1、VDA Recommendation February 2007 Geometrical Product Specifications Surface Texture “Robust Gaussian Regression Filter“ Definition and Application VDA 2008 Descriptors: shape deviations, robust profile filter, rules, methods Page 1 of 11 GERMAN ASSOCIATION OF THE AUTOMOTIVE INDUSTRY (VDA) Westendstr
2、ae 61, 60325 Frankfurt Distribution: DOKUMENTATION KRAFTFAHRTWESEN E.V. (DKF) Ulrichstrae 14, D-74321 Bietigheim-Bissingen Preface This VDA Recommendation describes the application of the robust Gaussian regression filter for surface profiles according to ISO DTS 16610-31. Utilizing the robust Gauss
3、ian regression filter al-lows for the determination of a reliable reference line for the roughness of plateau-like surface pro-files of manufactured components. The filter does not take into account deep pores and protruding peaks, which may lead to a falsification of the reference lines position. I
4、t works without running-in and running-out lengths and is able to approximate form components with up to second-degree accuracy. 1 Scope This guideline describes the evaluation of surfaces exhibiting a structured or plateau-like surface roughness, which were measured using the stylus method. Such su
5、rface structures include, for example, hone marks but also laser-molten recesses or silicon crystals of an Al-Si alloy exposed as a result of the machining process. The filter method described in this Recommendation extracts the roughness profile from a plateau-like surface profile without geometric
6、al distortions caused by the filter itself, thereby facilitating a reasonable geometric evaluation of surface roughness according to DIN EN ISO 4287, DIN EN ISO 13565-2, VDA 2005 and VDA 2006. The use of the robust Gaussian regression filter is mandatory if specified in the drawing note in combinati
7、on with the Rk parameters according to DIN EN ISO 13565-2 (see Section 4.2). In this case, the combination of parameter calculation with the special filter method according to DIN EN ISO 13565-1 is not applied. Note: It is recommended to continue using linear profile filters (e.g. acc. to DIN EN ISO
8、 11562) for the evaluation of surfaces showing either a symmetrical amplitude density or a homogeneous roughness structure, such as e.g. ground, turned or milled surfaces. 2 Normative references The following normative documents contain specifications that, through reference in this text, con-stitut
9、e provisions of this VDA Recommendation. For dated references, subsequent amendments or revisions to this publication do not apply. Users of this VDA Recommendation are nevertheless requested to check whether it is possible to use the latest versions of the following normative documents. For undated
10、 references, the latest edition of the normative document referred to ap-plies. Members of ISO and IEC maintain directories of the valid international standards. VDA 2005: 2006-11, Geometrical Product Specifications, Engineering Drawings, Specification of Surface Texture VDA 2006: 2003-07, Geometris
11、che Produktspezifikation (GPS), Oberflchenbeschaffenheit, Regeln und Verfahren zur Beurteilung der Oberflchenbeschaffenheit (Geometrical Product Specification (GPS), Surface Texture, Rules and Meth-ods for Evaluating Surface Texture - only available in German) DIN EN ISO 3274: 1998-04 Geometrical Pr
12、oduct Specifications (GPS), Surface Texture: Profile Method - Nominal Char-acteristics of Contact (Stylus) Instruments (ISO 3274:1996); German Version ENISO ISO3274: 1997 DIN EN ISO 4287: 1998-10 Geometrical Product Specifications (GPS), Surface Texture: Profile Method Terms, Defini-tions and Surfac
13、e Finish Parameters (ISO 4287: 1997); German Version EN ISO 4287: 1998 DIN EN ISO 4288: 1998-04 Geometrical Product Specifications (GPS), Surface Texture: Profile Method Rules and Procedures for the Evaluation of Surface Texture (ISO 4288: 1996); German Version EN ISO 4288: 1997 DIN EN ISO 11562: 19
14、98-09 Geometrical Product Specifications (GPS), Surface Texture: Profile Method - Metrological Characteristics of Phase Correct Filters (ISO 11562: 1996); German Version EN ISO 11562: 1997 The English translation is believed to be accurate.In case of discrepancies the German version shall govern. Nu
15、merical notation according to ISO practice (seeVW 01000). Page 2 VDA 2008: 2007-02 DIN EN ISO 13565-1: 1998-04 Geometrical Product Specifications (GPS) - Surface Texture: Profile Method Surfaces having Stratified Functional Properties Part 1: Filtering and General Measurement Conditions (ISO 13565-1
16、: 1996); German Version EN ISO 13565-1: 1997 DIN EN ISO 13565-2: 1998-04 Geometrical Product Specifications (GPS) - Surface Texture: Profile Method Surfaces having Stratified Functional Properties Part 2: Height Characterization Using the Linear Material Ratio Curve (ISO 13565-2: 1996); German Versi
17、on EN ISO 13565-2: 1997 ISO DTS 16610-31: Geometrical Product Specification (GPS) Filtration Part 31: Robust Profile Filters: Gaussian Filters (ISO DTS 16610-31: 2005) 3 Definitions The following definitions as well as the definitions according to VDA 2005 and VDA 2006 apply to the application of th
18、is standard. 3.1 Robust profile filters A profile filter is referred to as robust, if distinctive profile peaks and profile marks (frequently re-ferred to as outliers) have no considerable falsifying influences on the formation of the reference line. The mean value is determined by an additional amp
19、litude-dependent weighting of profile ordi-nates. This process is referred to as non-linear profile filtering. Due to the non-linear profile filtering, the position of the reference line for roughness evaluation in the primary profile and, accordingly, the roughness profile itself are largely indepe
20、ndent of outliers. 3.2 Difference between linear and robust profile filters In the case of linear profile filters, the average value of profile ordinates is calculated using an am-plitude-independent moving averaging process. The filtering behavior of linear profile filters can thus be characterized
21、 by a transfer function for sine waves of different wavelengths. Due to the amplitude-dependent weighting of profile ordinates, such transfer function does not exist for the robust profile filter. 3.3 Filter running-in and running-out lengths If no additional measures are taken, so called filter run
22、ning-in and running-out lengths, which lead to a reduction of the assessable evaluation length, occur during the profile filtering process. In the case of standardized profile filters according to DIN EN ISO 11562, the filter running-in as well as running-out length ranges between half a limit wavel
23、ength c and an entire one, depending on filter implementation. In contrast, no filter running-in and running-out lengths are involved in the application of the robust Gaussian filter. 3.4 Structural elements relevant to function Surface structures having a significant influence on surface function a
24、re referred to as structural elements relevant to function. An example for such a structural element relevant to function is a hone mark on a cylinder barrel which, due to the fact that it retains oil just like a reservoir, ensures lubrication between cylinder liner and piston ring. 4 Robust Gaussia
25、n regression filter The robust Gaussian regression filter takes into account local characteristics of profile ordinates and can thus be assigned to the class of robust profile filters. Furthermore, the robust Gaussian filter approximates form components with up to second-degree accuracy, which facil
26、itates an un-problematic elimination of metrologically acquired form components. Filter running-in and running-out lengths are not involved in the application of the robust Gaussian filter. Figure 1 illustrates the different filter effects of the linear Gaussian filter according to DIN EN ISO 11562
27、and the robust Gaussian regression filter. The course of the linear filters mean line (illustrated on the left) follows distinct structural elements relevant to function such as profile Page 3 VDA 2008: 2007-02 peaks and valleys. As a consequence, the roughness profile shows protrusions at valley en
28、ds as well as indentations on profile peaks (indicated on the left). Such profile characteristics, which only arise as a result of the filtering process, may have a significant influence on the characteristic val-ues for roughness. Local roughness amplitudes do not have an impact on the course of th
29、e robust Gaussian filters mean line (illustrated on the right). Accordingly, the roughness profile is not falsi-fied and characteristic values for roughness are determined in accordance with the actual surface characteristics. Furthermore, no filter running-in and running-out lengths occur where thi
30、s filter is used. Figure 1 Left: Filter line of the Gaussian filter acc. to DIN EN ISO 11562. The respective roughness profile, from which filter running-in and running-out lengths were removed, is illustrated be-low. Right: Filter line of the robust Gaussian regression filter with the respective ro
31、ughness pro-file illustrated below. In both cases, the wavelength limit was set to (c=0,8 mm). 4.1 Choice of wavelength limit The robust Gaussian regression filter is primarily used in cases where aforementioned distinct structural elements have a significant influence on the filter line position of
32、 the linear Gaussian filter according to DIN EN ISO 11562. The width of structural elements included in the roughness profile should be taken as a guideline when determining the wavelength limit c in the drawing note. In this case, what is taken into ac-count are structural elements relevant to func
33、tion and not distortions. In order to obtain an ap-proximate value for the determination of the wavelength limit, the width of the structural element with the largest lateral dimension in the primary profile is estimated and then multiplied by the fac-tor three. Subsequently, the set of standardized
34、 wavelength limits .; 0,08 mm; 0,25 mm; 0,8 mm; 2,5 mm; 8 mm; . is used as a reference list, from which the next higher wavelength that most closely approximates the triple structural element width is chosen. Example: Let 0,2 mm be the structural element width. Multiplied by three, this yields 0,6 m
35、m. The corresponding wavelength limit is c = 0,8 mm. Further examples can be found in the Appendix. Note: On principle, visual testing of the filter line in the primary profile must be carried out during trial stage in order to ensure correctness of the chosen wavelength limit. In the ideal case, th
36、e filter line only follows the long-wave section of the profile without being influenced by structural elements. If the course of the filter line is significantly influenced in the area of structural elements, the wavelength limit shall be increased accordingly. In contrast, the fil-ter lines wavele
37、ngth limit shall be decreased in cases where the filter line can no longer follow the long-wave section of the profile. If necessary, a compromise between both crite-ria shall be found. The evaluation length shall always be chosen such that a reliable statis-Surface profile with peaks and score mark
38、s Filter lines Roughness profile Roughness profile Gaussian filter acc. to ISO 11562 Robust Gaussian filter Running-in length Running-out length Page 4 VDA 2008: 2007-02 tical evaluation of the surface profile is possible. To this effect, the evaluation length should be taken from the set of standar
39、dized lengths .;0,4mm; 1,25mm; 4mm; 12,5mm; 40mm; . If the surface does not exhibit any distinct structural elements, wavelength limit and evaluation length are chosen according to DIN EN ISO 4288 or DIN EN ISO 13565-1. 4.2 Drawing note In accordance with the specifications concerning drawing notes
40、in VDA 2005, the filter name should always be specified in such notes. In case measuring conditions deviate from “normal“, the filter wavelength limit as well as the number of sampling lengths represent additional items to be specified. In drawing notes, the filter is referred to as “FPRRG“. FPRRG /
41、 Rz 6,3 Figure 2 Example of a drawing note specifying the use of the robust Gaussian regression filter. FPRRG 0.8 x 3 / Rz 6,3 Figure 3 Example of a drawing note specifying the use of the robust Gaussian regression filter in connection with particular measuring conditions. Page 5 VDA 2008: 2007-02 A
42、ppendix A Informative On the following pages, three different surfaces are evaluated using the robust Gaussian regres-sion filter. For comparison, the same surfaces are also evaluated using the Gaussian filter accord-ing to DIN EN ISO 11562. It should be taken into consideration that filter running-
43、in and running-out lengths are involved in the use of the Gaussian filter according to DIN EN ISO 11562. Page 6 VDA 2008: 2007-02 Example 1: Sintered surface Structure-oriented evaluation: width of structure = 0,16 mm; multiplication by three yields 0,48 mm; next higher standard value for wavelength
44、 limit: c = 0,8 mm. Robust Gaussian regression filter Profile 1 with mean line drawn in (robust filtering) Roughness profile (robust filtering) Gaussian filter according to DIN EN ISO 11562 Profile 1 with mean line drawn in (linear filtering) Roughness profile (linear filtering) Page 7 VDA 2008: 200
45、7-02 Example 2: Al-Si surface with structural elements Structure-oriented evaluation: width of structure = 35 m; multiplication by three yields 105 m; next standard value for wavelength limit: c = 0,25 mm. Robust Gaussian regression filter Profile 2 (section) with mean line drawn in (robust filterin
46、g) Roughness profile (robust filtering) Gaussian filter according to DIN EN ISO 11562 Profile 2 (section) with mean line drawn in (linear filtering) Roughness profile (linear filtering) Page 8 VDA 2008: 2007-02 Example 3: Surface with hone marks Structure-oriented evaluation: width of structure = 25
47、 m; multiplication by three yields 75 m; next standard value for wavelength limit: c = 0,08 mm. Robust Gaussian regression filter Profile 3 (section) with mean line drawn in (robust filtering) Roughness profile (robust filtering) Gaussian filter according to DIN EN ISO 11562 Profile 3 (section) with
48、 mean line drawn in (linear filtering) Roughness profile (linear filtering) Page 9 VDA 2008: 2007-02 Appendix B Informative B.1 The general filter equation for the robust Gaussian regression filter The general filter equation for the robust Gaussian regression filter is described by the following op
49、timization problem: () ()11Min :=kk,ipnil k k ,i l ,k l ,k l ,kw,lizw x sx x ,x lk x= . (1) For every point of the filter line w(x0) over the range 0x0lt, the minimization problem shall be solved. Variables and their respective meanings: n number of profile points k position within profile ( 1,.,kn= ) lz l th profile ordinate ( 1,.,ln= ) p degree of polynomial function kw filter line value at position k ,ki i th polynomial coefficient ( 1,.,ip= ) at position k ()sx Gaussian weighting function x scanning length The func
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