Model-Based Sensitivity Analysis of the Temperature in Laser Powder Bed Fusion.

To quantitatively evaluate the effect of the process parameters and the material properties on the temperature in laser powder bed fusion (LPBF), this paper proposed a sensitivity analysis of the temperature based on the validated prediction model. First, three different heat source modes-point heat source, Gaussian surface heat source, and Gaussian body heat source-were introduced. Then, a case study of Ti6Al4V is conducted to determine the suitable range of heat source density for the three different heat source models. Based on this, the effects of laser processing parameters and material thermophysical parameters on the temperature field and molten pool size are quantitatively discussed based on the Gaussian surface heat source. The results indicate that the Gaussian surface heat source and the Gaussian body heat source offer higher prediction accuracy for molten pool width compared to the point heat source under similar processing parameters. When the laser energy density is between 40 and 70 J/mm3, the prediction accuracy of the Gaussian surface heat source and the body heat source is similar, and the average prediction errors are 4.427% and 2.613%, respectively. When the laser energy density is between 70 and 90 J/mm3, the prediction accuracy of the Gaussian body heat source is superior to that of the Gaussian surface heat source. Among the influencing factors, laser power exerts the greatest influence on the temperature field and molten pool size, followed by scanning speed. In particular, laser power and scan speed contribute 38.9% and 23.5% to the width of the molten pool, 39.1% and 19.6% to the depth of the molten pool, and 38.9% and 21.5% to the maximum temperature, respectively.

Process Analysis and Topography Evaluation for Monocrystalline Silicon Laser Cutting-Off.

Due to the characteristics of high brittleness and low fracture toughness of monocrystalline silicon, its high precision and high-quality cutting have great challenges. Aiming at the urgent need of wafer cutting with high efficiency, this paper investigates the influence law of different laser processes on the size of the groove and the machining affected zone of laser cutting. The experimental results show that when laser cutting monocrystalline silicon, in addition to generating a groove, there will also be a machining affected zone on both sides of the groove and the size of both will directly affect the cutting quality. After wiping the thermal products generated by cutting on the material surface, the machining affected zone and the recast layer in the cutting seam can basically be eliminated to generate a wider cutting seam and the surface after wiping is basically the same as that before cutting. Increasing the laser cutting times will increase the width of the material's machining affected zone and the groove width after chip removal. When the cutting times are less than 80, increasing the cutting times will increase the groove width at the same time; but, after the cutting times exceed 80, the groove width abruptly decreases and then slowly increases. In addition, the lower the laser scanning speed, the larger the width of the material's machining affected zone and the width of the groove after chip removal. The increase in laser frequency will increase the crack width and the crack width after chip removal but decrease the machining affected zone width. The laser pulse width has a certain effect on the cutting quality but it does not show regularity. When the pulse width is 0.3 ns the cutting quality is the best and when the pulse width is 0.15 ns the cutting quality is the worst.

A Ti-6Al-4V Milling Force Prediction Model Based on the Taylor Factor Model and Microstructure Evolution of the Milling Surface.

In this paper, a milling force prediction model considering the Taylor factor is established, and the Ti-6Al-4V milling force predicted by the model under different milling parameters is presented. In the study, the milling experiment of Ti-6Al-4V was carried out, the milling force was collected by the dynamometer, and the microstructure evolution of the milling surface before and after milling was observed by EBSD. Through the comparative analysis of the experimental results and the model prediction results, the reliability of the prediction model proposed in this study was verified, and the influences of the milling parameters on the milling force were further analyzed. Finally, based on the EBSD observation results, the effects of the milling parameters on the microstructure evolution of the milling surface were studied. The results show that both the tangential milling force and normal milling force increase with the increase in the milling depth and feed rate. Among the milling parameters selected in this study, the milling depth has the greatest influence on the milling force. The average errors of the tangential milling force and normal milling force predicted by the milling force model are less than 10%, indicating that the milling force prediction model established in this paper considering Taylor factor is suitable for the prediction of the Ti-6Al-4V milling force. With the change in the milling parameters, the grain structure, grain size, grain boundary distribution, phase distribution, and micro-texture of the material surface change to varying degrees, and the plastic deformation of the milling surface is largely coordinated by the slip.

Force Prediction and Material Removal Mechanism Analysis of Milling SiCp/2009Al.

In recent years, medium- and low-volume fraction silicon carbide particle-reinforced aluminum matrix composites (SiCp/Al) have increasingly become a key material in the aerospace industry. Force prediction and material removal mechanism analysis of milling SiCp/Al are necessary to improve the surface integrity of products. An orthogonal experiment of SiCp/2009Al with a volume fraction of 20% was carried out, and the effect of the milling parameters on milling force was studied with the input parameters of milling speed, feed rate, and milling depth. Thereby, the empirical force model of milling SiCp/2009Al is established by fitting the experiential data based on the multiple linear regression analysis methods. Moreover, the effects of the milling parameters on the force were analyzed. Finally, the material removal mechanism of milling SiCp/Al is analyzed based on dislocation theory. The analyzed results reveal that the removal mechanism of the SiCp/Al composites includes plastic deformation of the aluminum matrix, cutting of particles, fragmentation, and deboning. Based on dislocation theory and maximum undeformed thickness theory, the effect of cutting parameters on the form of material removal was analyzed, which serves as a guide for selecting appropriate machining parameters to obtain improved machining quality of SiCp/Al composites.

Surface Topography Prediction Model in Milling of Thin-Walled Parts Considering Machining Deformation.

With the continuous improvement of the performance of modern aerospace aircraft, the overall strength and lightweight control of aircraft has become a significant feature of modern aerospace parts. With the wide application of thin-walled parts, the requirements for dimensional accuracy and surface quality of workpieces are increasing. In this paper, a numerical model for predicting surface topography of thin-walled parts after elastic deformation is proposed. In view of the geometric characteristics in the cutting process, the cutting force model of thin-walled parts is established, and the meshing relationship between the tool and the workpiece is studied. In addition, the influence of workpiece deformation is considered based on the beam deformation model. Cutting force is calculated based on deformed cutting thickness, and the next cutting-meshing relationship is predicted. The model combines the radial deflection of the workpiece in the feed direction and the changing meshing relationship of the tool-workpiece to determine the three-dimensional topography of the workpiece. The error range between the experimental and the simulation results of surface roughness is 7.45-13.09%, so the simulation three-dimensional morphology has good similarity. The surface topography prediction model provides a fast solution for surface quality control in the thin-walled parts' milling process.

Study on the Formation Mechanism of Surface Adhered Damage in Ball-End Milling Ti6Al4V.

Ball-end cutters are widely used for machining the parts of Ti-6Al-4V, which have the problem of poor machined surface quality due to the low cutting speed near the tool tip. In this paper, through the experiments of inclined surface machining in different feed directions, it is found that the surface adhered damages will form on the machined surface under certain tool postures. It is determined that the formation of surface adhered damage is related to the material adhesion near the cutting edge and the cutting-into/out position within the tool per-rotation cycle. In order to analyze the cutting-into/out process more clearly under different tool postures, the projection models of the cutting edge and the cutter workpiece engagement on the contact plane are established; thus, the complex geometry problem of space is transformed into that of plane. Combined with the case of cutting-into/out, chip morphology, and surface morphology, the formation mechanism of surface adhered damage is analyzed. The analysis results show that the adhered damage can increase the height parameters Sku, Sz, Sp, and Sv of surface topographies. Sz, Sp, and Sv of the normal machined surface without damage (Sku ≈ 3) are about 4-6, 2-3, and 2-3 µm, while Sz, Sp, and Sv with adhered damage (Sku > 3) can reach about 8-20, 4-14, and 3-6 µm in down-milling and 10-25, 7-18, and 3-7 µm in up-milling. The feed direction should be selected along the upper left (Q2: ß ∈ [0°, 90°]) or lower left (Q3: ß ∈ [90°, 180°]) to avoid surface adhered damage in the down-milling process. For up-milling, the feed direction should be selected along the upper right (Q1: ß ∈ (-90°, 0°]) or upper left (Q2: ß ∈ [0°, 90°)).

Analytical Modelling of Temperature Distribution in SLM Process with Consideration of Scan Strategy Difference between Layers.

In the practical selective laser melting (SLM) manufacturing process, the scan strategy often varies between layers to avoid overlapping of the melted area, which affects the residual stress and deflection of the final build. Yet not much modelling work has been done to accommodate the angle between layers. The paper proposed an analytical thermal model to address the scan strategy difference, such as laser scan direction difference between layers, which brings the model closer to the practical scan situation. The analytical transient moving point heat solution is adopted in this model. The laser movement is first considered in a laser coordinates, which originates at the laser radiation spot, and then transferred into a stationary coordinate, which originates at the starting point of the build. The model takes account of multi-track and multi-layer effect by considering thermal property changes caused by remaining heat, which is further adopted for temperature distribution calculation. The scan direction difference leads to different laser path at each layer, and alters heating and cooling time for a specific point on the build. The proposed model is validated by comparing the predicted melt pool geometries to documented experimental data. The effect of scan direction difference between layers is further discussed in the later part. It is found that the uni- and bi- directional scan leads to diverse temperature profile but its effect on melt depth is not significant. Although the laser rotation angle between layers leads to changes in the melt depth, it is not in a large scale. The proposed model shows that scan strategy does not change melt pool geometry in a significant scale but affects the thermal profile as well as thermal history. It can be used as a step for further modelling work for porosity and deflection.

Temperature prediction of ultrasonic vibration-assisted milling.

Machining temperature is a key factor in ultrasonic vibration-assisted milling as it can significantly influence tool wear rate and residual thermal stresses. In current study, a physics-based analytical predictive model on machining temperature in ultrasonic vibration-assisted milling is proposed, without resorting to iterative numerical simulations. As the tool periodically loses contact with the workpiece under vibration, three types of tool-workpiece separation criteria are first examined based on the tool trajectory under ultrasonic vibration. Type I criterion examines whether the relative velocity between tool and workpiece in cutting direction is opposite to the tool rotation direction. Type II criterion examines whether the instantaneous vibration displacement in radial direction is larger than instantaneous uncut chip thickness. Type III criterion examines whether there is overlap between current and previous tool paths due to vibration. If no contact, the instantaneous temperature rise is zero. Otherwise, the temperature rise is predicted under shearing heat source in shear zone and secondary rubbing heat source along machined surface. A mirror heat source method is applied to predict temperature rise, considering oblique band heat sources moving in a semi-infinite medium. The proposed predictive temperature model in ultrasonic vibration-assisted milling is validated through comparison to experimental measurements on Al 6063 alloy. The proposed predictive model is able to match the measured temperature with high accuracy of 1.85% average error and 5.22% largest error among all cases. Sensitivity analysis is also conducted to study the influences of cutting and vibration parameters on temperature. The proposed model is valuable in terms of providing an accurate and reliable reference for the prediction of temperature in ultrasonic vibration-assisted milling.

Correction: Li, Q. and Liang, S.Y. Microstructure Images Restoration of Metallic Materials Based upon KSVD and Smoothing Penalty Sparse Representation Approach. Materials 2018, 11, 637.

The authors were not aware of some errors and imprecise descriptions made in the proofreading phase, therefore, we wish to make the following corrections to this paper [1][...].

Analytical Thermal Modeling of Powder Bed Metal Additive Manufacturing Considering Powder Size Variation and Packing.

This work presents a computationally efficient predictive model based on solid heat transfer for temperature profiles in powder bed metal additive manufacturing (PBMAM) considering the heat transfer boundary condition and powder material properties. A point moving heat source model is used for the three-dimensional temperature prediction in an absolute coordinate. The heat loss from convection and radiation is calculated using a heat sink solution with a mathematically discretized boundary considering non-uniform temperatures and heat loss at the boundary. Powder material properties are calculated considering powder size statistical distribution and powder packing. The spatially uniform and temperature-independent material properties are employed in the temperature prediction. The presented model was tested in PBMAM of AlSi10Mg under different process conditions. The calculations of material properties are needed for AlSi10Mg because of the significant difference in thermal conductivity between powder form and solid bulk form. Close agreement is observed upon experimental validation on the molten pool dimensions.

Analytical Thermal Modeling of Metal Additive Manufacturing by Heat Sink Solution.

Metal additive manufacturing can produce geometrically complex parts with effective cost. The high thermal gradients due to the repeatedly rapid heat and solidification cause defects in the produced parts, such as cracks, porosity, undesired residual stress, and part distortion. Different techniques were employed for temperature investigation. Experimental measurement and finite element method-based numerical models are limited by the restricted accessibility and expensive computational cost, respectively. The available physics-based analytical model has promising short computational efficiency without resorting to finite element method or any iteration-based simulations. However, the heat transfer boundary condition cannot be considered without the involvement of finite element method or iteration-based simulations, which significantly reduces the computational efficiency, and thus the usefulness of the developed model. This work presents an explicit and closed-form solution, namely heat sink solution, to consider the heat transfer boundary condition. The heat sink solution was developed from the moving point heat source solution based on heat transfer of convection and radiation. The part boundary is mathematically discretized into many heats sinks due to the non-uniform temperature distribution, which causes non-uniform heat loss. The temperature profiles, thermal gradients, and temperature-affected material properties are calculated and presented. Good agreements were observed upon validation against experimental molten pool measurements.

Adaptive online dictionary learning for bearing fault diagnosis.

One of the most common parts to maintain system balance and support the various load in rotating machinery is the rolling element bearing. The breakdown of the element in bearings leads to inefficiency and sometimes catastrophic events across various industries. The main challenge over the last few years for fault diagnosis of bearings is the early detection of fault signature. In this paper, an adaptive online dictionary learning algorithm is developed for early fault detection of bearing elements. The dictionary is trained using a set of vibration signal from a heavily damaged bearing. The enveloped signal of the bearing is obtained using the Kurtogram and split into several sections. The K-SVD algorithm is implemented to the dictionaries corresponding to the enveloped signal. OMP is implemented with the calculated dictionaries to obtain the sparse representation of the testing signal. Then the envelope analysis is implemented to obtain the fault signal from the recovered signal by the dictionaries. The adaptive algorithm is added to the dictionary learning to update the dictionary based on newly acquired data with the weighted least square method. Without retraining the dictionaries using the K-SVD algorithm, the computation speed is significantly improved. The proposed algorithm is compared with a traditional dictionary learning algorithm to show the improvement in detection of new fault frequency and improved signal to noise ratio.

Bearing fault diagnosis with nonlinear adaptive dictionary learning.

The monitoring of rotating machinery condition has been a critical component of the Industry 4.0 revolution in enhancing machine reliability and facilitating intelligent manufacturing. The introduction of condition-based monitoring has effectively reduced the catastrophic events and maintenance cost across various industries. One of the major challenges of the diagnosis remains as majority of the diagnostic model requires off-line analysis and human intervention. The offline analysis, which is normally done by previous experience, involves tuning model parameters to improve the performance of the diagnostic model. However, for newly developed models, the knowledge of the unknown parameters does not exist. One way to resolve this issue is through learning using adaptation. The adaptation algorithm adjusts itself by newly acquired data. Hence, improvement of the model performance is achieved. In this paper, a nonlinear adaptive dictionary learning algorithm is proposed to achieve early fault detection of bearing elements without using the conventional computation heavy algorithm to update the dictionary. Deterministic and random data separation is implemented using the autoregressive model to reduce the background noise. The filtered data is further analyzed by the Infogram to reveal the impulsiveness and cyclostationary signature of the vibration signal. The dictionary is initialized using random parameters. Instead of using the k means singular value decomposition algorithm to compute the dictionary for adaptation, the unscented Kalman filter (UKF) is implemented to update the dictionaries using the filtered signal from the Infogram. The updating algorithm does not require computation of the dictionary, and no previous knowledge of the dictionary's parameters is needed. The updated dictionary contains the detected fault signature from the Infogram and, therefore, is used for further fault analysis. The proposed algorithm has the advantage of self-adaptation, the capability to map the non-linear relationship of the signal and dictionary weights. The algorithm can be used in the various condition-based monitoring of rotating machineries to avoid additional human efforts and improve the performance of the diagnostic model.

Heat Source Modeling in Selective Laser Melting.

Selective laser melting (SLM) is an emerging additive manufacturing (AM) technology for metals. Intricate three-dimensional parts can be generated from the powder bed by selectively melting the desired location of the powders. The process is repeated for each layer until the part is built. The necessary heat is provided by a laser. Temperature magnitude and history during SLM directly determine the molten pool dimensions, thermal stress, residual stress, balling effect, and dimensional accuracy. Laser-matter interaction is a crucial physical phenomenon in the SLM process. In this paper, five different heat source models are introduced to predict the three-dimensional temperature field analytically. These models are known as steady state moving point heat source, transient moving point heat source, semi-elliptical moving heat source, double elliptical moving heat source, and uniform moving heat source. The analytical temperature model for all of the heat source models is solved using three-dimensional differential equations of heat conduction with different approaches. The steady state and transient moving heat source are solved using a separation of variables approach. However, the rest of the models are solved by employing Green's functions. Due to the high temperature in the presence of the laser, the temperature gradient is usually high which has a substantial impact on thermal material properties. Consequently, the temperature field is predicted by considering the temperature sensitivity thermal material properties. Moreover, due to the repeated heating and cooling, the part usually undergoes several melting and solidification cycles, and this physical phenomenon is considered by modifying the heat capacity using latent heat of melting. Furthermore, the multi-layer aspect of the metal AM process is considered by incorporating the temperature history from the previous layer since the interaction of the layers have an impact on heat transfer mechanisms. The proposed temperature field models based on different heat source approaches are validated using experimental measurement of melt pool geometry from independent experimentations. A detailed explanation of the comparison of models is also provided. Moreover, the effect of process parameters on the balling effect is also discussed.

Analytical Modeling of In-Process Temperature in Powder Bed Additive Manufacturing Considering Laser Power Absorption, Latent Heat, Scanning Strategy, and Powder Packing.

Temperature distribution gradient in metal powder bed additive manufacturing (MPBAM) directly controls the mechanical properties and dimensional accuracy of the build part. Experimental approach and numerical modeling approach for temperature in MPBAM are limited by the restricted accessibility and high computational cost, respectively. Analytical models were reported with high computational efficiency, but the developed models employed a moving coordinate and semi-infinite medium assumption, which neglected the part dimensions, and thus reduced their usefulness in real applications. This paper investigates the in-process temperature in MPBAM through analytical modeling using a stationary coordinate with an origin at the part boundary (absolute coordinate). Analytical solutions are developed for temperature prediction of single-track scan and multi-track scans considering scanning strategy. Inconel 625 is chosen to test the proposed model. Laser power absorption is inversely identified with the prediction of molten pool dimensions. Latent heat is considered using the heat integration method. The molten pool evolution is investigated with respect to scanning time. The stabilized temperatures in the single-track scan and bidirectional scans are predicted under various process conditions. Close agreements are observed upon validation to the experimental values in the literature. Furthermore, a positive relationship between molten pool dimensions and powder packing porosity was observed through sensitivity analysis. With benefits of the absolute coordinate, and high computational efficiency, the presented model can predict the temperature for a dimensional part during MPBAM, which can be used to further investigate residual stress and distortion in real applications.

Predictive Modeling of Machining Temperatures with Force⁻Temperature Correlation Using Cutting Mechanics and Constitutive Relation.

Elevated temperature in the machining process is detrimental to cutting tools-a result of the effect of thermal softening and material diffusion. Material diffusion also deteriorates the quality of the machined part. Measuring or predicting machining temperatures is important for the optimization of the machining process, but experimental temperature measurement is difficult and inconvenient because of the complex contact phenomena between tools and workpieces, and because of restricted accessibility during the machining process. This paper presents an original analytical model for fast prediction of machining temperatures at two deformation zones in orthogonal cutting, namely the primary shear zone and the tool⁻chip interface. Temperatures were predicted based on a correlation between force and temperature using the mechanics of the cutting process and material constitutive relation. Minimization of the differences between calculated material flow stresses using a mechanics model and a constitutive model yielded an estimate of machining temperatures. Experimental forces, cutting condition parameters, and constitutive model constants were inputs, while machining forces were easily measurable by a piezoelectric dynamometer. Machining temperatures of AISI 1045 steel were predicted under various cutting conditions to demonstrate the predictive capability of each presented model. Close agreements were observed by verifying them against documented values in the literature. The influence of model inputs and computational efficiency were further investigated. The presented model has high computational efficiency that allows real-time prediction and low experimental complexity, considering the easily measurable input variables.

Microstructure Images Restoration of Metallic Materials Based upon KSVD and Smoothing Penalty Sparse Representation Approach.

Microstructure images of metallic materials play a significant role in industrial applications. To address image degradation problem of metallic materials, a novel image restoration technique based on K-means singular value decomposition (KSVD) and smoothing penalty sparse representation (SPSR) algorithm is proposed in this work, the microstructure images of aluminum alloy 7075 (AA7075) material are used as examples. To begin with, to reflect the detail structure characteristics of the damaged image, the KSVD dictionary is introduced to substitute the traditional sparse transform basis (TSTB) for sparse representation. Then, due to the image restoration, modeling belongs to a highly underdetermined equation, and traditional sparse reconstruction methods may cause instability and obvious artifacts in the reconstructed images, especially reconstructed image with many smooth regions and the noise level is strong, thus the SPSR (here, q = 0.5) algorithm is designed to reconstruct the damaged image. The results of simulation and two practical cases demonstrate that the proposed method has superior performance compared with some state-of-the-art methods in terms of restoration performance factors and visual quality. Meanwhile, the grain size parameters and grain boundaries of microstructure image are discussed before and after they are restored by proposed method.

Multichannel Signals Reconstruction Based on Tunable Q-Factor Wavelet Transform-Morphological Component Analysis and Sparse Bayesian Iteration for Rotating Machines.

High-speed remote transmission and large-capacity data storage are difficult issues in signals acquisition of rotating machines condition monitoring. To address these concerns, a novel multichannel signals reconstruction approach based on tunable Q-factor wavelet transform-morphological component analysis (TQWT-MCA) and sparse Bayesian iteration algorithm combined with step-impulse dictionary is proposed under the frame of compressed sensing (CS). To begin with, to prevent the periodical impulses loss and effectively separate periodical impulses from the external noise and additive interference components, the TQWT-MCA method is introduced to divide the raw vibration signal into low-resonance component (LRC, i.e., periodical impulses) and high-resonance component (HRC), thus, the periodical impulses are preserved effectively. Then, according to the amplitude range of generated LRC, the step-impulse dictionary atom is designed to match the physical structure of periodical impulses. Furthermore, the periodical impulses and HRC are reconstructed by the sparse Bayesian iteration combined with step-impulse dictionary, respectively, finally, the final reconstructed raw signals are obtained by adding the LRC and HRC, meanwhile, the fidelity of the final reconstructed signals is tested by the envelop spectrum and error analysis, respectively. In this work, the proposed algorithm is applied to simulated signal and engineering multichannel signals of a gearbox with multiple faults. Experimental results demonstrate that the proposed approach significantly improves the reconstructive accuracy compared with the state-of-the-art methods such as non-convex Lq (q = 0.5) regularization, spatiotemporal sparse Bayesian learning (SSBL) and L1-norm, etc. Additionally, the processing time, i.e., speed of storage and transmission has increased dramatically, more importantly, the fault characteristics of the gearbox with multiple faults are detected and saved, i.e., the bearing outer race fault frequency at 170.7 Hz and its harmonics at 341.3 Hz, ball fault frequency at 7.344 Hz and its harmonics at 15.0 Hz, and the gear fault frequency at 23.36 Hz and its harmonics at 47.42 Hz are identified in the envelope spectrum.

Detection of weak fault using sparse empirical wavelet transform for cyclic fault.

The successful prediction of the remaining useful life of rolling element bearings depends on the capability of early fault detection. A critical step in fault diagnosis is to use the correct signal processing techniques to extract the fault signal. This paper proposes a newly developed diagnostic model using a sparse-based empirical wavelet transform (EWT) to enhance the fault signal to noise ratio. The unprocessed signal is first analyzed using the kurtogram to locate the fault frequency band and filter out the system noise. Then, the preproc signal is filtered using the EWT. The l q -regularized sparse regression is implemented to obtain a sparse solution of the defect signal in the frequency domain. The proposed method demonstrates a significant improvement of the signal to noise ratio and is applicable for detection of cyclic fault, which includes the extraction of the fault signatures of bearings and gearboxes.

A split-optimization approach for obtaining multiple solutions in single-objective process parameter optimization.

It can be observed from the experimental data of different processes that different process parameter combinations can lead to the same performance indicators, but during the optimization of process parameters, using current techniques, only one of these combinations can be found when a given objective function is specified. The combination of process parameters obtained after optimization may not always be applicable in actual production or may lead to undesired experimental conditions. In this paper, a split-optimization approach is proposed for obtaining multiple solutions in a single-objective process parameter optimization problem. This is accomplished by splitting the original search space into smaller sub-search spaces and using GA in each sub-search space to optimize the process parameters. Two different methods, i.e., cluster centers and hill and valley splitting strategy, were used to split the original search space, and their efficiency was measured against a method in which the original search space is split into equal smaller sub-search spaces. The proposed approach was used to obtain multiple optimal process parameter combinations for electrochemical micro-machining. The result obtained from the case study showed that the cluster centers and hill and valley splitting strategies were more efficient in splitting the original search space than the method in which the original search space is divided into smaller equal sub-search spaces.