Introduction

In recent years, the global installed capacity of wind power has been growing rapidly, and wind power bearings, as the key transmission components in the top of the wind turbine tower, play an important role in the smooth operation of wind turbines1. Wind power bearing rolling body and bearing inner and outer ring long-term friction contact, not only in high speed, high load conditions with good wear resistance and high hardness, but also in high temperature, low speed and heavy load, such as lack of oil and oil, emergency braking situation with a certain degree of self-lubricating properties, and the working environment of the wind power bearings often need to withstand the role of high humidity, high temperature, high corrosion, etc., which will result in the contact surface of the rolling body of the bearing to produce a certain amount of corrosion and damage, so that the distribution of lubricant medium is not uniform, the lubrication effect is reduced, resulting in increased friction and wear of the rolling body of wind power bearings, fatigue resistance is reduced, and the service life is rarely up to 20 years2,3.

In order to obtain wind power bearing rolling bodies with good mechanical properties, the magnetron sputtering technology can be used to prepare uniformly dense films with excellent mechanical properties such as stress, hardness, wear resistance, etc. The results of the studies by Ohtake4 and Wang5 show that the DLC films with sp3 diamond structure exhibit excellent wear resistance and ultra-high hardness, which is the reason why they are used in the surface coating reinforcement of various types of high-end bearing rolling bodies. In addition, during high-temperature friction, the DLC film is transformed into a soft film containing sp2 graphite structure with good lubrication performance6, but the DLC film also has its own limitations. When the film is loaded, the high residual stress will easily cause cracks and gaps, and in serious cases, the film will fall off directly, which largely reduces the bonding strength between the film and the substrate.

Erdemir7 et al. analyzed the reason for the excessive residual stress in DLC thin films and concluded that argon ion bombardment led to structural changes in the carbon atoms, forming different hybrid structure sp2, sp3, and sp2/sp3, and the existence of these hybrid structure generated a large difference in the residual stresses, especially the chemical bonding strength of the sp3 structure was higher than that of the sp2 structure, and with the sp3 structure the carbon atom increases, the residual stress of DLC films increases. Guo8 et al. in order to reduce the excessive residual tensile stress in DLC films, used DC magnetron sputtering technique to deposit Cu-DLC films with different Cu doping on Si substrate, and found that the residual stress value of Cu-DLC films was less than 0.6 GPa, which was much lower than 2.0 GPa when no Cu doping.Pau9 et al. In order to reduce the residual stress of DLC films, 2–7% nanogold was doped into the DLC deposited on Si substrate, which reduced the residual stress of the films from 2.3 to 0.48 Gpa, and it was concluded that this reduction was caused by the change in the content of sp2/sp3 hybrid structure in the thin-film organization.

From the above, it can be seen that the sp2 and sp3 hybrid structure have an important influence on the improvement of the comprehensive performance of DLC films, while the ratio of hybrid structure of the films is related to the deposition parameters in addition to the influence of the doping elements. Ma et al. concluded that a low-temperature substrate is favorable for the deposition of DLC films on various metal surfaces when depositing the films10, which is due to the fact that the temperature has a large influence on the ionization motion of argon ions, and the different argon ion densities largely affect the sp2/sp3 content in DLC films. Suitable magnetic field and voltage effects can enhance the bonding of the film to the substrate11. In addition to the effects of sputtering temperature and electromagnetic field, the deposition air pressure also has a certain effect on the properties of DLC films12, and the energies of both sputtered ions and deposited particles increase with the increase of deposition air pressure13,14, and the accumulation of deposited particles with high energies to the surface of the substrate will increase the temperature of the growing film, cause the thermal migration of the atoms in the mixed layer, and destroy the diamond structure that has been formed (sp3), while the diamond structure of the DLC film has high hardness and high wear resistance, this good wear resistance is attributed to the hybridization bond of the sp3 structure of carbon atoms, the C–H covalent bond will break and fail during the friction process, and the H atoms are able to quickly combine with the carbon atoms that appear to have dangling bonds to form the sp3 structure again and maintain the original diamond structure15. Therefore, reasonable control of process parameters such as sputtering temperature, deposition air pressure, and voltage magnetic field has a direct impact on the performance of DLC films.

In this paper, the molecular dynamics simulation technique of LAMMPS was introduced to simulate the process of preparing diamond-like thin films on 42CrMo substrate by magnetron sputtering technique, and the effects of different deposition parameters on the residual stress and film-base bonding strength of DLC/Ni-DLC thin films were investigated on an atomic scale, and the sp2/sp3 hybridization ratios and film thicknesses of DLC/Ni-DLC thin films were Statistical analysis was carried out on the sp2/sp3 hybridization ratio and film thickness of the DLC/Ni-DLC films, and the relationship between the film organization and film residual stress and film-base bonding strength was analyzed, so as to obtain diamond-like films with low residual stress, good self-lubricating performance and high film-base bonding strength by adjusting the deposition parameters, and then to improve the comprehensive performance of the diamond-like films and prolong the service life of the wind turbine bearings.

LAMMPS-MD simulation

LAMMPS is a large-scale parallel processor for molecular/atomic dynamics, which can support the setting of potential functions, initial conditions, boundary conditions and other parameters of interaction between different atoms, with high simulation accuracy, fast operation speed, and the visualization and analysis of simulation results using OVITO software, which has its unique advantages for the study of nanoscale DLC/Ni-DLC thin films prepared by magnetron sputtering. The simulation process is shown in Fig. 1.

Figure 1
figure 1

LAMMPS simulation of magnetron sputtering for the preparation of DLC thin film streams.

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In order to scientifically carry out the MD experiments for the preparation of DLC/Ni-DLC thin films by magnetron sputtering, a three-factor, four-level L16 (34) orthogonal experiment was designed by full factorial analysis for the main process parameters of magnetron sputtering technology: sputtering temperature T (K), sputtering voltage U (V), and deposition air pressure P (Pa), and the process parameters and level settings are shown in Table 1.

Table 1 Process parameters and level settings.
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Analog and output calculation parameter settings

This MD simulation uses a hybrid potential hybrid composed of SiC.tersoff, lj/cut, FeNiMoCr.eam.alloy and other potential functions as the interaction potentials between the 42CrMo substrate and the pure carbon target as well as the argon ions to solve the motion trajectories of each atom.

During the MD process, the conjugate method gradient method is used to minimize the energy of the model so that each atom has a certain initial velocity, the unit is set to metal, the time step is set to 0.001, and the initial temperature is set to 273.15 K. The 42CrMo substrate is generated by the create-atoms command, and there are a total of 6454 alloy atoms in the substrate with the dimensions of 5 × 5 × 3 nm, and the carbon target has a total of 3000 atoms, and the system size is 5 × 5 × 4.4 nm. A total of 6454 atoms of alloy with the size of 5 × 3 nm and 3000 atoms of carbon target with the size of 5 × 5 × 4.4 nm were generated by the create-atoms command, the substrate had a total of 6454 alloy atoms with the size of 5 × 5 × 3 nm, the carbon target had 3000 atoms with the size of 5 × 5 × 4.4 nm, the system was equilibrated by 2 ps in NPT system, and then the system was equilibrated by 6 ps in NVT system, and the argon ions with 1 eV were bombarded by 5000 carbon atoms of the pure carbon target and Ni target composed of 500 Ni atoms to simulate the sputtering and deposition process of magnetron sputtering in a vacuum chamber, and the sputtered atoms are deposited onto the substrate to grow into a DLC/Ni-DLC film, and the thermodynamic information of the film is output through the thermo-style command, and the thermodynamic information of the film is output through the compute-stress/atom and fix-box/relax aniso commands, respectively, the residual stress calculation and binding energy output for the atoms of DLC/Ni-DLC films including the substrate hybrid layer, statistics of film thickness, film residual stress along the film thickness direction and film substrate binding force under different parameters, post-processing of the output files by using OVITO, and combining with Python to analyze and statistic the organization of sp2 of DLC/Ni-DLC films, sp3 hybrid structure ratio.

Results and analysis

Simulation results

The results of the MD experiments of DLC/Ni-DLC with different process parameters are shown in Tables 2, 3.

Table 2 MD simulation results of orthogonal experimental DLC films.
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Table 3 MD simulation results of orthogonal experimental Ni-DLC films.
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After the magnetron sputtering MD simulation, the simulation results were visualized and post-processed by OVITO, and the final stable DLC/Ni-DLC-42CrMo structural model was obtained as shown in Fig. 2, and the thickness of the Ni-doped film was about 4 nm.

Figure 2
figure 2

(a) Ni-DLC, (b) DLC, and 42CrMo composite models.

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As shown in Fig. 3, during the growth of DLC/Ni-DLC films, the formation of a mixed film layer between DLC/Ni-DLC and 42CrMo substrate surface layer was randomly observed at 3 ps, 81 ps, 196 ps, 282 ps, and the thickness of such a mixed layer reaches about 2 nm before generating a DLC/Ni-DLC film layer without 42CrMo alloy, and the existence of such a mixed layer is the key to the good adhesion of the films to the substrate, the nature of its residual stress, the distribution of its mechanical properties such as bonding force, and the distribution of sp2/sp3 hybrid structure. The existence of the hybrid layer is the key to the good adhesion of the film on the substrate, and the size, nature and distribution of its residual stress, the mechanical properties such as the size of the bonding force and the distribution of the sp2/sp3 hybrid structure have an important influence on the wear resistance and self-lubrication of the diamond-like film.

Figure 3
figure 3

Growth process of DLC/Ni-DLC thin films.

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Figure 4 shows the distribution of residual stresses in atomic scale DLC/Ni-DLC films under a certain set of parameters in the MD simulation, it is observed that the outermost layer of carbon atoms have less stress, while the subsurface layer is a mixture of carbon atoms and 42CrMo, and the stresses of the carbon atoms are not uniform, and it can be determined in Fig. 5 that the overall compressive stresses of the non-Ni doped DLC films in the mixed layer of 0–1.5 nm is dominated, and with the increase of thickness after 1.5 nm, it shows tensile stress and the stress value increases rapidly, and decreases along the thickness after statistical calculation. With the increase of thickness, after 1.5 nm for tensile stress and stress value increases rapidly, the film residual compressive stress along the thickness of the first increase and then reduce the film residual stress after statistical calculation of the film residual stress of the average residual stress of the film for the 1.516 Gpa. While the Ni-DLC film thickness of about 3.678 nm, the internal tensile and compressive stress of the film is lower and the distribution of the film is more uniform, the average residual stress value is − 0.969 Gpa.

Figure 4
figure 4

Residual stress distribution of each carbon atom in DLC/Ni-DLC films.

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Figure 5
figure 5

Residual stress distribution along film thickness for DLC/Ni-DLC films. (a) DLC. (b) Ni-DLC.

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The proportion of sp2, sp3, and sp2/sp3 hybrid structure of the films were counted by the OVITO module in Python, and the results are shown in Fig. 6, the proportion of sp3, sp2/sp3 hybrid structure in the DLC after Ni doping increased from (3.87%; 42.35%) to (14.65%; 51.70%), and the proportion of sp2 hybrid structure increased from 38.65 to 28.37%, and the proportion of sp3 hybrid structure in the film organization is about 2.56 times higher after Ni doping than without Ni doping.

Figure 6
figure 6

Proportion of sp2, sp3 hybridized structures of DLC/Ni-DLC films. (a) DLC. (b) Ni-DLC.

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As shown in Fig. 7, fix-box/relax aniso calculations show that there are 4405 atoms of C and Fe, Cr, Mo, etc. in the DLC film, with an average binding energy of about 11.81 eV, and the film-based binding force per unit cm length of the mixed layer is calculated as 3.372 N through the relationship between the distance and the energy; in the Ni-DLC film, there are 6421 atoms of C and Fe, Cr, Mo, Ni, etc., with an average binding energy of about 9.26 eV, and the film-based binding force per unit cm length of the mixed layer is 3.854 N through the distance and energy relationship. In the Ni-DLC film, there are 6421 atoms of C and Fe, Cr, Mo, Ni, etc., and the average binding energy is about 9.26 eV, and the film-based binding force of the mixed layer per unit cm length is 3.854 N calculated from the distance-energy relationship. The number of deposited atoms increases within the same deposition time after Ni doping and the inter-atomic binding energy decreases in the thin film organization, which may be an important factor for the reduction of the residual stress of the film.

Figure 7
figure 7

Calculated results of membrane base bonding force of thin films.

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Verification of molecular dynamics simulation results

In order to verify the reliability of the simulated experimental data, the Ni-DLC films were deposited using a PCVD8060 high vacuum multifunctional coater under the same experimental parameters, and the residual stresses of 16 groups of Ni-DLC films were measured using a TD-3500 X-ray polycrystalline diffractometer. The deposition system is shown in Fig. 8, the coated 42CrMo pads are shown in Fig. 9, and the X-ray polycrystalline diffractometer is shown in Fig. 10.

Figure 8
figure 8

PCVD8060 high vacuum multi-functional coating.

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Figure 9
figure 9

42CrMo gasket after coating.

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Figure 10
figure 10

X-ray diffractometer and measurement of thin films. (a) TD-3500 X-ray polycrystalline diffractometer. (b) Scanning process of thin film samples.

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The errors between the deposition experiments and the MD results are shown in Fig. 11. In the case of nickel doping, the residual stresses of the Ni-DLC films are overall in the form of residual compressive stresses or lower tensile stresses. The maximum error between the experimental results and the simulated stress values is 29.65%, the minimum error is 1.28%, and the average error is about 8.8%. The small error proves the accuracy and reliability of the molecular dynamics simulation method to analyze the residual stresses of Ni-DLC films prepared by magnetron sputtering.

Figure 11
figure 11

Error chart of experimental and simulation results.

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The cross-sectional morphology of the Ni-DLC films was observed using a JSM-IT800 SHL field emission scanning electron microscope (SEM) made in Japan, and the thick layers were obtained under the experimental conditions, and the SEM equipment is shown in Fig. 12. From the cross-sectional morphology of Ni-DLC films shown in Fig. 13, it can be clearly observed that in the thick layer, near the 42CrMo substrate, the film shows better densification by deposition of small particles, and the densification in the part of the film near the substrate after Ni doping has been improved to a certain extent. After continuous growth, a large number of tiny particles are extruded into each other under cryo-extrusion, and the films begin to grow in a columnar organization. This growth pattern can explain the phenomenon that the film tensile stress increases with the film thickness.

Figure 12
figure 12

Scanning electron microscope.

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Figure 13
figure 13

Thick layer of Ni-DLC film with deposition temperature of 348.15 K, sputtering voltage of 300 V and deposition air pressure of 0.2 Pa.

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Effect of process parameters and Ni doping on the structure and mechanical properties of Thin Films

By analyzing the results of MD simulation, the effects of sputtering temperature, sputtering voltage, and deposition air pressure on the proportion of sp2, sp3, and sp2/sp3 hybrid structure in the organization of DLC/Ni-DLC thin films as well as the residual stresses in their thin films were obtained, and the magnitude of the film-base bonding and the film thicknesses were compared between Ni-doped and non-Ni doped diamond-like thin films.

As shown in Fig. 14, keeping the temperature constant and under different deposition air pressures, the sp2 hybridized structure in the Ni doped film gradually decreases with the increase of air pressure and voltage; while without Ni doping, the sp2 hybridized structure in the film shows an overall trend of increasing with the increase of air pressure, and gradually less with the increase of voltage.

Figure 14
figure 14

Proportion of sp2 hybridized structures at different deposition air pressures.

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As shown in Fig. 15, keeping the deposition pressure unchanged and under different sputtering temperatures, the sp2 hybrid structure in the Ni doped film increases with the increase of temperature; when the film is not doped with Ni, the sp2 hybrid structure in the film increases slowly with the increase of temperature, and combined with Fig. 14, it can be seen that the overall decrease of sp2 hybrid structure in the film is observed after doping with Ni.

Figure 15
figure 15

Proportion of sp2 hybridized structures at different sputtering temperatures.

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As shown in Fig. 16, keeping the sputtering temperature unchanged, under different deposition air pressure, the sp3 hybridized structure in the Ni doped film decreases and then increases with the increase of air pressure, and increases and then decreases with the increase of voltage; when the film is not doped with Ni, the sp3 hybridized structure in the film increases slowly with the increase of air pressure, and gradually increases with the increase of voltage.

Figure 16
figure 16

Proportion of sp3 hybridized structures at different deposition air pressures.

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As shown in Fig. 17, keeping the deposition air pressure constant, at different sputtering temperatures, the sp3 hybridized structure in the Ni-doped film increases and then decreases with the temperature, while the sp3 hybridized structure in the film increases slowly with the increase of the temperature when the film is not doped with Ni. Combined with Fig. 16, it can be seen that the overall increase of sp3 hybridized structure in Ni-doped films. It has been shown that the sp3 hybridized structure will be transformed into an sp2 graphite structure when the temperature exceeds 500°C16,17, therefore, the sp3 hybridized structure can effectively ensure the self-lubricating performance of the DLC film on the surface of the rolling body of wind turbine bearings.

Figure 17
figure 17

Proportion of sp3 hybridized structures at different sputtering temperatures.

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As shown in Fig. 18, keeping the deposition air pressure unchanged, under different sputtering temperatures, the residual stress of the Ni doped film decreases slowly with the increase of temperature, and decreases and then increases with the increase of voltage; when the film is not doped with Ni, the residual stress of the film increases and then decreases with the increase of temperature and voltage.

Figure 18
figure 18

Residual stresses in thin films at different sputtering temperatures.

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As shown in Fig. 19, keeping the sputtering temperature unchanged, the residual stresses of the Ni doped thin films under different deposition air pressures do not change much with the increase of air pressure, while the residual stresses of the thin films without Ni doping fluctuate greatly with the increase of air pressure. Combined with Fig. 18, it can be seen that after Ni doping, the residual stress of the films is dominated by compressive stress, and the average stress value is lower than that of the non-Ni doped diamond-like films, which may be due to the formation of antibonds between Ni and C as well as the relaxation of the distorted bond angles and bond lengths leading to the reduction of the residual stress.

Figure 19
figure 19

Residual stresses of films at different deposition air pressures.

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As shown in Figs. 20, 21, for the same deposition conditions and time, the thickness of the Ni-doped film increased by about 82% and the film base bonding force increased by about 32.78% compared to the non-Ni-doped film, with the thickness of the Ni-DLC film ranging from 3.4 to 3.75 nm, and the film base bonding force ranging from 38.54 N to 45.36 N.

Figure 20
figure 20

Thickness of diamond-like films before and after Ni doping.

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Figure 21
figure 21

Membrane base bonding of DLC before and after Ni doping.

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Conclusions

In this paper, the molecular dynamics simulation method was used to complete the magnetron sputtering preparation process of DLC/Ni-DLC thin films, and the variation rules of hybrid structure, residual stress and film base bonding force of the films under the conditions of nickel element and different deposition parameters were obtained as follows:

  1. 1.

    In terms of film organization, nickel doping changes the ratio of the hybrid structure of the film, the ratio of sp3 hybrid structure is about 2.56 times higher than that of the undoped nickel, and this rhombic structure gives the film high hardness and good wear resistance. Meanwhile, the hybridized layer produced by the DLC/Ni-DLC film and the 42CrMo substrate is observed to be about 2 nm thick on the atomic scale, which indicates the possibility of the existence of a film-based hybrid layer.

  2. 2.

    In terms of the mechanical properties of the film, the energy between the carbon atoms decreases after Ni doping, causing a decrease in the interatomic force, leading to a certain degree of reduction in the residual stress of the film, and mainly compressive stress, under different deposition parameters, the value of the film stress decreases from 0.504–5.003 Gpa to − 2.11–0.065 Gpa, and the thickness of the same film with the same deposition time increases by about 82%, leading to an increase in the overall bond energy between carbon atoms and an increase in the film base bonding force by about 32.78%.

  3. 3.

    Inspired by the MD study, the effect of deposition parameters on the residual stress of the mixed layer of DLC films and the membrane base bonding strength is only one aspect, the doping of different elements can reduce the potential energy between the atoms of the film, change the bond angle between the atoms and the bonding strength, which has an important effect on the structural distribution and mechanical properties of the DLC films, the subsequent research should be centered on the reduction of the film residual stress to start with, the use of the MD means from the subsequent research should be centered on reducing the residual stress of the film, using MD means to prepare DLC films from the perspective of doping Ni, Si and other elements, as well as introducing transition layer, multilayer film, multi-element, etc., in order to reduce the residual stress of the film, improve the stability of the membrane-based bonding of the DLC film and the membrane-based bonding force, and further improve the operational stability and service life of the wind turbine bearings.