Mathematical Model For Surface Roughness Research Articles

Influence of tool wear on geometric surface modeling for TC4 titanium alloy milling

Addressing the insufficient accuracy of milling surface roughness prediction model, the formation causes of different roughness were analyzed, and a surface roughness prediction model which takes tool wear into account was established based on an improved Z-MAP algorithm. Combining tool geometry and tool wear morphology, a mathematical model of surface profile was built; And the motion trajectory equations of the milling cutter teeth were established via machining kinematics. The servo rectangular encirclement and Newton iterative method were adopted to improve the Z-MAP algorithm. Combining the Z-MAP algorithm with the insert motion trajectory equations, the values at different height coordinates of the workpiece grid nodes were obtained, allowing numerical simulation of workpiece surface geometry and analysis of the effect of cutting trajectory overlap on the machined surface morphology. TC4 titanium alloy milling experiment was conducted to validate the simulation model. The simulated surface roughness Sa exhibited significant deviation from experimental values before tool wear, with a maximum error of 53.08 %. Nevertheless, the simulated values of Sa were closer to experimental values after tool wear, with a maximum error of 15.45 % and a minimum of only 3.07 %. Additionally, the predicted results for the bearing length ratio Rmr(c) were consistent with experimental values. The mathematical model for surface roughness taking tool wear into account effectively predicted the shape profile and surface roughness of the machined surface, providing theoretical guidance and technical support for practical production.

A Multiscale Statistical Analysis of Rough Surfaces and Applications to Tribology

Mathematical modelling of surface roughness is of significant interest for a variety of modern applications, including, but not limited to, tribology and optics. The most popular approaches to modelling rough surfaces are reviewed and critically examined. By providing counterexamples, it is shown that approaches based solely on the use of the fractal geometry or power spectral density have many drawbacks. It is recommended to avoid these approaches. It is argued that the surfaces that cannot be distinguished from the original rough surfaces can be synthesised by employing the concept of the representative elementary pattern of roughness (REPR), i.e., the smallest interval (or area) of a rough surface that statistically represents the whole surface. The REPR may be extracted from surface measurement data by the use of the “moving window” technique in combination with the Kolmogorov–Smirnov statistic.

Study of Effect of Graphite Based Magnetorheological Fluids on Braking Performance and Rotor Surface of Magnetorheological Disk Brake Using Full-Scale Brake Inertia Dynamometer

The performance of magnetorheological (MR) brakes depends on the rheological and tribological properties of MR fluid. An additive-free MR fluid does not offer better braking performance, which limits the commercial application of MR brake. In view of these issues, MR fluids were prepared in this present work employing graphite flakes as an additive. The required rheological properties of these MR fluids were measured on the magneto rheometer, and their braking performances were measured as per braking standard IS13453 using a fabricated MR disk brake on a 2/3-wheeler brake inertia dynamometer. Due to the interaction of MR fluid with the rotor and housing surface, the MR gap (i.e., another performance parameter) varies. Therefore, the effect of the interaction of prepared MR fluids on the rotor surface properties of the MR disk brake was also investigated. The constituents of MR fluids generate roughness on the rotor and housing surface. As a result, a mathematical model for surface roughness was presented and verified with experimental results. Based on the study, it is found that 0.5% (w/w) of graphite flake is better than additive-free MR fluid.

Novel Algebraic Matrix Method Used to Generate Linear Equation for Surface Roughness and Material Removal Rate during Wet/Dry Turning Operation on MMCs Al6061-T6/SiC

Stir casting process is well known for reinforcement of ceramic particle in aluminium. Due to improved properties of Al6061-T6/SiC particulate metal matrix composites have attracted by industry as well as received wider attention of material expertise. The purpose of this study is to evaluate the turning process parameters through algebraic matrix which is unique approach. Also studied effects of spindle speed, feed, SiC silicon carbide-3% and 6%, depth of cut and nose radius on modifier element for instance surface roughness Ra and material removal rate MRR in both dry and wet condition. In addition to optimize the turning process parameters are on Al6061-T6/SiC 3% and 6% with a coated tungsten tool. The experimental runs are designed using the taguchi based multiple factorial design DOE and their outcomes are analyzed using Analysis of Variance ANOVA. Mathematical models are established using algebraic matrix to represent the relationship among turning process parameters as independent variables, surface roughness and material removal rate as dependent variables. For every experimental run, a same cutting insert was used to encourage accurate reporting of the surface roughness and material removal rate. The statistical variations revealed that the main effect of spindle speed, feed, SiC silicon carbide-3% and 6%, depth of cut and nose radius are influenced the surface roughness and material removal rate. Moreover, Built-up-edge BUE formation was observed at every combinations of machining parameters such as spindle speed, feed, SiC silicon carbide-3% and 6%, depth of cut and nose radius which affected the surface quality negatively. The proximity of predicted results and experimental results provide proof that the algebraic matrix – DOE method has successfully established the predictive models. It is strongly suggested SiC silicon carbide 3% and 6% are successfully reinforced in Al6061 as well as optimize turning process parameters in wet condition than dry condition. Mathematical models for surface roughness and material removal rate are found to be statistically significant in wet condition.

Optimization of Process Parameters Wire Cut Electro Discharge Machining (WEDM) on HCHCr-D2 Steel Material

With the increasing demands of high surface finish and machining of complex shape geometries, conventional machining process are now being replaced by non-traditional machining processes. Wire EDM is one of the non-traditional machining processes which is basedon Electrical Discharge Machining Process, which is also called electro-erosion machining process In the present research parametric analysis of wire EDM parameter is performed by Taguchi method on surface roughness (SR) and material removal rate (MRR). The Design of experiments is carried out considering Taguchi technique with four input parameters, namely, pulse-on, pulse off, and voltage. L9 orthogonal array is used to conduct experiments. ANOVA is used to find out the most significant parameter that affects the surface roughness. Optimizations of parameters are done by finding out the S/N ratios of each experiment runs. Regression Analysis is carried out togenerate a mathematical model of surface roughness, material removal rate and to predict the value obtained from the optimal parameter settings. Keywords: WEDM, Taguchi method, Annova, SR, MRR

Mathematical Modeling of Material Removal and Surface Roughness in Ultrasonic-Assisted Magnetic Abrasive Flow Machining Process

Abstract Ultrasonic-assisted magnetic abrasive flow machining (UAMAFM) process shows enhanced finishing performance compared to conventional abrasive flow machining (AFM). In this present research paper, mathematical models for M˙R and Ra have been developed for the UAMAFM process by considering both steady-state and transient phenomena. The external ultrasonic and magnetic field assistance enhanced the velocity and length of contact of active abrasives, calculated from the kinematic analysis. The resultant finishing forces have also been evaluated by considering these external aids. The steady-state material removal per finishing cycle remains constant and depends on the velocity of motion, length of contact, resulting forces, number of active abrasives, and work material hardness. The transient material removal per finishing cycle was calculated in terms of the volume of irregularities present over the work surface, i.e., initial surface roughness. The mathematical model for surface roughness was developed in terms amount of material removed (MR), and initial (Ra0) and critical surface roughness (Racr). The predicted values of material removed and surface roughness from developed mathematical models agreed with experimental results with a deviation of 7.80% and 2.44%, respectively.

Mathematical modeling of surface roughness in polystyrene foam machining

Mathematical modeling of surface roughness in polystyrene foam machining

Response parameters modeling of abrasive jet machined composite using artificial neural network

Machining of polymer based nanocomposite is very challenging. Though these materials possess unique properties and developed for specific applications. Therefore analysis of material processing performance of a particular machining process is become essential. Performance of a process can be understood by establish a mathematical relationship between input and output parameters. This empirical relationship can be useful for election of significant variable factors. Once these factors elected then better quality characteristics can be obtained at economical cost. In present study mathematical models for surface roughness and kerf taper of abrasive jet machined nanocomposite are developed using artificial neural network. To check the accuracy of developed models the predicted values of consider quality characteristics are compared with previous published experimental values. Input parameters jet pressure, traverse rate, weight percentage of multi-walled carbon nanotubes and stand of distance for abrasive jet machining of carbon fiber reinforced polymer composite are considered. Average percentage prediction error found less than 5% that shows predicted values from developed models are accurate.

Modeling and analysis of surface roughness in fused deposition modeling based on infill patterns

This paper presents an approach of modeling for surface roughness of Polylactic Acid (PLA) polymer components printed with Fused Deposition Modeling (FDM) based Additive Manufacturing (AM) process. With additive manufacturing technology one can build the components of metal, polymers and variety of composites with good dimensional accuracy. FDM is one of the additive manufacturing process which is used to build products of various polymers. In this investigation PLA components are built using FDM with different Infill Patterns viz. Zigzag, Triangles and Gyroid. Based on surface roughness measurement of components, predictive mathematical models for surface roughness are generated for different infill patterns. The analysis of surface roughness based on layer thickness and infill pattern is presented. The error between predictive surface roughness and experimental surface roughness ranges between 0.1 to 9.5%. For this investigation Gyroid infill pattern shows favourable results for surface roughness. The workable ranges for process parameter under investigation are infill percentage of 70 to 90 %, layer thickness of 0.2 to 0.22 mm and printing speed of 70 to 90 mm/s.

Optimal Selection of Cutting Parameters for Surface Roughness in Milling Machining of AA6061-T6

Due to its ability to remove material quickly while maintaining optimum surface quality, end milling is considered one of the most frequent metal cutting procedures in industry. The present study aimed to investigate the impacts of cutting parameters and tool geometry on milling of Aluminum Alloy 6061-T6 to examine the impact surface roughness by utilizing response surface methodology (RSM). RSM was used to create a second-order mathematical model of surface roughness for this purpose. A multiple regression analysis used the analysis of variance to demonstrate the effect of machining settings on surface roughness and determine experiment performance. The trials for optimizing surface roughness were set up utilizing the central composite design (CCD) method and various cutting parameters such as spindle speed, feed rate and depth of cut. Also the parameters used in tool geometry are the radial rake angle (10, 13, 16, 19 and 22 degrees), and nose radius (0, 0.2, 0.4, 0.6 and 0.8 mm). The result shows that the nose radius has more significant effect on the surface roughness followed by the radial rake angle. Moreover, the effect of the depth of cut on surface roughness is more dominant than cutting speed. The optimum combinations of cutting and tool geometry parameters were cutting speed (60.53 m/min), feed rate (0.025 mm/tooth), depth of cut (0.84 mm), radial rake angle (12.72 degree) and nose radius (0.34 mm).

Investigation of cutting temperature, cutting force and surface roughness using multi-objective optimization for turning of Ti-6Al-4 V (ELI)

Titanium alloys are getting prime importance in the areas like aerospace, biomedical, marine and many other applications where superior properties like higher strength to weight ratio, good fracture toughness and excellent corrosion resistance. Ti-6Al-4 V Because of the controlled interstitial element of iron and oxygen, Extra Low Interstitial (ELI) has exceptional qualities. During the turning of Ti-6Al-4 V, the impacts of four cutting parameters, namely cutting speed, feed, depth of cut, and tool nose radius, on responses such as surface roughness, cutting temperature, and cutting force, are explored (ELI). A total of 81 trials were carried out in a dry environment. Mathematical models for surface roughness, cutting temperature and cutting force are developed. Genetic algorithm toolbox of MATLAB is used for Multi objective optimization of cutting force, cutting temperature and surface roughness. The minimum cutting force of 12kgf, the least surface roughness as 0.307 µm and the lowest cutting temperature is 43.1 °C have been reported. The optimum values for cutting force, cutting temperature and surface roughness for multi-objective optimization have been presented by Pareto optimal solutions. The research work presented in this paper determines the values of process parameters of turning for achieving desirable combination of surface roughness, cutting force and cutting temperature on Ti-6Al-4 V(ELI)

Optimization of Cutting Parameters Affecting Surface Roughness in Turning of Inconel 625 Superalloy by Cryogenically Treated Tungsten Carbide Inserts

This work focuses on developing the mathematical model of surface roughness (Ra) in the turning of Inconel 625 superalloy with cryogenically treated tungsten carbide inserts. The influence of cryogenic treated on the microstructure and hardness of tungsten carbide tools was also investigated for the as-received inserts and deep cryogenic treatment at − 196 °C for 12, 24, and 36 h conditions. Turning experiments have been performed according to an orthogonal array L16 with three parameters (cutting tool, feed rate, cutting speed) at different levels with a 1 mm depth of cut. The ideal cutting tool and cutting parameters were evaluated in terms of the surface roughness (Ra). Analysis of Variance has been applied to determine the percentage of each cutting factor. It has been observed that the cutting speed has a maximum with 66.28% contribution on Ra. The best optimal turning parameters are obtained as A3B3C1 according to S/N ration. The mathematical model of Ra has been developed by regression analysis. The developed model is tested with verification experiments and found to be in good agreement with the experimental results.

Analytical modeling and experimental verification of surface roughness in the ultrasonic-assisted ball burnishing of shaft targets

Ultrasonic-assisted ball burnishing (UABB) is a promising surface strengthening technology for improving the properties of components. This method superimposes ultrasonic vibration to the traditional deep rolling; it can improve the surface roughness of a material, enhance its surface hardness, and introduce a high compressive residual stress, thereby improving the fatigue performance of components. A mathematical model should be established to predict and analyze the relationship between the experimental process parameters and results and to predict the effect of UABB on surface roughness. In the present work, a mathematical model of surface roughness after UABB was established on the basis of Hertz contact theory, comprehensively considering the process parameters, dynamic vibration forces, and elastic rebound of the targets. UABB experiments were carried out to verify the correctness of the mathematical model. Results showed that UABB can significantly reduce the surface roughness of the material, and the values calculated from the derived mathematical model showed good agreement with the experimental findings. The surface roughness decreased with the burnishing force (50–250 N) and amplitude (4–10 μm) increased, whereas the feed rate decreased. The increases of radii of component and ball were detrimental to the improvement of the surface roughness. And elastic rebound was not conducive to roughness reduction and its influence was negligible. Finally, the derived surface roughness model can be used to predict the component values after UABB and understand the effects of machining parameters on the shaft targets during processing.

Mathematical model of surface roughness at a flat grinding by periphery of a circle of metal-polymer parts

This scientific work focused on determination grinding modes for metal polymer products that are filled aluminium. Also it is necessary to ensure required surface roughness and the highest performance. We used three factor planned experiment to get equation surface roughness metal polymer product at a flat grinding. The analysis and processing the results of the experiment was performed using statistical methods. Preparation of the products for experiments based on previously obtained scientific data. We used only calibrated measuring instrument for taking readings. In this scientific work was obtained the equation of surface roughness and table feed and cut depth at flat grinding of metal polymer products. Also it’s been got values of grinding modes of metal polymer surfaces on the joint of the molding tool, according to required surface quality. An obtained curve was built.Comparisons with common relationships are made. The scope of the results has been determined. The values of grinding modes for processing metal polymer surface on the joint of the molding tool based on surface roughness also given in the scientific work.

Investigation of Vibration, Sound Intensity, Machine Current and Surface Roughness Values of AISI 4140 During Machining on the Lathe

The AISI 4140 steel is one of the most widely used alloys in various applications due to its good formability, high-strength, weldability and excellent corrosion resistance properties. In this study, the effects of cutting parameters (feed rate, depth of cut and cutting speed) were investigated on surface roughness, vibration, sound intensity and machine current during turning of AISI 4140 using coated carbide cutting tools under dry test condition. The response surface methodology, analysis of variance and statistical methods of main effect plot were applied to investigate the effects of input parameters on the response variables. Mathematical models for surface roughness, vibration, sound intensity and machine current were developed using multiple linear regression methods. In addition, the confirmation test was carried out in order to validate reasonable degree of approximation between predicted and experimental results. The results of this study showed that feed rate has the most significant impact on output parameters followed by depth of cut. Therefore, according to the experimental data, vibration, sound intensity, surface roughness and current values increase as the amount of feed rate and the depth of cut increases.

Machining characteristics and optimization of process parameters in die-sinking EDM of Inconel 625

Inconel 625 superalloy is a versatile austenitic nickel-based superalloy with excellent strength and good ductility. It possesses excellent mechanical properties at both extremely low and extremely high temperatures with excellent resistance to pitting, crevice corrosion, cracking and crystalline corrosion. Inconel 625 superalloy is an important and frequently used material for an automobile, aerospace industries and marine application due to its excellent mechanical, chemical and physical properties. In the present research, empirical mathematical model for surface roughness and material removal rate (MRR) has been developed to study the influence of die-sinking electrical discharge machining (EDM) parameters, viz. peak current, pulse on time and pulse off time on Inconel 625. Central composite design is employed to plan experimental layout, and a quadratic model is adopted for empirical mathematical modeling. ANOVA is performed to test the adequacy of the model using F-test and p-test. Optimal setting of EDM parameters is obtained using composite desirability. ANOVA analysis reveals that peak current is the most dominating factor for MRR followed by pulse on time, while surface roughness is mostly influential by pulse on time followed by pulse off time. Surface roughness increases with the increase in pulse on time. MRR firstly increases with an increase in pulse on time and start decreasing after mid value (0), i.e., 15 µs whereas surface roughness continuously increases with an increase in pulse on time. Optimal setting of EDM parameters is obtained by composite desirability function. The goal is to minimize surface roughness and maximize MRR simultaneously. Results are validated by the confirmation experiment using the optimal set of EDM parameters. The confirmation experiments reveal that the experimental and predicted results are very close with error amounting of 2.19% and 2.58% for MRR and surface roughness respectively.

Mathematical Modeling of Surface Roughness in the Forming of Innovative Materials

Vacuum moulding (VM) process has many potential engineering applications. Not much work hitherto has been reported for modeling the surface roughness (SR) in VM process. In the present study, outcome of Taguchi model has been used for developing a mathematical model for SR; using Buckingham’s π-theorem. Three input parameters namely type of metal / pouring temperature; shape factor and vacuum pressure were selected to give output in form of SR. This study provides main effect of these variables on SR and shed light on the mechanism of SR in VM process.

Numerical analysis of contact plastic bodies made by aluminium alloy with taking account of micro-roughness surfaces

The following article describes selected aspects of numerical modeling of the process of bonding metal alloys with consideration for micro-roughness. Plastic contact between two deformable bodies is studied within a DEFROM FEM environment. The paper presents selected numerical analysis results for an aluminum alloy. The mathematical model of surface roughness has been created on the basis of the surface real profile. The dependence between the tool lathe angle and the feed has been used to build a numerical model of roughness after completion of the turning process. The article investigates the impact of wave roughness in respect to the size effect and the possibility of cold welding as well as the simplification process of real surface roughness.

A Numerical Approach to Measure the Surface Roughness of FDM Build Part

Abstract The fused deposition modelling (FDM) technology is used to fabricate 3D physical models from CAD data by adding material one over another within a reasonable time and less material waste. Since FDM is an additive manufacturing process, build parts are severely affected by stair case effect produced during part fabrication. While any inclination parts are fabricated this stair case effect plays a vital role in determining surface roughness of build parts. Since FDM is a parametric dependent process its performance characteristics are largely influenced by various controllable as well as uncontrollable process parameters. In this research work, the effect of four controllable process parameters i.e. layer thickness, raster width, overlap distance and part orientation on the surface roughness of fused deposition modelling (FDM) is numerically investigated and the mathematical modelling of surface roughness is formulated. Design of experiment (DOE) with face centered central composite design (FCCCD) is adopted to minimize the number of experiments. Result shows that layer thickness has most influencing parameters on surface roughness. Mathematical modelling are suggested to measure the surface roughness of FDM build parts.

Experimental verification of a numerical surface roughness model for metallic bodies under large plastic strain

The present work describes selected aspects of numerical modelling of the process of bonding metal alloys with consideration for micro-roughness, as well as experimental verification. The plastic-elastic contact between two deformable bodies was investigated in a DEFROM FEM environment, and verified at the test stand. The present paper demonstrates selected results of contact modelling investigated using aluminium-copper samples, in relation to their elastic-plastic range. The real surface profile helped to create a mathematical model of surface roughness measured using a laser microscope. Dependency between a blade of a tool and a feed was used to build a numerical model of roughness based on the arithmetic average value of the roughness profile. The work presents also a process of simplification of real surface roughness for the needs of numerical calculations. The paper investigates an impact of wave roughness at obtained values on effective plastic strain and stress. Additionally, numerical analysis shows a need to enter a new roughness wave correction factor assuming a zero value of the coefficient of friction. This is due to the interaction of metallic surfaces within the plastic contact zone. The obtained results allow the estimation of the impact of surface force interaction expressed by the wave coefficient factor. The experimental verification of numerical calculations allowed the estimation of the actual impact of the micro-cutting process in the entire friction process. Further analysis of obtained results permits the author to explain the surface phenomena occurring during the friction process, such as adhesion or diffusion, and outline the development direction of numerical methods.