Influence of Dressing Parameters on Surface Roughness and Wheel Life in Internal Grinding SKD11 Tool Steel

Abstract

This paper presents a multi-objective study on internal grinding to achieve minimum surface roughness (SR) and maximum wheel life (WL) at the same time. This study looked at six input parameters: coarse dressing depth a_r, coarse dressing time n_r, fine dressing depth a_f, fine dressing time n_f, non-feeding dressing n₀, and dressing feed rate S_d. The effect of these parameters on the SR and WL of the grinding process was investigated. Furthermore, optimal input parameters to achieve SR and WL at the same time were proposed. It was also reported that the optimal set of input dressing parameters was appropriate for use.

1 Introduction

Grinding is a common machining process used in practice to achieve a high-quality surface finish. It is especially useful for machining annealed products with high hardness and strength. It accounts for approximately 20–25% of total mechanical part expenditures in industries. Researchers have been interested in improving performance and lowering machining costs for general and internal grinding while maintaining accuracy requirements for these reasons.

There have been numerous studies on the optimization of the internal grinding process to date. The monitoring and optimization of internal grinding process have been done in [1]. To reduce production time while maintaining part quality requirements, an online optimization system for cylindrical plunge grinding was developed [2]. A study on optimal determination of replaced grinding wheel diameter in internal grinding was presented in [3]. The effects of grinding process parameters such as wheel life, total dressing depth, radial grinding wheel wear per dress, and initial grinding wheel diameter on the exchanged grinding wheel diameter were investigated in the study. The effect of coolant parameters on surface roughness in internal cylindrical grinding of annealed 9CrSi steel was evaluated in [4]. The work’s findings led to the identification of optimal input parameters for achieving the lowest surface roughness. The authors in [5] determined the optimum replaced wheel diameter in stainless steel internal grinding. The effects of input process factors and cost components were investigated in this work. In [6] presented a study on optimizing internal traverse grinding of valves based on wheel deflection. Many single-objective [7] and multi—objective [8] optimization studies on internal grinding have been conducted. The optimum parameters of dressing process for internal grinding was proposed in several studies [9, 10]. Recently in [11] have applied the multi-criteria decision making (MCDM) method to determine the best dressing setup for internal grinding process.

This paper presents the results of a multi-objective optimization study on dressing process for internal grinding. In this work, the minimum SR and maximum WL were selected for the objectives of the optimization study. The effect of the input parameters of the dressing process were evaluated. In addition, an optimum set of input dressing factors for internal grinding SKD11 tool steel was proposed.

2 Experimental Work

Fig. 1.

Experimental setup

An experiment was carried out in order to solve the multi-objective optimization problem. This experiment was designed using the Taguchi method and the L16 orthogonal array (4⁴ × 2²). The input factors and their levels are shown in Table 1. Figure 1 depicts the experimental setup, with the dressing parameters shown in Table 1. The experiment was carried out as follows: the dressing process was carried out according to the plan shown in Table 2. After dressing, the grinding wheel was used to grind test samples at the following speeds: wheel speed of 12000 (rpm); workpiece speed of 150 (rpm); radial wheel speed of 0.0025 (mm/stroke); and axial feed speed of 1 (mm/min.). Following the completion of the experiments, the SR (in this case, Ra (μm)) was measured and WL (min.) was calculated. Table 2 shows the experimental plan as well as the output results (RS and WL).

Table 1. Input dressing parameters and their levels

Table 2. Experimental plan and output results

Multi-objective Optimization

For multi-objective optimization, the gray relational analysis (GRA) method combined with the Taguchi method were used. In the study, two objectives including the minimum surface roughness and the maximum durability of the grinding wheel were selected for the investigation.

The signal to noise (S/N) ratio for each test can be calculated using the surface roughness expectation that “the smaller the better”:

$$ {S / N} = -10log_{10} \left( {\frac{1}{n}\sum_{i = 1}^n {y_i^2 } } \right) $$

(1)

conversely for WL is “the larger is better”:

$$ SN = -10log_{10} \left( {\frac{1}{n}\sum_{i = 1}^n {\frac{1}{y_i^2 }} } \right) $$

(2)

where n is the total of test runs, yi the observed data.

The normalized values of grey relation for both SR and WL can be determined by $\rm{Z}_{\rm{ij}} \left( {0 \le \rm{Z}_{\rm{ij}} \le 1} \right):$

$$ Z_{ij} = \frac{{SN_{ij} - \min \left( {SN_{ij} ,j = 1,2, \ldots k} \right)}}{{\max \left( {SN_{ij} ,j = 1,2, \ldots n} \right) - \min \left( {SN_{ij} ,j = 1,2, \ldots n} \right)}} $$

(3)

Table 3 displays the S/N ratio and the normalized grey relation values. The grey relation coefficient, (y(k)) which express the relationship between reference and experimental data normalized data is found as follows:

$$ \gamma \left( k \right) = \frac{\Delta min + \zeta \Delta max}{{\Delta_j \left( k \right) + \zeta \Delta max}} $$

(4)

Table 3. Grey relational coefficient and grey grade values

In which:

$\Delta {\text{oj}}$ is the deviation of reference data.

$\Delta_j \left( k \right) = \left\| {Z_0 \left( k \right) - Z_j \left( k \right)} \right\|$ and Z0(k) is the reference data or best data.

(+) $\Delta \min = \mathop {\min }\limits_{\forall j \in i} \mathop {\min }\limits_{\forall k} \left\| {Z_0 \left( k \right) - Z_j \left( k \right)} \right\|$ minimum value of $\Delta_i \left( k \right).$

(+) $\Delta \max = \mathop {\max }\limits_{\forall j \in i} \mathop {\max }\limits_{\forall k} \left\| {Z_0 \left( k \right) - Z_j \left( k \right)} \right\|$ maximum value of $\Delta_i \left( k \right).$

(+) ζ is distinguishing or identification coefficient; ζ = 0÷1 (In this case ζ = 0.5).

Calculating the gray relational grade:

$$ \overline{\gamma }_j = \frac{1}{k}\sum_{i = 1}^m {\gamma_{ij} } $$

(5)

wherein k is the number of objectives optimized.

3 Results and Analysis

The Taguchi method is used to assess how dressing parameters affect mean gray relation values. The S/N value of is calculated using formula (2) in order to maximize the average gray relation value. Table 4 shows the calculated results of the effect of input parameters on the average gray relation value using the ANOVA method.

Table 4. Effect of dressing parameters on the gray relation values $\overline{y}_i$.

Table 5. Influence order of the dressing parameters on $\overline{y}_i$.

According to Table 4, the two parameters that have the greatest influence on $\overline{y}_i$ are n_f (39.98%) and n > (32.24%); followed by the influence of n_r (16.71%), a_f (5.31%), and a_r (1, 79%). Furthermore, S_d has no discernible effect on $\overline{y}_i$ (0.27%). The order of influence of the parameters on the gray relation value is described in Table 5. This table shows that the order of influence of input parameters is nf, n0, nr, af, ar, and Sd, in that order.

Figure 2 depicts the influence of input parameters across levels. From Fig. 2 it is easy to see that when n₀ increases from level 1 to level 3 increases; However, when it increases further to level 4, it reduces $\overline{y}_i$; With n_f: when n_f increases from level 1 to level 2, $\overline{y}_i$ increases sharply; however, when it continues to increase from level 2 to level 4, $\overline{y}_i$ decreases; With a_f: when a_f increases from level 1 to level 2, $\overline{y}_i$ increases insignificantly; a_f increases from level 2 to level 3 causing $\overline{y}_i$ to increase; Nonetheless, if it increases to level 4, $\overline{y}_i$ decreases sharply; The impact of n_r is described as follows: If it increases from level 1 to level 2 and from level 3 to level 4, $\overline{y}_i$ changes little; Nevertheless, when n_r increases from level 2 to level 3, $\overline{y}_i$ decreases sharply; The effect of a_r as follows: when a_r increases from level 1 to level 2, $\overline{y}_i$ will decrease. Besides, when S_d increases from level 1 to level 2, $\overline{y}_i$ increase slightly.

To determine the best dressing mode, take into account the effect of the input parameters on the S/N ratio. As previously discussed, the set of parameters with the highest value for each input factor is the most reasonable. The larger value S/N corresponds to $\overline{y}_i$ being as large as possible. This also implies that the effect of noise is reduced. Figure 3 depicts the effect of input parameters on the S/N value. Also, this Figure identifies the optimal set of parameters for the multi-objective function (Table 7).

Fig. 2.

Effect of input parameters on $\overline{y}_i$.

Fig. 3.

Effect of input parameters on S/N ratio

Table 6. Optimum dressing parameters

Table 7. Prediction of values RS and WL corresponding to the optimal parameters

Using Minitab 19, the optimal set of parameters can be used to calculate and predict the results of the objective functions (Table 6). The surface roughness Ra = 0.1821 (μm) and the wheel life T_w = 12.8431 (min.) were obtained from the predictive analysis results with the optimal set of dressing parameters.

Evaluation of Experimental Models:

The Anderson–Darling method was used to assess the suitability of the experimental model (Fig. 4). Figure 4 shows that the experimental points (the blue points) on the histogram are very close to the normal distribution line (the red solid line). It demonstrates that the deviation is very small. The Histogram graph of error frequency shows that the majority of errors are in the −0.1 to 0.1 range. The experimental errors in the other two graphs are distributed at random. This means that the built model is heavily influenced by the input parameters chosen and is unaffected by the order of experiments.

The Anderson–Darling method was used to validate the experimental model’s fit (Fig. 5). The results on this figure show that the experimental points (blue dots) are all within a 95% confidence interval bounded by two limit lines. Furthermore, the value of P of 0.185 is greater than a = 0.05, indicating that the empirical model used is appropriate.

Fig. 4.

Residual plots for S/N ratios

Fig. 5.

Probability plot of the fit of proposed model

4 Conclusions

The results of a multi-objective optimization study in the dressing process for internal grinding SKD11 tool steel are presented in this article. For the investigation, six input dressing parameters were chosen. The Taguchi technique is used in conjunction with GRA to reduce the surface roughness and increase the wheel life. The following conclusions can be drawn from the findings of this work:

• The influence of the dressing factors on the SR and WL of the grinding process was investigated.

• The most affected factors on $\overline{y}_i$ are n_f (39.98%) and (32.24%); followed by n_r (16.71%), a_f (5.31%), a_r (1, 79 %), and S_d (0.27%).

• The following input factors were proposed for the best dressing process when internal grinding to achieve minimum SR and maximum MRR simultaneously: a_r = 0.03 (mm/l); n_r = 2 (times); a_r = 0.025 (mm); a_f = 0.015 (mm); n_f = 1 (times); n₀ = 2 (times); and S_d = 1.2 (m/min).