Sage Journals: Discover world-class research

Abstract

The present study focuses on the experimental investigation and optimization of compressive residual stress on ball burnished Mg Ze41A alloy. The optimum compressive residual stress value of −182 MPa is obtained at burnishing force of 50 N, speed of 1200 r/min, feed of 150 mm/min and 4 number of passes. Burnishing force and speed are found to be the most sensitive parameters in affecting the compressive residual stress, followed by number of passes and burnishing feed. The demarcation lines in residual stress-burnishing maps of Mg Ze41A alloy are non-parallel and non-uniform, indicating significant interactions among burnishing parameters. Ball burnishing process imparted desired amount of work hardening, which resulted in homogenized (σ_x₁ = σ_x₂) and isotropic stress (σ₁ = σ₂) state. Additionally, the fuzzy logic model has been deployed to estimate the compressive residual stress values at different burnishing conditions. Fuzzy logic model estimated the results with an error of 6.11%. The results demonstrate that ball burnishing process is an effective method in inducing compressive residual stresses on Mg alloy. The outcome of this study can be of great help in enhancing the fatigue performance of small size products.

Keywords

Biomaterials magnesium burnishing residual stress burnishing maps fuzzy interface system

Introduction

The behaviour of metallic components against fatigue performance in automotive, aerospace and power generation industries is determined by fatigue strength. Hence, these industrial sectors always aim at improving the fatigue limit to avoid crack nucleation and fatigue failure of critical components.¹ The most popular methods to improve the service life of the components against cyclic loading are mechanical surface treatments.² They are being used widely to enhance the physical, mechanical and metallurgical properties of cyclic loaded components. The plastic deformation during mechanical treatments results in compressive residual stresses (CRSs), work hardening effect and microstructure changes; thereby improving the fatigue strength significantly. Eventually, these mechanical methods hinder the crack initiation and propagation. On the other side, they also improve corrosion and wear resistance. Among the mechanical surface treatments, burnishing, shot peening, laser shock peening and laser cladding are the popular methods.³ Ball burnishing is a simple, rapid, flexible and economical mechanical surface treatment, which can be performed by using a computer numerical control (CNC) or vertical machining centre (VMC) machine. The process involves the plastic flow of material from “peaks or ridges” to “valleys or depressions” by virtue of small plastic deformation. Ball burnishing process has multiple benefits, as depicted in Figure 1. Ball burnishing process improves the surface finish, surface hardness and induces high CRSs on the surface. As a result, significant improvement in fatigue life, corrosion and wear behaviour can be observed. Also, it can be realized that ball burnishing process can replace shot peening, laser shock peening and laser cladding in inducing CRS.⁴

Figure 1.

Benefits of ball burnishing process.

Ball burnishing process found to induce CRS up to 1 mm, as depicted in Figure 2. The CRS is not maximum on the surface but at a certain depth. In order to balance the stresses in the material, tensile residual stresses are formed after the CRS.⁵ Numerous researchers have explored the potentiality of burnishing process in inducing the CRS on a material. For instance, the effect of burnishing parameters in inducing CRS has been investigated on AISI 8620 steel.⁶ It has been observed that the burnishing force and feed have strong influence on CRS while the effect of speed is nominal. The CRS is highest at highest burnishing force and lowest feed. This might be due to the predominant plastic deformation at higher burnishing force and desirable surface roughness at lower burnishing feed.⁶ Similarly, ball burnishing process has been deployed on 17-4 PH stainless steel to impart CRS on the surface. Burnishing force is found to be the highly influential factor affecting CRS.⁷ A maximum CRS value of −994.6 MPa is observed at a depth of 0.1 mm and also, it has been realized that the residual stresses are more compressive in circumferential direction than axial direction for a cylindrical workpiece.⁷ Similar conclusions are obtained during slide diamond burnishing of 41Cr4 steel. Burnishing force has the strongest effects on CRS and subsequently on fatigue strength and fatigue life.⁸ The state of residual stress during roller burnishing of hot-rolled Mg–12Gd–3Y alloy has been studied to determine its significance against fatigue properties.⁹ It is observed that the maximum CRS (−410 MPa) induced on the hot-rolled surface is greater than that of tensile strength (362 MPa).

Figure 2.

Compressive residual stress (CRS) of ball burnishing process.

The number of passes during burnishing process has an effect on CRS as well. For instance, ball burnishing of EN series steels have revealed that the CRS increases with increase in passes up to certain extent. A maximum CRS of 280 MPa has been observed after two passes in EN series steels.¹⁰ Apart from passes, burnishing speed also has its prominence on CRS. This has been observed during burnishing of TA2 alloy, where the CRS value increases significantly with decrease in burnishing speed. The maximum CRS of −501 MPa is obtained at burnishing speed of 150 mm/min.¹¹ Not only burnishing parameters but also the direction of motion of the burnishing tool on the surface has an effect on CRS. The amount of CRS induced on the surface or sub-surface during burnishing process depends on nature of the material. The magnitude of CRS will be higher for harder materials and lower for soft materials. But, the depth of CRS will be higher for softer materials than that of harder materials.¹² The assistance of ultrasonic vibration during burnishing will have a significant change on the intensity of CRS than the conventional burnishing. For example, ultrasonic assisted ball burnishing of AA6061-T6 alloy induced a maximum CRS of −217 MPa, while the conventional ball burnishing process induced −163 MPa.¹³ In another example, ultrasonic assisted ball burnishing has induced a maximum CRS of 110 MPa on AA6061-T6 alloy at a penetration depth of 0.7 mm, static load of 120 N, vibration amplitude of 14 μm and tungsten carbide ball diameter of 3 mm.¹⁴ Ball burnishing process can be a useful process in transforming the TRS induced during machining process such as turning, milling and grinding etc., into CRS. For instance, the TRS of 1223 MPa formed during turning of AISI 4130 steel has been transformed into CRS of −223.7 MPa by deploying ball burnishing process.¹⁵ Also, it has been observed that the ball burnished surface delayed the fatigue crack propagation in stress concentration zones, thereby improving the fatigue strength drastically.¹⁶

In recent times, machine learning techniques have become quite popular in modelling complex engineering problems precisely and are being regarded as a substitution for classical modelling methods.¹⁷ The popular machine learning techniques can be artificial neural network, adaptive neuro-fuzzy interface system, Fuzzy Logic, Cellular Automata, Hybrid Systems, etc. The fuzzy logic model is an inexact interpretation of an engineering problem by using human linguistic conditions. The fuzzy logic model predicts the response characteristics by a set of fuzzy rules. The fuzzy logic rules are developed by establishing the inter-connection between input variables and response characteristics. Therefore, the fuzzy rules are formulated by the degree of truth rather than Boolean logic.¹⁸ With the ability of estimating the response characteristics quite effectively, the fuzzy logic model has been instrumental for wide range of industrial applications. For instance, the material removal rate of high speed steel during electrochemical machining has been estimated by fuzzy logic model effectively. The model predicted the material removal rate with an accuracy of 97.25%.¹⁹ The choice of linguistic terms and membership function (MF) decide the precision of fuzzy logic model. Fuzzy logic modelling of multi-responses of AISI 1095 steel during electric-discharge machining has revealed that the best predicted results are obtained by considering triangular MF for input parameters and trapezoidal MF for output responses.²⁰ The UTS and elongation of friction stir welded copper joints has been estimated by fuzzy modelling. The maximum UTS of 276.1 MPa and elongation of 44.6% is obtained by fuzzy model.²¹ Similarly, mechanical properties of abaca fibre reinforced polymer composites is predicted by fuzzy logic with an accuracy of 87%. The results obtained are slightly inaccurate as the input data is not sufficient enough to model the problem. Therefore, sufficient data sets are to be created before adopting fuzzy logic modelling.²²

From the state of the art review, it can be understood that the experimental investigation on CRS during ball burnishing process is very limited. In fact, there are no studies related to the optimization of ball burnishing process for maximum CRS. Also, the effect of major burnishing parameters on CRS has been studied to an extent, but deep insights into the relationship are yet to be reported. The rare earth base Mg alloy, Ze41A alloy was originally developed for gear box applications in the aerospace industry. However, with the nature of biodegradability and biocompatibility, it is now being explored for biomedical applications such as orthopaedic implants and cardiovascular stents. In the current study, attention is paid to examine the capability of ball burnishing process in inducing CRS on Mg Ze41A alloy at different burnishing conditions. Also, the effect of each burnishing parameter on CRS has been explored. An attempt has been made to optimize the ball burnishing process for maximum CRS using Taguchi method. Finally, the popular soft computing technique, fuzzy logic is deployed to estimate the CRS value of ball-burnished magnesium alloy in different test cases. The predictive capability of the technique has been determined by a validation study.

Methodology

CNC burnishing process

The ball burnishing process has been carried out in a vertical head CNC machine. The process is deployed on rare earth base magnesium (Ze41A) alloy, which has a chemical composition of Zirconium 0.54%, Cerium 0.61%, Zinc 5.4%, Manganese 0.02%, Iron 0.003%, and rest Magnesium. The workpiece of dimensions 70 × 70 × 25 mm³ has been parted off from the casted block of Mg Ze41A alloy with a plan of executing 25 burnishing experiments, as shown in Figure 3(a). Each burnishing experiment is performed on 8 × 8 mm² and parted by 5 mm on the workpiece consecutively. After the ball burnishing operation, each burnishing region is separated by wire-EDM cut, as shown in Figure 3(b). Now, each sample has been evaluated for CRS on the burnished surface (Figure 3(c)). It is important to mention that the workpiece is milled before performing burnishing operation, such that the surface roughness of R_a = 0.941 μm has been obtained initially. Figure 4 represents the innovative ball burnishing tool used for experimentation. The shank with circular cross section has been designed for mounting the tool into the tool holder and the mandrel is designed in such a way that it holds the rotating tungsten carbide ball (ϕ8 mm) firmly. The rotating ball will be assisted during the contact with workpiece by three tungsten balls (ϕ4 mm).

Figure 3.

(a) Design of workpiece, (b) burnished samples, (c) burnished sample geometry.

Figure 4.

Ball burnishing tool for burnishing operation.

The ball burnishing experiments are conducted on ‘CNC Fanuc series oi Mate-MC’, which is having an accuracy of 1 μm. Ball burnishing process demands for such high precession CNC machines as burnishing force is highly sensitive parameter. The other specifications include spindle power 11 kW and maximum spindle speed 4000 r/min. The preliminary experiments have provided great assistance in selecting the range of each burnishing parameter. The burnishing parameters and their corresponding levels are provided in Table 1. Each burnishing parameter has been varied in five levels to apprehend the non-linear interactions in ball burnishing process appropriately.⁴ An illustration of experimental set-up has been showcased in Figure 5(a)–(c). The workpiece is fixed firmly on the CNC machine to ensure no fluctuations during operation. The initial milled and burnished surfaces are cleaned with alcohol to remove foreign contaminants and hard particles from the surface. The initial milling experiments are also performed on the same CNC machine with a speed of 1000 r/min, feed of 100 mm/min and depth of cut 1 mm. Surface integrity measurements after milling operation has revealed the microhardness of 75.2 HV and surface roughness (R_a) of 0.941 μm.

Figure 5.

An illustration of (a), (b) experimental set-up in VMC (c), (d) workpiece and burnished samples after wire-EDM cut.

Table 1.

The levels of the burnishing parameters.

Parameter	Unit	Level
Parameter	Unit	1	2	3	4	5
Burnishing force	N	30	40	50	60	70
Burnishing feed	mm/min	100	125	150	175	200
Burnishing speed	r/min	1000	1100	1200	1300	1400
Number of passes	—	1	2	3	4	5

CRS measurement

Compressive residual stress during ball burnishing process has been evaluated by PANalytical X-pert diffractometer. X-rays of wavelength (λ = 0.1542 nm) are being generated by applying current of 35 mA and voltage of 40 kV with copper (Cu) as the anode material. During burnishing operation, the surface will be subjected to stress, which results in crystal lattice structure changes due to the plastic flow of the material. This results in change of crystallographic interplanar spacings between the planes. These crystallographic spacings behave as internal strain gauges and change the strain consequently based on Bragg's law of diffraction. Bragg's angle of 2θ = 104.37° and the corresponding crystallographic planes {1 1 2} have been used to determine residual strains. The X-rays are diffracted on the sample at different tilt angles (ψ), and the corresponding crystallographic interplanar distance (d_ψ) is recorded and then sin² ψ method is deployed to evaluate residual stresses. The residual stress from sin² ψ method has been evaluated by equation (1).

σ_{R S} = \frac{E}{(1 + ν) S i n^{2} φ} (\frac{d_{φ} - d_{0}}{d_{0}})

(1)

E represents Young's modulus and

ν

represents Poisson's ratio of the ball-burnished Mg Ze41A alloy. ψ is the angle between the normal vectors of the sample surface and diffraction plane and d₀ is the distance between crystallographic planes when ψ is zero. The features of the burnished surface are determined and plotted as ‘d_ψ-sin² ψ’ at different ψ angles. The Young's modulus (E) and poisson's ratio (

ν

) are considered as 44 GPa and 0.35 respectively.

Results and discussion

The Taguchi method is a powerful and robust tool for process optimization in an industry. It designs the experiments using an orthogonal array and subsequently, the analysis is carried out by using signal-to-noise ratio (S/N). The quantities ‘signal’ and ‘noise’ indicate the desirable and undesirable value of the performance characteristics respectively. The optimum process condition derived from the S/N ratios of Taguchi method is found to be stable, robust, and results in minimum process variation. In the current investigation, Taguchi method with L₂₅ orthogonal array has been used for ball burnishing process optimization. The orthogonal array is designed by considering the levels of parameters, as depicted in Table 1. The main focus of the study is to maximize the CRS induced during ball burnishing process. Therefore, ‘larger the better’ type characteristic is chosen for obtaining the best CRS value. Positive value of CRS has been considered for computing S/N ratio of CRS. The experimental data and S/N ratio of each test have been presented in Table 2. The S/N ratio of CRS has been evaluated from equation (2).

η = - 10 \log_{10} ({CRS}^{- 2})

(2)

Table 2.

Taguchi results of ball burnishing process.

S No	Burnishing force (N)	Burnishing speed (r/min)	Burnishing feed (mm/min)	No of passes	Mean compressive residual stress (MPa)	S/N ratio of compressive residual stress
1	30	1000	100	1	−48	33.62
2	30	1100	125	2	−73	37.27
3	30	1200	150	3	−145	43.23
4	30	1300	175	4	−137	42.73
5	30	1400	200	5	−56	34.96
6	40	1000	125	3	−109	40.75
7	40	1100	150	4	−141	42.98
8	40	1200	175	5	−110	40.83
9	40	1300	200	1	−61	35.71
10	40	1400	100	2	−85	38.59
11	50	1000	150	5	−81	38.17
12	50	1100	175	1	−131	42.35
13	50	1200	200	2	−125	41.94
14	50	1300	100	3	−149	43.46
15	50	1400	125	4	−129	42.21
16	60	1000	175	2	−113	41.06
17	60	1100	200	3	−89	38.99
18	60	1200	100	4	−121	41.66
19	60	1300	125	5	−117	41.36
20	60	1400	150	1	−93	39.37
21	70	1000	200	4	−74	37.38
22	70	1100	100	5	−77	37.73
23	70	1200	125	1	−97	39.74
24	70	1300	150	2	−101	40.09
25	70	1400	175	3	−61	35.71

Role of burnishing force in inducing CRS

The influence of burnishing force on CRS has been depicted in Figure 6. It can be observed that the CRS value increases with an increase in burnishing force up to 50 N and decreases further. When the burnishing force is low, the penetration of the rotating ball into the work surface will be very little, thereby cause incomplete deformation of the asperities. As a result, the strain hardening induced on the burnished surface is low and hence, the CRS value is low. As the force increases steadily, the protrusion of the rotating ball will be high and the deformation zone widens, resulting in high-strain hardening. This phenomenon has been observed up to a burnishing force of 50 N. Therefore, the maximum value of CRS has been obtained at 50 N burnishing force. However, the CRS value decreases as the rotating ball advances further, due to severe plastic deformation and excessive strain hardening of the burnished layers of Mg Ze41A surface. This leads to distortion and flaking at extremely high burnishing forces and apparently the value of CRS is low. Therefore, the CRS value decreases beyond 50 N burnishing force. The earlier reports on the burnishing of non-ferrous materials have revealed that the CRS value has been reduced up to a certain burnishing force. Experimental exploration on ball burnishing of Mg Ze41A alloy also compliments these findings. The interactions between the burnishing force and other burnishing parameters are presented in Figure 7. The crossed lines in the interaction plot represent that the burnishing force interacts with the other burnishing parameters significantly. Similar findings are also observed during analysis of variance (ANOVA) analysis, as described in the ‘ANOM and ANOVA of CRS’ section. Hence, the burnishing force has to be rightly chosen for achieving the best CRS value. Also, a comprehensive analysis related to interaction of burnishing force and burnishing speed has been provided in section ‘RsB maps’ as residual stress-burnishing (RsB) map.

Figure 6.

Main effects plot of compressive residual stress (CRS).

Figure 7.

Interaction effects plot of compressive residual stress (CRS).

Role of burnishing speed in inducing CRS

The effect of burnishing speed on CRS value can be found in Figure 6. The CRS value at the initial burnishing speed is observed to be lower. Although the penetration time of the burnishing ball is high at low speeds the plastic deformation induced on the surface is quite less. The burnishing effect has been found to impart elastic deformation at low burnishing speeds. As a result, the elastic recovery is found to be higher and subsequently low work hardening and thereby low residual stress. However, with the increase in burnishing speed, the CRS value increases. This is perhaps due to the increase in plastic deformation and the lateral material flow of the strain hardened surface. Also, the interfacial temperature at the junction of the rotating ball and the workpiece rises. All these factors contribute for the high residual stresses on the burnished surface. The results reveal that the burnishing speed of 1200 r/min has yielded the best CRS value. But, the CRS value decreases with increase in burnishing speed further. This might be due to excessive strain hardening and lateral material flow. At higher burnishing speeds, the lateral material flow will be higher due to heavy centrifugal action. As a result, the material gets dispersed laterally to long distances, which results in excessive strain hardening. Consequently, the surface gets damaged and results in low CRS value. Therefore, it is advisable to adopt medium burnishing speed for achieving the best CRS value. The reduction in CRS value at higher burnishing speeds has been observed during burnishing of AISI 8620 Steel⁶ and Mg-0.8Ca alloy, which closely concur with the results of Mg Ze41A alloy. The interaction plot (Figure 8) of Mg Ze41A alloy showcases very severe interactions between burnishing speed and other process parameters as the lines are crossed at multiple locations. Therefore, the burnishing speed has to be chosen accurately for achieving the best CRS value. In order to elucidate the interaction further, a detailed discussion has been presented in the ‘RsB maps’ section as RsB map.

Figure 8.

RsB maps of ball burnished Mg Ze41A alloy (the unit of CRS is MPa). RsB: residual stress-burnishing; CRS: compressive residual stress.

Role of burnishing feed in inducing CRS

Along with burnishing force and speed, burnishing feed also has an influence on surface roughness, microhardness, and CRS during ball burnishing operation. The role of burnishing feed in inducing CRS has been explicitly represented in Figure 6. The lowest CRS value at low burnishing feed is pertaining due to excessive cold work and large plastic deformation. This might be due to the burnishing ball deformations at a particular place are higher at lower burnishing feed. As a result, the longitudinal material flow is higher, which resulted in severe strain hardening. However, with increase in burnishing feed, the CRS value increases and attains maximum value at burnishing feed of 150 mm/min. The longitudinal material flow decreases with increase in burnishing feed, which results in desirable plastic deformation and cold work. Therefore, the ball burnishing process yields the best CRS value at medium burnishing feed. On the other hand, the CRS value is lower at higher burnishing feeds. This could be due to insufficient burnishing at higher burnishing speeds. This results in less material flow in longitudinal direction and inadequate cold work. Also, at high burnishing feeds, incoherent deforming action of the rotating ball has been observed, which resulted in instability of burnishing tool. Burnishing feed has been found to interact with the most influential burnishing parameters such as burnishing force and speed profoundly, as depicted in Figure 7. Therefore, the burnishing feed has to be chosen in synchronize to burnishing force and speed. Similar research work related to ball burnishing of engineering materials support the findings of present study on Mg Ze41A alloy.

Role of passes in inducing CRS

The elastic recovery during plastic deformation of ball burnished surface can be monitored by number of passes. Hence, it is always recommended to adopt multiple passes during burnishing of metals. However, it is essential to know the influence of multiple passes on CRS. Figure 6 shows the state of residual stress with increase in passes. The elastic recovery in plastic zone can not be prevented by single pass. Therefore, the intensity of strain hardening will be lowered, resulting in lower cold work. Apparently, the lower CRS value has been attained at single pass. As the passes increase, the elastic recovery increases and thereby the intensity of strain hardening increases, subsequently the cold work will be higher. Therefore, increase in the CRS value has been observed for multiple passes and this phenomenon continues till four passes. This shows that the elastic recovery in plastic zone has been prevented completely by four passes. On the other hand, the CRS value decreases after four passes. This could be due to over-strain hardening effect and flaking of the surface. The interaction plot (Figure 7) reveals that the interactions of passes with other burnishing parameters is reasonable and has to considered during ball burnishing operation. The experimental investigation on ball burnished Mg Ze41A alloy establishes that the intensity of CRS increases with increase in burnishing force, speed, feed and passes, reaches the highest value and decreases further. Also, it has been found that the basic characteristics of CRS for burnished MgCa0.8 alloy in the literature can be transferable to Mg Ze41A alloy.

Analysis of means and ANOVA of CRS

The analysis of means (ANOM) has been carried out by using S/N ratios of CRS to decide the optimal level of parameters in the ball burnishing process. The optimum level of the burnishing parameter is chosen based on the highest S/N ratio. The ANOM results based on the S/N ratios of CRS have been presented in Table 3. It can be revealed that the best CRS value has been obtained at 50 N burnishing force, 1200 r/min burnishing speed, 150 mm/min burnishing feed and four passes. Further, the ANOVA has been carried out based on the S/N ratio of CRS value to elucidate the prime importance of each burnishing parameter and the results are tabulated in Table 4. The analysis is performed at confidence level of 95%, such that the level of significance is maintained as 0.05. In the present investigation, the significance level is found to be less than 0.05, which indicates that the burnishing parameters will have a direct influence on CRS value. The results emphasize that burnishing force (26.78%) and burnishing speed (26.08%) have the high relative importance in maximizing the CRS value; while burnishing feed and number of passes have low-relative importance.

Table 3.

ANOM of CRS.

Level	Burnishing force	Burnishing speed	Burnishing feed	Number of passes
1	38.36	38.20	39.01	38.16
2	39.77	39.86	40.27	39.79
3	41.63	41.48	40.77	40.43
4	40.49	40.67	40.54	41.39
5	38.13	38.17	37.80	38.61
Delta	3.50	3.31	2.97	3.24
Rank	1	2	4	3

ANOM: analysis of mean; CRS: compressive residual stress.

Table 4.

ANOVA of CRS.

Source	DF	Adj SS	Adj MS	F-value	P-value	Percentage cont
Burnishing force	4	49.94	12.48	2.58	0.012	26.78
Burnishing speed	4	48.64	12.16	2.54	0.011	26.08
Burnishing feed	4	37.25	09.31	1.85	0.021	19.97
Number of passes	4	40.86	10.21	2.06	0.017	21.97
Error	8	09.78	01.22			05.24
Total	24	186.47				100

ANOVA: analysis of variance; CRS: compressive residual stress.

Evaluation of optimum results

The optimum level of burnishing parameters has been determined from ANOM results of CRS. However, the optimum burnishing condition obtained for the best CRS value has not been in the list of L₂₅ orthogonal array. Therefore, the CRS value at optimum burnishing condition has been estimated using S/N ratios. The S/N ratio (η_opt) of CRS at optimum CRS condition is estimated by equation (3).

η_{o p t} = m + \sum_{j = 1}^{p} [{(m_{i, j})}_{max} - m]

(3)

where (m_i,j)_max is the S/N ratio of the best combination level (i) of burnishing parameter (j), m is the mean S/N ratio and p is the number of ball burnishing parameters. Now, the estimated value of CRS has been calculated by using equation (1). The estimated value at optimum burnishing condition is found to be −188 MPa. The estimated value of Taguchi method has been validated by experimental trials and tabulated in Table 5. It can be realized that Taguchi method estimated the CRS value at optimum condition with an error of 3.30%. As the percentage error is quite low, Taguchi method can be considered as a reliable and feasible method for optimizing the residual stresses during ball burnishing of metallic alloys.

Table 5.

Optimum burnishing parameters for compressive residual stress (CRS).

Parameter	CRS
Optimum condition	3,3,3,4
Burnishing force	50 N
Burnishing feed	150 mm/min
Burnishing speed	1200 r/min
No of passes	4
S/N ratio (η_opt)	46.23
Observed	−188 MPa
Actual	−182 MPa
Error (%)	3.30

RsB maps

The CRS of Mg Ze41A alloy is profoundly affected by burnishing force and speed, as depicted in ANOVA table. Further, the literature lacks in analytical modelling of residual stresses during burnishing process. Hence, an effort is made to correlate the residual stresses with regards to highly influencing burnishing parameters. Therefore, the RsB maps are designed based on burnishing force and speed. This map is designed by considering burnishing force on abscissa and burnishing speed on ordinate. When a hard rotating ball moves over a surface repeatedly, the plastic deformation occurs, which in turn induces strain hardening effect and results in residual stress. However, the intensity of residual stress depends on mechanical load, material deformation and material flow of work piece. This residual stress will be isotropic in nature and it is subjected on all the grains because of the grain constraints in each direction. The RsB map of ball burnished Mg Ze41A alloy is depicted in Figure 8. This map basically represents the interactions encountered during ball burnishing operation. The demarcation lines are highly non-parallel and non-uniform, indicating the dominant interactions during burnishing of Mg Ze41A alloy.

The value of CRS is varied from one burnishing condition to another. Therefore, it is essential to identify the range of parameters for best CRS value. An attempt has been made to propose the range of parameters for best CRS value by designing burnishing zones, as represented in Figure 9. The burnishing zones are categorized based on the range of CRS values marked as Unlikely zone, Likely zone and Most Likely zone. The unlikely zone is observed to be predominant at extreme burnishing force and speed conditions. At low extreme conditions, the intensity of strain hardening is quite low because of the poor burnishing effect. In contrary, the burnished surface gets distorted due to excessive strain hardening at higher extreme conditions. As a result, the burnished Mg Ze41A surface exhibited low CRS value at extreme burnishing conditions. However, a clear transition has been observed from unlikely to likely zone, as moved away from unlikely zone. This could be possible because of improvement in the strain hardening, when shifted from extreme conditions. However, the intensity of strain hardening is not at the optimum level in likely zone, which resulted in moderate values of CRS. Meanwhile, the shift from likely to most likely zone is inevitable, when drifted towards the centre. The amount of strain hardening induced in likely zone is of desirable value, which resulted in best CRS value. It can be concluded that the best CRS value can be achieved, when the ball burnishing operation is performed in most-likely zone. Further, these burnishing zones can assist in process parameters selection for any equivalent strength material. The most-likely zone for an equivalent strength material (σ_y = 140 MPa) can be found in between 45 and 55 N of burnishing force and 1150–1250 r/min for burnishing speed.

Figure 9.

Burnishing zones based on residual stress.

Fuzzy logic modelling

The information in FIS is processed by linguistic reasoning. A linguistic term describes the state of a phenomenon by a word rather than numerical values. However, the words are classified further into numerical values by the help of fuzzy sets. In the present study, the CRS of magnesium alloy is modelled by considering four major ball burnishing parameters. The linguistic values of ball burnishing parameters are represented in Table 6. The input parameters are partitioned according to the levels of Taguchi method. Similarly, the linguistic terms of CRS are presented in Table 7. CRS has been fuzzified into seven linguistic terms to ensure great predictive response. The fuzzy sets have been represented graphically by MFs. Also, the MFs can be used to present the degree of fuzziness in a fuzzy set by mapping the value between 0 and 1 by a curve in the input space. The selection of MF and its value is exclusively based on the process knowledge and the experimental data. Triangular MFs are generally preferred as it has been gradually decreasing on either sides with only one definite value. In the current study, each burnishing parameter and CRS has been modelled by triangular MF. A triangular MF, μ_A(x), is defined in equation (4). The triangular MF is found to be suitable as it suffices to evaluate the slope and the central value. As a result, burnishing parameters and CRS values are constrained to two fuzzy sets and hence, their summation always remains unity. In addition, the triangular MF outperformed the other MF's in estimating the results of multi-performance characteristic problems. Fuzzy logic model in Matlab-R2016a has been developed by mamdani type inference system.

μ_{A} (x) = {\begin{matrix} \frac{(x - l)}{(m - l)}, & l \leq x < m \\ \frac{(u - x)}{(u - m)}, & m l t x \leq u \\ 0, & otherwise \end{matrix}

(4)

Table 6.

Linguistic values of burnishing parameters.

Levels		Force (N)	Speed (r/min)	Feed (mm/min)	Passes
VS	Very small	30	1000	100	1
S	Small	40	1100	125	2
M	Medium	50	1200	150	3
L	Large	60	1300	175	4
VL	Very large	70	1400	200	5

Table 7.

Linguistic values of compressive residual stress (CRS).

Levels		CRS (MPa)
P	Poor	50
VB	Very bad	70
B	Bad	90
F	Fair	110
G	Good	130
VG	Very good	150
E	Excellent	170

The linguistic terms of burnishing parameters and CRS are interrelated by heuristic rules as If ‘condition’ then ‘consequence’. A rule base comprising 25 fuzzy rules has been formulated by considering the experimental data. For example, Rule 15: If burnishing force is medium, burnishing speed is very large, burnishing feed is small and passes are large then the surface roughness is good.

Prior to defuzzification process, the outcome of the fuzzy rule base has been integrated by aggregation process. The aggregation method used for unification of fuzzy rule bank is max (maximum) method for its easiness and adoptability. Additionally, the MF of the ‘consequence’ part of fuzzy rule base is unified by fuzzy-union operator. Further, the cumulative response of fuzzy rules obtained through unification process undergoes defuzzification. The term ‘defuzzification’ represents the conversion of fuzzified value into real value. The cumulative response will be transformed into crisp value. The crisp value represents the CRS of ball burnished MgZe41A alloy. The commonly used defuzzification methods are mean of maxima method, bisector method and centroid method. In the present investigation, centroid method is used, for its adoptability, execution and accuracy. The governing equation for centroid method has been provided in equation (5). The experimental data and aforesaid linguistic terms with triangular MF have been used to simulate the fuzzy logic model in the Matlab software on the basis of mamdani interface system. The generated model has been validated by predicting the values at three unknown test cases and the outputs generated are represented in Figure 10.

x^{*} = \frac{\sum_{i = 1}^{n} x_{i} \cdot μ (x_{i})}{\sum_{i = 1}^{n} μ (x_{i})}

(5)

Figure 10.

Prediction results of fuzzy logic model.

where x_i is centroid value, x*is crisp value, μ(x_i) is firing level of the ith rule among ‘n’ rules fired.

Validation of FIS model

After the successful generation of fuzzy logic in Matlab software, the models are tested for accuracy. The CRS values at three unknown burnishing conditions have been predicted by the models, as represented in Table 8. The predicted CRS values are compared with experimental values to validate the models. The percentage error for the results has been calculated to compare accuracy between the models. The average absolute percentage error for the developed fuzzy logic model is found to be 6.11%, as depicted in Table 8. The least errors prove that the fuzzy logic results are nearer to the actual experimental results. The close assent of predicted and measured values of CRS emphasizes that the fuzzy logic model can be effective in predicting the residual stresses under different burnishing parameters satisfactorily. Thus, the developed fuzzy logic model can be a promising alternative for predicting the CRS value in the specified range of burnishing parameters. The number of arithmetic operations is substantially low during implementation of fuzzy logic model. Similar estimation capabilities of fuzzy logic models were observed during machining of ferrous materials.

Table 8.

Validation of FIS model.

Force (N)	Speed (r/min)	Feed (mm/min)	Passes	Experimental CRS (MPa)	Predicted CRS (MPa)	Percentage error
50	1200	150	4	−182	−167	−8.24
50	1300	150	3	−124	−130	4.84
60	1100	100	5	−95	−90	−5.26
Avg. absolute error						6.11

CRS: compressive residual stress; FIS: fuzzy interface system.

Conclusion

Ball burnishing process was found to impart CRSs on the surface successfully. Based on the results, the following conclusions are derived:

Burnishing force and speed are found to be the most sensitive parameters in affecting the CRS with a contribution of 26.78% and 26.08%, respectively, followed by burnishing passes and feed with a contribution of 21.97% and 19.97%, respectively. The optimum CRS value of −182 MPa has been obtained at burnishing force of 50 N, speed of 1200 r/min, feed of 150 mm/min and 4 passes.

The demarcation lines in RsB maps are found to be non-parallel and non-uniform, indicating significant interactions among burnishing parameters during ball burnishing of Mg Ze41A alloy. Based on RsB maps, it has been proposed that the ball burnishing process for an equivalent material (σ_y = 140 MPa) can be performed at burnishing force of 45–55 N and burnishing speed of 1150–1250 r/min for obtaining the best CRS value.

The fuzzy logic model with triangular MF and centroid method of defuzzification has yielded the results with the lowest error of 6.11%. The FIS model can be of great help in generating the global database for process improvements during CRS estimation of ball burnished Mg Ze41A alloy.

The ball burnishing process is effective and economical in inducing the CRS and hence, can be recommended for industrial applications, where fatigue strength and corrosion resistance are of high importance. However, further research is required to explore the applicability and feasibility of the burnishing process in the case of complicated parts consisting of free-form surfaces.

Footnotes

Acknowledgements

The authors would like to acknowledge Meda Hemalatha for her support during fuzzy logic modelling

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Srinivasu Gangi Setti

References

Delgado

Cuesta

Alegre

, et al. State of the art of deep rolling. Precis Eng 2016; 46: 1–10.

Salimi

Bahemmat

Haghpanahi

. Study on residual stresses caused by underwater friction stir welding: fe modeling and ultrasonic measurement. Proc IMechE, Part E: J Process Mech Eng 2019; 233: 118–137.

Jagadeesh

Gangi Setti

. A current status of the residual stress characterization by the crystal lattice strain (diffraction) method. J Struct Chem 2020; 61: 262–273.

Jagadeesh

Gangi Setti

. Surface integrity of ball burnished bioresorbable magnesium alloy. Adv Manuf 2022. doi:10.1007/s40436-021-00387-6

Teimouri

Amini

Ashrafi

. An analytical model of burnishing forces using slab method. Proc IMechE, Part E: J Process Mech Eng 2019; 233: 630–642.

Alshareef

Marinescu

Basudan

, et al. Ball-burnishing factors affecting residual stress of AISI 8620 steel. Int J Adv Manuf Technol 2020; 107: 1387–1397.

Zhang

Bugtai

Marinescu

. Burnishing of aerospace alloy : a theoretical – experimental approach. J Manuf Syst 2015; 37: 472–478.

Maximov

Duncheva

Anchev

, et al. Improvement in fatigue strength of 41Cr4 steel through slide diamond burnishing. J Brazilian Soc Mech Sci Eng 2020; 42: 1–20.

Zhang

Lindemann

Ding

, et al. Effect of roller burnishing on fatigue properties of the hot-rolled Mg-12Gd-3Y magnesium alloy. Mater Chem Phys 2010; 124: 835–840.

10.

Ravindra Babu

Ankamma

Siva Prasad

, et al. Effects of burnishing parameters on the surface characteristics, microstructure and microhardness in en series steels. Trans Indian Inst Met 2011; 64: 565–573.

11.

Yuan

Sun

, et al. Experimental investigation into the effect of low plasticity burnishing parameters on the surface integrity of TA2. Int J Adv Manuf Technol 2017; 88: 1089–1099.

12.

Teimouri

Amini

Guagliano

. Analytical modeling of ultrasonic surface burnishing process: evaluation of residual stress field distribution and strip deflection. Mater Sci Eng A 2019; 747: 208–224.

13.

Teimouri

Amini

Bami

. Evaluation of optimized surface properties and residual stress in ultrasonic assisted ball burnishing of AA6061-T6. Measurement 2018; 116: 129–139.

14.

Teimouri

. Optimization of residual stress field in ultrasonic assisted burnishing process. Int J Light Mater Manuf 2019; 2: 346–354.

15.

Arsalani

Razfar

Abdullah

, et al. Fatigue behavior improvement of hardened parts using sequential hard turning, grinding, and ball burnishing operations. Proc IMechE, Part L: J Materials: Design Appl 2021; 235: 87–99.

16.

Boozarpoor

Elyasi

Hosseinzadeh

. An investigation of the surface quality of burnished AISI 4340 steel. Proc IMechE, Part E: J Process Mech Eng. 2018; 232: 299–313.

17.

Tunckaya

. An experimental modelling and performance validation study: top gas pressure tracking system in a blast furnace using soft computing methods. Proc IMechE, Part E: J Process Mech Eng 2021; 235: 2154–2164.

18.

Jagadeesh

Setti

. Modeling the surface integrity of ball burnished biocompatible magnesium alloy by soft computing techniques. Trans Indian Inst Met 2022; 75: 1603–1618.

19.

Leyva-Bravo

Chiñas-Sanchez

Hernandez-Rodriguez

, et al. Electrochemical discharge machining modeling through different soft computing approaches. Int J Adv Manuf Technol 2020; 106: 3587–3596.

20.

Belloufi

Mezoudj

Abdelkrim

, et al. Experimental and predictive study by multi-output fuzzy model of electrical discharge machining performances. Int J Adv Manuf Technol 2020; 109: 2065–2093.

21.

Heidarzadeh

Testik

ÖM

Güleryüz

, et al. Development of a fuzzy logic based model to elucidate the effect of FSW parameters on the ultimate tensile strength and elongation of pure copper joints. J Manuf Process 2020; 53: 250–259.

22.

Sinha

Narang

Bhattacharya

. A fuzzy logic approach for modelling and prediction of mechanical properties of hybrid abaca-reinforced polymer composite. J Brazilian Soc Mech Sci Eng 2020; 42: 1–11.

Experimental investigation and estimation of compressive residual stress of ball burnished rare earth based magnesium alloy

Abstract

Keywords

Introduction

Methodology

CNC burnishing process

CRS measurement

Results and discussion

Role of burnishing force in inducing CRS

Role of burnishing speed in inducing CRS

Role of burnishing feed in inducing CRS

Role of passes in inducing CRS

Analysis of means and ANOVA of CRS

Evaluation of optimum results

RsB maps

Fuzzy logic modelling

Validation of FIS model

Conclusion

Footnotes

Acknowledgements

Declaration of conflicting interests

Funding

ORCID iD

References