Wheel wear related instability in grinding of quartz glass

Grinding is a popular method for producing high-quality parts made of hard and brittle materials. A lot of researchers have focused on the impact of grinding parameters on surface quality. However, only a few studies discussed the surface quality instability caused by the grinding wheel wear during a long grinding process. In this paper, through wheel state monitoring and surface quality testing of ground samples, it is found that the relationship between ground surface roughness and theoretical undeformed chip thickness is significantly affected by the grinding wheel wear state, rather than maintain steady as described in most available models. By introducing the normal grinding force, a linearly relationship was found among normal grinding force, undeformed chip thickness and ground surface roughness. Besides, sensitivity analysis was conducted to guide the parameter adjustment to maintain the stability of ground surface roughness and grinding state. The mechanism of the effect of wheel wear on normal grinding force was also studied in detail. This study will help to further understand the mechanism of the

positively correlated with the contact area between abrasive grits and workpiece. This research was helpful to understand why the grinding force increases with grinding wheel wear progresses.
These research results have shown that it is feasible to use the grinding force to characterize the grinding wheel wear.
Additionally, it is necessary to know whether the change in grinding force due to wheel wear has a significant effect on the ground surface roughness. Sevaraj et al. [32] studied the changes in cutting force and surface roughness with wheel wear. Their results showed that cutting force and surface roughness have similar trends with the wheel wear exacerbating. Zhu et al. [33] found a certain relationship between grinding force and machined surface roughness. Therefore, the normal grinding force could be used as the characteristic parameter of grinding wheel wear to learn the further relationship between wheel wear and ground surface roughness. However, how to use the grinding force to judge the wear state of the grinding wheel and predict the roughness more accurately remains to be studied.
With the development of artificial intelligence, intelligent manufacture will be an important form of processing in the future. To achieve the purpose, the grinding situation should be monitored online and the wheel wear is then an important factor that affects the grinding quality.
When the grinding wheel is worn and the shape of abrasive grits changes, the prediction results of the models that considering only processing parameters will have a large deviation. To fill this gap, the changes caused by grinding wheel wear is monitored through the normal grinding force.
Through the introduction of the normal grinding force, the wear factor is incorporated into the roughness prediction model to achieve a more accurate prediction result. Besides, the sensitivity of ground surface roughness and normal grinding force to machining parameters and grinding wheel wear is also analyzed in this paper. And the results can be used to guide the adjustment of grinding parameters and ensure the stability of the grinding process.

Experimental materials
The material of specimens used in this experiment was quartz glass. The quartz glass had a hardness of 5.5 HM, bending strength of 67 MPa, and elasticity modulus of 72 GPa, as presented in Table 1. The specimens had dimensions of 15 mm×15 mm×10 mm.

Experiment setup and conditions
The grinding experiment was conducted on a computer numerical control (CNC) milling machine NHM 800, 10 kW. Firstly, the specimens were glued on an iron block. Secondly, the iron block was clamped with a flat-nose plier. Thirdly, the flat-nose plier was fixed on the dynamometer, shown in Fig. 1. respectively. The grinding process was conducted without coolant. The levels of three grinding parameters are listed in Table 2. In the long grinding process, grinding wheel wear will affect the stability of the grinding quality. However, the wear of grinding wheel is not obvious in a short time grinding of quartz.
Therefore, before the quartz grinding test, the grinding wheel was used to grind a 41Cr4 steel sample to accelerate the wheel wear. When the material removal volume of 41Cr4 steel (MRV41Cr4) was 735, 3045, 13545, 29295, and 50295 mm 3 , the grinding wheel was marked as stage 1, stage 2, stage 3, stage 4, and stage 5 respectively. In different wear stages, grinding experiments of quartz samples were carried out and two workpieces were ground without coolant for each set of processing parameters.

Measurement method
In different wear stages, the grinding wheel topography was measured in a laser scanning confocal microscope (KEYENCE VK-X260K). Five busbars were evenly chosen on the cylindrical surface of the grinding wheel, and three positions on each busbar were taken for the wheel topography measurement. After the wheel topography measurement, the grinding experiment of quartz glass was performed.
During the grinding process, the grinding force was measured using a piezoelectric dynamometer Kistler 9139 AA2, and the sampling frequency was set to 10kHz to collect the grinding force signal. Then the force signal was subjected to Butterworth low-pass filtering with a cut-off frequency of 2 Hz, and the mean and standard deviation value of the force signal was calculated from the filtered force signal.
After grinding, the surface roughness of the workpiece was measured by a profilometer (Talysurf CLI2000). Every workpiece was tested in 5 different positions. The sampling length was randomly select to pre-measure the roughness of the ground surface. Results showed that the roughness was in the range of 3 to 9 microns. According to this result, the final sampling length was selected as 2.5 mm and the data length was selected as 8 mm. The topography of the ground surface was measured by a laser scanning confocal microscope (KEYENCE VK-X260K) and a scanning electron microscope (FEI QUANTA 450).

The influences of wheel wear on grinding force and surface roughness
During the grinding process, the abrasive grits were continuously worn, showing as attrition wear, fracture, and grits dropped-out. At the same cutting depth, the greater the wear, the larger the contact area between abrasive grits and workpiece will be, thus the grinding force increases with abrasive grits wear [31].
The experiment data were shown in Table 3. The topography of the grinding wheel and ground surface in different wear stages were shown in Fig. 2 and Fig.3. In stage 2, the attrition wear of abrasive grits was observed. In this stage, most of the abrasive grits have sharp edges, and the normal grinding force was 35.11N in trail No. 2. Obvious groove marks and significant material fragmentation were also observed on the ground surface in stage 2 ( Fig. 3). As the wear intensified, the attrition wear of abrasive grits gradually exacerbated, which was manifested as the increase of the wear area. Besides, the abrasive grits fracture and dropped-out ( Fig. 2) occurred. These phenomena caused the abrasive cutting edge to become blunt, which in turn led to an increase in the grinding force and the material was broken into finer pieces (Fig. 3). As the wear of the grinding wheel increased, the grinding force further increased, while the grinding surface tended to be flat and the fragment became finer.  where tm is the maximum undeformed chip thickness, C is the number of cutting points per area, r is the aspect ratio of the chip section, Vw is the infeed rate of the workpiece in m/s, Vs is the speed of grinding wheel in m/s, Ap is the nominal depth of cut in m, de is the equivalent diameter of grinding wheel in m.
Defining a grinding processing parameter-related factor , then the maximum undeformed chip thickness is The parameter k is determined by three grinding parameters, which reflects the influence of processing parameters on the maximum undeformed chip thickness. The normal grinding force increases with the aggravation of grinding wheel wear and has a non-linear positive correlation with MRV41Cr4. On the contrary, the ground surface roughness has a non-linear negative correlation with MRV41Cr4. All nine groups of parameters show similar trends, as is shown in Fig. 4. Before stage 3, the normal grinding force increases rapidly, then, the normal grinding force increases slower as the wheel wear exasperates. On the opposite, the ground surface roughness decreases rapidly at first, then decreases slower as the wear aggravates.
Therefore, the normal grinding force can be used to evaluate the wear state of the grinding wheel.

The influences of wheel wear on existing surface roughness prediction models
Roughness is an important characteristic parameter to evaluate the grinding quality. Surface roughness prediction models have attracted the attention of many scholars. Most researchers believe that the ground surface roughness is proportional to the undeformed chip thickness. The where E(Ra) is the expected value of surface roughness Ra, f is the overlap factor, E(t) is the expected value of undeformed chip thickness which obeys a Rayleigh distribution.
This model is in good agreement with experimental results when the ground surface roughness is between tens of nanometers and a few microns [34]. However, this model did not consider the effect of grits wear. Considered that the wheel wear changes the distribution of maximum undeformed chip thickness, the relationship needs further research.  In existing research, it shows that there is a certain relationship between grinding force and machined surface roughness [33], but few studies have quantified this relationship. The relationship among normal grinding force Fn, parameter k, and surface roughness Ra is shown in where a, b, c are the coefficients obtained by data fitting. The value of these coefficients and Rsquare (COD) is shown in Table 4. The R-square shows that the two-dimension linear relationship among Fn, k, and Ra is valid. In addition, the value of the coefficient a is positively related to MRV41Cr4, so a can be used to indicate the degree of grinding wheel wear. In conclusion, three sets of processing parameters can be selected for pre-experiment to determine the relationship among Fn, k, and Ra which is only related to the wear state of grinding wheel. Then, the ground surface roughness Ra can be predicted by the normal grinding force Fn and parameter k during the grinding process.

Sensitivity analysis
In grinding process, as the wheel wear exacerbates, the surface roughness decreases.
However, the grinding force increases with the wheel wear intensifies, which will increase the probability of surface quality instability. Therefore, the sensitivity analysis of the grinding process is helpful to ensure the stability of workpiece quality in a long-time grinding process.

Sensitivity of surface roughness to grinding parameters
When the grinding surface roughness fluctuates or deteriorates, it is necessary to adjust the processing parameters to ensure the ground surface roughness meets demand. Theoretically, adjusting any of the three parameters can achieve the goal, but priority should be given to adjusting the most sensitive parameter. respectively.
When grinding with a new grinding wheel, the effect of processing parameters on roughness is not obvious, as shown in Table 5. When the wheel wear reaches to stage 2, the workpiece infeed rate has a significant influence on the ground surface roughness. In stage 3 and stage 4, the wheel speed is the only parameter that has a significant influence. When it comes to stage 5, all the parameters have a great impact on ground surface roughness and the depth of cut is the primary significant parameter, followed by workpiece infeed rate. Therefore, in different wear stages, the operator should give priority to adjusting the most significant parameters to make the grinding quality meets the requirements.

Sensitivity of grinding force to grinding parameters and wheel wear
The increase of normal grinding force will increase the subsurface damage and the deformation of low stiffness parts. Therefore, the sensitivity of normal grinding force to grinding parameters should be analyzed to guide the adjustment of grinding parameters to reduce the grinding force. Moreover, a long-term steady grinding state is beneficial to maintain the consistency of product quality. So, the sensitivity of normal grinding force to wheel wear should be studied to maintain the steady grinding state for a longer time.  In order to reduce the grinding force, the sensitivity of the grinding force to processing parameters was analyzed. To maintain the steady grinding state in a long-term grinding process, the sensitivity of grinding force to grinding wheel wear need to be further studied.
The change in normal grinding force is defined as where n and n+1 stand for different wheel wear stages, n=1, 2, 3, 4. If δn,n+1 is the smallest under a certain set of processing parameters when the grinding wheel wear increases, the grinding state determined by this set of parameters is called steady state.
While sensitive state appears when δn,n+1 is the biggest. Table 7 shows the change in normal grinding force δn,n+1 as the wheel wear exacerbates. Then ANOVA on the change of Fn is carried out to determine the sensitive state and steady state. The result is shown in Fig. 7. Fig. 7 shows that in early wear stage (before stage 2), the steady state of normal grinding force appears with the parameters that the grinding wheel speed is 1000rpm, the workpiece feed rate is 500mm/min, and the cutting depth is 50μm. Then the steady state changes to the parameters that the grinding wheel speed is 1000 rpm, the workpiece feed rate is 500 mm/min, and the cutting depth is 150μm between stage 2 and stage 3. As the wear of grinding wheel further increases, the steady state gradually moves to the parameters that the grinding wheel speed is 5000 rpm, the workpiece feed rate is 500 mm/min, and the cutting depth is 150μm. The steady state is influenced by wheel wear. The mechanism of the influence of grinding wheel wear on the steady grinding state needs to be studied to deepen the understanding of the mechanism of grinding process.
In different wheel wear stages, the processing parameters that determine the steady grinding state are different, which means that the mechanism that affects the steady state is different during different wear stages. For a new grinding wheel, the protrusion height of abrasive grits is highly random, fewer effective abrasive grits are involved in grinding and it is difficult to accurately characterize it by a certain distribution. (stage 1), shown in Fig. 8 (a). Due to the high randomness of abrasive grits protrusion height, the processing parameters that determine the steady state in this wear stage have no general regularity. As the wear intensifies, the protrusion height of abrasive grits can be described by a specific distribution. In this state, the parameters that determine the steady grinding state begin to show regularity (after stage 2). The mechanism of the sensitivity of grinding force to wheel wear in early stages (stage 2~stage 3) and late stages (stage 4~stage 5) need to be studied to deepen the understanding of grinding mechanism. When the grinding wheel is in early wear stages (stage 2~stage 3), the number of effective abrasive grits involved in the grinding processing is less. Therefore, the reduction of abrasive grits protrusion height caused by grinding wheel wear hw is significant, shown in Fig. 8. As a result, the grinding force generated by the parameters with a bigger actual cutting depth aa is less sensitive to grinding wheel wear. Because the actual cutting depth aa has a positive correlation with parameter k, so the relationship between δn,n+1 and aa can be qualitatively described by the relationship between δn,n+1 and k. As shown in Fig. 9, with the increase of parameter k, the grinding steady tends to be steady in early wheel wear stages (stage 2~stage 3). It is consistent with the trend of experimental data analysis. However, when the wheel wear is severe (stage 4~stage 5), the trend from experimental analysis is contrary to this theory. So, the mechanism should be further studied.  The wheel wear will cause variation in parameter Sw and Nd. The total differential of fn to the wheel wear w can be expressed as Eq. (7). The partial derivatives of fn with respect to Sw and Nd are also calculated to analyze the sensitivity of grinding normal force to wheel wear. Shown in Eq. (8) and Eq. (9). When the state of the grinding wheel is determined, the wear area Sw can be treated as a constant. So, NdVw/Vs and Vw/Vs are the key parameters of influence on the sensitivity of Fn to wheel wear.
The change in fn (dfn) has a positive correlation with δn,n+1 because fn is the main component of Fn when the wheel wear is severe. So, NdVw/Vs and Vw/Vs will have an influence on δn,n+1.
Because Nd has a positive relationship with parameter k, the relationship between δn,n+1 and NdVw/Vs can be qualitatively described by the relationship between δn,n+1 and kVw/Vs, shown in Fig. 10 (a), and the relationship between δn,n+1 and Vw/Vs is shown in Fig. 10 (b). The grinding state determined by parameters that have a smaller value of kVw/Vs and Vw/Vs is less sensitive to the grinding wheel wear. This trend is confirmed by the experimental results. Based on the above analysis, the operator should give priority to adjusting the most significant parameters towards the steady state to maintain the stability of grinding state. Benefit from this adjustment, the increase in the grinding force will be smaller when the grinding wheel continues to wear, and the stability of machining state and grinding quality can be maintained for a longer time, reducing the number of adjustments.
In this paper, the influence of grinding wheel wear on grinding force and surface roughness is studied, and a semi-empirical roughness prediction model is proposed considering the influence of grinding wheel wear. To ensure the stability of the grinding process, sensitivity analysis was conducted to guide the adjustment of grinding parameters. Following conclusions are achieved: (1) The normal grinding force can be used to evaluate the degree of grinding wheel wear.
There is a non-linear positive relationship between the normal grinding force and material removal volume during grinding wheel accelerated wear treatment, while the surface roughness is the opposite.
(2) The capability of existing ground surface roughness prediction models is affected by the grinding wheel wear. The distribution of maximum undeformed chip thickness is changed in different wear status due to the change of abrasive grits protrusion height distribution.
Consequently, the linear relationship between ground surface roughness and maximum undeformed chip thickness also changes due to the wheel wear.
(   in different wear status. The red symbol stands for sensitive state and the blue symbol stands for steady state. In the early stage of grinding wheel wear (before stage 2), the steady parameters of grinding force appear when the grinding wheel speed is 1000rpm, the workpiece feed rate is 500mm/min, and the cutting depth is 50μm. As the wear of the grinding wheel increases, the steady parameters gradually move to the parameters that the grinding wheel speed is 5000 rpm, the workpiece feed rate is 500 mm/min, and the cutting depth is 150μm Fig. 8 shows the change of abrasive grit protrusion height in different wear stages. Before stage 3, the number of effective abrasive grits involved in the grinding processing is less. Therefore, the reduction of abrasive grits protrusion height caused by grinding wheel wear hw is significant.
As a result, the grinding force generated by the parameters with a bigger actual cutting depth aa is less sensitive to grinding wheel wear Fig. 9 shows the relationship between δ and k. With the increase of parameter k, the grinding state tends to be steady in early wheel wear stages (stage 2~stage 3). It is consistent with the trend of experimental data analysis. However, when the wheel wear is severe (stage 4~stage 5), the trend from experimental analysis is contrary to this theory Fig. 10 shows the relationship between the change in normal force δ and kVw/Vs ( Fig. 10 (a)), Vw/Vs (Fig. 10 (b)). The grinding state determined by parameters that have a smaller value of kVw/Vs and Vw/Vs is less sensitive to the grinding wheel wear. This trend is confirmed by the experimental results Table captions list Table 1 shows the properties of the quartz workpiece used in the experiment Table 2 shows the process control parameters and their range in the experiment Table 3 shows the experiment parameters and the normal grinding force Fn during grinding process, Ra value of the ground surface in different wear stages Table 4 shows the values of fitting coefficients a, b, c in Eq. (3) and their R-square in different wear stages. The R-square shows that the two-dimension linear relationship among grinding force Fn, parameter k, and surface roughness Ra is valid. In addition, the value of the coefficient a is positively related to MRV41Cr4, so coefficient a can be used to indicate the degree of grinding wheel wear Table 5 shows the F value from ANOVA of the normal grinding force Ra in different wear stages.
The symbol'+', '++', and '+++' indicate the significance level of F test is 0.1, 0.05, 0.01, respectively. When grinding with a new grinding wheel, the effect of processing parameters on roughness is not obvious. When the wheel wear reaches to stage 2, the workpiece infeed rate has a significant influence on the ground surface roughness. In stage 3 and stage 4, the wheel speed is the only parameter that has a significant influence. When it comes to stage 5, all the parameters have a great impact on ground surface roughness and the depth of cut is the primary significant parameter, followed by workpiece infeed rate Table 6 shows the F value from the ANOVA results of the normal grinding force indifferent wear stages. The results show that the grinding wheel speed has a remarkable influence on normal grinding force in all wear stages. Before stage 2, wheel speed is the only parameter that significantly affects the normal grinding force. With the wheel wear further increases, the workpiece infeed rate and depth of cut show a significant influence on normal grinding force Table 7 shows the change in normal grinding force Fn when the wheel wear exacerbates. The ANOVA was conducted based on these data to analyze the sensitivity of grinding normal force to wheel wear