機(jī)械加工外文翻譯

1、<p>　　Selection of optimum tool geometry and cutting conditions</p><p>　　using a surface roughness prediction model for end milling</p><p>　　Abstract : </p><p>　　Influence of t

2、ool geometry on the quality of surface produced is well known and hence any attempt to assess the performance of end milling should include the tool geometry. In the present work, experimental studies have been conducted

3、 to see the effect of tool geometry (radial rake angle and nose radius) and cutting conditions (cutting speed and feed rate) on the machining performance during end milling of medium carbon steel. The first and second or

4、der mathematical models, in terms of machining</p><p>　　1、Introduction</p><p>　　End milling is one of the most commonly used metal removal operations in industry because of its ability to remove

5、 material faster giving reasonably good surface quality. It is used in a variety of manufacturing industries including aerospace and automotive sectors, where quality is an important factor in the production of slots, po

6、ckets, precision and dies. Greater attention is given to dimensional accuracy and surface roughness of products by the industry these days. Moreover, surface finish </p><p>　　Surface finish resulting from t

7、urning operations has traditionally received considerable research attention, where as that of machining processes using cutters, requires attention by researchers. As these processes involve large number of parameters,

8、it would be difficult to correlate surface finish with other parameters just by conducting experiments. Modeling helps to understand this kind of process better. Though some amount of work has been carried out to develop

9、 surface finish prediction mo</p><p>　　Establishment of efficient machining parameters has been a problem that has confronted manufacturing industries for nearly a century, and is still the subject of many s

10、tudies. Obtaining optimum machining parameters is of great concern in manufacturing industries, where the economy of machining operation plays a key role in the competitive market. In material removal processes, an impro

11、per selection of cutting conditions cause surfaces with high roughness and dimensional errors, and it is even po</p><p><b>　　2 、Review</b></p><p>　　Process modeling and optimization

12、are two important issues in manufacturing. The manufacturing processes are characterized by a multiplicity of dynamically interacting process variables. Surface finish has been an important factor of machining in predict

13、ing performance of any machining operation. In order to develop and optimize a surface roughness model, it is essential to understand the current status of work in this area. </p><p>　　Davis et al. [3] have

14、investigated the cutting performance of five end mills having various helix angles. Cutting tests were performed on alloy L 65 for three milling processes (face, slot and side), in which cutting force, surface roughness

15、and concavity of a machined plane surface were measured. The central composite design was used to decide on the number of experiments to be conducted. The cutting performance of the end mills was assessed using variance

16、analysis. The affects of spindle speed</p><p>　　As end milling is a process which involves a large number f parameters, combined influence of the significant parameters an only be obtained by modeling. [5] h

17、ave developed a surface roughness model for the end milling of EN32M (a semi-free cutting carbon case hardening steel with improved merchantability). The mathematical model has been developed in terms of cutting speed, f

18、eed rate and axial depth of cut. The affect of these parameters on the surface roughness has been carried out using respo</p><p>　　Since the turn of the century quite a large number of attempts have been mad

19、e to find optimum values of machining parameters. Uses of many methods have been reported in the literature to solve optimization problems for machining parameters. Jain and Jain [8] have used neural networks for modelin

20、g and optimizing the machining conditions. The results have been validated by comparing the optimized machining conditions obtained using genetic algorithms. Suresh et al. [9] have developed a surface rou</p><

21、p>　　3 Methodology</p><p>　　In this work, mathematical models have been developed using experimental results with the help of response surface methodology. The purpose of developing mathematical models rel

22、ating the machining responses and their factors is to facilitate the optimization of the machining process. This mathematical model has been used as an objective function and the optimization was carried out with the hel

23、p of genetic algorithms.</p><p>　　3.1 Mathematical formulation</p><p>　　Response surface methodology (RSM) is a combination of mathematical and statistical techniques useful for modelling and an

24、alyzing the problems in which several independent variables influence a dependent variable or response. The mathematical models commonly used are represented by:</p><p>　　where Y is the machining response, ?

25、 is the response function and S, f , α, r are milling variables and ∈ is the error which is normally distributed about the observed response Y with zero mean.</p><p>　　The relationship between surface roughn

26、ess and other independent variables can be represented as follows， where C is a constant and a, b, c and d are exponents.</p><p>　　To facilitate the determination of constants and exponents, this mathematica

27、l model will have to be linearized by performing a logarithmic transformation as follows:</p><p>　　The constants and exponents C, a, b, c and d can be determined by the method of least squares. The first ord

28、er linear model, developed from the above functional relationship using least squares method, can be represented as follows:</p><p>　　where Y1 is the estimated response based on the first-order equation, Y i

29、s the measured surface roughness on a logarithmic scale, x0 = 1 (dummy variable), x1, x2, x3 and x4 are logarithmic transformations of cutting speed, feed rate, radial rake angle and nose radius respectively, ∈ is the ex

30、perimental error and b values are the estimates of corresponding parameters.</p><p>　　The general second order polynomial response is as given below:</p><p>　　where Y2 is the estimated response

31、based on the second order equation. The parameters, i.e. b0, b1, b2, b3, b4, b12, b23, b14, etc. are to be estimated by the method of least squares. Validity of the selected model used for optimizing the process paramete

32、rs has been tested with the help of statistical tests, such as F-test, chi square test, etc. [10].</p><p>　　3.2 Optimization using genetic algorithms</p><p>　　Most of the researchers have used t

33、raditional optimization techniques for solving machining problems. The traditional methods of optimization and search do not fare well over a broad spectrum of problem domains. Traditional techniques are not efficient wh

34、en the practical search space is too large. These algorithms are not robust. They are inclined to obtain a local optimal solution. Numerous constraints and number of passes make the machining optimization problem more co

35、mplicated. So, it was dec</p><p>　　1.GA work with a coding of the parameter set, not the parameter themselves.</p><p>　　2.GA search from a population of points and not a single point.</p>

36、<p>　　3.GA use information of fitness function, not derivatives or other auxiliary knowledge.</p><p>　　4.GA use probabilistic transition rules not deterministic rules.</p><p>　　5.It is ver

37、y likely that the expected GA solution will be the global solution.</p><p>　　Genetic algorithms (GA) form a class of adaptive heuristics based on principles derived from the dynamics of natural population ge

38、netics. The searching process simulates the natural evaluation of biological creatures and turns out to be an intelligent exploitation of a random search. The mechanics of a GA is simple, involving copying of binary stri

39、ngs. Simplicity of operation and computational efficiency are the two main attractions of the genetic algorithmic approach. The computations are carri</p><p>　　In order to use GA to solve any problem, the va

40、riable is typically encoded into a string (binary coding) or chromosome structure which represents a possible solution to the given problem. GA begin with a population of strings (individuals) created at random. The fitn

41、ess of each individual string is evaluated with respect to the given objective function. Then this initial population is operated on by three main operators – reproduction cross over and mutation – to create, hopefully,

42、a better popu</p><p>　　4 Experimental details</p><p>　　For developing models on the basis of experimental data, careful planning of experimentation is essential. The factors considered for exper

43、imentation and analysis were cutting speed, feed rate, radial rake angle and nose radius.</p><p>　　4.1 Experimental design</p><p>　　The design of experimentation has a major affect on the number

44、 of experiments needed. Therefore it is essential to have a well designed set of experiments. The range of values of each factor was set at three different levels, namely low, medium and high as shown in Table 1. Based o

45、n this, a total number of 81 experiments (full factorial design), each having a combination of different levels of factors, as shown in Table 2, were carried out.</p><p>　　The variables were coded by taking

46、into account the capacity and limiting cutting conditions of the milling machine. The coded values of variables, to be used in Eqs. 3 and 4, were obtained from the following transforming equations:</p><p>　　

47、where x1 is the coded value of cutting speed (S), x2 is the coded value of the feed rate ( f ), x3 is the coded value of radial rake angle(α) and x4 is the coded value of nose radius (r).</p><p>　　4.2 Experi

48、mentation</p><p>　　A high precision ‘Rambaudi Rammatic 500’ CNC milling machine, with a vertical milling head, was used for experimentation. The control system is a CNC FIDIA-12 compact. The cutting tools, u

49、sed for the experimentation, were solid coated carbide end mill cutters of different radial rake angles and nose radii (WIDIA: DIA20 X FL38 X OAL 102 MM). The tools are coated with TiAlN coating. The hardness, density an

50、d transverse rupture strength are 1570 HV 30, 14.5 gm/cm3 and 3800 N/mm2 respectively.</p><p>　　AISI 1045 steel specimens of 100×75 mm and 20 mm thickness were used in the present study. All the specime

51、ns were annealed, by holding them at 850 ?C for one hour and then cooling them in a furnace. The chemical analysis of specimens is presented in Table 3. The hardness of the workpiece material is 170 BHN. All the experime

52、nts were carried out at a constant axial depth of cut of 20 mm and a radial depth of cut of 1 mm. The surface roughness (response) was measured with Talysurf-6 at a 0.8 mm cu</p><p>　　5 Results and discussio

53、n</p><p>　　The influences of cutting speed, feed rate, radial rake angle and nose radius have been assessed by conducting experiments. The variation of machining response with respect to the variables was sh

54、own graphically in Fig. 1. It is seen from these figures that of the four dependent parameters, radial rake angle has definite influence on the roughness of the surface machined using an end mill cutter. It is felt that

55、the prominent influence of radial rake angle on the surface generation could be due </p><p>　　5.1 The roughness model</p><p>　　Using experimental results, empirical equations have been obtained

56、to estimate surface roughness with the significant parameters considered for the experimentation i.e. cutting speed, feed rate, radial rake angle and nose radius. The first order model obtained from the above functional

57、relationship using the RSM method is as follows:</p><p>　　The transformed equation of surface roughness prediction is as follows:</p><p>　　Equation 10 is derived from Eq. 9 by substituting the c

58、oded values of x1, x2, x3 and x4 in terms of ln s, ln f , lnα and ln r. The analysis of the variance (ANOVA) and the F-ratio test have been performed to justify the accuracy of the fit for the mathematical model. Since t

59、he calculated values of the F-ratio are less than the standard values of the F-ratio for surface roughness as shown in Table 4, the model is adequate at 99% confidence level to represent the relationship between the mach

60、ining</p><p>　　The multiple regression coefficient of the first order model was found to be 0.5839. This shows that the first order model can explain the variation in surface roughness to the extent of 58.39

61、%. As the first order model has low predictability, the second order model has been developed to see whether it can represent better or not.</p><p>　　The second order surface roughness model thus developed i

62、s as given below:</p><p>　　where Y2 is the estimated response of the surface roughness on a logarithmic scale, x1, x2, x3 and x4 are the logarithmic transformation of speed, feed, radial rake angle and nose

63、radius. The data of analysis of variance for the second order surface roughness model is shown in Table 5.</p><p>　　Since F cal is greater than F0.01, there is a definite relationship between the response va

64、riable and independent variable at 99% confidence level. The multiple regression coefficient of the second order model was found to be 0.9596. On the basis of the multiple regression coefficient (R2), it can be concluded

65、 that the second order model was adequate to represent this process. Hence the second order model was considered as an objective function for optimization using genetic algorithms. This sec</p><p>　　Using th

66、e second order model, the surface roughness of the components produced by end milling can be estimated with reasonable accuracy. This model would be optimized using genetic algorithms (GA).</p><p>　　5.2 The

67、optimization of end milling</p><p>　　Optimization of machining parameters not only increases the utility for machining economics, but also the product quality toa great extent. In this context an effort has

68、been made to estimate the optimum tool geometry and machining conditions to produce the best possible surface quality within the constraints.</p><p>　　The constrained optimization problem is stated as follow

69、s: Minimize Ra using the model given here:</p><p>　　where xil and xiu are the upper and lower bounds of process variables xi and x1, x2, x3, x4 are logarithmic transformation of cutting speed, feed, radial r

70、ake angle and nose radius.</p><p>　　The GA code was developed using MATLAB. This approach makes a binary coding system to represent the variables cutting speed (S), feed rate ( f ), radial rake angle (α) and

71、 nose radius (r), i.e. each of these variables is represented by a ten bit binary equivalent, limiting the total string length to 40. It is known as a chromosome. The variables are represented as genes in the chromosome.

72、 The randomly generated 20 such chromosomes (population size is 20), fulfilling the constraints on the variab</p><p>　　where xi is the actual decoded value of the cutting speed, feed rate, radial rake angle

73、and nose radius, x(L) i is the lower limit and x(U) i is the upper limit and li is the substring length, which is equal to ten in this case.</p><p>　　Using the present generation of 20 chromosomes, fitness v

74、alues are calculated by the following transformation:</p><p>　　where f(x) is the fitness function and Ra is the objective function.</p><p>　　Out of these 20 fitness values, four are chosen using

75、 the roulette-wheel selection scheme. The chromosomes corresponding to these four fitness values are taken as parents. Then the crossover and mutation reproduction methods are applied to generate 20 new chromosomes for t

76、he next generation. This processof generating the new population from the old population is called one generation. Many such generations are run till the maximum number of generations is met or the average of four select

77、ed fitn</p><p>　　Table 7 shows some of the minimum values of the surface roughness predicted by the GA program with respect to input machining ranges, and Table 8 shows the optimum machining conditions for t

78、he corresponding minimum values of the surface roughness shown in Table 7. The MRR given in Table 8 was calculated by</p><p>　　where f is the table feed (mm/min), aa is the axial depth of cut (20 mm) and ar

79、is the radial depth of cut (1 mm).</p><p>　　It can be concluded from the optimization results of the GA program that it is possible to select a combination of cutting speed, feed rate, radial rake angle and

80、nose radius for achieving the best possible surface finish giving a reasonably good material removal rate. This GA program provides optimum machining conditions for the corresponding given minimum values of the surface r

81、oughness. The application of the genetic algorithmic approach to obtain optimal machining conditions will be quite us</p><p>　　6 Conclusions</p><p>　　The investigations of this study indicate th

82、at the parameters cutting speed, feed, radial rake angle and nose radius are the primary actors influencing the surface roughness of medium carbon steel uring end milling. The approach presented in this paper provides n

83、impetus to develop analytical models, based on experimental results for obtaining a surface roughness model using the response surface methodology. By incorporating the cutter geometry in the model, the validity of the m

84、odel has been en</p><p><b>　　中文翻譯</b></p><p>　　選擇最佳工具，幾何形狀和切削條件利用表面粗糙度預(yù)測(cè)模型端銑</p><p>　　摘要： 刀具幾何形狀對(duì)工件表面質(zhì)量產(chǎn)生的影響是人所共知的，因此，任何成型面端銑設(shè)計(jì)應(yīng)包括刀具的幾何形狀。在當(dāng)前的工作中，實(shí)驗(yàn)性研究的進(jìn)行已看到刀具幾何（徑向前角和

85、刀尖半徑）和切削條件（切削速度和進(jìn)給速度） ，對(duì)加工性能，和端銑中碳鋼影響效果。第一次和第二次為建立數(shù)學(xué)模型，從加工參數(shù)方面，制訂了表面粗糙度預(yù)測(cè)響應(yīng)面方法（丹參） ，在此基礎(chǔ)上的實(shí)驗(yàn)結(jié)果。該模型取得的優(yōu)化效果已得到證實(shí)，并通過了卡方檢驗(yàn)。這些參數(shù)對(duì)表面粗糙度的建立，方差分析極具意義。通過嘗試也取得了優(yōu)化表面粗糙度預(yù)測(cè)模型，采用遺傳算法（ GA ） 。在加文的程式中實(shí)現(xiàn)了最低值，表面粗糙度及各自的值都達(dá)到了最佳條件。</p>

86、;<p><b>　　1 導(dǎo)言</b></p><p>　　端銑是最常用的金屬去除作業(yè)方式，因?yàn)樗軌蚋焖偃コ镔|(zhì)并達(dá)到合理良好的表面質(zhì)量。它可用于各種各樣的制造工業(yè)，包括航空航天和汽車這些以質(zhì)量為首要因素的行業(yè)，以及在生產(chǎn)階段，槽孔，精密模具和模具這些更加注重尺寸精度和表面粗糙度產(chǎn)品的行業(yè)內(nèi)。此外，表面光潔度還影響到機(jī)械性能，如疲勞性能，磨損，腐蝕，潤(rùn)滑和導(dǎo)電性。因此，測(cè)量

87、表面光潔度，可預(yù)測(cè)加工性能。</p><p>　　車削過程對(duì)表面光潔度造成的影響歷來倍受研究關(guān)注，對(duì)于加工過程采用多刀，用機(jī)器制造處理，都是研究員需要注意的。由于這些過程涉及大量的參數(shù)，使得難以將關(guān)聯(lián)表面光潔度與其他參數(shù)進(jìn)行實(shí)驗(yàn)。在這個(gè)過程中建模有助于更好的理解。在過去，雖然通過許多人的大量工作，已開發(fā)并建立了表面光潔度預(yù)測(cè)模型，但影響刀具幾何方面受到很少注意。然而，除了切向和徑向力量，徑向前角對(duì)電力的消費(fèi)有著重

88、大的影響。它也影響著芯片冰壺和修改芯片方向人流。此外，研究人員[ 1 ]也指出，在不影響表面光潔度情況下，刀尖半徑發(fā)揮著重要作用。因此，發(fā)展一個(gè)很好的模式應(yīng)當(dāng)包含徑向前角和刀尖半徑連同其他相關(guān)因素。</p><p>　　對(duì)于制造業(yè)，建立高效率的加工參數(shù)幾乎是將近一個(gè)世紀(jì)的問題，并且仍然是許多研究的主題。獲得最佳切削參數(shù)，是在制造業(yè)是非常關(guān)心的，而經(jīng)濟(jì)的加工操作中及競(jìng)爭(zhēng)激烈的市場(chǎng)中發(fā)揮了關(guān)鍵作用。在材料去除過程中，

89、不當(dāng)?shù)倪x擇切削條件造成的表面粗糙度高和尺寸誤差，它甚至可能發(fā)生動(dòng)力現(xiàn)象：由于自動(dòng)興奮的震動(dòng)，可以設(shè)定在[ 2 ] 。鑒于銑削運(yùn)行在今天的全球制造業(yè)中起著重要的作用，就必要優(yōu)化加工參數(shù)。因此通過努力，在這篇文章中看到刀具幾何（徑向前角和刀尖半徑）和切削條件（切削速度和進(jìn)給速度） ，表面精整生產(chǎn)過程中端銑中碳鋼的影響。實(shí)驗(yàn)顯示，這項(xiàng)工作將被用來測(cè)試切削速度，進(jìn)給速度，徑向前角和刀尖半徑與加工反應(yīng)。數(shù)學(xué)模型的進(jìn)一步利用，尋找最佳的工藝參數(shù)，并

90、采用遺傳算法可促進(jìn)更大發(fā)展。</p><p><b>　　2回顧</b></p><p>　　建模過程與優(yōu)化，是兩部很重要的問題，在制造業(yè)。生產(chǎn)過程的特點(diǎn)是多重性的動(dòng)態(tài)互動(dòng)過程中的變數(shù)。表面光潔度一直是一個(gè)重要的因素，在機(jī)械加工性能預(yù)測(cè)任何加工操作。為了開發(fā)和優(yōu)化表面粗糙度模型，有必要了解目前在這方面的工作的狀況。</p><p>　　迪維斯等

91、人[ 3 ]調(diào)查有關(guān)切削加工性能的五個(gè)銑刀具有不同螺旋角。分別對(duì)鋁合金L65的3向銑削過程（面，槽和側(cè)面）進(jìn)行了切削試驗(yàn)，并對(duì)其中的切削力，表面粗糙度，凹狀加工平面進(jìn)行了測(cè)量。所進(jìn)行的若干實(shí)驗(yàn)是用來決定該中心復(fù)合設(shè)計(jì)的。切削性能的立銑刀則被評(píng)定采用方差分析。對(duì)主軸速度，切削深度和進(jìn)給速度對(duì)切削力和表面粗糙度的影響進(jìn)行了研究。調(diào)查顯示銑刀與左手螺旋角一般不太具有成本效益比。上下銑方面切削力與右手螺旋角，雖然主要區(qū)別在于表面粗糙度大，但不存

92、在顯著差異。 拜佑密等人[ 4 ]研究過工具對(duì)旋轉(zhuǎn)角度，進(jìn)給速度和切削速度在機(jī)械工藝參數(shù)（壓力，摩擦參數(shù)）的影響，為端銑操作常用三種商用工件材料， 11L17易切削鋼，62-35-3易切削黃銅和鋁2024年使用單一槽高速鋼立銑刀。目前已發(fā)現(xiàn)的壓力和摩擦法對(duì)芯片-工具接口減少，增加進(jìn)給速度，并與下降的氣流角，而切削速度已微不足道，對(duì)一些材料依賴參數(shù)，工藝參數(shù)，歸納為經(jīng)驗(yàn)公式，作為職能的進(jìn)給速度和刀具旋轉(zhuǎn)角度為每個(gè)工作材料。不過，研究人員也

93、還有沒有考慮到的影響，如切削條件和刀具幾何同步，而且這些研究都沒有考慮到切削過程的優(yōu)化。</p><p>　　因?yàn)槎算娺^程介入多數(shù)f參量，重大參量的聯(lián)合只能通過塑造得到。曼蘇爾和艾布達(dá)萊特基地[ 5 ]已開發(fā)出一種表面粗糙度模式，為年底銑EN32M（半自由切削碳硬化鋼并改進(jìn)適銷性）。數(shù)學(xué)模型已經(jīng)研制成功，可用在計(jì)算切削速度，進(jìn)給速度和軸向切深。這些參數(shù)對(duì)表面粗糙度的影響已進(jìn)行了響應(yīng)面分析法（丹參）。分別制定了一階

94、方程涵蓋的速度范圍為30-35米/分，一類二階方程涵蓋速度范圍的24-38米/分的干切削條件。 艾爾艾丁等人[ 6 ]開發(fā)出一種表面粗糙度模型，用丹參，為端銑190BHN鋼。為選擇適當(dāng)?shù)慕M合，切割速度和伺服，增加金屬去除率并不犧牲的表面質(zhì)量，多此進(jìn)行了模型建造并繪制隨層等高線圖。 瀚斯曼等人[ 7 ] ，還使用了丹參模式來評(píng)估工件材料表面粗糙度對(duì)加工表面的影響。該模型是銑操作進(jìn)行實(shí)驗(yàn)鋼標(biāo)本。表明表面粗糙度及各項(xiàng)參數(shù)，即切削速度，飼料和切

95、削深度之間的關(guān)系。上述模式并沒有考慮到對(duì)刀具幾何形狀對(duì)表面粗糙度的影響。</p><p>　　自從世紀(jì)之交的相當(dāng)多的嘗試已找到了最佳值的加工參數(shù)。許多方法已經(jīng)被國(guó)內(nèi)外文獻(xiàn)報(bào)道，以解決加工參數(shù)優(yōu)化問題。喬恩和賈殷[ 8 ]用神經(jīng)網(wǎng)絡(luò)建模和優(yōu)化加工條件。結(jié)果已得到驗(yàn)證，通過比較優(yōu)化的加工條件得到了應(yīng)用遺傳算法。 （蘇瑞等人[ 9 ]已開發(fā)出一種表面粗糙度預(yù)測(cè)模型，將軟鋼用響應(yīng)面方法，驗(yàn)證生產(chǎn)因素對(duì)個(gè)別工藝參數(shù)的影響。

96、他們還優(yōu)化了車削加工用表面粗糙度預(yù)測(cè)模型為目標(biāo)函數(shù)。考慮到上述情況，已試圖在這方面的工作，以發(fā)展一個(gè)表面粗糙度的模型與工具幾何形狀和切削條件，在此基礎(chǔ)上的實(shí)驗(yàn)結(jié)果，然后再優(yōu)化，在端銑操作中，它為選拔這些參數(shù)給定了限制。</p><p><b>　　3 方法論</b></p><p>　　在這項(xiàng)工作中，數(shù)學(xué)模型已經(jīng)開發(fā)使用的實(shí)驗(yàn)結(jié)果與幫助響應(yīng)面方法論。旨在促進(jìn)數(shù)學(xué)模型與

97、加工的反應(yīng)及其因素，是要促進(jìn)優(yōu)化加工過程。這個(gè)數(shù)學(xué)模型已被作為目標(biāo)函數(shù)和優(yōu)化進(jìn)行了借助遺傳算法</p><p><b>　　3.1數(shù)學(xué)表達(dá)</b></p><p>　　響應(yīng)面分析法（丹參）是一種有益建模和分析問題的組合數(shù)學(xué)和統(tǒng)計(jì)技術(shù)的方法，在這幾個(gè)獨(dú)立變量的影響力供養(yǎng)變或反應(yīng)。數(shù)學(xué)模型常用的是代表：</p><p>　　而Y是加工回應(yīng)，?是響應(yīng)

98、函數(shù)和S，f，α ， R的銑削變數(shù)和∈是錯(cuò)誤，通常是發(fā)給約觀測(cè)響應(yīng)y為零的意思。</p><p>　　之間的關(guān)系，表面粗糙度及其他獨(dú)立變量可以發(fā)生情況如下：</p><p>　　其中c是一個(gè)常數(shù)，并為A ， B ， C和D的指數(shù)</p><p>　　為方便測(cè)定常數(shù)和指數(shù)，這個(gè)數(shù)學(xué)模型，必須由線性表演對(duì)數(shù)變換如下：</p><p>　　常數(shù)和指