Study on friction and wear properties of cast iron material in line contact condition based on free abrasive grinding experiment

In order to study the friction and wear properties of cast iron in free grinding environment under the condition of line contact, this paper presented a new method to calculate the friction coefficient by measuring the friction torque. Through the self-developed free abrasive grinding experimental device in line contact condition, this work carried out friction and wear experiment with relative speed, load, abrasive particle diameter, and abrasive mass fraction as process parameters, and studied the evolution rules of friction coefficient and wear amount of cast iron materials under different process parameters. Based on the response surface method Box-Behnken experimental design, the significance of the experimental results was analyzed, and the prediction model of the friction coefficient and wear amount of cast iron was established. According to the significance of the prediction model, the influence degree of each process parameter on the friction coefficient and wear amount was revealed. The results showed that under the action of free abrasive, the friction coefficient of cast iron material in line contact with GCr15 was between 0.18 and 0.35. When the experimental time was 1.5 h, the removal amount of cast iron material was between 20 and 65 mg, which is significantly increased compared with that without abrasive and the wearing capacity of cast iron increased with the increase of relative speed, load, abrasive particle diameter, and abrasive mass fraction. The friction coefficient had a negative correlation with relative speed, and a positive correlation with abrasive particle diameter and abrasive mass fraction. With the increase of load, the change of friction coefficient decreased first and then increased. The influence degree of each process parameter on the friction coefficient and wear amount of cast iron material: the particle diameter and relative velocity of abrasive were relatively significant, the abrasive mass fraction was the second, and the load was the smallest. Through random experiments, the prediction model of friction coefficient and wearing capacity were verified to be highly accuracy, and could be used to predict the friction and wear performance parameters of cast iron in the process of free grinding under the condition of line contact. It provided a certain theoretical basis for the friction and wear behavior of cast iron as a grinding tool material in the grinding process.


Introduction
Cast iron has good self-lubrication, wear resistance, high vibration absorption, and excellent cutting performance. It is often used as grinding tools in the field of precision and ultra-precision manufacturing and processing [1][2][3][4][5]. As a grinding tool, cast iron is affected by many factors in the process of grinding and polishing, such as grinding motion and loading, the coupling effect of grinding liquid and solid-liquid, the requirements of mechanical properties of machined workpiece material, and the complexity of disassembly and assembly of grinding and polishing equipment. Under the coupling effect of multiple physical fields, the quantitative analysis of friction and wear performance of cast iron becomes extremely complex. However, the friction coefficient and wear behavior between the friction pair of cast iron and the machined material in the process of grinding and polishing directly affect the theoretical study of the forming mechanism of the machined material and the structural design and service life prediction of the cast iron grinding tool.
There were many researches on using cast iron as grinding disc in precision/ultra-precision machining technology. Some scholars applied cast iron grinding disc to the precision/ultraprecision machining of glass, ceramic, copper, cemented carbide, and other materials, and through experimental analysis, it was further verified that cast iron is suitable to be used as grinding disk material in precision/ultra-precision machining technology. The ultra-precision grinding machine Nano-400LappingMachine made by Li et al. [6] used cast iron grinding disc to polish the circular grating glass so that the surface roughness of Ra is 3 nm and the parallelism is 5 μm. Tang et al. [7] used cast iron grinding disc to polish the workpiece, and the surface roughness of the workpiece can be effectively reduced by coating diamond abrasive grains of different diameters on the cast iron disc, and this method can be used in a wide range of environment and high performance-to-price ratio. Zeng et al. [8] used nodular cast iron grinding disc to polish quartz bushing, and obtained high quality quartz film with thickness of 25.1 μm, and surface roughness reached 0.89 nm. Yuan et al. [9] studied the effects of machining load and rotational speed of abrasive tools on the surface roughness of SUS440C stainless steel samples during free abrasive machining with cast iron discs. The results showed that the surface roughness decreased rapidly after grinding for 10 s, and then tend to be stable when Ra reaches about 0.06 μm. Yu et al. [10] used a double-rotation precision sphere grinder with cast iron grinding discs to process the cemented carbide spheres, and the roundness of the spheres was 0.21 μm and the surface roughness Ra was 20.34 nm, achieving high dimensional accuracy and high surface quality. Batch processing.
In terms of friction and wear performance of cast iron as a grinding disc material during grinding and polishing, some scholars mainly tested and studied the friction coefficient of cast iron through friction and wear experiments. Deng et al. [11] tested the friction coefficient of cast iron material through the pin-on-disk friction and wear test, and used the cast-iron disk double-disk straight groove grinding test to achieve high-precision machining of cylindrical rollers. He [12] analyzed the spin and translation motion of double-disc eccentric straight groove grinding cylindrical rollers, selected 9 materials such as cast iron, glass, and mild steel, and the friction coefficient of each friction pair is tested by pin-ondisk friction and wear tester to realize the optimal selection of grinding disc materials. Chen [13] conducted an experimental analysis on the rotation of cylindrical rollers based on friction and wear experiments. When cast iron, glass, copper, and other materials were used as grinding disc materials, under the action of different process parameters, the relative slip rate between the cylindrical roller and the grinding disc was quite different. The above scholars all use the pin-on-disk friction and wear test, and the grinding fluid is not circulated; the actual contact state of the cylindrical roller and the working surface material of the grinding tool and the circulating grinding method of the grinding fluid are not considered.
From what has been discussed above, the research of cast iron in the grinding and polishing process shows that cast iron material is suitable for the workpieces of precision/ultra-precision machining as a grinding tool. There is little research on the friction and wear characteristics of cast iron grinding disc in the process of grinding and polishing. Although some scholars had studied the friction coefficient of cast iron materials based on friction and wear experiments, they had not fully considered the contact condition between friction pairs, process parameters and the influence of grinding fluid on the friction and wear properties of cast iron material. Ren et al. [14][15][16] proposed the bearing rolling element precision evolutionary grinding method, which points out that the stable rotation movement of the rolling element in the grinding process is a necessary condition to reduce the roundness error of the rolling element, and the contour of the working surface of the grinding tool and the contour of the rolling element copy each other and evolve cooperatively; The rotation stability of the rolling element is mainly realized by friction drive, and the coevolution of the working surface of the grinding tool and the contour of the rolling element is mainly guaranteed according to the wear behavior of the two friction pairs. It is particularly important to study the friction and wear properties of the working surface materials of the grinding tool. Therefore, according to the actual contact state between the rolling element and the working surface of the grinding tool, this paper designs a line contact friction and wear experimental device. The effects of process parameters and grinding fluid ratio on the friction and wear properties of cast iron are studied by free abrasive grinding experiment; Based on the response surface method, the influence of multi factor interaction on the friction and wear properties of cast iron material is analyzed. On this basis, the prediction model of friction coefficient and wear amount is established, and its accurate control is realized, which provides the basis for parameter selection for the study of the rotation movement and wear behavior of rolling elements in the grinding process of cast iron grinding disc.

Design principle of free abrasive grinding experimental device in line contact condition
At present, centerless grinding and centerless superfinishing are mainly used for the processing of rolling elements (such as cylindrical rollers, tapered rollers, spherical rollers), pins, and other rotating bodies. Some scholars also use flat plate grinding, double cone plate grinding, ring sleeve grinding, and other processing methods. In the above method, the contact surface between the rolling element and the lapping tool is in different forms of line contact [14][15][16]. Therefore, the experimental device is designed based on the line contact condition in the above grinding method, and its structure is shown in Fig. 1. The free abrasive grinding experimental device in line contact condition mainly includes stepper motor, dynamic torque sensor, driving shaft, intermediate shaft, driving wheel A/B, test shaft, test wheel A/B, counterweight block, and grinding fluid adding device. The driving shaft is parallel to the axis of the test shaft, and the two axes are respectively driven by a stepper motor, and the counterweight block acts on the middle shaft, resulting in a certain pressure between the test wheel A and the test wheel B. Driven by a stepper motor, the driving shaft rotates around its own axis at an angular velocity ω 1 . Because the driving wheel A/B is in contact with the driving shaft, it rotates at an angular velocity ω 2 around the intermediate axis under the action of friction. At the same time, under the drive of the stepper motor, the test shaft drives the test wheel B to rotate around its own axis with angular velocity ω 3 . Because the test wheel A is in contact with the test wheel B, there is friction between the test wheels. The dynamic friction torque produced by the friction force is tested by a dynamic torque sensor installed between the stepper motor and the test shaft. The magnitude of the friction between the test wheels can be achieved by replacing counterweights of different masses. The relative velocity between test wheel A and test wheel B is calculated by where v 1 is the linear speed of the test wheel B; v 2 is the linear speed of the test wheel A; R 1 is the radius of the test wheel B; R 2 is the radius of the test wheel A; n 1 is the speed of the test wheel B, which is adjusted by the stepper motor connected with the test shaft; n 2 is the speed of the test wheel A, which is adjusted by the stepper motor connected with the drive shaft and detected by the speed tester.
The force analysis of the linear contact free abrasive friction and wear experimental machine is shown in Fig. 2. According to the force analysis, the force balance equation is as follows: In the vertical direction: In the horizontal direction:   Table 1.

Experiment conditions
(1) Setting of experimental parameters The relative velocity n, load F, abrasive particle diameter D, and abrasive mass fraction W are selected as the process parameters in the linear contact friction and wear experiment; in order to study the influence of various process parameters on the friction and wear properties of the sample, the single factor experiment of each process parameter is set up as shown in Table 2.
(2) Measuring method First, the sample is cleaned with alcohol in an ultrasonic cleaning machine and dried; then the mass of the sample is measured by ZG-TP203 precision electronic balance, and each workpiece is measured three times. Then, the sample is installed on the experimental machine, and the experimental processing is carried out according to the setting of experimental parameters and the requirement of grinding time. After the end of the experiment, the workpiece is removed and the quality of the sample is cleaned and dried again, and the average difference of the measured mass of each sample before and after the experiment is the wear amount of the sample. The wear marks on the surface of the sample were observed by Alicona TM IFM-G4 three-dimensional surface measuring instrument, as shown in Fig. 3a. The surface roughness of the sample is measured by Taylor Hobson TM profilograph, as shown in Fig. 3b.

Experimental results and analysis
(1) Influence of different process parameters on friction coefficient According to the setting of experimental parameters in Table 2, the time domain characteristics of friction coefficient between contact surfaces under different relative velocity, load, abrasive particle diameter, and abrasive mass fraction are analyzed and studied. The evolution of friction coefficient under different process parameters within 3600 s is shown in Figs. 4, 5, 6, 7, 8. It can be seen from Fig. 4 that in the initial stage of grinding (0 ~ 1200 s), the friction coefficient fluctuates greatly, and the friction coefficient is dispersed at different relative velocities, and on the whole, the friction coefficient increases sharply and then decreases, and then decreases when the relative speed is 200 mm/s, as shown at position A in Fig. 4. When the relative velocity is 500 mm/s, the friction coefficient appears a relatively stable stage at 100-700 s, and then the gradient decreases gradually into a stable stage, as shown at position B in Fig. 4. Mainly due to the inconsistency of the original processing texture and surface quality of the sample surface, the friction coefficient fluctuated greatly and changed irregularly at the initial stage of grinding. In the grinding stabilization stage (1200-3600 s), the fluctuation of friction coefficient with different relative velocities tends to be stable, and the friction coefficient decreases with the increase of relative velocity. In the stable stage, the average friction coefficient decreased from 0.25 to 0.168, a decrease of about 32%.
At lower relative velocity, a slight plastic flow occurs between the contact surfaces, and there is no obvious material removal of the micro bumps between the contact surfaces, so that the original surface roughness has not been significantly improved; And at low speed, the micro convex contact time between the contact surfaces is long, which is easy to form adhesion behavior, resulting in a large friction coefficient. With the increase of relative velocity, the contact time of micro peaks on the surface of the sample decreases, reducing the adhesion between the contact surfaces [17]; the contact time of micro bumps between the contact areas becomes shorter, and the speed produces a high pressure on the micro bumps, so that the micro bumps on the surface are removed to form debris, and the debris adheres to the contact surfaces to form an oxide film, which plays a role of lubrication and wear reduction to a certain extent. At the same time, due to the existence of abrasive fluid, an adsorbed water film is formed on the surface of the sample, and the adsorbed water film, rough micro bumps, and abrasive particles jointly bear the load [18]. With the increase of relative speed, the  load shared by the water film gradually increases, and the low shear strength of water reduces the friction coefficient; Moreover, more abrasive fluid is involved in per unit time, resulting in dynamic pressure effect, which increases the thickness of adsorbed water film, improves the lubrication performance, and takes away more heat generated by friction, thus reducing the friction coefficient.
It can be seen from Fig. 5 that the friction coefficient decreases first and then increases with the increase of load. When the load is 40-100 N, the friction coefficient increases sharply in the whole grinding process, then decreases gradually, and finally tends to be stable; the fluctuation of friction coefficient tends to be stable at 1400 s. When the load reaches 20 N, the friction coefficient fluctuates greatly in the initial grinding stage of grinding, and it is roughly stable after 1400 s, and it still fluctuates to varying degrees in the stable stage, as shown in position A in the Fig. 5. When the load is between 20 and 80 N, the average friction coefficient in the stable stage is between 0.18 and 0.21. When the load is 100 N, the average friction coefficient increases significantly in the stable grinding stage.
Under the action of lower load, due to the small force between the abrasive particles and the sample, the material only has elastic deformation or a small degree of plastic deformation. At this time, the friction between the abrasive particles and the sample mainly comes from the adhesive friction between the contact surfaces, so it has a large friction coefficient. When the load increases beyond the critical load of elastic-plastic transformation, plastic deformation gradually contributes to the friction in the contact area, and at this time, it is mainly the furrow friction, and the adhesion friction coefficient is greater than the furrow friction coefficient [19]. Therefore, when the load increases to 40 N, the friction coefficient shows an obvious downward trend. As the furrow friction coefficient is related to the contact area [20], as the load continues to increase, the depth of the abrasive particles pressing into the sample surface increases, resulting in the increase of the contact area between the abrasive particles and the sample surface, which leads to the increase of the furrow friction coefficient. When the load is low, there are a lot of rolling phenomena between the contact surfaces, which makes the friction coefficient between the contact surfaces smaller; when the load increases, most of the abrasive particles change from rolling to sliding due to the greater constraint of the load between the contact surfaces, which increases the friction coefficient between the contact surfaces.
It can be seen from Fig. 6 that the friction coefficient increases with the increase of wear particle diameter. The friction coefficient is 0.12 with abrasive-free grinding. After adding abrasive particles, the friction coefficient increases significantly. With the increase of the particle diameter from 1 to 24 μm, the average friction coefficient increases from 0.185 to about 0.3. When the abrasive particle diameter is large, there is still a large fluctuation in the stable grinding stage. When there are abrasive particles, the friction resistance of abrasive between the contact surfaces is mainly composed of two parts: one part of the friction generated by the squeezing, cutting, and meshing of the abrasive particles on the contact surface, and the other part of the abrasive are in the rolling state, forming the rolling friction resistance. In the case of plastic metals, due to the high hardness of abrasive particles, they are easy to be pressed into the surface of cast iron material, which plays a major role in squeezing, cutting and meshing the surface of cast iron, and plays a minor role of abrasive particles rolling in a free state. With the increase of abrasive particle diameter, the depth of abrasive particles pressing into the surface of the sample increases, and the resistance of squeezing, cutting, and meshing increases. The resistance of squeezing, cutting, and meshing is approximately proportional to the cross-sectional area of abrasive particles. Therefore, the friction coefficient increases with the increase of abrasive particle diameter.
It can be seen from Fig. 7 that the friction coefficient increases with the increase of abrasive mass fraction, Fig. 9 The effect of load on wear capacity Fig. 10 The effect abrasive particle diameter on wear capacity Fig. 11 The effect abrasive mass fraction on wear capacity generally, the friction coefficient is less affected by the abrasive mass fraction, and the average friction coefficient is between 0.18 and 0.23. When the abrasive mass fraction is below 7%, the increase extent of friction coefficient is slight; when the abrasive mass fraction is greater than 7%, the increase extent of friction coefficient is relatively obvious. According to Eq. 5 in document [21], with the increase of abrasive mass fraction, the number of effective abrasive particles in the contact area of the friction pair increases, so that the total contact area between the effective abrasive particles and the sample surface increases, and the friction coefficient in the contact area increases.
where Nv is the number of effective abrasive particles; ρ f is the number of abrasives per unit volume of abrasive fluid; ρ m is the density of the grinding fluid.
(2) Wear capacity and wear morphology of cast iron material According to the process parameter settings in Table 2, the effects of different relative speeds, loads, abrasive particle The wear capacity of cast iron and GCr15 increases with the increase of relative speed, load, abrasive particle diameter and abrasive mass fraction. When the relative speed is 100-300 mm/s, the wear capacity of cast iron and GCr15 increases significantly; as the relative speed continues to increase, the wear capacity of cast iron and GCr15 increases slightly. With the increase of load, the increase of cast iron material is relatively gentle, while the increase of GCr15 material is relatively obvious. When the abrasive particle diameter is less than or equal to 1 μm. The wear ability of the material is not much different from that with abrasivefree grinding. When the abrasive particle diameter is greater than 1 μm, the wear capacity of the material increases step by step, and when the abrasive particle diameter reaches 24 μm, the wear capacity of GCr15 material increases abruptly. With the increase of abrasive mass fraction, the wear capacity of cast iron materials shows an increasing trend, and the increase range is small; The wear capacity of GCr15 material increases slightly when the abrasive mass fraction is less than 5%, and increases significantly when the abrasive mass fraction is greater than 5%.
As shown in Figs. 12, 13, 14, 15, the wear appearance and roughness of cast iron are analyzed. The X and Y coordinates in these figures are consistent with the coordinates of the test wheel in Fig. 1, and the measured roughness direction is along the axis of the test wheel. The wear mark of cast iron material is relatively uniform, as shown in position A in Fig. 12. The depth and width of the wear mark are not obvious, and the surface roughness of the sample is 0.2596 μm. When the relative speed is small, the mechanical action is small, and the attached film produced by the grinding fluid on the surface of the friction pair material cannot be removed in time, which reduces the interaction between machinery and chemistry, and makes the material wear less. At the same time, due to the weak mechanical action, the friction heat generated on the material surface is less, and the grinding fluid has a cooling effect, so the heat generated on the material surface cannot meet the energy of the chemical interaction between the grinding fluid and the sample material. Therefore, the friction chemical effect is very weak, which will also make the material wear less. With the increase of the relative speed, the contact frequency of the friction pair increases, and the wear frequency of the material surface increases, which increases the wear capacity of the material; at the same time, a large amount of friction heat will be generated on the surface of the friction pair at a large relative speed, and the grinding fluid cannot be cooled in time, resulting in the enhancement of the thermal softening effect on the surface of the material, the reduction of the physical and mechanical properties of the material, and the increase of the wear capacity of the material.
As shown in Fig. 13, when the load increases, the wear scar depth on the surface of cast iron material increases, as shown in position C in the Fig. 13, and the roughness slightly increases compared with the roughness value in Fig. 12. As the load increases, the pressure on a single abrasive particle increases. According to the elastic-plastic theory, the depth of the abrasive particle pressing into the material surface increases, and the scratching volume of the abrasive particle on the material surface increases at a certain relative speed; according to Preston equation [22], the amount of material removed is positively correlated with the relative speed and load. Therefore, with the increase of load and relative speed, the amount of material wear increases. However, with the increase of load between the contact surfaces, the gap between the contact surfaces will be reduced, so that the flow of abrasive fluid into the contact surfaces will be smaller. Therefore, with the increase of load, the surface wear of the sample will increase, but the extent of increase is not obvious.
where MRR is the material removal amount; K is Preston coefficient; P load between contact surfaces; V is the relative velocity between contact surfaces.
As shown in Fig. 14, when the abrasive particle diameter is 24 μm, the wear mark on the surface of cast iron material is obvious. As shown in position D in the Fig. 14, the width of the wear mark reaches more than 120 μm, and its surface roughness value Ra = 0.5872 μm, which is significantly changed compared with Fig. 12. According to Eq. 8 in document [23], with the (7) MRR = KPV increase of the particle diameter of the abrasive particles, the plastic deformation depth of the abrasive particles pressed into the material increases, and the wear capacity of the material increases; when the abrasive mass fraction is fixed, increasing the abrasive particle diameter will reduce the number of effective abrasive particles in the contact area, increase the pressure borne by a single abrasive particle under the same load, and increase the furrow depth of the abrasive particles pressed into the material surface, resulting in obvious wear marks on the material surface and increased material wear capacity.
where h is the pressed depth of spherical abrasive particles; D is the abrasive diameter, H is the hardness of the workpiece material; P is the load; E is the equivalent elastic modulus; B is the half width of the contact area under the load; l is the actual length of the contact area; R t is the workpiece dimension radius.
As shown in Fig. 15, when the abrasive mass fraction is 11%, compared with the abrasive mass fraction of 5% in Fig. 12, the width of the wear mark on the material surface increases and the roughness increases. With the increase of abrasive mass fraction, the number of effective abrasive particles in the grinding area increases, and there are more abrasives that have not been ground and crushed participating in the grinding process, thus increasing the wear capacity of material. Kuide et al. [24] deduced the CMP material removal model by using the method of contact mechanics, and obtained that the mass fraction of abrasive particles was positively correlated with the amount of material removed, which was consistent with the experimental analysis results.

Establishment and analysis of prediction model based on response surface method
The above single-factor experiment mainly conducts a qualitative analysis on the friction coefficient, wear capacity, and surface wear morphology of cast iron material under different process parameters, and expounds the evolution law of the friction coefficient and wear capacity of cast iron material with process parameters in line contact condition based on free abrasive grinding experiment. In this section, the response surface method is used to carry out the Box-Behnken experiment factors and levels design. Through the experimental results, the influence of various process parameters and their interaction on the friction and wear capacity of cast iron material is studied, and the relationship between process parameters and the wear amount and friction coefficient of cast iron materials is accurately established, so as to realize the quantitative analysis of process parameters on the friction and wear properties of cast iron material. According to the Box-Behnken experimental design, the wear capacity of cast iron material during grinding for 1.5 h and the average friction coefficient in the stable stage during this time are selected as the measured data of response surface method analysis, as shown in Table 3.
The regression analysis of the experimental data in Table 3 is carried out by Design-Expert 12 software, and the results of friction coefficient and wear quantity show that the quadratic term is significant.Therefore, the prediction model (Eq. 7) established by response surface method is used to fit and analyze the experimental results.
where y is the response value; x is the design variable; k is the number of design variables, and the design variables in this study are 4, that is, k = 4; β 0 is a constant, β j is the j linear coefficient; β jj is the second-order migration coefficient; β ij is the variable interaction coefficient.
Regression model of friction coefficient: Regression model of wear capacity:   16 Interaction diagram of load and abrasive particle diameter on friction coefficient Analysis of variance is used to detect and analyze the significance of the regression model of friction coefficient and wear capacity. The misfit coefficient of the regression model is an important data used to evaluate the reliability of the equation. The significance criterion of mismatch coefficient is P value. When P > 0.005, the significant confidence level of mismatch item is greater than 95%, which means that the equation is well fitted, subsequent data analysis can be conducted. When P < 0.005, it means that the equation is slightly fitted to the empirical results, subsequent data analysis cannot be conducted [25]. From the analysis of the significance of friction coefficient in Table 4 and the significance of wear capacity in Table 5, the P values of the model are less than 0.0001, which shows that the above two regression models can fit the friction coefficient and wear quantity more accurately. The misfit coefficients of the regression model are all greater than P f = 0.1719, P m = 0.3091, indicating that the misfit term is not significant, and the regression model fits well. The evaluation index of the significance of each factor on the response value mainly depends on the F-value. The larger the F-value, the more significant the influence of this factor on the response value. Through the F-value comparative analysis of the friction coefficient regression model, it can be seen that the influence degree of each process parameter on the friction coefficient is: the particle size of the wear particles is the largest, the relative speed is the second, and the load is the smallest. Through the F-value comparative analysis of the friction coefficient regression model, it can be seen that the influence degree of each process parameter on the wear capacity is that the abrasive particle diameter is the largest, the relative speed is the second, and the load is the smallest.
According to the significance analysis of the regression model of friction coefficient in Table 4, the relative velocity n, abrasive particle diameter D, and abrasive mass fraction W are extremely significant to the friction coefficient prediction model (P < 0.0001), and the interaction of D × F, D × n, n × W, and F × F is significant to the friction coefficient prediction model (P < 0.05). Other factors are not significant. The determination coefficient of the regression model is 0.9804 and the correction coefficient is 0.9609, both are close to 1, which further indicates that the fitting reliability of the model is high. The interaction effect of the significant factors in the friction coefficient prediction model is analyzed, as shown in Figs. 16, 17, 18. Through the analysis of the above response surface diagram, it can be seen that the influence law of each process parameter on the friction coefficient is consistent with the single-factor experimental analysis results. It is apparent from Fig. 16b that the friction coefficient is less affected by the load; the abrasive particle diameter has a more significant effect on the friction coefficient. When the load is greater than 80 N, the effect of Fig. 17 Interaction diagram of relative velocity and abrasive particle diameter on friction coefficient the abrasive particle diameter on the friction coefficient is more obvious, and when the abrasive particle diameter increases from 2 to 28 μm, the friction coefficient increased from 0.17 to 0.3. It is apparent from Fig. 17b that with the decrease of the relative velocity, the reduction degree of the friction coefficient when the abrasive particle diameter is less than 7 μm is much smaller than that when the abrasive particle diameter is larger than 7 μm. The effect of abrasive particle diameter on the friction coefficient is more obvious at lower relative speeds. It is apparent from Fig. 18b that when the abrasive mass fraction is greater  Interaction diagram of load and mass fraction on wear capacity than 7%, the friction coefficient decreases significantly with the increase of the relative velocity; when the relative velocity is greater than 400 mm/s, the friction coefficient changes with the increase of the abrasive mass fraction extremely inconspicuous.
According to the significance analysis of the regression model of wear capacity in Table 5, the relative velocity n, abrasive particle diameter D, and abrasive mass fraction W are extremely significant to the wear capacity prediction model (P < 0.0001), and the interaction of W × F, F × n, n × W, F × F, n × n, and D × D to the friction coefficient prediction model is more significant (P < 0.05). Other factors are not significant.  The determination coefficient of the regression model is 0.9824, and the correction coefficient is 0.9649, all close to 1, further indicating that the model has high fitting reliability. The interaction effect of the significant factors in the wear capacity prediction model is analyzed, as shown in Figs. 19, 20, 21. Through the analysis of the above response surface diagram, it can be seen that the influence law of each process parameter on the wear capacity is consistent with the single factor experimental analysis results. It is apparent from Fig. 19b that when the load is greater than 70 N, the wear capacity increases greatly with the increase of the abrasive mass fraction; when the abrasive mass fraction is greater than 8%, the wear capacity increases greatly with the increase of the load. It is apparent from Fig. 20b that when the relative speed is greater than 180 mm/s, the wear capacity increases greatly with the increase of the relative velocity. It is apparent from Fig. 21b that the abrasive mass fraction and relative velocity have significant effects on the wear capacity.
In order to verify the accuracy of the prediction model of friction coefficient and wear capacity, experimental processing is carried out with different combinations of process parameters, and the friction coefficient and wear capacity corresponding to different process parameters combinations are measured. The specific verified experimental process parameters combination design is shown in Table 6. And the experimental and predictive results of friction coefficient and wear capacity are shown in Fig. 22. The accuracy rates of the measured models are all above 85%, which further proves that the above-mentioned friction coefficient and wear capacity prediction models have high accuracy and can be used to predict the friction and wear performance parameters of cast iron in the line contact state during the free abrasive grinding.

Conclusions
This paper presents a new method of measuring friction coefficient by using friction torque, and self-developed free abrasive grinding experimental device in line contact condition. Through the free abrasive grinding experiment, the friction and wear properties of cast iron under line contact condition are studied, and the effects of various process parameters on the friction coefficient, wear capacity, and surface morphology of cast iron are analyzed; The response surface method is used to explore the influence of various process parameters on the friction coefficient and wear capacity, and the prediction model of friction coefficient and wear capacity is established to quantitatively analyze the friction and wear performance. (1) This paper presents a method of measuring the friction coefficient by measuring the friction moment between the contact surfaces of the friction pair. Based on the free grinding experiment of cast iron in line contact condition, the influence of process parameters on the friction coefficient and wear capacity of the contact surface of cast iron material is analyzed. The results show that the friction coefficient of cast iron material is between 0.18 and 0.35. When the experimental time is 1.5 h, the removal amount of cast iron material is between 20 and 65 mg. The abrasive particle diameter and abrasive mass fraction are positively correlated with the friction coefficient and wear capacity of the friction pair material; The friction coefficient decreases with the increase of relative velocity, and decreases first and then increases with the increase of load; the wear capacity increases with the increase of load and wear particle diameter. With the increase of process parameters, the significance of wear marks on the surface of cast iron and its roughness increase in varying degrees. (2) Through the Box-Behnken experimental design in response surface method, and the significance analysis of the experimental data, the results show that the influence of process parameters on the friction coefficient is: relative speed > abrasive particle diameter > abrasive mass fraction > load; the interaction between load and abrasive particle diameter, the interaction between abrasive particle diameter and relative velocity, and the interaction between relative velocity and abrasive mass fraction have significant effects on the friction coefficient. The influence degree of process parameters on wear is: abrasive particle diameter > relative velocity > abrasive mass fraction > load; the interaction between load and relative velocity, load and abrasive mass fraction, and relative velocity and abrasive mass fraction have significant effects on the wear capacity. (3) According to the response surface method, the friction coefficient and wear capacity prediction model are established, and the friction coefficient and wear capacity prediction model are verified by random parameter combination experiment. The results show that there is no significant difference between the friction coefficient and wear capacity obtained from the random experiment and the prediction model. The accuracy of the prediction model obtained by comparison is more than 85%, which shows that the established prediction model has high accuracy and can realize the quantitative study of the friction and wear performance parameters of friction pair cast iron and GCr15 material in the free abrasive grinding environment when they are in line contact.
In this paper, a new testing method and an experimental device are proposed. It studies the friction and wear performance of free abrasive grinding cast iron material under the condition of line contact, and realizes the reasonable control of process parameters, as well as the accurate prediction of friction coefficient and wear capacity. When cast iron is used as the grinding tool material to grind GCr15 parts in line contact condition with the grinding tool. This study provides theoretical support for the analysis of the motion characteristics and wear mechanism of parts, the wear mechanism and wear resistance of cast iron grinding tools, and mainly lays a theoretical foundation for the ultra-precision manufacturing of bearing rolling elements, pins, and other rotating bodies.
Author contribution Yongxiang Su: writing-original draft preparation, methodology, experiment, data collection and curation, results analysis, formal analysis; Guang Chen: writing-review and editing, conceptualization, supervision, project administration; Yuchong Chang: experimental work, data collection; Qian Gao: review and editing, supervision, results analysis; Chengzu Ren: review and editing, supervision, formal analysis.

Data availability
The data presented and/or analyzed during the current study are available from the corresponding author on reasonable request.
Code availability Not applicable.

Competing interests
The authors declare no competing interests.