Development of mathematical models for surface roughness parameter prediction in turning depending on the process condition

International Journal of Mechanical Sciences 113 (2016) 120–132

Contents lists available at ScienceDirect

International Journal of Mechanical Sciences journal homepage: www.elsevier.com/locate/ijmecsci

Development of mathematical models for surface roughness parameter prediction in turning depending on the process condition Mite Tomov a,n, Mikolaj Kuzinovski a, Piotr Cichosz b a b

“Ss. Cyril and Methodius” University in Skopje, Faculty of Mechanical Engineering-Skopje, Macedonia Institute of Production Engineering and Automation of the Wroclaw University of Technology, Poland

art ic l e i nf o

a b s t r a c t

Article history: Received 26 January 2016 Received in revised form 12 April 2016 Accepted 28 April 2016 Available online 29 April 2016

This paper presents mathematical models for predicting Rz, Rp, Rv, Ra, RSm and Rmr (c ) roughness parameters based on the kinematical–geometrical copying of the cutting tool onto the machined surface. The feed f , the radius rε and the angles λs , γo, κr have been used as input parameters in mathematical models. In order to increase the mathematical models’ accuracy, as well as their practical applicability, this paper proposes connecting the R-parameter prediction models with the condition of the surface roughness formation process. The parameter of statistic equality of sampling lengths in surface roughness measurement ( SE ) has been used for this purpose. The proposed mathematical models were verified using two different CNC lathes, working pieces made of the material 42CrMo (EN), using finishing inserts. The paper provides the theoretically calculated values, the measured values and the percentage differences between them for the considered R-parameters. The paper proposes an algorithm of steps for predicting and realizing the considered roughness parameters for industrial purposes. & 2016 Elsevier Ltd All rights reserved.

Keywords: Surface roughness R-parameters Mathematical models Surface roughness predication

1. Introduction Surface texture increasingly becomes a dominant factor in the successful operation of mechanical parts. Hence, surface texture or surface roughness becomes the most frequently used parts quality index. Therefore, a great deal of research [1–12] geared towards the development of various optimization methods for surface roughness prediction even in the parts formation stages becomes an increasingly current topic. Generally, the already developed surface roughness prediction methods can be systematized in three groups. The first group contains the experimental methods for surface roughness prediction, based on and developed by the design of experiments [1–3]. This type of research typically ends with a specific mathematical model for surface roughness prediction with a nonlinear shape or a linear shape (regression shape) after the application of logarithmic transformations. The mathematical models developed in such a way contain a certain constant and exponents of independent input values that apply exclusively to the experimental equipment used to perform the experiments. It is precisely this limitation that can be considered the greatest deficiency of this group of models. Another limitation relates to n

Corresponding author. E-mail addresses: [email protected], [email protected] (M. Tomov), [email protected], [email protected] (M. Kuzinovski), [email protected] (P. Cichosz). http://dx.doi.org/10.1016/j.ijmecsci.2016.04.015 0020-7403/& 2016 Elsevier Ltd All rights reserved.

the fact that the input independent values are being considered (change) in a specific hyperspace (framework), and therefore the obtained models pertain only to the researched hyperspace and not beyond it. The second group [4–10] includes the experimental surface roughness prediction methods again based on and developed by the design of experiments, but augmented and expanded using another mathematical method (technique). The most commonly used mathematical methods in this regard include response surface methodology [4,5], regression and neural networks [6–8], expert systems [9,10] etc. These mathematical methods enable the model to include a larger number of impact factors with a view of predicting surface roughness as accurately as possible. Still, the limitations for the first group apply here as well. The third group [11,12] of surface roughness prediction methods rely on the kinematical–geometrical copying of the cutting tool onto the processed surface. Usually, these surface roughness predictions can be found in the catalogs of cutting tools manufacturers. These methods do not have limitations with respect to a particular experimental equipment or hyperspace, but have serious accuracy deficiencies when predicting roughness in specific processing conditions, i.e. cutting regime values. The reason for this is that the analytical formulations for calculating the roughness parameters do not take into consideration the key values, such as the cutting speed V and the cutting depth ap , vital for the proper implementation of the process of transformation of the removed material into a chip.

M. Tomov et al. / International Journal of Mechanical Sciences 113 (2016) 120–132

Another deficiency may also relate to the fact that the research focuses, primarily, on the two parameters Ra and Rt , which cannot uniquely define the roughness profile. The research in this paper firstly aims at developing mathematical models for a specific number of roughness parameters, based on the kinematical–geometrical copying of the cutting tool onto the processed surface, taking into account the impact of as many input values (in addition to f and rε ) as possible, and secondly at linking these models to parameters that provide information on the stability of the process. This objective agrees with the essential reason for the metrology discipline which states that surface metrology must enable full control of surface constitution and provide an understanding of the functionally important surface characteristics.

121

constitution of the surface and its measurement. According to DIN 4760 [19], the real surface simultaneously and integrally contains all types of deviations from first to sixth order. Third to fifth order deviations together form the roughness of the surface. If we look at the explanation of the causes of the third to fifth order deviations (Fig. 1), we will conclude that we can only predict the causes for the third order deviations (cutting tool geometry, feed, cutting depth etc.). The causes of the fourth and fifth order deviations are unpredictable and different for different processes and some of them also depend on the causes for the third order deviations. From the surface roughness measurement point of view, roughness is a derived value, as shown in Fig. 1. The primary profile consists of deviations between the first and second order deviations (Fig. 1). The causes of the first and second order deviations also cannot be completely predicted and directly depend on numerous factors such as the condition of the machine, cutting tool, parameters etc. This suggests that the development of mathematical models for predicting the primary profile parameters (P-parameter), based on the principle of kinematical–geometrical copying of the cutting tool onto the processed surface is unjustified. We can only develop mathematical models that predict the roughness profile parameters (R-parameter) based on the principle of kinematical–geometrical copying.

2. Mathematical models for prediction of the primary profile or roughness profile parameters? The surface roughness prediction models presented in [1–12] refer to the roughness profile. According to international ISO standards, as well as other national standards (ANSI, JIS etc.), like the procedure for obtaining the primary profile, the roughness and waviness profiles presented in [13], the roughness profile is a derived value obtained from the total or the primary profile using the λc and λs profile filters. Many existing researches aim mainly at obtaining accurate roughness profiles and they refer to software filtration and the types of the λc profile filter [14,15], mechanical filtration [16–18] etc. Certain errors in obtaining the roughness profile and the roughness parameters can contribute to serious inaccuracies in the surface roughness prediction models. On the other hand, the contact phenomena (wear, lubrication, friction) occur on the real surface that integrally contains all kinds of first to sixth order deviations according to Tomov et al. [13]. Hence the dilemma: Whether mathematical prediction models for primary parameter (P-parameter), based on the principle of kinematical–geometrical copying, can be developed? To solve this dilemma we will use Fig. 1 which shows the location of the roughness of the surface from the aspect of the

3. Mathematical model postulates We will develop mathematical models for the Rz, Rp, Rv, Ra, RSm and Rmr (c ) R-parameters, as a function of the feed f , the radius rε and the angles λs , γo, κr . The angles λs , γo determine whether a circular part (if both of them equal zero) or an ellipse will be copying onto the processed surface. The angle κr additionally determines the position of the ellipse relative to the processed surface. The angles λs , γo directly impact the process of chip formation. All considered R-parameters, given above, will apply within the sampling length. As we mentioned previously, the mathematical formulations for calculating roughness parameters, based on kinematical–

According to DIN 4760

1. Nominal form removed (least square line or other techniques) 2. Application of the profile filter λs

3rd order: roughness Cutting edge shape, feed or depth of cut the tool.

4th order: roughness Process of chip formation, material deformation during shot peening, boss at galvanic treatment.

5th order: roughness Process of crystallization, surface alteration by chemical reaction, corrosion processes.

Application of the profile filter λc

Roughness profile

measurement

waviness Off-center clamping, form or concentric deviation of a milling cutter, machine or tool vibrations.

Primary profile

In terms of

form deviation Error in the guideways of the machine tool, machine or workpiece deflection, incorrect clamping of workpiece, hardening distortion, wear.

Total profile

constitution

2nd order:

Traced profile

In terms of

1st order:

According to several ISO standards (contact stylus instrument) Fig. 1. Location of the roughness from the aspect of surface constitution and measurement.

6th order: ,,Structure of the material’’.

122

M. Tomov et al. / International Journal of Mechanical Sciences 113 (2016) 120–132

geometrical copying of the cutting tool onto the processed surface, do not take into account processing parameters vital to the correct realization of the process of transformation of the removed material into a chip. These include the cutting speed V and the cutting depth ap . The formation of the surface, or more specifically the surface texture depends not only on the cutting parameters f , V , ap etc. Impact on the texture of the surface, and hence the roughness, have the work piece, with its mechanical properties and thermic preparation, the material of the inserts especially the coatings, the positioning of the tool, the working condition of the machine, the cutting force, the cutting temperatures, the tool wear, the vibrations of the work piece, and especially of the tool etc. The question is how to take into account all of these influential factors when predicting the surface roughness, when most of them depend on one or more other factors. In order to simplify the impacts of all these factors, this research accepts that the roughness profile comprises the roughness profile obtained by kinematical–geometrical copying of the cutting tool with the addition of (distorted by) the profile formed as a result of the other influential factors, i.e. expressed as

R = Rkinem . − geomet . + Rdistorting

(1)

The value of the parameters that describe the Rkinem . − geomet . profile will be determined by the suggested mathematical models, while the influence of Rdistorting will be taken into account using the parameter of statistic equality of sampling lengths in surface roughness measurement ( SE ) [14]. Basically we will attempt to use the SE parameter to feed back to the models for predicting the roughness parameters depending on the stability and the condition of the surface roughness formation process. According to Raja et al. [14], the SE parameter is calculated as follows:

Ksm Ks

SE =

(2)

where Ksm and Ks are coefficients obtained as follows:

Ksm =

2 2 − smin smax 2 smax

(3)

where smax is the value of the maximal standard deviation calculated within the sampling lengths, while smin is the value of the minimal standard deviation calculated within the sampling lengths.

Ks =

s2 sR2

(4)

where s is the standard deviation calculated as the mean value of the individual standard deviations within the sampling length, while sR is the standard deviation calculated for evaluation length of the roughness profile. Eq. (1) expresses not only the simple sum of Rkinem . − geomet . and Rdistorting , but an interaction between Rkinem . − geomet . and Rdistorting , in particular the impact of Rdistorting on Rkinem . − geomet . The R-parameters for which mathematical models will be developed, will be expressed as Rzk − g , Rpk − g , Rvk − g , Rak − g , RSmk − g and Rmr (c )k − g .

4. Derivation of the mathematical models for the R-parameters 4.1. Kinematical–geometrical copying of the cutting tool Planes in the tool-in-hand system [20] and tool angles (turning tool) [20] represent a basis for the setup and the derivation of

mathematical models for different geometries (positive, negative and combined) of the cutting tool. The angles κr , λs and γo define the spatial position of the plane ACD (Fig. 2), containing the tool corner radius, approximated with point D . Fig. 2 shows different positions of the ACD plane relative to the tool reference plane Pr . These positions form the basis for the derivation of the mathematical models. Fig. 2a shows the case with positive λs and γo (greater than zero), Fig. 2b shows the case with negative λs and γo, Fig. 2c shows the case with λs positive and γo negative and Fig. 2d shows the case with λs negative and γo positive. The AB , BC and BD axes are mutually perpendicular. The planes Pr′ and Pr " are parallel to the tool reference plane Pr and the position of the ACD plane, i.e. the angles λs and γo is determined relative to them. The angles ω and σ are additional angles which define the spatial orientation of the plane АCD in relation to the tool reference plane and these angles are used in the mathematical models. The AC (i.e. AC ′ or A′C ) axis is the pivotal axis for the ACD ( AC ′D ; A′CD ) plane. The angle ω shows the rotation of the ACD plane, relative to the reference plane, around the AC (i.e. AC ′ or A′C ) axis. The angles ω and σ as a function of λs and γo are expressed by

⎛ tan λ ⎞ s⎟ σ = arctan⎜⎜ ⎟ ⎝ tan γo ⎠

(5)

⎛ tan γo ⎞ ω = arctan⎜ ⎟ ⎝ cos σ ⎠

(6)

The expressions (5) and (6) apply to all cases shown in Fig. 2. The angle φ is used to determine the position of the AC -axis relative to the rotation axis of the machined part (Fig. 3). Fig. 3 shows that κr = σ + φ , i.e.:

φ = κr − σ

(7)

When the angles λs and γo are different than zero or if only one of the angles is different than zero, the projection of the radius rε onto the reference plane will an ellipse. 4.2. Mathematical models In order to obtain the mathematical models for determining the R-parameters as a function of f , rε , λs , γo and κr we will consider a segment of the deterministic profile (Fig. 4). Angle κr serves solely to determine the angle φ i.e. the position of the axis around which the ACD plane rotates relative to the work piece axis. Because the nose radius of the cutting tool lies on the ACD plane, the angle φ determines the position of the ellipse axes around which it rotates. The Cartesian coordinate system is centered in the center of the ellipse and rotated by an angle φ relative to the rotation axis of the work piece. Because the rake face always rotates around the x-axis, the ellipse semi-major axis equals of the insert nose radius rε , while the semi-minor axis equals rϵ cos ω . To calculate the H value, which will help us determine the Rzk − g parameter, we need to determine the equation for the straight line y1. We know only the direction of the straight line. The location of the line y1 = − x⋅ tan φ + y0 will be determined from the relation of tangency with the ellipse

x2 rε2

In the ellipse equation

y2

+ x

rε2cos2ω 2

rε2

+

y

= 1. 2

rε2cos2ω

= 1, if we substitute the line

equation y = y1 = − x tan ϕ + y0 we obtain:

M. Tomov et al. / International Journal of Mechanical Sciences 113 (2016) 120–132

123

Fig. 2. Different positions of the ACD plane relative to the tool reference plane ( Pr ): (а) λs and γo are positive; (b) λs and γo are negative; (c) λs is positive, γo is negative; and (d) λs is negative, γo is positive;

Fig. 3. Determining the angle ϕ. Fig. 4. Roughness profile segment.

x2(cos2ω + tan2φ) − x2y0 tan φ + y02 − rε2cos2ω = 0 X1/2 =

2y0 tan φ ±

4y02tan2φ − 4(tan2φ + cos2ω)(y02 − rε2cos2ω) 2 2 2(tan φ + cos ω)

one touching (intersection) point we need: or since we have

4y02 tan2φ − 4(tan2φ + cos2ω)(y02 − rε2cos2ω) = 0

124

M. Tomov et al. / International Journal of Mechanical Sciences 113 (2016) 120–132

After

the

reducing

the

equation

we

see

that:

y0 = rε tan2φ + cos2ω . Now we can write that: 2

2

2

2

x

From the intersection of the ellipse

y2 = − x tan φ +

H − Rzk − g cos φ

rε2

+

y

2

rε2cos2ω

(8)

X1/2 =

(

H − Rzk − g cos ϕ

= 1 with the line

H − Rzk − g cos ϕ

2

⎛

) tan φ − 4(tan φ + cos ω)⎜⎝ ( 2

2

2

(

b

and b. In the considered case b − a = f and

H − Rzk − g cos φ

∫a f (x )dx = Psegment .

2

⎞

) − r cos ω⎟⎠ 2 ε

2

2(tg 2φ + cos2ω) the surface area of the triangle (PΔ) formed between the coordinate system center and the points (X1, Y1) and (X2 , Y2). This means

Using the equation X1 − X2 = f ⋅cos φ we obtain:

4

b

Therefore we need to find the surface area Psegment (Fig. 5). We will determine the surface area Psegment by determining the surface area of the sector ( Psector ) between the points (X1, Y1) and (X2 , Y2) minus

we get two intersection points with x-axis

)tan φ ± 4(

b

∫a f (x )dx . Indeed ∫a f (x )dx presents the

surface area bound by the function f (x ), the x -axis and the limits a

coordinates:

2

1 b−a

using the equation

2

H = cos φ⋅y0 = rε sin φ + cos φcos ω = rε 1 − cos φsin ω 2

The determination of the models of the other R-parameters requires the determination of the mean line of the roughness profile. We will determine the mean line of the roughness profile

H − Rzk − g 2

⎛

) tan φ − 4(tan φ + cos ω)⎜⎝ (

cos φ

2

2

2

H − Rzk − g 2 cos φ

⎞

) − r cos ω⎟⎠ 2 ε

2

Psegment = Psector − PΔ First we determine Psector . In order to simplify the calculation we will use polar coordinates, i.e. x = r cos ρ , y = r sin ρ , where

tan2φ + cos2ω = X1 − X2 = f ⋅ cos φ

x2

r = r (ρ) and by substituting in

rε2

+

y2 rε2cos2ω

Hence, after reducing the equation we can express Rzk − g as follows:

r (ρ ) =

Rzk − g = rε 1 − cos2φ⋅sin2ω

the point (X1, Y1)to the angle of the point (X2 , Y2) For the surface area we obtain

rε2(1 − cos2φ⋅sin2ω) −

−

f2 (1 − cos2φ⋅sin2ω)2 4cos2ω

Psector =

(9)

In order to further reduce the expression, we introduce the following replacement t = 1 − cos2φ⋅sin2ω . The reduced expression for Rzk − g will be as follows:

Rzk − g = rε t − If

rε2t −

γo = 0 and

X1/2 =

(

cos ϕ

f t2 4cos2ω

ρ2

r 2(ρ)dρ=

1

1

Psector = 2 rϵ2cos2ω ∫

1 2

∫ρ

ω = arctan

( )=0 tan γo cos σ

and

Psector =

H − Rzk − g cos φ

2

(11)

⎛

) tan φ − 4(tan φ + cos ω)⎜⎝ ( 2

2

2

rϵ2cos2ω 1 − cos2ρsin2ω

1

1 1 + t2

dρ

; dρ =

dt 1 + t2

and for the

t2

1 1 1 + t2

dt 2 sin2ω 1 + t

1

= 2 rϵ2cos2ω ∫

t2

dt

t1 1 + t 2 − sin2ω

t2 1 2 dt r cos2ω 2 ϵ t1 t 2 + cos2ω

∫

=

1 2 1 t ⎤ r cos2ω⎡⎣ cos ω arctg cos ω ⎦⎥ 2 ϵ t1

Psector =

f2 f2 ≈ rε2 − 4 8rε

ρ2

t2

(10)

λs = 0 , we obtain

)tan φ ± 4(

∫ρ

. The angular change ρ is bound by the angle of

t1 1 −

f2 rε2t − t 2 = rε − 4cos2ω

H − Rzk − g

1 2

= 1 we obtain

limits of ρ1 we get t1 = tgρ1 and for ρ2 we get t2 = tgρ2.

2

Eq. (11) is extensively used in the catalogs of cutting tool manufacturers, but also in a great deal of research in the past. In order to find the coordinates of the intersection points we need to go back to the calculated Rzk − g :

2

1 − cos2ρsin2ω

We substitute t = tan ρ; cos2ρ =

t = 1 − cos2φsin2ω = 1, and therefore Rzk − g will be as follows:

Rzk − g = rε t −

rε cos ω

tan ρ2 tan ρ1 ⎤ 1 2 2 ⎡ 1 1 rϵ cos ω⎢ ⎥ − arctan arctan ⎣ cos ω 2 cos ω cos ω cos ω ⎦

If the limits are reversed then we will obtain a negative value, and therefore we write:

Psector =

H − Rzk − g cos φ

2

⎡ tan ρ2 tan ρ1 ⎤ 1 2 − arctan rϵ cos ω⎢ arctan ⎥ ⎣ 2 cos ω cos ω ⎦

⎞

) − r cos ω⎟⎠ 2 ε

2

2(tan2φ + cos2ω) At the same time we know that tan ρ1 =

And we obtain

rϵ2 f2 f cos φ − ± , t 2 4cos2ω H − Rzk − g Y1/2 = − tan φ⋅X1/2 cos φ

Y1 X1

and tan ρ2 =

Y2 X2

and

the formula will be transformed into:

Psector =

X1/2 = sin φ

(12)

⎡ ⎛ ⎞ ⎛ ⎞⎤ Y2 Y1 1 2 rϵ cos ω⎢ arctan⎜ ⎟ − arctan⎜ ⎟⎥ 2 ⎝ X2 cos ω ⎠ ⎝ X1 cos ω ⎠⎦ ⎣

If the change of the function arctan(x )is between −90° and 90°, in order to capture all points we need to make the following

M. Tomov et al. / International Journal of Mechanical Sciences 113 (2016) 120–132

y

Similarly, we need to determine the surface area above the mean line. This, in fact, is equal to the one below the mean line. This will help us find the entire surface area, at a distance of the feed f above and below the mean line. Thus we can calculate the

y1

y2

1

Psegment R-profile

X3/4 =

A (X1,Y1)

P?

Y3/4 =

Psector D

C

(H − Rzk − g + Rpk − g )sin φ ± cos φ⋅cos ω rε2t − (H − Rzk − g + Rpk − g )2

H − Rz k − g+Rpk − g

x

corrections:

) …. (rad) If X < 0 ⇒ K = π + arctan( ) …. (rad) Yi Xi cos ω

Therefore we get

Psector =

1 2 rϵ cos ω( K2 − K1) 2

(16)

rε2 cos ω XY −X Y ( K4 − K3) − 3 4 f 4 3 f

(17)

RSmk − g ≈ f

We need to determine the surface area of the ΔOAB ( Fig. 5).

PΔOAB = PΔ = PΔOBC + PABCD − PΔOAD PΔOBC

− tan φ⋅X3/4

Since the theoretic roughness profile obtained from longitudinal turning is deterministically and periodically replicable, the mean width of the profile elements RSmk − g is adopted to be approximately equal to the feed:

Yi Xi cos ω

i

i

cos φ

The formulation of Rak − g will be the same as for Rpk − g , the only difference being the coordinates (X3, Y3) and (X4 , Y4 ) and we will have two such surface areas. Therefore the mathematical formulation for Rak − g will be as follows:

Rak − g =

(

(15)

t

Fig. 5. Surface area of the ellipse segment.

If Xi ≥ 0 ⇒ Ki = arctan

l

value for Rak − g = l ∫ f (x ) dx where, in the considered case, l = f . 0 In order to achieve this objective we need to find the new points intersecting the middle line:

B (X2,Y2)

O

125

XY = 2 2 2

(18)

If we take a random straight line parallel to y1 and y2 , located between them at a distance c relative to y2 , then the x-axis coordinates intersecting the ellipse can be expressed as

Xi / i + 1 =

2(H − Rzk − g + c )sin φ ± cos φ cos ω rε2t − (H − Rzk − g + c )2 t

The distance between this two points is

PABCD =

PΔOAD =

( X1 − X2)( Y1 + Y2)

2cos ω rε2t − (H − Rzk − g + c )2 Xi − Xi + 1 = cos φ t

2

X1Y1 2

Hence we can determine the material ratio of roughness profile by

PΔOAB = PΔ = PΔOBC + PABCD − PΔOAD =

X1Y2 − X2Y1 2

If we reverse these coordinates then we get a negative value, therefore we write:

PΔ =

X1Y2 − X2Y1 2

rϵ2 cos ω XY −X Y ( K2 − K1) − 1 2 2 2 1 2

Rpk − g =

f

r 2 cos ω XY −X Y = ε ( K2 − K1) − 1 2 2f 2 1 2f

(13)

We will determine the maximum valley depth of the roughness profile Rv , using the formula:

Rvk − g = Rzk − g − Rpk − g

⎞ ⎞2 ⎟ t 2 + c⎟ ⎟ ω ⎠ ⎟⋅100% ⎟ ⎟ ⎟ ⎠

2

4cos

(14)

(19)

( ) = 0 and tan γo cos σ

t = 1 − cos2φsin2ω = 1 and for Rmr (c )k − g we get:

Rmr (c )k − g

We will determine the maximal height of the roughness profile Rpk − g , using the formula:

Psegment

f2

If γo = 0 and λs = 0, we get that ω = arctan

The formula is correct for any position of the points with coordinates (X1, Y1) and (X2 , Y2) in then coordinate system. Now we can determine the surface area of the segment:

Psegment = Psector − PΔ =

Rmr (c )k − g

⎛ ⎛ ⎜ 2 cos ω rε2t − ⎜ rε2t − ⎜ ⎝ = ⎜1 − ⎜ f ⋅t ⎜ ⎜ ⎝

⎛ ⎛ ⎜ 2 rε2 − ⎜ rε2 − ⎜ ⎝ = ⎜1 − ⎜ f ⎜ ⎜ ⎝

f2 4

⎞ ⎞2 ⎟ + c⎟ ⎟ ⎠ ⎟⋅100% ⎟ ⎟ ⎟ ⎠

(20)

Because the mathematical expressions of the considered R-parameters are interdependent, we derived them using a systematically consecutive. 4.2.1. Constraints of the mathematical models When γo = 0, Eq. (5) becomes undefined (arctan 71), and therefore when using equations to calculate R-parameters when γo = 0, the calculations for γo should consider an angle close to zero

126

M. Tomov et al. / International Journal of Mechanical Sciences 113 (2016) 120–132

(for example 0.001°). Also, when the tool cutting edge angle κr = 45∘ , the angles γo and λs cannot have equal values with opposite signs (like γo = 8; λs = − 8), because then Y1 and Y2 in Eq. (12) become zero. In such a case it is recommended to take slightly different values for γo and λs . We have deliberately deviated from the definition of the material ratio of the roughness profile Rmr (c ) ( Rmr (c )k − g ) provided in [21]. The difference is that the parameter Rmr (c ) , according to ISO 4287:1997 [21] is calculated within the evaluation length, while here it is calculated within the sampling length. Therefore we replaced Rt with Rz . This deviation is inevitable because the mathematical formulation (19) directly depends on the other mathematical formulations used to derive the other parameters, derived from the sampling length. All previously mentioned mathematical models apply only when using cutting tools that have a nose radius of the cutting insert (rε ≠ 0), and only when the corner nose radius of the insert copying onto the processed surface (not major cutting edge or minor cutting edge). 4.3. Mathematical models including SE As previously mentioned, in these investigation propose the use of the SE parameter as an indicator of the stability and the conditions of the surface roughness formation process. The authors propose to calculate the roughness R-parameters as follows:

Rz = Rzk − g ⋅e

3SE

(21)

where the parameter Rzk − g is calculated using the formula (10).

Rp = Rpk − g ⋅e2SE

Table 1 Input parameters and their levels. Sr. no.

Parameters

Level 1

Central point

Level 2

1 2

Cutting speed ( V ) (m/min) Feed ( f ) (mm/rev) Tool nose radius ( rε ) (mm) Depth of cut ( ap ) (mm)

150 0.1

185.7 0.173

230 0.3

3 4

0.4 0.4

0.8 0.69

1.6 1.2

Table 2 Experimental plan. No. Piece Segments markings V (m/min)

f (mm/rev)

rε (mm)

ap (mm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0.1 0.1 0.3 0.3 0.1 0.1 0.3 0.3 0.1 0.1 0.3 0.3 0.1 0.1 0.3 0.3 0.173 0.173 0.173 0.173

0.4 0.4 0.4 0.4 1.6 1.6 1.6 1.6 0.4 0.4 0.4 0.4 1.6 1.6 1.6 1.6 0.8 0.8 0.8 0.8

0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 0.69 0.69 0.69 0.69

1

2

3

4

1.1 1.2 1.3 1.4 1.5 2.1 2.2 2.3 2.4 2.5 3.1 3.2 3.3 3.4 3.5 4.1 4.2 4.3 4.4 4.5

150 230 150 230 150 230 150 230 150 230 150 230 150 230 150 230 185.7 185.7 185.7 185.7

(22)

where the parameter Rpk − g is calculated using the formula (13).

Rv = Rvk − g ⋅e 3SE

(23)

where the parameter Rvk − g is calculated using the formula (14).

Ra = Rak − g ⋅e SE

(24)

where the parameter Rak − g is calculated using the formula (17).

RSm = RSmk − g , or

(25)

RSm = RSmk − g ⋅e SE

(26)

where the parameter RSmk − g is calculated using the formula (18).

Rmr (c ) =

Rmr (c )k − g e SE

Fig. 6. The work piece.

(27)

where the parameter Rmr (c )k − g is calculated using the formula (19). As (Eqs. (21)–27) show, here the paper proposes to express the SE parameter using the exponential function f (SE ) = e SE because of the following: – According to (Jack) Feng and Wang [1], Makadia and Nanavati [4], and Ozel and Karpat [6] the use of exponential models to model surface roughness has been generally accepted, – The exponential expression e SE in (Eqs. (21)–27) also preserves the “natural principle” of the roughness modeling process, i.e. in the event of a stable surface roughness formation process then we expect that SE → 0. When SE → 0, the expression e SE → 1, i.e. approaches the theoretically calculated roughness parameter values.

Fig. 7. CNC lathe model OKUMA LB 15-II (C-1S).

M. Tomov et al. / International Journal of Mechanical Sciences 113 (2016) 120–132

127

are multiplied with the expression e SE . The coefficient in front of SE is different for the considered height parameters because the directly measured parameters are more sensitive to the “distorting” of the profile than the average Ra parameter. In realistic conditions, due to “distorting, the Rmr (c ) parameter is expected to have smaller values than the theoretically calculated values and therefore the expression e SE is in the denominator in order to reduce the theoretically calculated values. The RSm parameter is expected to be the least sensitive to “distorting” of the roughness profile, to a certain extent of “distorting”. Therefore we propose two formulations (25) and (26) to calculate this parameter. The experimental verification will show the extent of “distorting” of the roughness profile, which represents the key element in calculating RSm according to the first or the second formulation (equation). Fig. 8. CNC lathe model MORI SEIKI SL-3H.

5. Experimental verification 5.1. Experimental plan

Fig. 9. Surf test model No. SJ-410 (Mitutoyo make).

In realistic processing conditions, the height parameters Rz, Rp, Rv and Ra are expected to have higher values than the theoretically calculated values due to the “distorting” of the roughness profile and therefore the theoretically calculated value

For the experimental verification of the obtained mathematical modules we adopted a planning principle identical to two-level full factorial experimental design. The input parameters are cutting speed (V ), feed ( f ), tool nose radius ( rε ) and depth of cut ( ap ). Although they do not participate in the mathematical models, the reason for inclusion of V and ap was elaborated in item 3. Therefore the number of experiments that will be implemented is 24 = 16, as well as four experiments as a repetition of the input values in the central point, or in total 24 = 16 + 4 = 20 experiments. Table 1 provides the values of the input variables. The input parameter values are in accordance with the recommendations of the insert manufacturer, but we also paid attention to obtain roughness profiles with as large a parameter value span as possible (for example from Ra ¼0.2 to 7.5 μm). Table 2 shows the detailed experiment plan. 5.2. Work piece material The work pieces used in this research are made of steel 42CrMo

Table 3 Roughness parameters – calculated and obtained by measurement of the segments and SE , for Lathe 1. No. Marking on segments

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

1.1 1.2 1.3 1.4 1.5 2.1 2.2 2.3 2.4 2.5 3.1 3.2 3.3 3.4 3.5 4.1 4.2 4.3 4.4 4.5

Roughness parameters – calculated

Roughness parameters – obtained by measurement of the segments

Rzk-g (μm) Rpk-g (μm) Rvk-g (μm)

Rak-g (μm) RSmk-g (μm)

Rmrk-g (30Rz) (%)

Rzm (μm)

Rpm (μm)

Rvm (μm)

Ram (μm)

RSmm (μm)

Rmrm (30Rz) (%)

3.153 3.153 29.347 29.347 0.785 0.785 7.082 7.082 3.153 3.153 29.347 29.347 0.785 0.785 7.082 7.082 4.714 4.714 4.714 4.714

0.808 0.808 7.471 7.471 0.202 0.202 1.816 1.816 0.808 0.808 7.471 7.471 0.202 0.202 1.816 1.816 1.209 1.209 1.209 1.209

16.3 16.3 15.9 15.9 18.4 18.4 16.3 16.3 16.3 16.3 15.9 15.9 15.9 18.4 16.3 16.3 16,3 16.3 16.3 16.3

3.871 3.330 29.026 30.042 1.824 1.638 7.325 7.582 3.724 3.767 29.812 28.192 1.214 1.383 7.632 7.780 6.072 5.927 5.259 5.187

2.397 2.035 19.454 19.960 0.99 0.906 4.696 4.958 2.427 2.328 20.405 18.594 0.622 0.714 4.740 5.051 3.464 3.324 3.301 3.191

1.473 1.290 9.572 10.027 0.834 0.731 2.629 2.623 1.298 1.440 9.406 9.598 0.592 0.669 2.893 2.729 2.608 2.604 1.958 1.997

0.800 0.836 7.292 7.171 0.307 0.379 1.781 1.795 0.805 0.837 7.309 7.004 0.241 0.299 1.815 1.763 1.381 1.405 1.210 1.168

99.4 99.4 299.8 298.9 66.6 94.8 300.5 298.7 98.8 100.9 300.2 298.9 77.5 99.8 297.7 297.9 173.0 172.9 173.0 172.8

13.4 17.2 15.3 14.5 14.2 19.2 15.1 16.4 9.8 13.8 14.3 15.6 15.3 21.2 16.4 14.2 19.4 20.1 15.3 15.3

2.104 2.104 19.713 19.713 0.524 0.524 4.723 4.723 2.104 2.104 19.713 19.713 0.524 0.524 4.723 4.723 3.144 3.144 3.144 3.144

1.049 1.049 9.633 9.633 0.262 0.262 2.359 2.359 1.049 1.049 9.633 9.633 0.262 0.262 2.359 2.359 1.569 1.569 1.569 1.569

100 100 300 300 100 100 300 300 100 100 300 300 100 100 300 300 173 173 173 173

SE

0.059 0.063 0.046 0.049 0.322 0.163 0.062 0.040 0.052 0.059 0.040 0.048 0.287 0.150 0.047 0.042 0.071 0.028 0.032 0.026

128

M. Tomov et al. / International Journal of Mechanical Sciences 113 (2016) 120–132

Table 4 Roughness parameters – calculated and obtained by measuring the segments and SE for Lathe 2. No. Marking on segments

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

1.1 1.2 1.3 1.4 1.5 2.1 2.2 2.3 2.4 2.5 3.1 3.2 3.3 3.4 3.5 4.1 4.2 4.3 4.4 4.5

Roughness parameters – calculated

Roughness parameters – obtained by measurement of the segments

Rzk-g (μm) Rpk-g (μm) Rvk–g (μm)

Rak–g (μm) RSmk-g (μm)

Rmrk-g (30Rz) (%)

Rzm (μm)

Rpm (μm)

Rvm (μm)

Ram (μm)

RSmm (μm)

Rmrm (30Rz) (%)

3.153 3.153 29.347 29.347 0.785 0.785 7.082 7.082 3.153 3.153 29.347 29.347 0.785 0.785 7.082 7.082 4.714 4.714 4.714 4.714

0.808 0.808 7.471 7.471 0.202 0.202 1.816 1.816 0.808 0.808 7.471 7.471 0.202 0.202 1.816 1.816 1.209 1.209 1.209 1.209

16.3 16.3 15.9 15.9 18.4 18.4 16.3 16.3 16.3 16.3 15.9 15.9 15.9 18.4 16.3 16.3 16.3 16.3 16.3 16.3

3.698 3.783 28.693 28.816 1.540 1.767 7.457 8.000 3.798 3.688 31.065 28.640 28.693 1.736 7.401 7.711 5.301 5.843 6.340 5.931

2.123 2.341 19.555 19.449 0.760 0.955 4.659 4.787 2.296 2.299 20.557 19.466 19.555 0.929 4.760 4.789 3.051 3.508 4.083 3.673

1.582 1.441 9.138 9.355 0.779 0.811 2.810 3.213 1.502 1.391 10.508 9.173 9.138 0.806 2.642 2.922 2.250 2.314 2.257 2.257

0.926 0.876 7.070 7.113 0.261 0.356 1.876 1.808 0.866 0.825 7.265 6.948 7.070 0.334 1.679 1.652 1.211 1.239 1.414 1.351

100.0 100.6 280.7 299.8 53.0 65.5 300.4 300.6 99.2 100.2 289.9 288.5 280.7 106.7 297.9 296.3 173.5 173.1 172.7 173.8

17.8 15.3 14.1 13.5 13.4 16.0 17.8 16.3 15.3 12.6 11.6 13.6 9.9 8.4 13.3 15.9 19.2 13.6 13.2 15.7

2.104 2.104 19.713 19.713 0.524 0.524 4.723 4.723 2.104 2.104 19.713 19.713 0.524 0.524 4.723 4.723 3.144 3.144 3.144 3.144

1.049 1.049 9.633 9.633 0.262 0.262 2.359 2.359 1.049 1.049 9.633 9.633 0.262 0.262 2.359 2.359 1.569 1.569 1.569 1.569

100 100 300 300 100 100 300 300 100 100 300 300 100 100 300 300 173 173 173 173

SE

0.054 0.097 0.040 0.053 0.526 0.239 0.048 0.060 0.119 0.129 0.073 0.045 0.415 0.456 0.064 0.070 0.041 0.054 0.041 0.065

Table 5 Differences between the highest and the lowest measured value from five measurements of parameters expressed as percentages (%). No.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Marking on segments

1.1 1.2 1.3 1.4 1.5 2.1 2.2 2.3 2.4 2.5 3.1 3.2 3.3 3.4 3.5 4.1 4.2 4.3 4.4 4.5

Lathe 1

Lathe 2

Rzm (%)

Rpm (%)

Rvm (%)

Ram (%)

RSmm (%)

Rmrm (30Rz) (%)

Rzm (%)

Rpm (%)

Rvm (%)

Ram (%)

RSmm (%)

Rmrm (30Rz) (%)

2.1 3.8 3.3 1.1 13.8 9.4 4.5 1.7 2.9 2.3 1.7 1.1 3.3 20.4 3.0 3.4 1.4 3.2 3.5 3.7

3.9 3.9 3.7 1.3 10.3 12.1 3.0 1.0 6.1 1.7 1.6 2.3 3.7 22.5 3.4 3.3 2.3 2.4 2.1 3.5

3.3 4.2 2.3 4.7 21.9 5.8 7.6 3.8 6.8 6.4 2.7 3.7 2.3 31.3 4.1 4.5 3.6 5.1 6.2 5.0

1.9 1.2 2.5 1.5 8.7 1.8 1.6 1.8 1.8 1.3 1.2 1.8 2.5 3.9 1.1 1.9 0.9 1.2 0.8 0.9

3.6 2.6 0.9 1.5 23.0 8.9 1.0 0.7 2.1 2.8 1.2 0.7 0.9 1.4 1.5 1.2 0.9 0.4 0.6 0.7

14.6 11.0 3.2 9.9 35.5 25.3 9.4 7.0 30.2 14.3 5.5 7.3 3.2 27.0 8.8 10.5 3.0 8.7 4.5 16.0

3.1 3.3 1.0 2.5 14.6 15.7 1.3 1.5 2.7 5.5 2.7 1.7 1.0 13.8 4.6 4.6 3.4 2.3 2.2 5.5

6.1 8.0 1.5 3.9 15.5 12.9 1.6 2.1 3.2 6.3 3.9 2.1 1.5 17.8 3.8 4.4 2.2 2.5 1.2 5.5

5.1 10.6 2.3 3.2 17.8 18.9 3.7 1.9 5.2 9.3 1.3 3.5 2.3 12.7 6.7 4.9 9.6 8.0 5.9 11.5

0.4 2.9 2.1 2.2 21.1 3.6 2.2 1.5 4.3 2.2 1.2 2.4 2.1 10.4 0.8 3.3 1.1 2.0 1.8 1.8

2.1 3.9 33.5 1.5 44.6 30.1 0.8 0.9 1.1 4.6 2.1 1.5 33.5 21.3 1.4 5.1 0.5 1.0 0.8 1.4

32.0 13.8 9.0 7.1 33.5 28.1 9.2 3.0 21.5 37.1 25.2 11.9 48.2 48.2 9.4 4.9 9.4 31.2 11.3 11.0

(EN), or АISI 4140 (USA). The hardness of all piece segments along the entire length ranges from 32 to 34 HRC. The pieces have a special design (Fig. 6), each featuring five segments for processing and one segment for clamping to chuck. The segments for processing are appropriately marked as shown in Table 2. 5.3. Machine and cutting tool The work pieces are processed using two different CNC lathes. The lathe shown in Fig. 7, model OKUMA LB 15-II (C-1S) has variable spindle speed of 38–3800 rpm, feed rate 0.001–1000 mm/ rev and 15 kW spindle drive motor, and will be indicated as Lathe 1 hereinafter in the text. The lathe shown in Fig. 8, model MORI SEIKI SL-3H has a variable spindle speed 37–4000 rpm, feed rate 0.0001–500 mm/rev and 15 kW spindle drive motor, will be

indicated as Lathe 2 hereinafter in the text. The research involves two different CNC lathes in order to increase the reliability of the practical verification, i.e. to get two processing systems with different Rdistorting . The four work pieces are positioned identically in both lathes. From one side the work pieces are clamped in the chuck, while, on the other side, they lean on the tailstock (Figs. 7 and 8). Before processing starts in accordance with the experimental plan, the pieces were processed in order to remove the circular run out from the clamping of the pieces. A coolant was applied during the machining of the pieces. The pieces were processed using a holder designated PSSNR/L 2020-12K (PAFANA), with κr = 45∘ , γo = − 8∘ , λs = 0∘ and cutting finishing inserts designated SNMG 120404-MF, SNMG 120408-MF and SNMG 120416-MF from the Sandvik Coromant.

M. Tomov et al. / International Journal of Mechanical Sciences 113 (2016) 120–132

129

Table 6 Percentage difference between theoretical value and measured average values. No.

Segments marking

Rz

Rp

Lathe 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1.1 1.2 1.3 1.4 1.5 2.1 2.2 2.3 2.4 2.5 3.1 3.2 3.3 3.4 3.5 4.1 4.2 4.3 4.4 4.5

No.

Markingon segments

Lathe 2

A (%)

B (%)

A (%)

 22.8  5.6 1.1  2.4  132.4  108.7  3.4  7.1  18.1  19.5  1.6 3.9  54.6  76.2  7.8  9.9  28.8  25.7  11.6  10.0

 2.9 12.7 13.8 11.7 11.6  28.1 14.1 5.2  1.0  0.2 10.0 16.8 34.7  12.3 6.3 3.0  4.2  15.5  1.5  1.8

 17.3  20.0 2.2 1.8  96.2  125.0  5.3  13.0  20.5  17.0  5.9 2.4  90.3  121.1  4.5  8.9  12.5  24.0  34.5  25.8

1.1 1.2 1.3 1.4 1.5 2.1 2.2 2.3 2.4 2.5 3.1 3.2 3.3 3.4 3.5 4.1 4.2 4.3 4.4 4.5

B (%) 0.1 10.3 13.4 16.2 59.5  10.0 8.9 5.7 15.8 20.6 14.9 14.8 45.2 43.6 13.6 11.8 0.4  5.4  19.0  3.6

C (%)

1.0  3.4 2.4 4.0  52.2  87.6 1.9 1.2 0.4  3.6 2.2 6.2  19.1  48.2 0.1 2.9  14.2  16.2  0.1 3.4

Lathe 2 D (%)

 13.9 3.3 1.3  1.3  89.0  73.0 0.6  5.0  15.3  10.6  3.5 5.7  18.7  36.3  0.4  7.0  10.2  5.7  5.0  1.5

 1.3 14.8 10.0 8.2 0.7  24.9 12.2 3.2  3.9 1.6 4.5 14.3 33.2  0.9 8.6 1.6 4.3 0.1 1.4 3.6

C (%)  0.9  11.2 0.8 1.3  45.1  82.2 1.4  1.4  9.1  9.3  4.3 1.3  40.8  77.4  0.8  1.4 3.0  11.6  29.9  16.8

Lathe 1 D (%) 9.4 8.3 8.5 11.3 49.3  13.1 10.5 10.1 14.0 15.6 9.8 9.8 38.6 28.7 11.3 11.9 10.5  0.1  19.7  2.6

RSm

Lathe 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Lathe 1

Ra

G (%)

Rv

Lathe 2 H (%) 6.7 2.9 6.8 8.6  10.3  59.4 7.8 5.1 5.4 2.3 6.0 10.6 10.6  27.5 4.6 6.9  6.4  12.9 3.0 5.9

G (%)  14.6  8.4 5.4 4.8  29.0  76.2  3.3 0.5  7.2  2.2 2.8 7.0  33.3  65.5 7.5 9.0  0.1  2.5  16.9  11.7

 8.6 1.6 9.1 9.7 23.8  38.8 1.6 6.3 4.9 10.2 9.6 11.1 12.0  5.0 13.2 15.2 3.9 2.9  12.2  4.7

 40.4  23.0 0.6  4.1  218.2  179.2  11.4  11.2  23.7  37.3 2.4 0.4  125.9  155.4  22.6  15.7  66.2  65.9  24.8  27.3

F (%)  17.7  1.7 13.4 10.2  21.1  71.3 7.5 1.5  5.8  15.1 13.4 13.7 4.6  62.8  6.6  2.1  34.5  52.4  13.5  17.8

E (%)  50.8  37.3 5.1 2.9  197.5  209.7  19.1  36.2  43.2  32.6  9.1 4.8  188.3  207.8  12.0  23.8  43.4  47.5  43.9  43.9

F (%)  28.4  2.7 16.0 17.2 38.6  51.4  3.0  13.7  0.2 9.9 12.3 16.9 17.0 21.5 7.5  0.3  26.9  25.4  27.3  18.5

Rrm(30Rz)

Lathe 1 H (%)

E (%)

Lathe 2

I (%)

Lathe 2 J (%)

0.6 0.6 0.1 0.4 33.4 5.2  0.2 0.4 1.2  0.9  0.1 0.4 22.5 0.2 0.8 0.7 0.0 0.0 0.0 0.1

 5.4  5.9  4.6  4.6 8.1  11.6  6.6  3.7  4.1  7.0  4.2  4.5  3.2  16.0  4.0  3.5  7.3  2.8  3.2  2.5

I (%) 0.0  0.6 6.4 0.1 47.0 34.5  0.1  0.2 0.8  0.2 3.4 3.8 32.7  6.7 0.7 1.2  0.3 0.0 0.2  0.5

Lathe 1 J (%)  5.5  10.8 2.6  5.4 10.3 16.8  5.1  6.4  11.7  14.0  3.9  0.6  1.9  68.3  5.8  5.9  4.4  5.6  4.0  7.2

K (%) 17.8  5.9 3.2 8.8 22.7  4.0 7.3  0.8 39.7 15.4 10.1 1.5 23.7  15.2  0.8 13.1  19.3  23.6 6.2 6.2

Lathe 2 L (%) 12.9  12.8  1.3 4.2  6.6  22.4 1.4  5.0 36.5 10.3 6.4  3.4  1.7  33.9  5.6 9.4  28.0  27.1 3.2 3.8

K (%)  9.4 6.2 10.9 14.6 27.2 13.3  9.4 0.1 6.3 22.8 26.7 14.1 46.2 54.6 18.6 2.4  17.9 16.4 18.9 3.9

L (%)  15.4  3.4 7.3 10.0  23.1  10.0  14.8  6.1  5.6 12.2 21.1 10.1 18.5 28.4 13.2  4.7  22.8 11.8 15.5  2.5

A—Percentage difference between theoretical values calculated according to Eq. (10) and measured average values. B—Percentage difference between theoretical values calculated according to Eq. (21) and measured average values. C—Percentage difference between theoretical values calculated according to Eq. (13) and measured average values. D—Percentage difference between theoretical values calculated according to Eq. (22) and measured average values. E—Percentage difference between theoretical values calculated according to Eq. (14) and measured average values. F—Percentage difference between theoretical values calculated according to Eq. (23) and measured average values. G—Percentage difference between theoretical values calculated according to Eq. (17) and measured average values. H—Percentage difference between theoretical values calculated according to Eq. (24) and measured average values. I—Percentage difference between theoretical values calculated according to Eq. (18) and measured average values. J—Percentage difference between theoretical values calculated according to Eq. (26) and measured average values. K—Percentage difference between theoretical values calculated according to Eq. (19) and measured average values. L—Percentage difference between theoretical values calculated according to Eq. (27) and measured average values.

Every workpiece segment is processed using a new cutting edge of the insert, in order to eliminate the effect from the wear of the inserts. 5.4. Measurement equipment and conditions The roughness of the processed segments was measured using

Surf test model No. SJ-410 (Mitutoyo make) ( Fig. 9). The surface roughness was measured at five equally spaced locations around the circumference of the work pieces to obtain the statistically significant data for the test. The measured roughness parameters shown in Tables 3 and 4 are average values from five measurements. The roughness

130

M. Tomov et al. / International Journal of Mechanical Sciences 113 (2016) 120–132

parameters were measured and calculated in accordance with the ISO standard recommendations, i.e. in accordance with the procedure for obtaining the primary profile, the roughness profile and waviness profile presented in [13]. A Gaussian filter of appropriate size equal to the sampling length was used as a λc profile filter. We used two sampling lengths of 0.25 mm and 0.8 mm depending on the value of the RSm. The Rmr (c ) parameter was calculated at a level of 30% of Rz ( 30Rz ) from the highest peak of the roughness profile, i.e. c ¼30% of Rz μm, for all considered roughness profile. A pick-up stylus used had a top angle of 60° and a top radius of 2 μm. A skidless pick-up was used. During the measurements, the instrument was mechanically levelled with respect to the measured surface. The measuring system was calibrated using a type C etalon with Ra ¼2.97 μm, and was verified using a type C etalon with Ra ¼ 6 μm. The used calibration etalons have a measuring uncertainty of 5%. The parameter SE was calculated for a roughness evaluation length (ln ) greater than ln for which the roughness parameters were measured, i.e. the next largest ln recommended by ISO 4288:1996 [22]. The SE value provided in Tables 3 and 4 is an mean value of the five measurements around the circumference of each segment. 5.5. Result and discussion Tables 3 and 4 systematize the values for the considered roughness parameters calculated in accordance with (Eqs. (10), (13), 14), (17), (18) and (19), and the measured values (averages from five measurement) of the processed segments for Lathe 1 and Lathe 2. The roughness parameters obtained by measuring the processed segments will be expressed as Rzm, Rpm , Rvm, Ram , RSmm and Rmr (c )m . In order to obtain information about distortion of the measured R-parameter values, Table 5 provides the differences between the highest and the lowest measured value from five R-parameter measurements expressed in as percentages (%). Table 6 provides the percentage differences between the theoretically calculated values for the parameters Rzk − g , Rpk − g , Rvk − g , Rak − g , RSmk − g , Rmr (c )k − g and the measures values for the roughness parameters, as well as the percentage differences between the theoretical values calculated for the parameters Rz, Rp, Rv, Ra, RSm, Rmr (c ) and the measured values of the roughness parameters for both CNC lathes. The minus sign in front of the percentage differences indicates a measured value greater than the theoretically calculated value. The experiments show that the SE parameter can successfully be used as an indicator of the condition of the process referring to the formation of the surface roughness, i.e. an indicator of the roughness profile condition. For example, this can be seen in Figs. 10–12. Fig. 10 shows a roughness profile with SE ¼0.26, obtained from measuring the segment marked 1.5 from the first work piece. Fig. 11 shows a roughness profile with SE ¼0.09, obtained from measuring the segment marked 2.5 from the second work piece and Fig. 12 shows a roughness profile SE ¼ 0.04, obtained from measuring the segment marked 3.2 from the third work piece. This does not mean that thee roughness profile shown in Fig. 10 was obtained from an unstable machining process. The main reason for the “distortion” of the shape and the deviation from the strictly deterministic shape relates to the ratio between the values of f and rε .The radius of the insert rε ( rε ¼1.6 mm) is multiple times greater than the feed f ( f ¼0.1 mm/rev), and therefore the kinematical–geometrical copying of the cutting tool onto the processed surface is much less apparent than the process of transforming the material into a chip. The results show that increasing the value of the SE parameter leads to greater percentage differences between the highest and lowest measured value out of the five measurements for each

segment (Table 5), as well as greater percentage differences between the theoretically calculated values and the measured values (Table 6). The experiments showed that the inclusion of the input variables V and ap is justified, although they do not participate in the theoretical calculations for the R-parameters. The percentage differences shown in Table 6 suggest that the inclusion of SE in the R-parameter calculation models is quite justified. Perhaps if one considers the percentage differences between the theoretically calculated and the measured values in both cases separately, one may find examples where the theoretical values that do not take into account the SE parameter provide smaller percentage differences. However, if we look at the entire hyperspace of input variables, we can clearly and visibly see the tendencies of obtaining smaller differences between the theoretically calculated values that the take the SE parameter into account, and the measured values, for both lathes. Another positive effect is the change of the sign in front of the percentage differences from “–” to “þ ” in some cases, which suggests that the theoretically calculated value is greater than the measured value which is particularly important when applying the “max-rule” to indication the roughness parameters in technical product documentation. This confirms the expectation that the RSm parameter least sensitive to the “distortion” of the roughness profile. When SE is less than 0.1, then the theoretical calculation of the value of RSm should not include the impact of the “distortion” of the profile, or SE . When SE is greater than 0.1, then the inclusion of SE in the theoretical calculation of the value for RSm is justified. The different approach to the theoretical calculations and measurements also impact the percentage differences of the parameter Rmr (c ) . The theoretic calculation of Rmr (c ) considers the sampling length while the measurements consider the mm 1 0 -1 -2 0

0.5

1

1.5

2

2.5

3

3.5

4 mm

Fig. 10. Roughness profile with SE ¼ 0.26 and Ra ¼ 0.32 μm.

mm 2 0 -2 0

0.5

1

1.5

2

2.5

3

3.5

4 mm

Fig. 11. Roughness profile with SE ¼0.09 and Ra ¼0.84 μm.

mm 20 10 0 -10 0

2

4

6

8

10

12 mm

Fig. 12. Roughness profile with SE ¼0.04 and Ra ¼7.09 μm.

M. Tomov et al. / International Journal of Mechanical Sciences 113 (2016) 120–132

131

theoretically developed models to the real machining process condition, different for different processing systems (machines). This approach facilitates a radical expansion of the area of practical applicability of the developed models. Here the research focuses on the development of mathematical models based on the principle of kinematical–geometrical copying of the cutting tool onto the processed surface. Nevertheless, in the future we need to investigate whether and how this idea can expand to the other methods for predicting roughness parameters. The authors think that the scientific contribution of this research is reflected in the fact that it sets the models for predicting the Rp, Rv and Rmr (c ) parameters, something rarely seen in the research on this topic. Usually, the researchers focus on finding prediction models for the Ra and Rz (Rt ) parameters. Parameter of statistic equality of sampling lengths in surface roughness measurement ( SE ) has proven here to be a successful index that provides information about the condition of the process with respect to surface roughness formation, i.e. an indicator of the roughness profile condition that can be successfully implemented in surface roughness prediction models. We should point out that the obtained percentage differences between the theoretically calculated values for the R-parameters and the measured values do not express only the difference between them, but they also include the errors that occurred during the measurement of the R-parameters. The used type C measurement equipment calibration etalons have a calibration certificate that certifies that they have an uncertainty level of the Ra -parameter of 5%. In addition, the measuring device (Surf test SJ410) can have a specific error (uncertainty). Therefore when the percentage differences between the theoretically measured values are small, we cannot ascertain that they reflect only the differences between the theoretical and the measured values. In addition, we have to emphasize the impact of the selection of a large hyperspace for the input variables, especially f and rε , on the occurrence of large percentage differences between the theoretically calculated values for the R-parameters and the measured values in some cases. During the practical verification, if the authors focused on a carefully selected smaller hyperspace for the input variables, then they could expect to obtain smaller differences between the calculated and the measured values.

Acknowledgments Fig. 13. Algorithm of steps for predicting and realizing the considered roughness parameters for industrial purposes.

evaluation length. 5.5.1. Practical applicability of the research Based on the obtained results and the discussion above, and in order to make this research applicable, Fig. 13 proposes an algorithm of steps for predicting and realizing the considered roughness parameters for industrial purposes. From a practical standpoint, the existence of a “test processing” step may be considered a shortcoming of the algorithm. However this step is unavoidable because it indicates the condition of the process for a specific machine, i.e. SE . In the future, perhaps we should investigate the possibility of modeling (for example through Design of Experiment (DOE)) of SE and instead of having a “test processing” step, obtain the values for SE from the SE model. 6. Conclusion The research presented in this paper further develops the models for predicting surface roughness by directly linking the

The authors would like to use this opportunity to express a great deed of gratitude to the companies SVEMEK DOOEL-Skopje and METALKEJ-Skopje for the technical assistance provided in the processing of the work pieces and measuring the surface roughness.

References [1] (Jack) Feng CX, Wang X. Development of empirical models for surface roughness prediction in finish turning. Int J Adv Manuf Тechnol 2002;20:348–56. [2] Sundaram RM, Lambert BK. Mathematical models to predict surface finish in fine turning of steel, Part 1. Int J Prod Res 1981;19(5):547–56. [3] Choudhury IA, El-Baradie MA. Surface roughness prediction in the turning of high-strength steel by factorial design of experiments. J Mater Process Technol 1997;67:55–61. [4] Makadia AJ, Nanavati JI. Optimisation of machining parameters for turning operations based on response surface methodology. Measurement 2013;46:1521–9. [5] Kahraman F. The use of response surface methodology for prediction and analysis of surface roughness of AISI 4140 steel. Mater Technol 2009;43 (5):267–70. [6] Ozel T, Karpat Y. Predictive modeling of surface roughness and tool wear in hard turning using regression and neural networks. Int J Mach Tools Manuf 2005;45:467–79.

132

M. Tomov et al. / International Journal of Mechanical Sciences 113 (2016) 120–132

[7] Feng CX, Wang XF. Surface roughness predictive modeling: neural networks versus regression. IIE Trans 2003;35:11–27. [8] Lee SS, Chen JC. On-line surface roughness recognition system using artificial neural networks system in turning operations. Int J Adv Manuf Technol 2003;22(7–8):498–509. [9] Liao YG, Hu SJ. An integrated model of a fixture–workpiece system for surface quality prediction. Int J Adv Manuf Тechnol 2001;17:810–8. [10] Rosen B-G, Ohlsson R, Westberg J. Interactive surface modelling, an implementation of an expert system for specification of surface roughness and topography. Int J Mach Tools Manuf 1995;35:317–24. [11] Kuzinovski M, Stamboliska Z, Cichosz P. Engineering of surface layer in material removal machining. J Mater Process Technol 2004;155–156:1451–8. [12] Miko E, Nowakowski Ł. Analysis and verification of surface roughness constitution model after machining process. Procedia Eng 2012;39:395–404. [13] Tomov M, Kuzinovski M, Cichosz P. A new parameter of statistic equality of sampling lengths in surface roughness measurement. Stroj Vestn – J Mech Eng 2013;59(5):339–48. [14] Raja J, Muralikrishnan B, Fu Shengyu. Recent advances in separation of roughness,

waviness and form. J Int Soc Precis Eng Nanotechnol 2002;26:222–35. [15] Raja J, Radhakrishnan V. Digital filtering of surface profiles. Wear 1979;57:147 15. [16] Pawlus P. Mechanical filtration of surface profiles. Measurements 2004;35:325–41. [17] Whitehead SA, Shearer AC, Watts DC, Wilson NH. Comparison of two stylus methods for measuring surface texture. Dent Mater 1999;15:79–86. [18] Pawlus P, Śmieszek M. The influence of stylus flight on change of surface topography parameters. Precis Eng 2005;29(3):272–80. [19] DIN 4760. Gestaltabweichungen. Begriffe. Ordungssustem. Juni 1982. [20] ISO 3002/1-1982 (Е). Basic quantities in cutting and grinding – Part 1: Geometry of the active part of cutting tools – general terms, reference systems, tool and working angles, chip breakers. [21] ISO 4287:1997. Geometrical Product Specifications (GPS) – surface texture: profile method – terms, definitions and surface texture parameters. [22] ISO 4288:1996. Geometrical Product Specifications (GPS) – surface texture: profile method – rules and procedures for the assessment of surface texture.