Indian Journal of Engineering & Materials Sciences Vol. 25, February 2018, pp. 59-68

Simulation of surface patterns imprinted by wheel grinding which dressed by rounded tools

Md Mofizul Islama, Hochan Kima* & Tae Jo Kob

aDepartment of Mechanical and Automotive Engineering, Andong National University, 1375 Gyeongdong-ro, Andong, Gyeongbuk 760-749, South Korea

bSchool of Mechanical Engineering, Yeungnam University, 214-1 Daedong, Gyoungsan, Kyoungbuk, 712-449, South Korea

Received 21 October 2015; accepted 14 June 2017

Surfaces having more precise pattern are effective for lubrication, friction or drag, being designed by engineers and incorporated into the components specification. Therefore, it is very important to develop such precise surface patterns in a repeatable and economically viable way. The aim of this research work is to develop rounded groove surface pattern model by grinding with the grooved wheel based on dressing. In order to grooving of grinding wheel, a rounded tip dresser is used instead of sharp tip dresser. The developed grooved wheel geometry model can be integrated with a grinding process model for simulating rounded groove surface patterns. A computer based simulation program is developed using Matlab according to proposed mathematical model to display 3D geometry of the patterned surface. The simulation results of resulting surface pattern with rounded groove can be realized by interactively inputting parameters in to the developed software. An experiment has been carried out for the verification of the simulation results and it is found that the simulation results agree well with the experiment. The simulation results could be used to predict the rounded groove surface patterns by the given grinding parameters.

Keywords: Grinding wheel, Dressing, Surface patterns, Rounded groove, Simulation, Modeling

Surface pattern scan be generated by a controlled grinding process with the wheel shaped in a particular way. Patterned surface has been successfully used in many applications to improve the performance of surfaces. The mechanical parts having regular and repeated pattern is classified into dimple or riblet which are effectual in terms of lubrication, friction or drag. Grinding with grooved wheels produced by dressing arises as a potential alternative by combining its inherent finishing process characteristics, its capacity of cutting hard materials, with relative low process technical requirements, low investment and short cycle times. User defined patterns can be imprint on the wheel surface during dressing and later transferred to the parts by grinding, which promotes a freedom of choices for transferring patterns to the work-piece during regular grinding1. Surfaces having local, regular groove cavities arranged in a regular way show many advantageous features, regarding mainly tribological effects such as: reduction of fluid and boundary friction coefficients, absorption of small hard particles from the lubricant, reduction of residual stress and shape deviation, better leak-tightness of

static and dynamic couplings and better adherence of coating and adhesive bonds. Surface patterns may be generated by several ways, such as: precise diamond turning2, rolling3, embossing4,5, etching6,7, vibrorolling8, abrasive jet machining9 and electro discharge machining (EDM)10. Impressive results of laser surface texturing were demonstrated in many papers11-16. Pattern grinding with the wheel shaped in a special way was first presented in 1989 which is simple, cheap and productive methods for surface pattern generation17.

There are many examples of successful practical application of specially grooved surfaces. One of the most known is the so-called "plateau" surface, applied in honed surfaces in cylinder liners of two-stroke engines18,19. Chamorro et al.20 showed that riblet could provide an overall reduction of skin friction drag and the amount of the drag reduction varied with riblet height and geometry. Also, Denkena21 created riblet pattern on a surface by grinding with wheel dressed by patterned diamond roller, and the riblet pattern was applied to a turbine blade21. Jannone et al.22 developed the strategies for producing textured surfaces by grinding with the patterned wheel for industrial application. Bruzzone et al.23 reported a

——————— *Corresponding author (E-mail: hckim@anu.ac.kr)

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comprehensive view of the surfaces functionalities and processes that can be applied for texturing. One of the topics discussed on that publication was the application of textures for the improvement of lubrication showing good perspectives23. Costa and Hutchings24 showed that the use of small cavities uniformly distributed over the sliding surface offers the best tribological results for hydrodynamic bearings . Ren et al.25 showed that the simulation results of narrow short grooves with sinusoidal profile perpendicular to the motion direction give the most performing lubrication results for traditional automotive applications. Chakrabarti and Paul26 developed a simulation methodology for generation of the ground surface and also studied the effect of different grinding parameters on ground surface topography. Nguyen and Butler27 proposed a numerical procedure for the kinematic simulation of the grinding process in which wheel-work-piece interaction is taken into consideration in the generation of the work-piece surface. A number of researches have been implemented by Stephen28-31

regarding process modeling, computer simulations, and technological experiments of grinding. Salisbury et al.32 proposed a geometric-kinematic model for the generation of surface patterns incorporating the effects of process parameters such as table speed and wheel speed and also takes into account the wheel topography and original work-piece surface texture32.

Since wheel working surface has a direct impact on the quality of the ground surface pattern, hence it is significant to establish a proper geometry model of the grinding wheel at first. The generation of the work-piece surface is started with the generation of the grinding wheel surface. Therefore, this paper proposes a rounded groove surface pattern model generated by grinding with the wheel which is dressed by rounded tip tool. In order to making grooves on the wheel surface a rounded tip dressing tool is applied instead of sharp tip dresser of previous work33 in the dressing process. The structure of the grooved wheel yielded three dimensional surface patterns on the work-piece. Also an experiment is carried out for the verification of the obtained simulation results.

Simulation of Wheel Dressing by Rounded Tool Actually, the tip of the dressing tools are initially in

sharp in shape, but after dressing a while, the tip of the tool become rounded to some extent. Hence, it can be more effectual to use rounded tip tool to obtain precise groove on the wheel surface and consequently

rounded patterns on the work-piece. Therefore, it is significant to use rounded tip dresser for the generation of groove by dressing process. However, in the previous study of surface patterning, sharp tip dresser was used for wheel grooving33. To generate the rounded patterns on the work-piece, it is necessary to make rounded groove on the wheel working surface by the dresser in advance. The process of wheel dressing was described as grinding wheel is work-piece and dresser is the thread tool 34. The rounded groove on the wheel surface formed by the dressing was established by the relative motion between the grinding wheel and dresser35. Figure 1(a) shows the schematic shape of a rounded tip dresser and the kinematic relationship between the grinding wheel and the diamond dresser is represents by Fig. 1(b). The rounded tip dresser having a crest angle of αt, width of dressing b, radius of the rounded tip of the tool is r, the distance between the crest of the tool and the reference point is t which represent the depth of dressing, maximum depth of dressing is h, and other related symbols used during the simulation of dressing process are described in Fig. 1.

The shape of the rounded tip dressing tool is a combination of a circular portion and a linear portion. Therefore, the maximum depth of dressing h can be derived from an equation of a circle and a straight line equation as described by Eq. (1).

; where … (1)

; where

Here, 2;

2; and

22

The schematic shape of the cross-section of the grooved wheel after dressing by the rounded tip dresser is represents by Fig. 2. The cross-section

Fig. 1—(a) Schematic shape of the rounded tip dresser, (b) Relationshipbetween the wheel and dresser [35]

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having the maximum radius of the original grinding wheel is Rmax, the minimum radius at the deepest region of grooveis represent by Rmin, and Rθ be the radius of the grooved wheel at an arbitrary rotational position θ from the minimum radius. The linear relationship exists between the angle of dressed region and the width of dressing and also a linear relationship exist between the wheel rotation (2π) and wheel screw pitch p as like 2π: p= θ: x. From this linear relationship, x can be computed with respect to an arbitrary rotation angle θ35.

Accordingly, from this linear relationship the angle of machined area by the rounded segment of the tool θt2 can be determined by Eq. (2) and the angle of machined region by the linear portion of the tool θt1

can be estimated using Eq. (3). Therefore, the total angle of dressing region θt’ can be expressed by the Eq. (4). The width of dressing b can be computed with respect to αt and t34.

. … (2)

∙ … (3)

∙ … (4)

The position at which an arbitrary rotational angle θ is zero degree represents the maximum dressing depth and alternatively dressing depth is zero at the position of half of the dressed region. Hence, the radius of the grooved wheel cross-section Rθ at the rotational position θ can be computed using Eq. (5) under two conditions, where ht(θ) is the maximum depth of dressing with respect to an arbitrary rotation angle θ.

; Where, … (5)

Otherwise;

The relationship between the wheel screw pitch p and the distance along the wheel axis z is like that 2π: p= α: z, and from that relationship the rotational angle α with respect to z that appears at every pitch p can be computed using Eq. (6).

2 … (6)

In cylindrical coordinate system, the rotational angle ∅ of the grooved wheel at the z distance from the origin can be estimated using Eq. (7)

∅ 2 … (7)

Simulation of Rounded Patterns Generation

Grinding depth of patterning The reproduction of textured surface is realized by

the relative motion between the grooved wheel and work-piece during grinding33. Figure 2 shows the grinding depth dθ while patterning of surface and dθ

can be computed using Eq. (8), where H is the height of the center of the wheel to the upper surface of the work-piece.

; Where 0 … (8)

0; where 0 Grinding width and angle of patterning

Figure 3 shows the schematic of the grinding starting distance and grinding accelerating angle of the patterning. The half of the contact angle between the wheel and work-piece θs is the grinding accelerating angle and can be determined using Eq. (9). The grinding starting distance Gap that is the distance from the start of the wheel rotation to the center of the wheel can be computed using Eq. (10). Also the initial position of the center point of the roll can be represent as, xint = -Gap.

… (9)

Fig. 2—Cross-sectional shape of grooved wheel in a planeperpendicular to the axis

Fig. 3—Schematic of the grinding starting width and accelerating angle of patterning

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∙ … (10)

Simulation process of surface patterning

The generation of rounded groove surface patterns is dependent on the wheel active surface geometry, work-piece geometry and grinding condition. A schematic of the surface grinding process on which the model is based is shown Fig. 4. Figure 4(a) shows the schematic of the grinding process with the wheels having rounded helical grooves for shaping rounded patterns on work-piece surfaces. Figure 4(b) shows the schematic mapping of the wheel trajectories to the work-piece surface. The position of the wheel and work-piece and also the model parameters associated with them at an initial time and after a short interval of time is represent by Fig. 4(c). The structure of the wheel can be incorporated into the work-piece surface by inputting the array of surface heights representing the wheel surface. The work-piece surface geometry is represented as a grid and is basically computed as an array of points. When starting rotation the center of the wheel is located at a distance equal to the Gap as

mentioned in Eq. (10). The execution of the simulation process is based on time, therefore, the rotation of wheel and the corresponding points on the work-piece are updated by the specified time interval. Hence, the corresponding grinding depth on the work-piece surface is updated with the passing of time. Therefore, the desired pattern on the work-piece surface can be obtained by updating the points on the work-piece surface.

In this study, the grinding process is simulated using Matlab programming language. The parameters used as inputs for the simulation program are wheel dressing condition, work-piece data, cutting conditions and resolution required for calculating and plotting the surface pattern. For the progress of surface patterning, the grinding starting distance Gap

need to be computed first as mentioned in Eq. (10). The grinding operation is accelerating by the evaluation of half amount of the contact angle between the wheel and the work-piece θs as mentioned in Eq. (9). In the simulations, a perfectly flat surface (no initial roughness) is assumed and while passing of time all the points on the work-piece should be marked for patterned out. This assumption does not affect the performance of the model. The details of the simulation process of the surface patterning with a flow diagram are exposed in the previous study33.

Simulation Results

Simulation conditions for generation of rounded patterns Based on the proposed mathematical model of

wheel dressing and surface patterning, the program on numerical simulation and three dimensional image displays were developed using Matlab. A grooved wheel geometry model, an input for the simulation was developed using the parameters are as follows: depth of dressing t, rounded tip radius of the dressing tool r, radius of the grinding wheel D, pitch of the wheel screw p, crest angle of the rounded dressing tool αt, and the direction of the wheel screw dir35.The simulated grooved wheel based on the above parameters was used to simulate the grinding patterning process, with the grinding parameters are as follows: depth of dressing t, radius of the rounded tip of the tool r, the radius of the wheel D, pitch of the wheel screw p, crest angle of the dressing tool αt, grinding wheel rotational speed ω, moving speed or feed rate of the work-piece v, the height of the center of the wheel to the upper surface of the work-piece H, the direction of the wheel screw dir, number of screw threads of the wheel threads, and the

Fig. 4—Schematic of the surface pattern reproduction process onthe work-piece

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number of rotations of the wheel screw turns. And also the number of points per rotation of wheel pt_turns, the number of points per threads pt_threads, splitting the grinding starting angle θs into number of section pt_theta, was needed for the simulation of surface patterning.

The desired rounded patterns on the work-piece surface is obtained by grinding with the proposed grooved wheel as shown in Fig. 5 according to the input parameters are as follows: t: 2 mm, r: 0.4 mm, D: 4 mm, p: 1.66 mm, αt: 45 degree, ω: 2π rad/s, v: 100 mm/s, H: 2 mm, consider right hand direction of the wheel screw with 10 threads and 2 turns of the wheel. Also, pt_turns: 50, pt_threads : 70, pt_theta: pt_turns/2.

Moreover, the obtained standard feature of rounded groove patterns (Fig. 5) is compared with the surface

pattern model with V-groove as shown in Fig. 6. The surface pattern model of V-shaped groove33 was obtained by grinding using the same input parameters as rounded groove model. With the view of geometrical aspect, the rounded groove surface patterns shown in Fig. 5 is significantly different and advanced than the V-shape patterned surface of previous work33 as shown in Fig. 6.

Comparison of rounded groove patterns The input parameters used to simulate surface

patterns can be varied and accordingly simulation results in the desired grinding condition can also be varied. Several simulation results are displayed by varying inputs parameters in order to make comparison with the standard features of the surface patterns. The varying simulation conditions of the obtained rounded groove surface patterns are summarized in Table 1.

Table 1 – Simulation conditions of the obtained surface patterns with rounded groove.

Obtained surface model

Dressing depth, t (mm)

Rounded tip radius of tool, r (mm)

Radius of wheel,D (mm)

Wheel screw pitch, p (mm)

Crest angle of tool, αt (degree)

Screw direction of wheel (dir)

Fig. 5 2 0.4 4 1.66 45 Right handed Fig. 6 2 - 4 1.66 45 Right handed Fig. 7 1 0.4 4 1.66 45 Right handed Fig. 8 2 0.8 4 1.66 45 Right handed Fig. 9 2 0.4 8 1.66 45 Right handed Fig. 10 2 0.4 4 3.32 45 Right handed Fig. 11 2 0.4 4 1.66 30 Right handed Fig. 12 2.8 0.4 4 1.66 45 Right handed Fig. 13 2 0.4 4 1.66 45 Left handed

Fig. 5—Standard feature of grooved wheel (a) and resulting rounded groove surface patterns (b)

Fig. 6—Comparison of standard feature with V-shape groove patterns [33]

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If the depth of dressing is reduced to half than the standard features (Table 1), noteworthy change is observed in the surface pattern model as shown in Fig. 7. Due to reduced dressing depth, the obtained rounded groove surface with flat bottom and reduced groove depth is observed. Alternatively, a significant reduction of the groove depth was found in the obtained rounded groove patterns as shown in Fig. 8, when rounded tip radius of the tool was increased to double than the standard features (Table 1).

On the other hand, Fig. 9 shows the enlarged diameter of the wheel and corresponding rounded groove surface patterns, due to increased wheel radius by two times (Table 1) than the standard features. If the pitch of the wheel screw is increased to double than the standard features (Table 1), the resulting simulation results of the rounded patterns was changed as shown in Fig. 10. As a result of increased screw pitch, the width of flat bottom surface of the

obtained patterns was increased considerably. For comparison with the standard features of the surface patterns, the crest angle of the dressing tool is reduced from 45o to 30o (Table 1), and the obtained surface patterns with wide flat bottom and reduced groove depth was observed as shown in the Fig. 11.

It is possible to obtain surface patterns with flat top by shaping deeper grooves on the wheel surface. Accordingly, Fig. 12 shows the surface patterns with

Fig. 7—Comparison of surface patterns by reducing dressing depth t (2to 1 mm)

Fig. 8—Comparison of surface patterns by increasing tip radius of tool r (0.4 to 0.8 mm)

Fig. 10—Comparison of surface patterns by increasing wheel screw pitch p (1.66 to 3.32 mm)

Fig. 9—Comparison of surface patterns by changing radius of the wheel D (4 to 8 mm)

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flat top, by increasing depth of dressing from 2 mm to 2.8 mm (Table 1).The simulation results discussed in the above was the right hand direction of wheel screw, where as Fig. 13 demonstrated the rounded groove surface patterns with left hand direction of the wheel screw.

In Figs 5-13, it is shown that the geometry of the obtained surface patterns varied with the varying simulation conditions as summarized in Table 1. The simulation results in this paper can be used to guide the actual grinding process in order to improve the machined surface quality. On the other hand, one can predict the surface patterns by using the given grinding parameters. Numerical evaluations of the rounded groove surface patterns

To perform numerical analysis, the cross-section of the different surface patterns obtained by varying simulation conditions as mentioned in

Figs 5-13, are shown in Fig. 14 (a-i).The numerical evaluation was carried out on the geometric features of the obtained rounded groove patterns. The geometric features of the obtained rounded groove patterns such as: depth of the groove dg, top width of the groove wt, bottom width of the groove wb, and the distance between the top of work-piece to the top of the grooves are summarized in Table 2. The numerical evaluation of the rounded groove patterns revealed that the geometry of the obtained surface patterns varied with varying simulation conditions.

Verification of the simulation results

An experiment was carried out for the verification of the obtained simulation results. The experiments of the wheel dressing for making grooves as well as grinding of surface patterning were done with the

Fig. 11—Comparison of surface patterns by reducing crest angle of tool αt (45o to 30o)

Fig. 12—Flat upper surface of the patterns by increasing dressing depth t(2to 2.8 mm)

Fig. 13—Comparison of surface patterns by changing screw direction (right hand to left hand)

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same machine tool, a 3-axis machining center. A GC180J8V grinding wheel was used for grooving as well as surface patterning, and was clamped to the spindle with a special device for chucking the grinding wheel. The work-piece material was carbon steel (AISI 1045). The experimental set-up for the wheel dressing and surface patterning process is shown in Fig. 15.

In the experiment, a diamond dresser was mounted onto the table which was operated by NC code for making grooves on the grinding wheel and after that the desired patterns was obtained by single pass of the grooved wheel on the work-piece. Since the wheel dressing and patterning is done at the same machine tools, the errors from loading and unloading of the grinding wheel were reduced. Before making grooves

Fig. 14—(a-h) Comparison of geometric features among the obtained rounded groove patterns.

Table 2 – Numerical evaluations of the obtained rounded groove surface patterns

Obtained surface model

Depth of groove, dg

(mm) Top width of groove, wt

(mm) Bottom width of groove, wb

(mm) Distance between top of work-piece

to top of the groove, s (mm)

Fig. 5 1.3547 1.66 0 0.6453 Fig. 6 1.9065 1.66 0 0.0935 Fig. 7 0.3550 1.66 0.830 1.6450 Fig. 8 0.7090 1.66 0 1.2910 Fig. 9 1.3547 1.66 0 0.6453

Fig. 10 1.3547 3.32 1.660 0.6453 Fig. 11 0.8550 1.66 0.581 1.1450 Fig. 12 1.2040 1.079 0 0 Fig. 13 1.3547 1.66 0 0.6453

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on the grinding wheel surface, the whole surface was dressed in order to assure the concentricity of the wheel surface to the center of the machine spindle. After that, the thread grooving was done with groove pitch of 1 mm, and depth of groove 60 μm. Since the dressing depth for one cycle was 2 μm, a total of 30 cycles was necessary for making groove. The details of the experimental process were described elsewhere36.

Figure 16 compares the noncontact measurement results with the simulation results of the single groove surface patterns for verification in the case of feed rate 4800 mm/min and wheel speed 1200 rpm. Figure 17 shows the comparison between the cross-section of the measurement and simulation results of the single groove patterns. In the cross-section, it was observed that the depth and pitch of the groove is same in the simulation and experimental results. In the comparison, it was found that the experimental results agreed well with the simulations results of the

surface patterns. A comparison regarding pitch, depth and angle of pattern between the simulation and experimental results are given in Table 3. The measured angle of pattern has a small deviation due to the measuring error.

Fig. 16—Comparison between the simulation and experimental results of the surface patterns for verification, (a) measurement (b) simulation

Fig. 15—Experimental setup [36]

Table 3 – Comparison between the simulation and experimental results

Parameters Simulation Experiment Deviation (%)

Depth of the groove (μm)

18.034 18.034 0

Pitch of the groove (mm)

1 1 0

Angle of the pattern (degree)

14.04 14.2 1.12

Fig. 17—Comparison between the cross section of the patterns, (a) measurement (b) simulation

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Conclusions In this study, a new surface pattern model with

rounded groove has been proposed based on the wheel geometry which was dressed by rounded tip tool. The wheel work-piece interaction is taken into consideration for the generation of the rounded groove patterns on the work-piece. In the simulation results, it was observed that the dressed rounded groove on the wheel working surface is well transferred to the work-piece surface during simulation of grinding process. For validation of the standard features of rounded groove patterns, several simulation results were displayed by varying simulations conditions. The three dimensional geometry of the resulting surface patterns with rounded groove displayed in this paper is mainly considered from the geometric point of view. The numerical evaluations of the obtained rounded patterns indicated that, the geometry of the patterned surface varied with the varying grinding conditions or wheel geometry. It was observed that, the experimental results agreed well with the simulation results of the surface patterns. The simulation model could be used to control the actual grinding patterning process or to predict the rounded groove surface patterns by the given grinding parameters. Acknowledgements

We would like to acknowledge the support of the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (NRF-2013R1A1A2012654). We would also like to thank Mr. Han Dosup for his help to carry out the experiment. References 1 Oliveira J F G, Bottene A C & Franca T V, Ann CIRP,

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