolerance zone indicator. For example, the orientation of a plane around vector u~ , which belongs to this plane, by indicator r~u would require parallelism of this plane to a line D both belonging to this plane and normal to u~ . When placed near indicators, the arrows represent degrees of freedom (translation and rotation), which leave the tolerance zone invariant. For curved surfaces, the tolerance zone is defined by the envelope of a sphere whose diameter is equal to the tolerance exhibited at the nominal surface. This tolerance zone can be freely displaced in order to adjust it onto the real surface. The proposed indicator defines the available degrees of freedom. 2.3.2. Rules of vectorial indicator assignment on the studied requirement The studied requirement consists of either a position or orientation specification in relation to a datum reference frame. The toleranced feature is initially characterized directly by means of a vectorial indicator as in Fig. 3. Next, the function of every reference frame datum is characterized by a vectorial indicator. According to this approach, it is necessary to determine if a datum is able to locate or orientate the tolerance zone. A complex algorithm, based on geometrical tests, has been computerized; nonetheless, a convenient method is available for the process planner to establish these properties, as follows: † Delete useless tertiary datum of the reference frame, provided this datum is of no utility in defining the tolerance zone with respect to the datum reference frame. To the extent possible, delete useless tertiary and secondary datum.
Fig. 3. Vectorial representation of tolerance zones.
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Table 1 Surfaces of the studied requirement
Table 3 Surfaces after the second transfer
Set
E0
Set
E2
Surface number Phase number Indicator
7 Raw p~x
Surface number Phase number Indicator
7 Raw p~x
D(4) 30 p~x
B(10) 10 r~z
A(15) 10 o~z
† Place all usable theoretical dimensions between the toleranced feature and datum surfaces. These selected datum surfaces serve as positioning references in this direction or in many directions. † All other datum surfaces are orientating references. Two complementary rules must also be applied: † Whereas the preponderant datum orientates the reference system in two directions (o~u ), the complementary reference only orientates around one axis (generally r~u ). † In datum reference systems that include two parallel cylinders, both cylinders must be associated in order to yield one orientating datum. In the third table of Fig. 2, the vectorial indicator is placed near both the toleranced feature and useful datum surfaces of the studied requirement (Table 1). Useless datum must be deleted. This vectorial indicator has been defined according to the type of datum surface (plane, cylinder and point) and the reference function (position or orientation), by use of Fig. 3. 2.4. Transfer rules 2.4.1. Definition of active surfaces Within a given phase, machined surfaces and set-up surfaces are both considered active [13]. In this work, the active surfaces of a given phase are identified in the process plan (Table 2, Fig. 2) by either a cross or a point on the row corresponding to this phase. 2.4.2. Cases of direct specification If all surfaces of the requirement are active during the same phase, the manufacturing specification is then direct and identical to the requirement. The requirement is duplicated as a manufacturing specification within this phase. The tolerance value is not even known and may possibly be reduced as a result of tolerance optimization. Table 2 Surfaces after the first transfer Set
E1
Surface number Phase number Indicator
7 Raw p~x
B(10) 10 r~z
A(15) 10 o~z
H(1) Raw p~x
G(8) Raw r~z
F(19) 20 To ~z
B(10) 10 r~z
A(15) 10 o~z
H(1) Raw p~x
G(8) Raw r~z
2.4.3. Transfer rules The studied requirement is defined by a set of surfaces called E0 and has been represented on the first row of Table 3. For each surface of E0, it is necessary to determine both the vectorial indicator and number of the phase within which it had been completed. The determination of manufacturing specifications requires an iterative procedure, as follows: – Let i be the surface machined last during Phase n. Surface i must be localized or orientated in relation to the reference frame corresponding to the fixturing surfaces in this same phase. The vectorial indicator of surface i and Fig. 3 provide the symbol and shape of the tolerance zone. The datum reference frame must thus be reduced to just those truly useful surfaces for purposes of this specification. – This first machining specification can be represented on a new row placed under the studied requirement. An arrow marks the toleranced surface while points indicate the useful datum surfaces. – This specification can be represented on the machining drawing of Phase n. The symbol of the tolerance frame may be made more explicit depending on the relative position of both the toleranced feature and references (e.g. angularity, perpendicularity or parallelism). For a position specification, the theoretical dimension must be placed between the toleranced surface and the datum surfaces. – The vectorial indicator must be determined for every datum surface of this new manufacturing specification by applying the set of rules proposed in Section 2.3.2. – To obtain another manufacturing specification, the new set E1 is built starting from set E0, and then by removing the i machined surface and adding useful datum surfaces into the manufacturing specification along with their vectorial indicators. This iterative procedure gets repeatedly applied until all surfaces of set Ek are active within the same phase, thereby providing a direct specification. 2.4.4. Difference between target datum and a simple datum The functional requirements are defined in ISO tolerancing standards with a simple datum. Such a datum, for example, could be a plane tangent to the actual surface. In machining, the fixture surfaces in contact with the partholder are limited to one, two or three small surfaces; the corresponding reference constitutes a target datum.
B. Anselmetti, H. Louati / International Journal of Machine Tools & Manufacture 45 (2005) 1124–1131
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Fig. 4. Gap between various datum surfaces.
This type of datum may be different from a simple datum, in taking into account the flatness of the primary plane or the perpendicularity of a secondary plane. In Fig. 4 for example, the datum A used for this functional parallelism is very different from the datum C being displayed by the simple datum B and different from the datum E being displayed by the target datum D. A gap consequently exists between the simple datum of the studied requirement and the target datum used for fixturing. It then follows that there are two distinct levels of depth for applying transfer rules: – Both simple datum and target datum are considered to be identical, in neglecting form and orientation deviations; – Datum surfaces are considered to be different, which generates more complex transfers. The example from Section 3 neglects the deviation between datum.
3. Application example 3.1. Part and process planning definition The proposed procedure is applied to a jaw of a NC-lathe chunk machined on a three-axis milling machine. First of all, the top of Fig. 2 defines the geometry of workpieces,
including reference surfaces, and then the process plan encompasses both the surface marks and reference names (Fig. 5). Fig. 6 depicts the shapes of workpieces after each phase and set-up. 3.2. Determination of machining specifications The studied requirement is the localization of Plane 7 in relation to a datum reference frame composed of the primary datum A(15), the secondary datum B(10) and the tertiary datum D(4). The toleranced plane (7) must lie in a zone at a distance of 30 mm from D, the ~x -axis direction, defined by two planes 0.2 mm apart. The Plane 7 indicator is p~x . Datum A orients both the datum reference frame and the tolerance zone, in addition to eliminating rotations around ~x and ~y . We therefore assign it the vectorial indicator o~z . Datum B orients the tolerance zone around ~z and receives the indicator r~z . The tertiary reference D locates the zone in the axis direction and is assigned indicator p~x . These studied requirements then allow defining the initial table containing the first set of surfaces E0 (Table 1). All surfaces of this set E0 are not active within the same phase. The iterative transfer procedure must therefore be applied. In this set, Cylinder 4 is machined last (Phase 30), with indicator p~x . According to Fig. 3, this cylinder must be located in relation to the fixturing system of Phase 30 F G H. Datum H is used for inserting the theoretical dimension
Fig. 5. Definition drawing of a jaw.
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Fig. 6. Manufacturing drawings.
between H and Plane 7. The datum frame cannot be reduced. Vectorial indicators of these datum surfaces are defined using the set of rules described in Section 2.3. Manufacturing specification no. 1 can be represented both in Fig. 6 and in manufacturing drawing Fig. 6, Phase 30. In order to construct the set E1 presented in Table 2, Cylinder 4 has been extracted from E0 and the fixturing surfaces of Phase 30 F(19), G(8) and H(1) have been included. In this set E1, Plane 19 is machined last (Phase 20), with indicator ~z requiring, according to Fig. 3, an orientation specification in relation to the fixturing system of Phase 20 A G H. Datum surfaces H and G are not used for this specification; the datum frame is thus reduced to the primary fixturing reference A with vectorial indicator o~z . Manufacturing specification no. 2 can be represented both in Fig. 2 and in manufacturing drawing Fig. 6, Phase 20. To build set E2, Surface 19 is deleted; A(15) must be added, yet it already exists in set E1 with the same vectorial indicator o~z . According to Table 3, it is necessary to orientate Surfaces 10 and 15, machined in Phase 10, in relation to the fixturing system of Phase 20 I G H. Set E4 only contains surfaces of the raw workpiece (Table 4). This last table contains datum frame I G H of the preceding manufacturing specification in Phase 10. According to indicator p~x , Surface 7 must be located relative to this datum frame (manufacturing specification no. 5). The manufacturing specifications obtained for the studied requirement can be represented on manufacturing drawings (Fig. 6).
4. Distribution of tolerances The method presented herein yields manufacturing specifications for each functional or production requirement. In order to proceed with the synthesis of tolerances, a series of equations that provide the results of each tolerance chart with 3D influences must be written, as follows Ri Z
X
kij tij % Ci
where tij is the tolerance of a manufacturing specification, kij a coefficient of influence and Ci the limit of the studied requirement. The distribution of tolerances is optimized according to the capability of machine tools and processes. For this last step, the part fixture on a machine tool often induces the most significant source of uncertainty [14–16]. According to our approach, we estimate the influence of tool-holder deviations and dispersions for each manufacturing specification defined with ISO standards [17]. This error is calculated using an Excel solver by applying the concept Table 4 Surfaces of the raw workpiece Set
E4
Surface number Phase number Indicator
7 Raw p~x
I(20) Raw To ~z
H(1) Raw p~x
G(8) Raw r~z
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of small displacement torsor on the boundary points of the toleranced feature. The tolerance distribution can then be optimized by introducing manufacturing costs into the solver [18] Cost Z
X lij tij
where lij is the global machining dispersion for this machining specification.
5. Conclusion As a contribution to the future CAD/CAM system, this paper has proposed a graph that associates machine part definition, process plan representation, and functional and production requirements. A simple transfer procedure determines the 3D manufacturing specification defined with ISO tolerancing standards. The machined surfaces are either located or orientated with respect to a datum reference frame that must be reduced whenever possible. This method utilizes a vectorial representation of the tolerance zone that describes the surface set-up function within a phase. The range of potential uses for this approach appears to be very broad in assembly, for example. Proposed rules must be validated and completed for more complex examples and industrial parts. This algorithm must now be programmed within an Excel environment in VBA language and then coupled with CATIA V5, in order to import part geometry.
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[4] O. Legoff, F. Villeneuve, F. Geiskopf, Three Dimensional Quantification of Machining Defects, Geometric Product Specification and Verification: Integration of Functionality, Kluwer Academic Publisher, Dordecht, 2003, pp. 185–196. [5] F. Vignat, F. Villeneuve, Application du torseur des petits de´placements a` l’e´tude 3D des tole´rances de fabrication: application au process de tournage 8e`me colloque national—AIP primeca (2003) pp. 238–258. [6] S. Tichadou, O. Legoff, J. Hascoe¨t, Process planning geometrical simulation: compared approaches between integrated CAD/CAM system and /Small Displacement Torsor[ model, Bath, UK, April 5–7, 2004 IDMME, 2004 [7] R. Benea, C. Fortin, C. Cloutier, Analyse de tole´rances en fabrication tenant compte des proce´de´s et des erreurs machines outils, Revue internationale de CFAO et d’informatique graphique, vol. 17, 2002, pp. 39–59. [8] L. Laperrie`re, W. Ghie, A. Desrochers, Projection of Torsors: a Necessary Step for Tolerance Analysis Using the Unified JacobianTorsor Model, Eighth CIRP International Seminar on Computer Aided Tolerancing, (2003) pp. 14–23. [9] F. Villeneuve, F. Vignat, 3D Synthesis of Manufacturing Tolerances Using a SDT Approach, Eighth CIRP International Seminar on Computer Aided Tolerancing (2003) pp. 279–290. [10] L. Pino, F. Bennis, C. Fortin, De´finition et calcul de la pie`ce virtuelle et re´sultante en assemblage, IDMME 2000, Montre´al, Canada, CD Rom. [11] B. Anselmetti, cotation de fabrication et me´trologie, Editions Herme`s Lavoisier, 2003. [12] T. Raulin, Formalisation d’une me´thodologie de spe´cification ge´ome´trique des e´tats interme´diaires des pie`ces fabrique´es, Bibliographie de DEA de Production Automatise´e, Ecole Normale Supe´rieure de Cachan, LURPA, 2002. [13] D. Duret, De´termination des intervalles de tole´rance en fabrication par une approche graphique, Actes se´minaire Tole´rancement et chaıˆnes de cotes, ENS Cachan, fe´v, 1995. [14] R. Ramesh, M.A. Mannan, A.N. Poo, Error compensation in machine tools—a review: part I: geometric, cutting-force induced and fixturedependent errors, International Journal of Machine Tools and Manufacture 40 (9) (2000) 1235–1256. [15] S.H. Huang, Q. Liu, Rigorous application of tolerance analysis in setup planning, The International Journal of Advanced Manufacturing Technology 2003; 196–207. [16] V. Bhat, E. De Meter, An analysis of the effect of datumestablishment methods on the geometric errors of machined features, International Journal of Machine Tools and Manufacture 40 (13) (2000) 1951–1975. [17] H. Louati, Elaboration et traitement de la cotation de fabrication en 3D en fraisage 3axes, me´moire de recherche, DEA Production Automatise´e, Ecole Normale Supe´rieure de Cachan, juillet, 2004. [18] B. Anselmetti, P. Bourdet, Optimization of a workpiece considering production requirements, Computers in Industry 21 (1993) 23–24.