Study on the influence of vibration characteristics on surface roughness in quick-point grinding and prediction model

The characteristic frequency of vibration was obtained by extracting the vibration characteristics of fluorophlogopite in quick-point grinding, and the characteristic frequency deviation rate was proposed to study the effect of vibration characteristics on surface roughness. Meanwhile, the influence of five process parameters, such as the grinding speed, table feed speed, grinding depth, deflection angle, and inclining angle, on the characteristic frequency deviation rate and surface roughness was also investigated. It reflected the relationship between deviation rate and surface roughness. The experimental results indicated that the process parameters influenced the deviation rate and surface roughness, and the changes of both were synchronized. Moreover, the modified model of the quick-point grinding surface roughness was proposed in the paper, which was based on the prediction model of several scholars. The model included vibration characteristic parameters and five process parameters, which not only kept the accuracy of the prediction model but also realized the introduction of vibration characteristics. It was proved that the prediction effect of the modified model was accurate and reliable. Based on the prediction model of surface roughness including vibration features, the idea of monitoring and controlling surface roughness by real-time vibration signal was put forward.


Introduction
Surface roughness, as one of the significant indexes to evaluate precision and ultra-precision manufacturing technology, has always been a research hotspot in the field of machinery [1].Suitable surface machining quality can effectively reduce stress concentration and improve assembly accuracy and service life of parts.As an advanced finishing technology, the point contact characteristic of quick-point grinding can drastically reduce the grinding force and heat and greatly improve the machining quality [2].For this kind of high-speed grinding process, grinding vibration is one of the main factors that lead to the deterioration of surface quality.Excessive vibration, resonance, and chatter often directly increase the reject rate [3].Therefore, it is necessary to fully understand the relationship between machining vibration and surface roughness.
Many scholars have studied the prediction of grinding surface roughness, mainly focusing on the influence of process parameters on surface roughness.Malkin and Hwang [4], based on the grinding process of metal material, established a surface roughness prediction model from the perspective of kinematics and geometry, which did not include the properties of the grinding wheel and workpiece materials.The model first quantitatively predicted the grinding surface roughness from the theoretical point of view.Snoeys et al. [5] offered an empirical model of surface roughness based on grinding experiments.The model took linear speed, Shuai Pan, XueqiaoYu, and Quan Shan contributed equally to this work.
feed speed, and grinding depth as the main variables, which greatly improved the prediction accuracy.Agarwal and Rao [6] proposed a mathematical model of surface roughness for grinding ceramic materials by considering the random distribution of the exposed height of grinding grains.Öktem et al. [7] combined response surface methodology and genetic algorithm to determine the process conditions for obtaining the best surface quality in metal milling.
To predict the roughness of different materials, the researchers turned the perspective to the mechanical properties of materials and fracture removal mechanisms.According to the Rayleigh distribution and indentation theory, Shao et al. [8] established a grinding surface roughness model for brittle materials, which included the ductile-brittle transition, the grinding wheel microstructure, the process conditions, and the material properties.In the process of grinding silicon carbide, Wu et al. [9] used the Rayleigh distribution function to calculate the proportion of grains involved in ductile and brittle removal and established a surface roughness model for the coexistence of brittleness and plastic.Based on the oblique turning process of potassium dihydrogen phosphate crystal, Zhang and Zong [10] established a theoretical roughness model of soft and brittle materials including kinematics, plastic side-flow, elastic recovery of materials, and cracks effect.Ma et al. [11,12] studied the removal mechanism of engineering ceramics based on the fracture mechanics of brittle solids and the energy conservation principle.The relationship between variable angle and machining surface quality was analyzed by quick-point grinding of fluorophlogopite.Moreover, the theoretical model and modified empirical model of surface roughness were put forward in multi-dimension, and the sensitivity of each process parameter to surface roughness was also mentioned.The prediction accuracy of surface roughness in this kind of research is improving continuously, but the characteristic parameters used to represent machining vibration are not included yet.
The research on the relationship between machining vibration and surface quality usually starts from the perspective of kinematics, focusing on the consistency of the tool-path equation and machining surface texture.Thomas et al. [13] investigated the relationship between tool vibration and surface finish and the interaction between independent variables by turning carbon steel samples with different process parameters.Kim et al. [14] put forward the influence form of tool vibration on surface quality at a microscopic level and gave a systematic method to identify tool vibration frequency by surface profile.Hassui and Diniz [15] not only analyzed the relationship between the vibration signal and the workpiece quality when the grinding wheel was worn but also determined the best time for dressing the grinding wheel.Hessainia et al. [16] discussed the coupling effect of cutting parameters and tool vibration on surface roughness.
They refined the surface roughness model of hard turning by response surface methodology and determined the best cutting parameters and tool vibration values.Upadhyay et al. [17] considered the correlation between the vibration acceleration components in different directions and the surface quality.In the turning process of Ti-6Al-4V, the vibration signal was used to predict the surface roughness, and a firstorder multiple regression model was established.
Many scholars have used intelligent algorithms and computer techniques to make empirical predictions of key parameters such as surface quality with a huge amount of vibration data.Risbood et al. [18] introduced vibration and cutting force signals into the neural network for high-density training and realized the prediction of surface roughness and dimensional deviation in the turning process of low-carbon steel.Based on an artificial neural network, Elango et al. [19] predicted the vibration quantity of the high-speed steel turning tool with different process parameters and geometric parameters and obtained the criteria for measuring tool life from the angle of vibration.Lin et al. [20] established a surface roughness model based on cutting parameters and machining vibration of end milling through multiple regression analysis and an artificial neural network.This kind of research explored the influence of vibration on surface roughness through the geometric interference between the tool and the workpiece from the perspective of dynamics.The tool vibration was regarded as an ideal time function, so the prediction accuracy still has room for improvement.
In this paper, the characteristic quantity of representing vibration was proposed on the basis of previous work through the extraction experiment of vibration characteristics of fluorophlogopite in quick-point grinding.A prediction model of surface roughness was established which considered the grinding speed v s , feed speed v w , grinding depth a p , deflection angle α, inclining angle β, and vibration characteristic parameters.The model was verified by an orthogonal experiment, and the effect of grinding vibration on surface quality was also investigated.

The selection of vibration characteristic parameter
Both the impact of the cutting process and the imbalance in the machining system will cause the relative vibration between the tool and the workpiece.This kind of vibration will feed back to the machining link, interfere with the normal machining process, and worsen the surface quality of the workpiece.In the study of machining vibration, the tool vibration trajectory is usually used to characterize the actual machined surface topography of the workpiece, as shown in Fig. 1.When the effect of vibration on surface quality is completely neglected, the cutting marks appear as simple geometric interference (Fig. 1A), which is often regarded as the basic assumption in the traditional theoretical calculation [4].When considering the influence of vibration on surface quality, the vibration was often represented only by the dynamic quantity of the system, such as tool vibration velocity and acceleration [16,17].Or the prediction model of these factors was established by defining process parameters as variables [21], which was tantamount to taking random vibration as an ideal harmonic motion in equivalent form (Fig. 1B).Especially for brittle materials such as engineering ceramics, there are crystal gaps, tiny cracks, and different sizes of internal grain [22,23].In the actual machining process, when the ceramic material is impacted, the surface and sub-surface cracks propagate, and the chips formed by the envelope of the cracks and the unmachined surface flow out [24].Therefore, the vibration signals produced by the contact between the workpiece at different positions and the tool differ greatly (Fig. 1C).The vibration frequency ω is mainly determined by the rotation period of the machine tool spindle, which is little affected by random factors.In order to preserve the accuracy and randomness of the original signal, choosing frequency ω to characterize the actual vibration state is superior to the ideal trajectory method.However, the correspondence between frequency ω and surface roughness is still unclear and needs further proof.

Extraction of vibration characteristic
To explore the influence of vibration frequency on the quality of the machined surface, the vibration characteristics were extracted by the experiment of quick-point grinding.And the relationship between grinding vibration frequency ω and surface roughness R a under different process parameters was also studied in this paper.The experiment equipment was a MK9025A profile grinder.The workpiece material was fluorophlogopite ceramic, whose main component was R 2 O-MgO-Al 2 O 3 -SiO 2 -F (R is an alkali metal).And the cutting tool in this study was a CBN grinding wheel.SD1413 threeway acceleration sensor was used to pick up the vibration, and DH5920 dynamic signal acquisition and analysis system was used to process signals, and the surface roughness was obtained on a three-dimensional non-contact surface topography measuring instrument, as shown in Fig. 2. The pre-experiment was a simple single-factor experiment.The vibration acceleration signal and surface roughness R a value were acquired under different grinding process parameters.The process conditions and results are given in Table 1.
The time domain signal of vibration acceleration obtained from the experiment is given in Fig. 3A.It was concluded that the signal was highly random and difficult to fit the analytical results.If the processing is idealized greatly, the accuracy will be lost.After the Fast Fourier Transform was performed on the time domain signal, the vibration frequency domain signal was obtained (Fig. 3B), and the set of stable characteristic peaks was extracted at the same time.Therefore, the frequency was less affected by random interference, and the waveform features were obvious.The frequency could be used as a characteristic parameter to represent the vibration.
It was found in the experiment that the characteristic frequency ω in the loading state was always less than the characteristic frequency ω 0 in the no-load state, as shown in Fig. 4A-C.The contact effect between the workpiece and grinding wheel always caused the characteristic frequency to redshift, and ω 0 was only affected by the spindle speed and the inherent properties of the machine tool.
For the purpose of studying this redshift phenomenon, the deviation rate of characteristic frequency ω was defined as e ω , whose expression is as follows: As shown in Fig. 5, the grinding wheel vibration under two kinds of loading states presented a trajectory deviation of Δl 1 ~Δl 4 , which reflected the change of grinding vibration frequency.
The comparison results of surface roughness R a , characteristic frequency ω, and deviation rate e ω are shown in Fig. 6.It was found that there was no obvious relationship between ω and R a , while e ω and R a had obvious correspondence.Thus, e ω was chosen as the characteristic value of vibration, which was used to analyze the relationship between vibration and surface roughness and establish the mathematical model.

Effect of process parameters on frequency deviation rate and surface roughness
In the process of extracting vibration characteristic parameters, the pre-experiment showed good results.So, the same experiment equipment and materials were used to explore the influence of process parameters on the frequency deviation rate e ω and surface roughness R a .The experiment process conditions are shown in Table 2.
In the experiment, all process parameters were selected within the conventional processing range.The relative range of e ω within this range was defined as the maximum influence rate RR of this parameter on e ω , so as to focus on the influence degree of different process parameters on characteristic parameters within the conventional range, and the equation was where e ωmax and e ωmin are the maximum deviation rate and minimum deviation rate in the processing interval and 0 is (2) RR = e max − e min ∕ 0 × 100%  the average value of no-load characteristic frequency in the interval.

Grinding speed v s
As shown in Fig. 7, with the increase of grinding speed v s , both e ω and R a decreased.When v s increased, the grinding volume of a single grain decreased, the impact load of grains on the workpiece surface reduced, the energy transfer weakened, the mechanical energy loss for maintaining vibration faded down, and the frequency change became smaller, so e ω decreased.At the same time, the number of grains involved in grinding on the grinding wheel surface in a unit time increased, and the material of the workpiece at the same position was evenly removed layer by layer several times, thus R a decreased.Moreover, when the grinding speed was low, it had a great impact on the workpiece.If the speed is too high, the vibration interference caused by the imbalance in the machining system will be amplified.Therefore, the change rate of surface roughness with time changed from negative to positive during the increase in the linear speed of the grinding wheel.According to the calculation, the maximum influence rate of grinding speed was RR(v s ) = 0.465%, which indicated that v s had a great influence on e ω .This was consistent with the existing conclusion [25].Therefore, in actual production, the grinding speed should be selected reasonably to reduce the machining error caused by vibration.

Feed speed v w
As shown in Fig. 8, when the feed speed increased, e ω and R a also increased.Increasing the feed speed increased the axial impact between the grinding wheel and the workpiece.The original elastic deformation of the micro-convex body broke and released energy, and the energy to maintain the vibration frequency decreased, and then, the e ω increased.With the increase of the impact, the fracture scale of the workpiece surface increased, and more pits appeared, so R a also increased.
When the feed speed increased, the side of the grinding wheel and the workpiece was pressed tightly, and the vibration caused by the coaxiality between the grinding wheel and the spindle was well controlled, which weakened the mechanical energy transfer of the vibration and slowed down the growth of e ω and R a .The maximum influence rate was RR(v w ) = 0.033%.Therefore, the feed  speed v w had little influence on e ω ; correspondingly, the accuracy of controlling e ω and R a into a reasonable range by adjusting v w was also the highest [26].

Grinding depth a p
As shown in Fig. 9, with the increase of grinding depth, e ω increased, and R a fluctuated.The volume removal rate of the workpiece was enhanced by the increase in grinding depth, and more plastic deformation and material fracture were generated.And energy transfer was intensified, vibration mechanical energy was reduced, so that the frequency was difficult to maintain, and then, e ω increased.Moreover, the increase in grinding depth produced a stronger crushing phenomenon, the radial load increased, and the crack expanded to the inside of the material.At this time, the crack deflection was often related to the defects inside the material.The defects were randomly distributed, which led to large fluctuations in the effect of grinding depth on the roughness.The maximum influence rate was RR(a p ) = 0.291%.It could be seen that a p had a great influence on e ω , and priority should be given to adjusting and selecting a small grinding depth within a reasonable range in actual processing.

Deflection angle α and inclining angle β
As shown in Figs. 10 and 11, when the deflection angle α and inclining angle β increased in positive and negative directions, the e ω showed a symmetrical increase trend at 0°.This was because when α and β were far away from the 0° position, the load area between the grinding wheel and the workpiece decreased, which increased the contact stress in the grinding zone and improved the material removal effect in the processing zone.The enhancement of energy transfer led to the increase of e ω .
The effect of variable angle on the surface roughness was slightly different.The surface roughness increased with the increase of α and decreased with the increase of β, and there was no similar phenomenon of symmetric increase about 0° position.This was because changing the deflection angle α affected the grinding length at any machining position, and the change of inclining angle β affected the pre-grinding zone of the workpiece entering the grinding wheel working area.
As shown in Fig. 12A-C, the cylindrical side of the workpiece was expanded along the busbar.An arbitrary point M on the workpiece moved through the grinding zone to point N.The width of the grinding wheel is b.The axial speed of the workpiece relative to the grinding wheel is v x = −v w , the Fig. 7 Effect of grinding speed v s on e ω and R a Fig. 8 Effect of feed speed v w on e ω and R a Fig. 9 Effect of grinding depth a p on e ω and R a circumferential speed is v y = −v s , and the angle θ between the direction of motion and the circumferential direction satisfies the equation When α = 0, the geometrical relationship indicated that the length l of any point of the workpiece moving in the grinding zone is When α changes, Eq. ( 4) becomes The longer the grinding length l was, the more grains acted on the same position of the workpiece during the machining process, the more times the workpiece was ground and polished, and the smaller the surface roughness was.Therefore, with the increase of deflection angle α, the grinding length became shorter, and the surface roughness increased, which was independent of the direction of grinding wheel deflection.
As shown in Fig. 13, when the grinding wheel was tilted from β = 0° to both sides in the grinding process, the working zone changed from the cylindrical surface of the grinding wheel to the side edge.Theoretically, the workpiece is only contacted with the side edge.In practice, the workpiece entered the pre-grinding zone before contacting the side edge because of the exposing height of grains.And the grains were uniformly cut into the workpiece layer by layer so that the effective grain number changed from instantaneous generation to uniform increase.The impact flexibility and polishing times were increased, and the machined surface roughness was reduced.As shown in Fig. 13, with the increase of inclining angle β, the grain number in the pre-grinding zone increased, and the pregrinding zone expanded; thus, the surface roughness was reduced.This trend was independent of the inclining direction of the grinding wheel.
After calculation, the maximum influence rate of α was RR(α) = 0.101%, and the maximum influence rate of β was

Relationship between e ω and R a
In the process of grinding, the impact load of a single grain could be changed by changing the relative speed and contact area between the grinding wheel and workpiece.In the transmission process of vibration, the larger the impact load of a single grain was, the more plastic deformation and breakage were generated by the contact between the micro-convex bodies.The elastic potential energy stored in the micro-convex body was converted into the energy that softened and deteriorated the micro-convex body materials and the surface energy generated by fracture, which led to the decrease of the mechanical energy that maintained the vibration frequency and the increase of the characteristic frequency deviation.Moreover, due to the crystal gaps and defects in ceramic materials, when the impact load of grinding wheel grains on the workpiece increased, the cracks generated on the workpiece surface expanded more in the direction of the minimum material bonding force and the lowest strength, and this direction tended to go deep into the material, rather than along the direction of the grinding wheel, and fed and created a new surface.The cracks did not deflect to the material boundary in time, resulting in bigger surface roughness.According to the experimental results and analysis, when the process parameters of the grinding process change, the vibration characteristics and the surface quality had the same variation trend, that was, when the process parameters caused the surface roughness R a to increase, the deviation rate e ω usually increased.The relationship between e ω and R a is shown in Fig. 14, indicating a significant positive correlation between e ω and R a .
Based on the analysis of deflection angle α and inclining angle β, it was concluded that e ω was more relevant to the surface roughness R a when the workpiece was initially removed at any processing position.The change of e ω caused by repeated polishing and pressing of the same position was covered up by the violent energy transmission of other first processing positions.The change of variable angle mainly changed the number of polishing, so the change law of e ω and R a was slightly different.

Surface roughness model of fluorophlogopite in point grinding
After mastering the influence of the process parameters of quick-point grinding on e ω and R a and their relationship, a mathematical model can be established to predict the surface quality in the machining process.This kind of prediction model has been studied by many scholars.

Chip thickness model model R a1
There are two classic models for surface roughness kinematics, Malkin and Snoeys.From the point of view of where L is the distance between continuous cutting edges of the grinding wheel and d s is the grinding wheel diameter.
The model reflected the geometrical relationship between the grinding wheel and the workpiece in the grinding process, but the logic was too idealized, which resulted in the low precision of the model.
In view of the low accuracy caused by ignoring material properties, Snoeys et al. [5] established an empirical model with the main grinding process parameters as variables based on experimental data, considering the nonuniformity of the grain distribution and other factors.The model is shown as where R 1 and x are empirical coefficients.
According to the surface formation mechanism of brittle materials and a large number of experimental studies, the maximum undeformed chip thickness h m played a major role in the final forming of the actual machined surface.Instead of the grinding depth a p in Eq. (7), it was more realistic and accurate, so a chip thickness model R a1 was obtained, which is as follows where d w is the workpiece diameter.

Empirical model R a2 considering variable angle
The influence of variable angle still needs to be considered in the surface roughness prediction of the quick-point grinding process.Ma et al. [11] first established the empirical model of surface roughness R a3 considering variable angle through the quick-point grinding experiment of engineering ceramics, breaking the view of some scholars that the surface roughness of point grinding was independent of variable angle [27] which is shown as where b and k are coefficients.

Modified model R a3 considering vibration characteristics
Based on the surface roughness prediction model proposed by the above scholars, the research on the process parameters of quick-point grinding, including grinding speed v s , feed speed v w , grinding depth a p , deflection angle α, and inclining angle β, has been quite comprehensive.However, the influence of grinding vibration on surface roughness has not been considered.15A-E.
From Fig. 15A-C, the changing trend of the modified empirical model R a3 was similar to the value of experimental R a0 , the chip thickness model R a1 , and the variable angle model R a2 .According to Fig. 15D, E, the influence of variable angle on surface roughness was not taken into account in the model R a1 , which resulted in a decrease in model ( 9) The advantage of the modified empirical model R a3 was that the influence of vibration characteristic frequency on surface roughness during grinding was considered.The five main process parameters of point grinding were set before machining.When they were considered only, the real-time machining process did not affect the predicted results of surface roughness.However, grinding vibration changed in real time during machining, which meant that not only the change of surface roughness could be predicted synchronously, but also the precise control of surface roughness could be realized by monitoring the vibration signal in real time.It was of great significance to understand the surface-forming mechanism, improve process parameters, and reduce processing costs [28,29].
In the real-time machining process of quick-point grinding, the accurate machined surface quality could be obtained by real-time monitoring e ω signal and adjusting process parameters based on the relationship between e ω and R a .According to the maximum impact rate RR of different process parameters on e ω in the quick-point grinding experiment of fluorophlogopite ceramics, v s , a p , and v w corresponded to different levels of adjustable parameters.The change of e ω signal could be observed in actual processing, and three process parameters could be appropriately adjusted to accurately obtain a product with a certain surface roughness.The deflection angle α and inclining angle β were limited by the production demand of parts and the difficulty of parameter

Verification of modified model R a3
To further demonstrate the accuracy of model R a3 , the standard deviations between each model value and the experimental values were calculated, and orthogonal experiments were designed.

Standard deviation comparison
In order to study the degree of deviation of models R a1 , R a2 , and R a3 from the experimental value R a0 , the standard deviations σ of each model under different process parameters were calculated, and the equation is In the equation, R aji represents the i-th experiment of the j-th model, j = 1, 2, 3, 4, and N represents the number of experiments.After calculation, the standard deviation σ of each model under different process parameters σ is shown in Table 3.
From the standard deviation results, it can be clearly seen that the R a3 model has the smallest standard deviation and the smallest deviation from the experimental value R a0 , indicating that the R a3 model has the highest accuracy.

Orthogonal experimental verification
On the basis of the single factor experiment, an orthogonal experiment L 16 (4 5 ) was used to verify the reliability of the modified model R a3 .The levels of each factor in the orthogonal experiment are shown in Table 4.
By substituting orthogonal experimental data into Eqs.( 8), (9), and (10), the predicted values of each model were compared with the experimental values, as shown in Fig. 16.It could be seen that the prediction accuracy of modified model R a3 was higher, the overall trend was consistent with the experimental values, and it had a certain reliability.

Conclusions
(1) The randomness of vibration in the grinding process of brittle materials was analyzed, and a reasonable characteristic value, namely, characteristic frequency ω, was given to characterize grinding vibration.(2) Proposed characteristic frequency deviation rate e ω through pre-experiment, and e ω had a strong correlation with the surface roughness R a .(3) Through the analysis of single factor experimental data, the deviation rate and surface roughness decreased with the increase in grinding speed and increased with the increase of feed speed.With the increase of grinding depth, the deviation rate increased, and the surface roughness showed a strong fluctuation.When the deflection angle and the inclining angle changed, the deviation rate increased symmetrically about the origin, Fig. 16 The comparison of different models in orthogonal experiment and verification of the modified model while the surface roughness increased with the increase of the deflection angle and decreased with the increase of the inclining angle.(4) The variation law of deviation rate and surface roughness was analyzed from impact load and polishing times.The deviation rate of characteristic frequency had a stronger correlation with the surface roughness of the workpiece when the material was initially removed and formed.The increase in polishing times could effectively reduce the surface roughness, but the deviation rate was not affected.

Fig. 1 A
Fig. 1 A-C Interference effect of the grinding wheel vibration on workpiece surface in different conditions

Fig. 2
Fig. 2 Experimental equipment and instruments

Fig. 6
Fig.6 Comparison of the vibration characteristics and surface roughness in pre-experiment

Fig. 13 Fig. 14
Fig.13 Effect of the change of inclining angle β on the pregrinding zone Combined with the relationship between the deviation rate of characteristic frequency e ω and surface roughness R a , the surface roughness empirical model R a3 considering vibration characteristics was established, which is shown as where R 1 ′, b′, k′, and x′ are coefficients.Define R 1 ′ = 1.8, b′ = 0.53, k′ = −2.6,x′ = 0.15, d s = 180, d w = 30, and L = 0.035.When calculating the maximum undeformed chip thickness h m , the equivalent feed speed v we , the equivalent grinding speed v se , the equivalent workpiece diameter d we , and the equivalent grinding wheel diameter d se considering the variable angle should be taken into account.The equation is shown as By comparing chip thickness model R a1 , point grinding variable angle model R a2 , vibration characteristic modified model R a3 , and single factor experimental value R a0 , the results are shown in Fig.
)⋅((dwe+dse)∕dwe))2 d se v we = v w ⋅ cos v se = v s d we = d w ∕cos 2 d se = d se ⋅ cosaccuracy.Compared with model R a2 , the modified model R a3 had a similar change trend.It could be seen that the new model considered the influence of variable angle on surface quality and had a good overall prediction accuracy.

Fig. 15 A
Fig. 15 A-E Comparison of predicted values of different models under different process parameters

( 5 )
Based on the Malkin kinematic model, Snoeys empirical model, chip thickness model, and variable angle model, the modified model of quick-point grinding considering vibration characteristics was established.The prediction results were compared by single factor experiment and orthogonal experiment, and the reliability of the model was verified.(6) The advantages of the new model are given in terms of timeliness, and a new idea for real-time monitoring and control of machined surface roughness was provided.

Table 3
Standard deviation of four kinds of modelsProcess parameters The standard deviations (σ)

Table 4
The factor level table of the orthogonal experiment