Performance Plus Software Parameter Definitions

Transcription

1 Performace Plus+ Software Parameter Defiitios/ Performace Plus Software Parameter Defiitios Chapma Techical Note-TG-5 paramete.doc ev-0-03

2 Performace Plus+ Software Parameter Defiitios/2 Backgroud ad Defiitios Total Profile The Total Profile represets the measuremet of a surface profilig istrumet. The Total Profile cotais both roughess ad waviess iformatio. Waviess Waviess is calculated from the Total Profile ad represets the loger spatial wavelegth features of the surface. Waviess over log distaces is typically called form, figure, or bow. Waviess parameters are calculated after removal of the mea Waviess value. Typically, waviess parameters are give by "W sub " where sub is the appropriate subscript for the parameter. For example, W a is the average waviess. oughess The roughess data is calculated by subtractig the Waviess from the Total Profile data. The oughess shows the fier, or shorter, spatial wavelegth features of the surface. Typically, roughess parameters are give by " sub " where sub is the appropriate subscript for the parameter. For example, a is the average roughess. Figure shows the relatioship of Total Profile, Waviess, ad oughess. Figure

3 Performace Plus+ Software Parameter Defiitios/3 Cutoff Filter Legth The cutoff filter legth is a iteratioal stadard defiitio for the filter legth used to produce the waviess ad roughess data. I moder profilig istrumets, this is a digital filter i the aalysis software. The cutoff filter is used to specify the rage of spatial wavelegths (or the spatial frequecies) i the waviess ad roughess data. Thus, roughess umbers, such as a ad MS, are meaigless without specifyig the cutoff filter used i the roughess calculatio. The cocept of the cutoff filter is similar to a high pass filter i electroics. A high pass filter will pass frequecies higher tha its cutoff ad block lower frequecies. For surface profile data, it is useful to describe a high pass filter as passig high spatial frequecies (or short wavelegths). Thus, the user must defie the cutoff filter ad the iteded spatial frequecies for aalysis i either the roughess or waviess data. It is possible to choose ay cutoff filter legth. However, there are five stadard cutoff filter legths that are defied by various stadard orgaizatios. These five cutoff legths represet a method to divide the spatial frequecy iformatio ito differet regios. The three orgaizatios have differet recommedatios for the umber of cutoff filter legths ad the correspodig overall evaluatio legth. Followig is the recommedatio for three curret stadards:! U.S. stadard: For proper statistics, the evaluatio legth should cotai a umber of cutoff filter legths.! ISO (Iteratioal Stadard): The evaluatio legth should cotai oe or more cutoff filter legths.! Germa (DIN 4768) stadard: The evaluatio legth is five times the cutoff filter legth. The followig table shows the five cutoff filter legths ad the recommeded evaluatio legth usig five segmets. The table also shows the umber of sectios for a full 00 mm sca. Our recommedatio is to use at least five cutoff legths for a good statistical evaluatio. Table Stadard Cutoff Filter Defiitios Cutoff Filter Legth (mm) Sca Legth with 5 Cutoff Legths (mm) Number of Sectios for a 00 mm Sca ,

4 Performace Plus+ Software Parameter Defiitios/4 Uits Vertical Scale The vertical scale is typically displayed i Agstroms (Å). Other uits that ca be used iclude, aometers (m), micrometers (µm) ad microiches (µi). Horizotal scale The horizotal scale is typically displayed i metric uits i micrometers (µm). Other possible uits are mm ad microiches (µi). Uit coversios micrometer.0 x 0-6 M µm Agstrom.0 x0-4 µm Å aometer 0 Agstroms m microich oe millioth of a ich µm 254 Å µi oughess Height Parameters oughess parameters are calculated from the roughess data ad typically defied by a "" variable. Followig are defiitios ad examples of these parameters. Several of these defiitios use the term y i to describe the height y at positio I, to describe the umber of poits i the sca (evaluatio legth), λ to describe the cutoff filter legth, ad k to describe the umber of cutoff filter legths. Geeral Parameters The followig parameters are calculated over the etire data set. The calculatio is ot depedet o the umber of cutoff filter legths.

5 Performace Plus+ Software Parameter Defiitios/5 a ad q (MS) Parameters a, oughess Average The roughess average is the most typically used oe umber descriptio to specify the roughess of a surface. The advatage to this parameter is that it teds to provide a average value, less depedet o small spikes such as foud with local defects. The a umber should oly be provided with it s associated cutoff filter legth. A a value quoted without the cutoff filter legth is meaigless. The roughess average does ot provide ay iformatio o the shape or size of surface features. For example, Figure 2 shows four profiles with obviously differet shapes, but the same a value. The formula for the a parameter is: a or a yi y + y2 + y3! + y q, root mea square (MS) roughess The MS value is aother geeral averaged roughess parameter. The MS value is obtaied from the formula:. q or q yi2 2 2 y + y2 + y3! + y 2 2

6 Performace Plus+ Software Parameter Defiitios/6 Figure 2

7 Performace Plus+ Software Parameter Defiitios/7 Peak ad Valley Parameters The followig peak ad valley parameters are calculated over the etire data set. They all provide the maximum or miimum values. p, maximum profile peak height The distace betwee the highest poit of the profile ad the mea lie withi the evaluatio legth. v, maximum profile valley depth The distace betwee the lowest poit of the profile ad the mea lie withi the evaluatio legth. t, maximum height of the profile (or Peak to Valley) The vertical distace betwee the highest ad lowest poits of the profile withi the evaluatio legth. Figure 3 shows a example of these three parameters. These parameters are most sesitive to ay defects, dirt, scratches, or high peaks or deep valleys. Correspodigly, these values will typically be the least repeatable of ay of the parameters. Figure 3 oughess Parameters Calculated Over Segmets

8 Performace Plus+ Software Parameter Defiitios/8 The followig roughess parameters are calculated over several cutoff filter legths to provide a better average value tha p, v ad t. pm, average maximum profile peak height pm is the average of the successive values of pi calculated over the evaluatio legth pm k k pi where pi is the distace betwee the highest poit of the profile ad the mea lie withi each cutoff filter legth. For example, pi is the highest peak i the first cutoff legth, p2 i the secod, etc. pm is the average of idividual p values calculated over successive cutoff filter legths. It provides a more repeatable value for the maximum profile height, especially for a large umber of segmets. Figure 4 shows a example of the pm value. Figure 4

9 Performace Plus+ Software Parameter Defiitios/9 vm, average maximum valley depth vm is the average of the successive values of vi calculated over the evaluatio legth. vm k k vi where vi is the distace betwee the lowest poit of the profile ad the mea lie withi each cutoff filter legth. vm is also a average, ad provides a more repeatable value for the miimum valley depth. Figure 4 shows a example of the vm value. tm, average maximum height tm is the average of the successive values of ti calculated over the evaluatio legth. This parameter is the same as z (DIN) whe there are five cutoff filter legths withi a evaluatio legth. tm k k ti where ti is the vertical distace betwee the highest ad lowest poits of the profile withi each cutoff filter legth. Figure 5 shows a example of the tm value. Figure 5 max is the largest ti withi the evaluatio legth.

10 Performace Plus+ Software Parameter Defiitios/0 max, like t, will ot be as repeatable because it will be more sesitive to local scratches, pits ad peaks. Figure 5 shows a example of max. 3z, average roughess depth This parameter is the mea of the idividual roughess depths. The roughess depth i each cutoff filter legth is defied as the distace betwee the third highest peak ad third lowest valley. Figure 6 k k 3z 3zi where 3zi is the vertical distace betwee the third highest peak ad the third lowest valley withi each cutoff legth. This parameter is useful to calculate a roughess depth, ot icludig the extreme peaks ad valleys. This may be useful for situatios where a wear process chages or smoothes the peaks, ad fills the valleys. See figure 6 for a example of the 3z parameter. z,te-poit oughess Height z is calculated by averagig the five highest peaks ad five lowest valleys over each cutoff legth. The total z is the calculated by averagig over all cutoff legths. z provides the most repeatable value of a peak to valley parameter, sice may averages are used i the calculatio. The equatio for z over oe cutoff legth is give by: 5 z pi + 0 vi

11 Performace Plus+ Software Parameter Defiitios/ The total z calculatio is provided over the etire evaluatio legth by averagig the cotributios of each segmet. Figure 7 shows a example of a z calculatio for oe cutoff filter legth. Figure 7 Waviess Height Parameters The waviess height parameters are calculated after removal of a mea value. The subscript o the W parameter has the same meaig as the parameters. W t W t is the peak to valley height of the waviess profile. W a W a is the waviess average ad the most typically used umber to describe waviess of the surface. The calculatio is similar to a. W q W q is the waviess MS with a calculatio similar to q. W p W p is the maximum peak height of the waviess. It is defied as the distace betwee the highest poit of the waviess profile ad the mea lie withi the evaluatio legth. The calculatio is similar to p. W v W v is the maximum valley depth. It is defied as the distace betwee the lowest poit of the waviess profile ad the mea lie withi the evaluatio legth. The calculatio is similar to v.

12 Performace Plus+ Software Parameter Defiitios/2 Spacig Parameters Several spacig parameters are provided to calculate a averaged spacig. This is especially useful for calculatig the spacig of irregularities o the surface. For example, two sie waves of the same amplitude but differet spacig would have the same a ad q (MS) values, but differet values for a spacig parameter. Two spacig parameters are defied, S m ad S. The spacig parameters are ot depedet o the profile height values. S m, mea spacig of profile irregularities S m is the mea distace of the spacig betwee successive poits as they cross the mea lie. The fial value of S m is calculated over the evaluatio legth. S m S mi where S mi is the legth of the mea lie sectio cotaiig a profile peak ad adjacet profile valley. S, mea spacig of local peaks of the profile The mea spacig of adjacet local peaks, S, is give by: S Si where S i is the spacig of local peaks ad the umber of local peaks. Figures 8 ad 9 show examples of both the S m ad S spacig parameters. These spacig parameters are most useful for examples such as rollig processes, platig, ad visual appearace. Figure 8

13 Performace Plus+ Software Parameter Defiitios/3 Figure 9 Shape Parameters sk, skewess A measure of the asymmetry of the profile about the mea lie sk N y 3 i Nq 3 If the profile is a perfect radom surface, the peaks ad valleys will be equally spread about a height histogram. I this case, sk (skew) 0. If the peaks have bee pushed dow by either a load o the surface, or a abrasio process of oe surface slidig over the other, the the profile peaks will be affected, but ot the valleys. I this case the skew will be egative. A coatig or platig process will typically fill i the valleys while leavig the peaks itact. This results i a positive skew. ku, kurtosis A measure of the sharpess of the histogram. ku N 4 q N y 4 i For a radom profile, the shape of the height histogram will be Gaussia ad the kurtosis 3. If the distributio has a sharp profile the the kurtosis will be greater tha 3. Correspodigly, if the distributio has a broad shape, the the kurtosis will be less tha 3. Oe example is that a sharp diamod tool will ted to produce a kurtosis of less tha 3.

14 Performace Plus+ Software Parameter Defiitios/4 Hybrid Parameters Peak Coutig Peak coutig ca be a useful parameter i situatios where the umber of peaks above a certai threshold ca be of iterest. Examples iclude texture of computer hard disk media, bearig surfaces, ad roll processes. Two peak cout methods or parameters are provided: the stadard Pc, or peak cout desity that icludes values both above ad below the mea lie, ad the High Spot Cout (HSC) that icludes oly values above the mea. Pc, peak cout desity Pc is the umber of couted peaks per uit legth (i cm or iches) measured at a specific peak cout level. The peak cout level is the vertical distace (user set) betwee boudary lies. A couted peak is the a profile irregularity where the profile itersects cosecutively a lower ad a upper boudary lie. Figure 0 shows a example of the upper referece level ad the lower referece level ad the associated umber of peaks. The value is always give as a desity, i peaks/cm. Figure 0

15 Performace Plus+ Software Parameter Defiitios/5 HSC, High Spot Cout The high spot cout couts oly the umber of profile peaks projectig above a user set lie parallel to the mea lie. Figure shows a example of the HSC. Figure Slope Parameters Δa, average absolute slope The average of the rate of chage of the profile height calculated over the evaluatio legth. a i ω where ω i is the surface slope at the ith locatio. The surface slope is the derivative of the height ad ca be expressed as ωi (y i+ -y i )/d where d is the samplig iterval of the data. Δq, root mea square slope The root mea square average rate of chage of the profile height calculated over the evaluatio legth.

16 Performace Plus+ Software Parameter Defiitios/6 q 2 ω i where ω i is the surface slope at the ith locatio. The surface slope is the derivative of the height ad ca be expressed as ω i (y i+ -y i )/d where d is the samplig iterval of the data. Parameter Curves All of the parameter curves ca be calculated o either the roughess, waviess, or total profile. Power Spectrum The power spectrum is a calculatio of the power of idividual spatial frequecies of the profile. The power spectrum is useful to examie the specific amplitudes of various spatial wavelegths. For example, the four profiles i Figure 2 have the same a but differet shapes. The power spectrum would show the distiguishig characteristics of these four profiles. Autocovariace Fuctio The autocovariace fuctio is useful to test for repeatig patters o the surface. Frequetly, a repeatig patter may be difficult to detect i the roughess plot if the amplitude is less tha the backgroud roughess. The autocovariace fuctio provides a method for accetuatig ay periodic features. Amplitude Distributio Fuctio The amplitude distributio fuctio, or height histogram, is useful to examie the distributio of surface features above ad below the mea lie. This fuctio is useful to examie surfaces with ether positive or egative skew, for example, machied surfaces ad/or plated or coated surfaces. Bearig Area Curve The bearig area curve, or cumulative height histogram, is the itegral of the amplitude distributio fuctio. This fuctio is also used to aalyze the cotributios of surface heights for applicatios such as platig, gridig, burishig, etc.