Determination of the Depth of Cut via Surface Integrity

Abstract

The present paper continues the authors’ research in machining process optimization, including the direction of machining parameters optimization. The paper develops an innovative method, via surface integrity, for determining the technological route and the related depths of cut, with respect to machining front faces of cast iron parts. For correctly establishing the depths of the cut, the errors that appear within surface and subsurface layers during the casting process, as well as during machining, must be gradually eliminated. These errors make it necessary to consider the concept of surface integrity. This paper presents the modality of integrating the components of surface integrity into the depth of cut. For the practical use of this method, a new software tool based on a series of mathematical models and a small database was conceived. A case study illustrates how the method is applied and the software tool used to solve a specific application in the case of a belt pulley.

1. Introduction and Literature Review

An important part of process planning refers to establishing the machining parameters. The depth of cut is the parameter that directly influences the machined-surface quality because it interacts with both the surface and subsurface layers of the processed material. The machined-surface quality must not be appreciated only by the surface roughness. A correct assessment must consider the condition and characteristics of the surface, as well as of the subsurface of the processed material. Thus, surface integrity becomes a very important criterion for assessing the quality of the machined surface [1,2]. Surface integrity refers to certain aspects of the surface, such as form, roughness, waviness, lay, and subsurface characteristics such as residual stress, granular plastic flow orientation, and defects (porosity, micro cracks, tears, laps, etc.) [3]. Surface integrity is influenced by various factors, including the machining parameters [4,5,6]. Dumas et al. [7] approach the connection between the rough and finishing tool passes considering the final surface integrity. The final surface integrity is influenced by the previous operations/passes. Surface integrity is specific to each operation. Thus, the concept of Current-Previous Machining Process—CPMP [8] becomes very important. This concept considers that surface roughness Rz_p and the components of S_p generated during the machining process and caused by the casting process must be considered when calculating d_cf (current depth of cut), following Figure 1. Rz_p refers to the surface roughness obtained after the previous operation. S_p refers to the subsurface layer degraded after the previous operation (subsurface defects). The depth of cut must also contain dimensional tolerance obtained at the previous operation (δ_p), flatness deviation obtained after the previous operation (εF_p), and axial clamping error related to the current operation (εCax_c). Among the first researchers who have considered the connection between the depth of cut and machined-surface quality was Kovan [9,10], whose ideas were overtaken by Picos [11], as well. However, at that time, the term surface integrity was not known. This term was first used by M. Field, J. F. Kahles in 1964. In accordance with these papers, the components of d_cf are colinear vectors, as Formula (1) illustrates.

$${\mathrm{d}}_{\mathrm{cf}}\ge {\mathrm{Rz}}_{\mathrm{p}}+{\mathrm{S}}_{\mathrm{p}}+{\mathsf{\delta }}_{\mathrm{p}}+{\mathsf{\epsilon }\mathrm{F}}_{\mathrm{p}}+{\mathsf{\epsilon }\mathrm{Cax}}_{\mathrm{c}}$$

(1)

index p is used for the previous operation, and index c is used for the current operation, so d_cf is to be calculated. In the literature, establishing the depth of cut is approached with respect to the issue of cutting parameters optimization. The depth of cut, as well as the other machining parameters, results based on a mathematical optimization model. Usually, the optimization criterion is an economic one (minimization of cost and time regarding machining operations). The constraints from the mathematical models are connection relations among the parameters related to machining operations. Pratihar [12] overviews the software for modeling certain parameters related to machining operations. The paper considers expert systems. Regarding the turning processes, the considered parameters are feed, depth of cut, speed, and surface roughness. Zhu et al. [13] present connection relations among surface roughness, work piece speed, tool speed, depth of cut, and feed. Baburaj et al. [14] created relations among surface roughness, cutting speed, feed rate, depth of cut, and nose radius. Prasad and Babu [15] have studied how vibration amplitude and tool flank wear were influenced by machining parameters.

Table 1. Optimization techniques for machining parameters.

Paper	Optimization Mathematical Methods
	Traditional	Non-Traditional
[16]	Dynamic programming
[17]		Neural network
[18]	Integer programming
[19]		Simulated annealing, Hooke–Jeeves pattern search
[20]		Genetic algorithm
[21]		Scatter search
[22]		Genetic algorithm
[23]		Genetic algorithm
[24]		genetic algorithm, simulated annealing, ant colony optimization
[25]		Evolutionary strategy
[26]		Particle swarm optimization
[27]		Simulated annealing, genetic algorithm, particle swarm optimization
[28]		Hybrid particle swarm optimization
[29]		Ant colony optimization, pass enumerating
[30]	Quadratic programming
[31]	Quadratic programming	Genetic algorithm
[32]	Dynamic programming
[33]		Hybrid robust differential evolution
[34]		Genetic algorithm, artificial neural network
[35]		Genetic algorithm, simulated annealing, particle swarm optimization
[36]		Cuckoo optimization
[37]		Genetic algorithm, simulated annealing
[38]		Improved flower pollination
[39]		Pareto optimization, artificial neural network
[40]		Genetic programming
[41]		Iterative search, multi-objective genetic algorithm, genetic algorithm
[42]		Intelligent evolutionary algorithm
[43]		Genetic algorithm, cuckoo search, accelerated particle swarm
[44]		Analysis of variance
[45]		Bat algorithm, divide and conquer strategy
[46]	Special linearization method, linear mathematical programming

presents an overview of optimization methods used by certain authors.

Most optimization methods from the analyzed papers consider manufacturing cost maximization as the objective function. However, other papers use other optimization criteria, such as maximization of material removal rate, minimization of production time, minimization of surface roughness, and minimization of cutting temperature. Based on the current literature, it might be appreciated that the optimization mathematical models do not contain enough elements regarding the insurance of the machined-surface quality because they do not consider surface integrity. From this viewpoint, the depth of cut must be understood differently from the speed and feed rate. The depth of cut is directly connected to the surface integrity (Figure 1), and surface integrity is a very important concept used for appraising the machined-surface quality. The present paper develops a method focused on the concept of surface integrity for determining the depth of cut related to the routing sheet for machining front faces of cast iron work pieces.

2. Method Development

This section of the paper develops ideas from previous authors’ research [8], approaching the determination of the technological sequences and the depths of cut for the front-face turning of cast iron parts. The considered basic criterion ensures the final surface integrity.

2.1. Mathematical Models

For determining the depths of cut for the current tool pass (d_cf), the components of surface integrity from the previous pass must be eliminated (integrated into d_cf following Figure 1) to obtain new surface integrity (related to the current pass). This mechanism must work for all passes of the technological route. The technological route contains chained pairs of current and previous operations. Thus, the couple of current and previous operations represents an important link in process planning. Each previous operation becomes current for determining a new depth of cut. The concept of CPMP works in this manner. The mathematical models related to d_cf calculation are structures of relations in which the components of the surface integrity and other variables related to the geometrical errors of the surface to be machined and fixing errors are found. For establishing these mathematical models, certain data gathered by the authors from industrial practice, the searched literature [10,11], and also work in progress results obtained by the authors were considered. These data have been mathematically modeled by regression analysis (using software tools from the Department of Manufacturing Engineering). It was convenient to obtain information regarding the whole layer Rz_p + S_p (sum of previous surface roughness and spoiled superficial layer). From the industrial experience, it resulted that the values of certain parameters from these models depend on the geometric features of the part/billet, as well as on the casting process accuracy grade. The paper considers five casting process accuracy grades in accordance with the industrial practice and ISO 8062-1994 [47]. Grade 1 refers to the most accurate casting process, and grade 5 refers to the less accurate casting process. The casting process accuracy grade is considered by variable cab. The mathematical models for calculating the depths of cut regarding the three types of front-face turning are presented below.

2.1.1. Calculation of the Depth of Cut for Rough Turning

The current operation is rough turning, and the previous operation refers to the cast billet.

$${\mathsf{\delta }}_{\mathrm{cib}}=2\cdot \mathrm{c}1\cdot {\mathrm{Dm}}^{\mathrm{b}1}\cdot {\mathrm{L}}^{\mathrm{b}2}\cdot {\mathrm{c}2}^{\mathrm{cab}},$$

(2)

$${\mathrm{Rz}}_{\mathrm{cib}}+{\mathrm{S}}_{\mathrm{cib}}=\mathrm{c}3\cdot \mathrm{Dm}\cdot \mathrm{cab}+\mathrm{c}4\cdot \mathrm{Dm}+\mathrm{c}5\cdot \mathrm{cab}+\mathrm{c}6,$$

(3)

$${\mathsf{\epsilon }\mathrm{F}}_{\mathrm{cib}}=\mathrm{c}20\cdot {\mathrm{D}}^{\mathrm{b}10},\hspace{1em}\mathrm{D}\in \left[10,\hspace{0.33em}800\right],$$

(4)

$${\mathsf{\epsilon }\mathrm{Cax}}_{\mathrm{rft}}=\mathrm{c}21\cdot {\mathrm{Df}}^{\mathrm{b}11}+\mathrm{c}22\cdot {\mathrm{Df}}^{\mathrm{b}11}\cdot \mathrm{cab},$$

(5)

$${\mathrm{d}}_{\mathrm{rft}}\ge {\mathsf{\delta }}_{\mathrm{cib}}+{\mathrm{Rz}}_{\mathrm{cib}}+{\mathrm{S}}_{\mathrm{cib}}+{\mathsf{\epsilon }\mathrm{F}}_{\mathrm{cib}}+{\mathsf{\epsilon }\mathrm{Cax}}_{\mathrm{rft}}.$$

(6)

2.1.2. Calculation of the Depth of Cut for Semi-Finishing Turning

The current operation is semi-finishing turning, and the previous operation is rough turning.

$${\mathsf{\delta }}_{\mathrm{rft}}=2\cdot \mathrm{c}11\cdot {\mathrm{L}}_{\mathrm{rft}}^{\mathrm{b}6},$$

(7)

$${\mathrm{Rz}}_{\mathrm{rft}}+{\mathrm{S}}_{\mathrm{rft}}=\mathrm{c}12\cdot {\mathrm{cab}}^{\mathrm{b}7},$$

(8)

$${\mathsf{\epsilon }\mathrm{F}}_{\mathrm{rft}}=\mathrm{c}23\cdot {\mathrm{D}}^{\mathrm{b}10},$$

(9)

$${\mathsf{\epsilon }\mathrm{Cax}}_{\mathrm{sft}}=\mathrm{c}24\cdot {\mathrm{Df}}^{\mathrm{b}12},$$

(10)

$${\mathrm{d}}_{\mathrm{sft}}\ge {\mathsf{\delta }}_{\mathrm{rft}}+{\mathrm{Rz}}_{\mathrm{rft}}+{\mathrm{S}}_{\mathrm{rft}}+{\mathsf{\epsilon }\mathrm{F}}_{\mathrm{rft}}+{\mathsf{\epsilon }\mathrm{Cax}}_{\mathrm{sft}}.$$

(11)

2.1.3. Calculation of the Depth of Cut for Finishing Turning

The current operation is finishing turning, and the previous operation is semi-finishing turning.

$${\mathsf{\delta }}_{\mathrm{sft}}=2\cdot \mathrm{c}16\cdot {\mathrm{L}}_{\mathrm{sft}}^{\mathrm{b}9},$$

(12)

$${\mathrm{Rz}}_{\mathrm{sft}}+{\mathrm{S}}_{\mathrm{sft}}=\mathrm{c}17,$$

(13)

$${\mathsf{\epsilon }\mathrm{F}}_{\mathrm{sft}}=\mathrm{c}25\cdot {\mathrm{D}}^{\mathrm{b}10},$$

(14)

$${\mathsf{\epsilon }\mathrm{Cax}}_{\mathrm{fft}}=\mathrm{c}24\cdot {\mathrm{Df}}^{\mathrm{b}12},$$

(15)

$${\mathrm{d}}_{\mathrm{fft}}\ge {\mathsf{\delta }}_{\mathrm{sft}}+{\mathrm{Rz}}_{\mathrm{sft}}+{\mathrm{S}}_{\mathrm{sft}}+{\mathsf{\epsilon }\mathrm{F}}_{\mathrm{sft}}+{\mathsf{\epsilon }\mathrm{Cax}}_{\mathrm{fft}}.$$

(16)

The coefficients and exponents from relations (2)–(16) are presented in

Table 2. Coefficients and exponents from relations (2), …, (16).

c1	b1	b2	c2	c3	c4	c5	c6	c20	b10	c21	b11	c22
0.031	0.153	0.359	1.34	0.0000163	0.000131	0.044	0.357	0.0004	1.3723	0.0274	0.205	0.00432
c11	b6	c12	b7	c23	b10	c24	b12
0.055	0.350	0.0174	1.79	0.000023	1.3723	0.0307	0.254
c16	b9	c17	c25	b10	c24	b12
0.023	0.342	0.05	0.000012	1.3723	0.0307	0.254

and were obtained by regression analysis in accordance with the above explanation.

2.2. CDFTCI Software Tool

The mathematical models (2)–(16) and the database (Table 2) have been integrated into the new software tool named CDFTCI (calculation of depth of cut for facing turning of cast iron), presented as the flow chart in Figure 2 and user interface in Figure 3.

Description of the module CDFTCI: After data input, the determination of the technological sequences for machining the considered front face follows. The decision variable is the roughness Ra. Then, for each technological sequence, calculated are the depths of cut (d_cf), previous dimensions (L_pre), standardized dimensions (L_pren), and the real depths of cut (d_cfreal). The results are stored in Table t(3,3). The coordinating parameter is surface integrity. After calculating a technological sequence, L1 and tft are updated, and the next technological sequence is calculated (if applicable). After closing the cycle controlled by counter p, the billet dimension (L_cib) and the related tolerance (δ_Lcib) are determined. The results are summarized as sequences of multi-pass-facing turning (Table t1(3,4)). The user interface is presented in Figure 3. Description of user–computer interface: The user interface contains four areas. The first area is for data entering (left side) and contains fields for numerical data, buttons for choosing the surface position, the roughness, and the casting process grade. The next area, on the right side, presents a passive image of the part, used as an aid for specifying the mode in which the surface position is established (internal/external), as well as for Dn and Ln. The third area contains three buttons: OK, Part Image, and Close. The Part Image button is for re-displaying the passive image as many times as required. After data validation, the fourth area automatically appears instead of the second area and contains the obtained results.

3. Results of the Case Study

For the belt pulley from din Figure 4 (material EN-GJL-200 cast iron), the following elements are determined: a) the routing sheet and the depths of cut for turning of the front faces having the following dimensions: • ϕ105 with the roughness Ra = 25 and L = 54; •• ϕ72^+0.074 with the roughness Ra = 3.2 and L = 54 and b) the dimensional characteristics of the billet (including the tolerances). By running the software module CDFTCI, the technological sequences for machining the two mentioned front faces were obtained in accordance with Figure 5 and Figure 6. These figures illustrate the obtained results, meaning the values of the depths of the cut, as well as the diameters of the two front faces after machining (the right sides of the figures). It is mentioned that for L = 54, the tolerances for the free dimensions have been adopted (±0.3). In the same manner, similar data have been obtained for the other front faces of the part (necessary for billet design). For determining the billet dimensions, there are also necessary data regarding the cylindrical surfaces of the part (the depths of cut). These data have been obtained using another software developed by the authors and presented in [8]. Thus, the billet shape from Figure 7 has been obtained.

4. Discussion

From the literature review (Section 1), it results that determining the depth of cut is done by machining parameters optimization, considering an economic criterion. The analyzed optimization mathematical models do not include the relationship between the depth of cut and the surface integrity. This aspect might lead to objective function optimization but does not guarantee to obtain the desired machined-surface quality. In the case of Figure 5, the dimension that must be obtained is ϕ105 (external front face), having the roughness Ra = 25 µm and L = 54 mm. CDFTCI software has determined the technological sequence—rough-facing turning with the total depth of cut = 2.5 mm divided into two passes (n = 2). The first pass is made with a depth of cut of 1 mm, and the second one is made with a depth of cut of 1.5 mm. The total depth of cut is determined by considering the surface integrity in accordance with Formula (6). In the case of Figure 6, the dimension that must be obtained is ϕ72^+0.074 (internal front face), having the roughness Ra = 3.2 µm and L = 54 mm. CDFTCI software has determined three technological sequences with depths of cut of 2.1 mm, 0.7 mm, and 0.6 mm, respectively. Rough turning is made by two passes with the depths of cut of 0.9 mm and 1.2 mm, respectively. The depths of cut are also determined by considering the surfaces integrity, in accordance with Formulas (6), (11), and (16). We mention that all these calculations are made by the CDFTCI software tool. The division of the depth of cut into two passes helps the tool protection. The results supplied by the CDFTCI software tool are found on the billet drawing (Figure 7); thus: 53.1 = 54 + 2.5 − 3.4. Final surface integrity is obtained by the process of successive transformations of the previous surface integrity into the current surface integrity, in accordance with Figure 1 and Formula (1). The industrial practice has confirmed the dependence of the components of surface integrity on the geometric features of the part and billet. This finding has allowed the determination of the mathematical models (2)–(16). The semi-finishing technological sequence might be excluded, but, in this case, the depths of cut for rough machining must increase.

5. Conclusions

The present paper falls within process planning and machining process optimization. In this way, the approaches from the paper are aimed at the automatic establishment of routing sheets and a novel modality for calculating the depths of cut. The main conclusions are presented as follows:

(a)

The quality of the machined surface must not be reduced only to the surface roughness;

(b)

Surface integrity is a very important indicator for the assessment of the machined-surface quality, and it is directly related to the performance of a product;

(c)

The surface integrity influences the depth of cut. This means that the material layer having the thickness of the depth of cut must contain all the errors obtained in the surface and subsurface layers in the case of the previous machining operation. This fact is ensured by relations (2)–(16) conceived by the authors;

(d)

Determining the depth of cut requires knowledge of the routing sheet. For the routing sheet, the decisional element is the roughness of the surface to be machined;

(e)

After the routing sheet is known, the CDFTCI software tool calculates the depth of cut for every technological sequence. In this case, the decisional element is surface integrity;

(f)

The present paper leads to a novel approach to machining parameters optimization. First of all, the depths of cut must be calculated in accordance with ensuring the surfaces integrity. Then, the results obtained in this manner must be integrated into mathematical models for machining parameters optimization (into the objective function or/and as constraints);

(g)

The novelty of the present paper refers to the use of the surface integrity concept for establishing the routing sheet and the related depths of cut for turning the front faces of cast iron work pieces. In this way, the authors have developed a new/original software tool named CDFTCI (conceived in Delphi environment). This software is based on a small database associated with the original mathematical relations (2)–(16), whose role is to model the components of surface integrity and other errors;

(h)

The CDFTCI software also contributes to the calculation of the billets’ dimensions regarding the front faces; with respect to the calculation of the billets’ dimensions regarding the cylindrical surfaces, TESEQ and CDCIM software tools must be used [8];

(i)

The CDFTCI software tool could be used as a standalone application, and it might be easily integrated into any CAP system and translated, if necessary, into other programming languages.