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Study on sliding friction characteristics of magnetorheological elastomer—copper pair affected by magnetic-controlled surface roughness and elastic modulus

To optimize the online friction coefficient adjustment, it is necessary to study the parameter change features of the magneto-sensitive polymer and its influence on the friction characteristics under magnetic field. A series of magnetorheological elastomers (MREs) with different initial surface roughness were prepared, and a sliding friction platform with MRE—copper block pair was built to carry out magnetic-controlled friction characteristic experiment. Results show that the sliding friction coefficient of MRE decreases with the increase of the magnetic field, but the degree of reduction is quite different under different initial surface roughness and elastic modulus. When the initial surface roughness of MRE is between 0.5 and 2.5 μm and the carbonyl iron particles volume fraction is between 10% and 15%, its magnetic-controlled friction coefficient has the largest reduced value of 22.75%. Moreover, features of elastic modulus and surface topography under magnetic field were tested and analyzed. By combining with the single peak contact model and the friction binomial law, the relationship between the surface roughness and elastic modulus of MREs and the sliding friction force is deduced, and it is proved that the friction coefficient is affected by the coupling effect of surface roughness and elastic modulus. The magnetic-controlled elastic modulus is the key factor, which determines the overall downward trend of the friction coefficient of MREs. Magnetic-controlled surface roughness also plays an important role in the adjustable range of friction coefficient, and reducing the initial surface roughness can increase the magnetic-controlled friction coefficient adjustable range.


Introduction
Exploring how to control friction [1] and reduce wear [2] has important engineering significance and value. With the rapid development of intelligent mechanical equipment and robot, the demand for regulation and utilization of friction has changed from simply increasing or reducing friction [3] to online reversible intelligent regulation. The traditional friction control methods (mechanical regulation [4], adding lubricant [5], surface texturing [6,7]) cannot enough to meet this requirement, and this has stimulated the development of technology for changing the surface friction characteristics of devices by external excitations, which mainly includes electric fields [8,9], magnetic fields [10] and temperature fields [11]. In those methods, electric field control requires a high voltage, with the safety risk, and temperature control needs a relatively long response time. Relatively speaking, the magnetic field control method takes into account both safety and rapid response [12], and it is one of the most promising regulation methods for controllable friction engineering applications.
The magnetorheological elastomer (MRE) is a new type of smart material fabricated by dispersed micron-sized ferromagnetic particles into a polymer matrix [13]. Under the action of magnetic field, dynamic mechanical properties of MREs can produce reversible changes within milliseconds [14], and have been widely used in various types of adjustable vibration isolation systems [15] and adaptive bridge bearings isolator [16]. Recently, scholars [17][18][19][20] have begun to study the friction characteristics of MREs, and found that the friction coefficient [19,20] and wear resistance [17,18] of MREs will be changed by an applied magnetic field. As a friction-controllable material, MREs can be applied to the key parts of mechanical structures, such as brake pads, conveyor belts, robot palms and rubber gaskets [21][22][23]. In order to achieve precise control, the sliding friction characteristics of MRE materials and their components in engineering applications, it is necessary to fully understand which factors will affect their friction characteristics after the applied magnetic field. Lee et al [17] designed and built a sliding friction experimental platform to measure the friction characteristics of MREs in the presence or absence of magnetic field. The results show that when there is a suitable magnetic field, the friction coefficient of MREs is reduced by about 0.1, and the variation range is about 40%. Further, Lian et al [18] tested the elastic modulus and friction of MREs prepared from different matrix materials. The experimental results show that by using the magnetic field, the four kinds of MREs have different elastic modulus, which leads to changes in friction properties. It can be inferred that the change of the elastic modulus to magnetic field may be an important reason for the magnetic-controlled friction. On this basis, our research group [19,20] derived that there may be some trend between the friction coefficient of the MREs and the elastic modulus by combining the elastic contact theory. Meanwhile, our research group [24] found that the surface morphology of the MREs also changed with the magnetic field, and the surface roughness can affect the friction characteristics. In addition to the mechanical properties of the contact surface, the topographical features of the surface and modulus are also important factors affecting the friction characteristics [25]. However, surface roughness and elastic modulus may not affect friction coefficient alone, and there may be some coupling relationship between the two factors, they are all worth to research and explore. Most of the existing researches have not involved and systematically studied the coupling change of the surface roughness and elastic modulus of MRE under the effect of magnetic field, and it is unclear how the surface roughness and elastic modulus coupled affect the friction properties of MREs. Therefore, it is necessary to deeply explore the influence of surface roughness and elastic modulus on the sliding friction characteristics of MRE under magnetic field.
In this study, a series of MRE samples with different initial surface roughness was prepared, and a sliding friction experimental platform was further built. Then, friction force measurement experiments were performed in the presence or absence of a magnetic field, and the optimal proportions of the MRE with different initial surface roughness were explored, and laid the foundation for revealing the mechanism. Moreover, a variety of characterization were performed on the material, and the experimental results that the coupling effects of two important factors namely elastic modulus and surface topography are theoretically analyzed from the macroscopic experimental. Finally, through the application of elastic mechanic equation and tribological equation, one magnetic-controlled sliding friction mechanism of the MREs was revealed, which will help to achieve precisely controllable sliding friction.

Fabrication of MRE samples with different roughness
The initial surface topography of the MREs has a decisive influence on the magnetic field-controlled surface roughness, and even a completely opposite change [20]. Therefore, in the preparation process, MRE samples with different surface Hereafter the mixture is ultrasonically to promote the bubble inside the mixture to float, and placed in a vacuum drying oven which the vacuum was 101 Pa to guarantee the bubbles were completely removed. In order to make the MREs have different initial surface topography, the 360 mesh and 12 000 mesh sandpapers were selected respectively, and the sandpaper is cut into a rectangle of 60 mm × 60 mm size, which is consistent with the internal dimensions of the mold, and the cut sandpaper is adhered to the bottom of the mold through the adhesive. For the isotropic MREs, the mixture after removing the bubbles was directly poured into a mold, sealed and placed in a vacuum drying oven at 80 • C for 2 h until solidification molding; While for anisotropic MREs, sealed and placed it in an electromagnet with magnetic induction of 0.7 T and heated it to 80 • C for 2 h to cure, and the specific operation flow is shown in figure 1. Isotropic and anisotropic MREs form certain initial surface morphologies after demolding. In addition, all MRE samples were cut into cuboid-like shapes with dimensions of 40 mm × 40 mm × 4 mm to facilitate experiment.

Characterizations
According to the above preparation process, the MRE samples with different initial roughness were prepared, and two isotropic MRE samples 2 and 6 with the particle volume ratio of 10% were selected. Because when the volume fraction of CIPs is 10%, the roughness of MRE changes more obviously [19]. An atomic force microscopy (AFM) image was taken with an NT-MDT NTEGRA Prima series atomic force microscope (Precision: Resolution can reach 1-3 µm; scanning range up to 200 µm × 200 µm) to characterize the microscopic surface morphology of MRE samples with different roughness. In short, first put the sample fixed on the iron sheet into the center of the magnetic sample table, so that it can attract the iron sheet and the sample. Then adjust the position of the optical microscope lens and adjust the four-quadrant detector. Finally, after initializing the scan parameters, scan the image and observe the microstructure.
A stylus contact measurement method was used to characterize the presence of a one-dimensional profile of the sample in the presence of a magnetic field. Measurements were performed using a surface roughness tester with an accuracy of 0.001 (TR210, Chongqing Libo Instruments Co., Ltd, China). The surface roughness tester is ready to start measurement by shaking the rocker behind the fixed stand so that the probe of the surface roughness tester touches the surface of the MRE sample. A microcomputer-controlled electromechanical universal testing machine (TSE-104B, Shenzhen Wance Testing Machine Co., Ltd, China) was applied to characterize the elastic modulus of the two MRE samples 2 and 6. The sample was placed in the middle of the electromagnet base, compressed with the machine's compression fixture, and the machine's program was set. The MRE samples were covered with different magnetic fields at different currents and compressed reciprocally for 2 min, and the compression force data and the degree of deformation were measured once. Young's modulus was calculated by taking the average of the effective values obtained through several tests.

Experimental setup 2.3.1. Construction of the sliding friction test platform.
A sliding friction experiment platform based on the friction pair of copper blocks was designed and built. The experimental platform is mainly composed of stepping motor, linear guide, tensile pressure sensor, pressure variable device, magnetic field applying device and a base. The principle and physical diagram of the experimental platform are shown in figure 2.
The surface friction force of the MREs is mainly tested by the planar constant force method. During the experiment, the sample is fixed on the center of the box. By placing different numbers of copper blocks in the pressure variable device to provide different positive pressures, the stepping motor in the horizontal direction is driven to move at a uniform speed, so that the non-magnetic copper friction pair performs sliding friction on the MRE surface. The dimension of the friction force is output by the pulled pressure sensor. By placing a permanent magnet larger than the samples in the magnetic box and adjusting the non-uniform magnetic field (approximately uniform) through the lifting device, the value of the friction force under the magnetic field with the same polarity of different strengths can be measured. According to the experimental requirements, the sliding friction characteristics of MRE samples with different roughness before and after the application of a magnetic field were tested. In order to ensure the accuracy of the test results, each experiment test is repeated ten times, and the average values are taken as the experimental result.

Friction force test method.
The experimental program was engineered in the following way. First, after cleaning the top surface of the MRE with alcohol to eliminate contaminants (such as grime and crumbs), the test sample was secured to a magnet box top, and then the horizontal motor is driven to push the pressure variable device in a uniform linear motion to the right. Next, the data capture software was used to record the full contact force data obtained through the force sensor during the process. Finally, loading was stopped at 180 s to end the test. In the test, the force when the top surface of the test sample hindered the pressure variable device was regarded as the friction force of the MRE. Before the experiment, the permanent magnet was placed on the lifting device in the magnet box to explore the influence of different magnetic field strength on the sliding friction characteristics. The test was performed at a fixed pushing speed of 0.2 mm s −1 , different positive pressures (0.95, 1.92, 2.89, 3.86, 4.81 N) and different magnetic field intensities (0, 150, 250 mT) and samples (table 1). Figure 3 shows the raw data for the pushing time and friction force curve of sample 7.

MRE sliding friction characteristics test results
Using the above-mentioned friction test platform, the prepared MRE samples were measured for surface friction force in positive pressures of 0.95, 1.92, 2.89, 3.86, 4.81 N and magnetic fields of 0, 150 and 250 mT. Each experiment was performed ten times under the same condition, and the mean value was denoted as the final value. The experimental results show that the sliding friction characteristics of the isotropic MRE and anisotropic MRE under different positive pressure conditions with an applied magnetic field are consistent, as shown in figures 4(a)-(d). In order to show more clearly, the experimental data of isotropic MRE with positive pressure of 2.89 N were analyzed and processed to obtain the specific variation of MRE friction coefficient under the action of magnetic field, as shown in figures 4(e) and (f).
The friction coefficient of MREs before and after application of magnetic field is obtained by Coulomb's law µ = f/P, f is friction force and P is positive pressure force. It can be found that in the absence of magnetic field, the MREs with different initial morphologies exhibit different friction coefficients, and the friction coefficient of S-MRE samples is larger than that of R-MRE samples. This result indicates that the surface roughness and friction force of MREs are related, and there has a certain suitable initial surface roughness that can help to reduce the friction coefficient.
The basic trend of the change in the initial friction coefficient increases and then decreases with increasing the particle fraction of CIPs. This phenomenon can be explained as follows: the initial elastic modulus is high when the volume fraction of CIPs particles is high, while the initial elastic modulus is low when the volume fraction of CIPs particles is low. And the initial friction coefficient is inversely proportional to the initial elastic modulus, and the initial friction coefficient should decrease as the volume fraction increases. However, when the volume fraction of CIPs particles of MRE is in the range of 5%-10%, the initial coefficient of friction increases. This is mainly due to the small increase in the initial elastic modulus, but the 5% sample has a small percentage of particles, and the surface is more likely to accumulate CIPs particles, and the friction factor of CIPs particles is lower than that of PDMS, so the initial friction coefficient exhibited smaller than that of 10%. However, when the volume fraction of CIPs particles in the MRE is in the range of 10%-20%, the sharp increase in the initial elastic modulus hardens the MRE and reduces the initial friction coefficient.
The friction coefficient of each MRE sample varied to different degrees under the increase of the magnetic field. In general, the magnetic field can control the reduction of the friction coefficient of the MREs. Further, the change degree of the friction coefficient under different magnetic fields was compared and analyzed, and the results are shown in table 2. It can be seen from table 2 that the friction coefficients of both S-MRE and R-MRE gradually decrease with increasing magnetic field, but there are large differences in the rates of change. Under the same other conditions, the decreasing trend of µ of S-MRE is as the volume ratio first increases and then decreases, and the decreasing trend of µ of R-MRE is increasing as the volume ratio increases. A possible reason is that with the increase of CIPs, the change of the elastic modulus under the magnetic field gradually increases, and the rate of change may decrease after a certain volume fraction [26]. The changing trend of the elastic modulus and that of the friction coefficient are almost in an inverse relationship, so whether there is a certain connection and influence between the two parameters. Under the magnetic field, the change of friction coefficient of the S-MRE samples observably more than the R-MRE samples, which may be caused by the different changes in the surface morphology of the two types samples with the magnetic field. Different surface roughness shows different friction coefficient change trend, which indicated that surface roughness can have some influence on the change of friction coefficient.
The rate of change is particularly small for both sample 5 and sample 13. This is mainly due to the slightly rough surface of sample 5 and sample 13 with more convex peaks, and then some convex peaks are reduced by the magnetic field. However, other slightly flat areas will produce new peaks, so the whole may still be rough. And the relative magnetic response effect is reduced by the small percentage of CIP particles in sample 5 and sample 13. When the volume fraction of S-MRE is 20%, the downward trend of friction coefficient slows down, but that of R-MRE still increases. It may be because the overall viscosity and other mechanical properties of MRE will increase when the volume fraction is 20%. When the surface is smooth, the influence of mechanical properties on the elastic modulus can be observed, and the upward trend of it decreases accordingly; when the surface is rough, the influence of mechanical properties on it is small due to the more convex surface, and the upward trend of it is still increasing. This also shows that elastic modulus and surface roughness are not a single effect on the friction coefficient, but a coupled influence on it.
Therefore, choosing S-MRE with CIPs volume of 10%-15% can more stably obtain an excellent friction coefficient variation range, which can reach about 23%. For instance, under a magnetic field of 250 mT, the µ change rate of sample 3 which with an initial smooth surface can be up to 22.75%. While, under the same magnetic field, for R-MRE samples, the largest friction coefficient change rate is only 9.04%.
Since surface roughness is a very important factor of MRE magnetic-controlled friction parameters, so a series of surface topography tests and analyses were carried out. The AFM images of the two MRE samples 2 and 6 were taken in order to visually see the comparison of different initial surfaces. From the figures 5(a) and (b), the sandpaper of 12 000 mesh was placed at the bottom of the mold, the surface of the prepared MREs is relatively smooth. While, after the sandpaper of 360 mesh was placed at the bottom of the mold, the surface of the prepared MREs is undulating and rough. It is indicated that the MRE samples with different initial morphology can be effectively prepared by treating the bottom of the mold with different meshes of sandpaper. In addition, the surface roughness tester was used to test the one-dimensional contour of samples under a magnetic field. It can be seen from figures 5(d) and (e) that, when there is no magnetic field, the surface of S-MRE sample 2 is relatively flat, and the surface of R-MRE sample 6 has large undulations, and there are a lot of convex peaks. Under a magnetic field of 250 mT, the surface morphology and contours of the two samples changed greatly. The surface of S-MRE sample 2 produced many convex peaks, and the surface unevenness increased compared to without magnetic field. On the contrary, the peak value of the surface convex peak of R-MRE sample 6 was weakened, compared without magnetic field, which the surface roughness is lower.
According to the statistical results shown in figure 5(c), the surface roughness of the MRE sample with a relatively smooth initial surface will increase with the increase of the magnetic field. For example, the maximum surface roughness change rate of S-MRE samples increased up to 84.35% under a magnetic field of 250 mT. However, when the initial surface is rough, the surface roughness of MRE will decrease with the magnetic field. For instance, maximum drop rate of R-MRE samples can reach 27.61%. By comparing and analyzing the samples with different initial surface roughness, the experimental results show that the initial roughness of MRE samples with different particle volume fractions are different, and the changing trend of magnetic-controlled surface roughness is also different. This means that the initial surface roughness may be an important factor affecting of the magnetic-controlled sliding friction characteristics. Furthermore, it is worth mentioning that, no matter how large the initial roughness is, after applying the magnetic field, the roughness is close to the critical value of about 3 µm. The surface roughness of S-MRE which has a better friction coefficient is between 0.5 and 2.5 µm.
The reason for this phenomenon is that when the initial roughness of the MRE is relatively small, the applied magnetic field generates uneven magnetic induction stresses due to the random distribution of the CIP particles in the PDMS. This leads to uneven micro-deformation of the PDMS surface, which causes the surface to become rough from a nearly smooth state, and the surface roughness of the MRE increases with the increase of the external magnetic field. However, the surface roughness of the MRE surface has CIP particles near each convex peak. The CIP particles are subjected to the magnetic field, which generates magnetically induced stresses at the convex peak through magnetic interactions. As a result, when the particles near the convex peak are attracted inward by nearby particles, strain occurs at the convex peak, leading to a decrease in the peak height, which results in a smooth surface and a decrease in surface roughness [20].
The elastic modulus is also an important factor affecting the magnetic-controlled sliding friction characteristics of MRE. For this reason, the elastic modulus of two MRE samples 2 and 6 were characterized by the instrument. The test generates different magnetic field strength by applying different drive currents in the coil, and the elastic modulus is the ratio of positive pressure to the deformation degree. It can be seen from figure 6 that the different initial surface morphology of the MREs have little effect on the change of magneto-elastic modulus, and the elastic modulus of the samples all increase with the increase of the magnetic field. It shows that the elastic modulus of MRE has the characteristics of adjustable and controllable under the magnetic field. It will increase with the increase of the magnetic field and the material will become hardness. Varieties in mechanical contact characteristics affect its sliding friction characteristics. Under the same test conditions (force, displacement, magnetic field, and volume ratio), the elastic modulus of S-MRE and that of R-MRE showed slightly different values.
Generally, under the magnetic field, the elastic modulus of MRE sample has a high rate of change, which can increase 123% with the 20% particles volume fraction [26]. Meanwhile, when the initial surface of MRE is different, the surface roughness will increase or decrease with the increase of magnetic field. However, the friction coefficient of all MREs decreases as the magnetic field increases. Therefore, the main factor affecting the magnetic-controlled sliding friction characteristics of MRE may be that the modulus increases with the increase of magnetic field. The difference in magneticcontrolled surface roughness caused by different initial surface roughness may only change the degree of friction coefficient reduction. S-MRE samples increase the surface roughness under the magnetic field and enhance the reduction of friction coefficient. However, under the magnetic field, the surface roughness of R-MRE samples is reduced, which reduces the tendency of the friction coefficient to decrease. It can be assumed and inferred that there is a coupling relationship between the elastic modulus and roughness.

Magnetic-controlled sliding friction theoretical analysis
Based on previous experimental research on friction coefficient, surface roughness and elastic modulus, it is found that the magnetic-controlled friction mechanism of MRE is related to the two factors, and there may be a coupling relationship between the two factors to affect the friction coefficient together [19]. Meanwhile, it is known that the surface morphology and mechanical properties of the object are important factors determining the friction characteristics [27]. In order to analyze the magnetic-controlled friction mechanism of MRE in principle, it is necessary to investigate the role and correlation between surface morphology and elastic modulus from theoretical analysis under assumed conditions. The microstructure of the MRE was observed by white light interferometer in the early stage. The results are shown in figure 7.
The results of white light interferometer test show that there are actually many microscopic peaks and valleys on the surface of the MRE sample which seemingly smooth. In the process of making contact with the friction pair, microscopically, the mutual contact of the two surfaces is actually the contact between the surface micro bulge.
It is assumed that the ideal initial surface topography of the MRE is composed of a number of rough peaks with neat rows, different height and the same radius. Under uniform stress, the rough peaks do not affect each other, and there is a critical point of initial surface roughness Ra 0 .When the roughness is Ra 0 , the number of peaks actually contacted is n 0 . Introducing relative roughness k 0 : where Ra represents the surface roughness of the MRE. When k 0 > 1, it represents that the initial surface of the MRE is relatively rough. When 0 < k 0 < 1, it represents that the initial surface of the MRE is relatively smooth. The actual contact position between the copper block and the MRE with different surface roughness under ideal conditions is shown in figure 8. The surface roughness Ra of the MRE mainly depends on the flatness of the surface topography. Small initial surface roughness indicates that the peak height of the surface of the MRE is small, and the height difference between the peaks is not obvious, as shown in figure 8(a). On the contrary, large initial surface roughness indicates that the peak height of the surface of the MRE is large, and the height difference between the peaks is large, as shown in figure 8(c).
Since the peak height of the MRE is on the order of micrometers, which is much smaller than the overall thickness of the material, it is reasonable to assume that the elastic modulus of each contact peak is the same as the elastic modulus of the  entire material. The actual contact area of the friction pair can be analyzed as follows, when the initial surface roughness is less than the critical value of Ra 0 , all the rough peaks with heights h 1 , h 2 , and h 3 are in contact with the friction pair under the action of pressure, and the number of contacts is n = n 1 + n 2 + n 3 . When the initial surface roughness is equal to the critical value of Ra 0 , the number of rough peaks in contact is n = n 0 = n 1 ′ + n 2 ′ . However, when the initial surface roughness is greater than the critical value of Ra 0 , since the difference between the peaks is too large, only n = n 1 ′ ′ rough peak having the height of h 1 ′ ′ are in contact with the friction pair. Therefore, it is concluded that the actual contact peak number n of the MRE has an inverse relationship with the relative roughness rate k 0 , which can be expressed as: where λ 1 and λ 2 are positive constants, the number of constants is determined by the actual contact situation.
Due to MRE is a kind of viscoelastic material, the contact problem with the friction pair of copper block during the sliding friction test can be converted into the contact between a plurality of elastic spheres which have a radius of curvature R and elastic modulus of E with a rigid plane, as shown in figure 9.
When the rough surface is pressed by the external load P and the rigid friction pair, the deformation due to the extrusion first occurs between the higher roughness peaks. The stress state of the single rough peak is analyzed, as shown in figure 9(a). As shown in the picture, the actual contact state of the rough peak changes from a broken line to a solid line, and the actual contact area is a circle with a radius r. The actual contact area between the single rough peak and the friction pair is derived by the analysis of the elastic mechanic equation [28]: However, the actual rough surface of the MRE is composed of a large number of rough peaks of different height, and during the contact process. Plurality of rough peaks is simultaneously involved in the contact. Therefore, the actual contact area between the MRE and the rigid friction pair is also related to the number of contact roughness peaks. Assuming that the number of surface peaks of the MRE in contact with the rigid friction pair is n under a certain pressure, the actual contact area of the surface of the MRE can be expressed as: When the MRE comes into contact with the friction pair, the friction force is generated under a certain thrust force, and the friction force can be considered as the sum of the mechanical action and the molecular action of contacting the rough peak [26]. According to the actual contact area derived, the friction force of the surface of the MRE can be determined as [29,30]: where α and β are constants, the number of constants is determined by the physical and mechanical properties of the surface of the MRE. It can be seen from the equation that the surface friction force of the MRE under a certain pressure is related to the elastic modulus E and affected by the number n of contact peaks. In the previous study [24], it was found that the MRE samples with different initial morphology will have different changes in surface morphology under an external applied magnetic field. The sample with a relatively smooth initial surface under the magnetic field, has an increased surface roughness and a large difference in height between the rough peaks. Conversely, the sample with a relatively rough initial surface under the magnetic field, has a decreased surface roughness and a small difference in height between the rough peaks. How the change in surface topography of the MRE under the magnetic field will affect the number of contact peaks, and the surface friction force will be further analyzed.
Taking equation (2) into equation (5), and the friction force of the surface of the MRE is further derived as follows: It can be seen from equation (6) that the change of the surface friction force of the MRE mainly depends on the change of the surface roughness and the elastic modulus under certain assumptions and ideal conditions. By adjusting the degree of change of these two important parameters, the effective control of the surface friction force of the MRE can be achieved. In general, the change rate of the elastic modulus of MRE under magnetic field is relatively high, which can increase 123% [26]. Although the surface morphology of the MRE is also controlled by the magnetic field to produce changes [24], compared with the changes in the elastic modulus, the range of surface morphology changes is smaller, which only within 30%. Since λ 1 and λ 2 are positive constants, the influence degree of elastic modulus is greater than that of surface roughness, so the changing trend of MRE friction force mainly depends on the magnetic-controlled elastic modulus, and the influence of magnetic-controlled surface morphology is relatively small. Combined with the previous experimental analysis under certain assumptions and ideal conditions, the changing trend among the friction force, the surface roughness and elastic modulus was obtained, as shown in table 3. The variation range of the friction force drop was roughly obtained based on the experimental data. Based on that the positive pressure force does not change, and then the degree of change in friction is equivalent to the degree of change in friction coefficient. The analysis shows that the variation of the magneticcontrolled friction coefficient is influenced by the coupling between surface roughness and elastic modulus. The reduction of the friction coefficient of MRE is mainly due to the observable increase in the magnetic-controlled elastic modulus. Affected by the change of the magnetic-controlled surface roughness, the friction coefficient of the S-MREs is reduced more than that of the R-MREs.
Both theoretical analysis and experimental tests show that the magnetic-controlled sliding friction characteristics of MREs is determined by two important factors: surface roughness and elastic modulus, and the elastic modulus plays a decisive role. Under certain conditions, the frictional characteristics of the MREs can be controlled more accurately by adjusting those two factors. It is beneficial to promote the engineering application of MREs with controllable sliding friction characteristics.

Conclusions
The sliding friction tests which regard MRE and copper block as friction pair were carried out on samples with different initial surface roughness. The experimental results show that the sliding friction coefficient of MRE decreases with the increase of the magnetic field, but the degree of reduction is quite different under different initial surface roughness and elastic modulus. The maximum change rate in S-MREs is 22.75% of sample 3, and sample 8 which has the largest change rate in R-MREs is only 9.04%. It is found that the frictional properties of MREs under the magnetic field are affected by surface roughness and elastic modulus. Moreover, change features of elastic modulus and surface topography under magnetic field were tested and analyzed. The elastic modulus of S-MREs and R-MREs both increased with the enhancement of a magnetic field, and the surface roughness of S-MREs was the same trend, but the surface roughness of R-MREs reduced when the magnetic field increased. Therefore, the friction coefficient of the S-MREs has a greater range of variation, and the R-MREs have a small change range of friction coefficient. When the initial surface roughness of MRE is between 0.5 and 2.5 µm and the CIPs volume fraction is between 10% and 15%, its magnetic-controlled friction coefficient change range is the largest, which can be reduced by about 23%. Under the condition of ignoring the effects of some other mechanical properties and non-uniform magnetic fields, and combined with the single peak contact model and the friction binomial law, the relationship between the surface roughness and elastic modulus of MREs and the sliding friction force is deduced. The results proved that the friction coefficient is mainly affected by the coupling effect of surface roughness and elastic modulus. It can be seen that the magneticcontrolled elastic modulus is the key factor, and the change rate of the elastic modulus is relatively large, which determines the overall downward trend of the friction coefficient of MREs. Although the surface roughness is not decisive, the magneticcontrolled surface roughness also plays an important role in the adjustable range of friction coefficient, and reducing the initial surface roughness can expand the magnetic-controlled friction coefficient adjustable range. The theoretical analysis results are consistent with the experimental data. The elastic modulus of MRE can be large, and the initial surface roughness should be as small as possible, which can obtain better magnetic-controlled sliding friction characteristics, and will help to research and promote the engineering application of MREs controllable sliding friction characteristics and interfacial contact fields.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.