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As an important part of rotating machinery, heat generation due to friction is inevitable during the rotating process of bearings. A large amount of heat causes the temperature of lubricating oil to increase, viscosity of lubricating oil to decrease, and lubricating performance decreases. Addressing the issue of inadequate lubrication between the rolling element and raceway due to increased lubricating oil temperature, this study focuses on full-ceramic ball bearings. It examines the impact of temperature fluctuations on the bearing's lubrication condition and investigates the vibration characteristics of the full-ceramic bearing. The variation in the viscosity of lubricating oil with respect to temperature is measured via a rotary viscometer. A dynamic model of the silicon nitride full-ceramic ball bearing, which considers the effects of elastohydrodynamic lubrication, is established. The impacts of changes in lubricating oil viscosity due to different temperatures on oil film pressure, oil film thickness, and bearing vibration are analyzed and then compared with experimental data. It is observed that under conditions of constant load and speed, the film thickness of the lubricating oil decreases as the viscosity decreases. Additionally, the second peak value of oil film pressure is reduced with the declining viscosity of the lubricating oil. As the viscosity decreases, the vibration of the bearing increases. The amplitude discrepancy between the simulated vibration signal and experimental vibration signal of the full-ceramic bearing is found to be less than 10 %, verifying the validity of the dynamic model.

In order to improve the processing accuracy of silicon nitride ceramic balls and to investigate the mechanism of forming ceramic balls by flexible support grinding method, a new cone-type flexible support grinding method with controlled deflection motion of grinding disc is proposed. Based on the new grinding method, a simulation model is established to deeply analyze the influence of the deflection motion of the grinding disc on the grinding trajectory and force state of the silicon nitride ceramic balls. Orthogonal experiments were conducted on a new cone-type flexible support grinding platform built to further analyze the effect of grinding disc motion characteristics on ball formation. Simulation and experimental results show that under the flexible support grinding method, As the increases of grinding disc deflection angle, the standard deviation of ball trajectory uniformity decreased from 43.58 to 35.49, the maximum contact force increased to 4 times the initial value, the average ball diameter variation increased from 1.466 μm to 2.382 μm, and the batch diameter variation increased from 4.98 μm to 10.27 μm. The lower grinding disc deflection motion is beneficial to optimize the grinding trajectory, but increases the unevenness of the ball force, which is not conducive to improving the average ball diameter variation and batch diameter variation of silicon nitride ceramic balls. In the actual process, the angle of deflection of the grinding disc must be controlled to within 0.02°.

In order to obtain the optimal process parameter combination of double-sided grinding Si3N4 cylindrical rollers, the orthogonal experiment method was used to explore the influences of the grinding disc speeds, the grinding pressures and the basic particle sizes of the abrasive particles on the surface quality and the removal efficiency of Si3N4 cylindrical rollers. The results of the surface roughness and the material removal efficiency of the specimen are taken as the basis for optimizing the grinding process parameters. The results show that the surface roughness of the specimen first decreases and then increases with the increase of the grinding disc pressure and the grinding speed. The basic particle sizes of the abrasive are positively correlated with the surface roughness of the specimen, while the grinding disc speed and the grinding pressure are positively correlated with the removal efficiency. The optimum combination of grinding parameters for Si3N4 cylindrical rollers is that the basic particle size of diamond abrasive is 2.6 μm, the grinding disc speed is 20 r/min and the grinding pressure is 0.15 MPa. Under the optimal parameters, the smooth and undamaged Si3N4 cylindrical rollers with surface roughness of 0.0486 μm and removal efficiency of 1.20 μm/min can be obtained.

Pure MoS _2 films exhibit disadvantages such as low densities, poor mechanical properties, and weak wear resistance under atmospheric environments. For this reason, Ti was chosen as the doping element in this work. Mo-S-Ti composite films with different Ti contents were deposited using the magnetron sputtering system, and the effects of Ti content on the chemical composition, mechanical and tribological properties of these films were analyzed by numerous characterization methods to determine the doping content of Ti elements. The results show that the tribological performance of Mo-S-Ti composite film under atmospheric environments reaches the best when the Ti content is 13.48 at%. In addition, the present work also found that longitudinal load and reciprocating frequency have a significant effect on the tribological properties of this film. It is easier to form high quality transfer film on GCr15 balls under higher longitudinal load and lower reciprocating frequency, thus transforming the friction between film and GCr15 ball into the friction between film and transfer film, resulting in excellent tribological performance.

The application feedback on existing silicon nitride ceramic bearings and RCF experimental research all indicate that the primary failure mode of silicon nitride ceramic bearings is material spalling on the contact surface. Spalling failure occurs due to the initiation and propagation of cracks under rolling contact. However, silicon nitride ceramic bearings, owing to their unique manufacturing method, inevitably exhibit defects and cracks. Therefore, as silicon nitride ceramic bearings are increasingly prevalent, reducing the probability of spalling failure is crucial for extending their service life. This can only be achieved by gaining a clear understanding of the crack initiation and expansion mechanisms in silicon nitride ceramic bearings. This paper is based on silicon nitride rolling friction experiments. It involves the joint simulation of Franc3D-V8.4 and ABAQUS2020, wherein the crack front SIFs are calculated for each load contact position of the surface crack on the silicon nitride ceramic bearing ring during cyclic movement. The study also delves into the determination of the maximum effective stress intensity factors and explores the influence of the initial crack depth on the cycle life and direction of crack propagation. The research yields several valuable conclusions. The findings of this research offer theoretical guidance for formulating grinding technologies for silicon nitride rings and adjusting and controlling working parameters of silicon nitride ceramic ball bearings. These insights are crucial for enhancing the reliability and longevity of silicon nitride ceramic bearings in practical applications.

Micro-diamond film, nano-diamond film and diamond-graphite composite film were deposited on silicon carbide substrate by hot filament chemical vapor deposition. The surface morphology and phase of the grown diamond films were analyzed using scanning electron microscope, atomic force microscope and Raman spectrometer. The friction coefficient and the wear rate of diamond films were measured by friction experiments. The friction and wear properties of diamond films were studied by comparing the experimental results. The results show that the diamond-graphite composite film has better friction and wear properties, the surface roughness of which is 53.8 nm. The friction coefficient (0.040) is similar to that of the nano-diamond film (0.037), while the wear rate is the lowest, 2.07×10−7 mm3·N−1·m−1. Compared with those of SiC substrate, the wear rate (9.89×10−5 mm3·N−1·m−1) and the friction coefficient (0.580) of the diamond films have been greatly improved, which indicates that depositing diamond on the surface of SiC substrate significantly improves the performance of the silicon carbide in the field of friction.

Full ceramic ball bearings are widely used in extreme and complex conditions, such as ultra-high/low temperature, ultra-high speed, corrosion and insulation, because of their material specificity. In order to reveal the friction and lubrication properties, improve the service performance life of all ceramic ball bearings, a mathematical model of the oil lubrication for full ceramic ball bearings has been established in this paper. The distribution rule of the lubricant film in the contact area under different speeds and loads were analysed. The main factors influencing the peak mutation of the lubricant film pressure are clearly defined. The results are compared and analysed by using a ball-disc rolling lubricant film test machine. The study found that the thickness of the lubricant film of a full ceramic ball bearing is positively correlated with the bearing speed and negatively correlated with the bearing loads. The bearing speed has a relatively large effect on the change in the lubricant film thickness. The pressure of the lubricant film in the contact area is positively correlated with the bearing speed, but it is not affected by the bearing load. Unlike metal ball bearings, the thickness and pressure of the lubricant film have a greater relative rate of change in different positions in the contact area of full ceramic ball bearings. With an increase in the bearing speed, the necking-down effect has a greater influence on the peak mutation of the oil pressure. Only one pressure peak occurs in the oil film in the contact area. The results of this paper play an important role in revealing the friction and lubrication properties of full ceramic ball bearings and improving their service performance and life under oil lubrication conditions.

Bearing as the core components of high-grade CNC machine tools, with the constant change of internal clearance of bearing wear increasingly aggravated, spindle rotation accuracy reduced. In this paper, the idea of control variable method is used to explore the dynamic change of bearing clearance from different speeds and different radial loads. Starting with the dynamic model of bearing vibration, the theoretical model of rolling bearing with five degrees of freedom is established in this paper. The interaction force between steel shaft and ceramic bearing inner ring is calculated by Runge-Kutta method with elastic wall thickness ring theory, and the reduction of radial clearance of bearing is obtained. Therefore, a dynamic model of ceramic bearing considering the extrusion force of ceramic bearing inner ring is proposed. At the same time, the vibration test of steel shaft-all-ceramic bearing is designed and carried out. The test results show that under the same load, the higher the rotating speed, the shorter the time for the bearing-rotor system to reach temperature stability, and the root mean square of ceramic bearing-rotor system is obviously reduced. At the same speed, the greater the load, the more obvious the root mean square increase of the bearing-rotor system.

A silicon nitride ceramic bearing has good self-lubricating characteristics. It still has a good operational status under the condition of a lack of oil. However, the temperature distribution of a silicon nitride ceramic bearing during its operation is unclear. To clarify the thermal distribution of a full-ceramic ball silicon nitride ceramic bearing under self-lubricating conditions, the changing trend of the rolling friction temperature between the rolling elements and channels with different accuracies is analyzed using the friction testing machine. The bearing heat generation model based on the silicon nitride material coefficient is established, and the life test machine measures the temperature of the bearing to verify the accuracy of the simulation model. The results show that the friction temperature between the ceramic ball and channel decreases with the increase in ceramic ball level. With an increase in the ceramic ball pressure and temperature, the friction temperature rises. Under self-lubrication, when the bearing bears a heavy load, the influence of the rotating speed on temperature rise tends to decrease. Under the condition of high speed, with the increase in load, the change range of temperature rise shows an upward trend. The important relationship between the bearing’s heat and bearing’s load and speed is revealed. It provides some theoretical guidance for the thermal analysis of a silicon nitride ceramic ball bearing under the self-lubricating condition to improve the service life and reliability of full-ceramic ball bearings.

Compared with metal ball bearings, full ceramic ball bearings have more outstanding service performance under extreme working conditions. In order to reveal the lubrication mechanism and improve the operation performance and service life of full ceramic ball bearings, in this paper, the friction, vibration, and temperature rise characteristics of 6208 silicon nitride full ceramic deep groove ball bearing, under the condition of oil lubrication, are studied experimentally. Based on the test results, and through theoretical calculation and simulation analysis, the distribution of the lubricating oil film in bearing contact micro-zone under different working conditions was simulated. After that, the surface of contact micro-zone of full ceramic ball bearing was analyzed. It was found that there is an optimal oil supply for full ceramic ball bearing oil lubrication in service. Under the optimal oil supply lubrication, full film lubrication can be achieved, and the bearing exhibits the best characteristics of friction, vibration, and temperature rise. Compared with the load, the rotational speed of the bearing has a decisive influence on the optimal oil supply. When the rotational speed and load are constant, the minimum oil film thickness and oil film pressure in the contact area of the rolling body decrease with the increase of angle ψ from the minimum stress point of the rolling body. Under the action of high contact stress, thin oil film will be formed in the bearing outer ring raceway. In the field of full ceramic ball bearings, the research content of this paper is innovative. The research results of this paper have an important guiding significance for revealing the oil lubrication mechanism of full ceramic ball bearing and enriching its lubrication theory and methods.

Working conditions such as lubrication, preload, and rotational speed have important influence on vibration and temperature rise of the spindle motor. In this study, controlled variable experiments are carried out on the silicon nitride (Si3N4) full-ceramic ball bearing and steel bearing of the same type, and the vibration signal characteristics and temperature rise of the spindle motor are tested and analysed, by changing the lubrication conditions, preloads, and rotational speeds of the spindle motor. Through the research, it is found that as the rotational speed increases, the vibration velocity of the Si3N4 full-ceramic bearing spindle motor under different preloads and lubrication conditions shows an overall increasing trend; kurtosis generally presents a downward trend and gradually flattens, indicating that although the vibration velocity increases at high speeds, the vibration signal shows a relatively stable state. As the rotational speed increases, the difference of vibration velocity under the condition of applying preload and no preload decreases, indicating that the influence of preload on the vibration of full-ceramic bearing spindle motor decreases with the increase in rotational speeds. At the same time, it is found that fr and 5fr have greater impact on the vibration of full-ceramic bearing spindle motor, where fr is the frequency of the bearing in normal operation, and 5fr is 5 times of the normal operating frequency. Lubrication conditions have little effect on the temperature rise of full-ceramic bearing spindle motor, and the temperature rise under nonlubricated conditions is even slightly lower than that under grease lubrication conditions. The research results show that the vibration velocity and temperature rise of Si3N4 full-ceramic bearing spindle motor are less than those of steel bearing with the same type, indicating that full-ceramic bearing has better performance than steel bearing under the same working conditions.

Diamond films were deposited on silicon nitride (Si3N4) substrates with three different roughnesses using the method of hot-filament chemical vapor deposition (HFCVD). The tribological properties of the film were studied by changing the deposition time, deposition distance, and methane (CH4) concentration. The friction coefficient, delamination threshold load, and wear rate of the diamond films were tested and calculated using the reciprocating friction and wear test under dry friction conditions. The results show that, when the deposition time is 12 h, the bonding force of the film is the lowest and the friction coefficient is the largest (0.175, 0.438, and 0.342); the deposition distance has little effect on the friction performance. The friction coefficients (0.064, 0.107, and 0.093) of nano-diamond films (NCD) prepared at a 40 sccm CH4 concentration are smaller than those of micro-diamond films (MCD) prepared at a 16 sccm CH4 concentration. The load thresholds before delamination of Ra 0.4 μm substrate diamond film are as high as 40 N and 80 N, whereas the diamond films deposited on Ra 0.03 μm substrates have lower wear rates (4.68 × 10−4 mm3/mN, 5.34 × 10−4 mm3/mN) and low friction coefficients (0.119, 0.074, 0.175, and 0.064). Within a certain load range, the deposition of a diamond film on a Ra 0.03 μm Si3N4 substrate significantly reduces the friction coefficient and improves wear resistance. Diamond film can improve the friction performance of a workpiece and prolong its service life.

Single layer diamond coatings, deposited on cobalt cemented tungsten carbide (WC-Co), with CH4 concentrations of 1%, 3% and 5% were prepared, by hot filament chemical vapor deposition (HFCVD). Moreover, according to the characteristics of different kinds of diamond structure, observed on the single layer coatings, multi-layer crystalline diamond films with micro-nano structures (composed of the 1% and 5%-type coatings) were prepared. The objective was to cumulate the increased interfacial adhesion and mechanical properties of each single layer diamond coating, into one multilayer coating, capable of resisting the efforts present between a milling tool and a hard-brittle material (natural marble). The coating morphology, structure, and resistance to crack propagation of the diamond films were evaluated. Furthermore, cutting tests with diamond-coated tools were performed, while observing the machining life and wear mechanism, on a hard-brittle material (marble). The results on the single layers showed that with the increase of the concentration of CH4, the adhesion to the WC-Co substrate, as well as the resistance to crack propagation is decreasing. The multilayer coating structure shows benefits from the single layer coatings, i.e. improved adhesion to the substrate and inhibition of crack propagation, while the tool life and machining stability are significantly better than the single diamond layer coated tools. Keywords: HFCVD, Diamond coating, Multilayer, Cutting tool, Hard-brittle material

Using response surface methodology, two-target parameter mathematical models for a 100MD60Y4 motorized spindle are established using biogeography-based optimization. Air supply pressure, fuel supply rate, and oil supply interval are the independent variables, while the spindle temperature increase and oil mist PM 2.5 cumulative volume distribution percentage are the response variables. Biogeography-based optimization is used to find a set of optimal lubrication system parameters with the constraint of a small temperature increase in the motorized spindle at 30,000 r/min while considering the influence of oil mist particle size on environmental quality. After lubrication system parameter optimization, comparing the particle size distribution density and temperature increase between the biogeography-based optimization model’s calculated values and the experimental test results, the errors were 1.8% and 1.17%, respectively.

Full ceramic bearing can work under a wide range of temperatures, but the thermal deformation difference between the ceramic outer ring and steel pedestal has a great increase with the rise of temperature and leads to obvious impact and friction. In this paper, the thermal deformation difference is considered and the fit clearance is taken as the boundary condition of the dynamic model. Investigations on the dynamic response of the outer ring are conducted, and the effect of thermal-related fit clearance is analyzed at different working temperatures and rotation speeds through parametric study and experiments. Results show that the vibration of the outer ring grows with the temperature and shows different changes with rotation speed as the temperature changes. The variation of working temperature brings difference in the interactions between the outer ring and the pedestal, and the trends of vibration with rotation speed also change at different temperatures. Impact and friction make great contributions to the interactions between the outer ring and the pedestal and show different changes with temperature. This study puts forward a method for the calculation of bearing vibration at variable temperatures and provides theoretical basis for the application of the full ceramic bearings.

The influence of some key parameters of hot filament chemical vapor deposition (HFCVD) on the temperature distribution during the deposition of diamond coatings on silicon nitride (Si _3 N _4 ) substrates was assessed with the help of the finite element method. Solid heat transfer, fluid heat transfer and surface radiation heat transfer mechanisms were used to calculate the substrate temperature in the steady state during the deposition process. The accuracy of the model was verified by comparing the simulation model with experimental measurements. The comparison shows that the deviation between the model and the actual substrate temperature measurements is within 3%. Furthermore, a Taguchi orthogonal experiment was designed (3 factors, 3 levels, L9). By changing the number of hot filaments, the distance between the filaments and the substrate, and the separation between two adjacent hot filaments, the influence trend of these parameters on the substrate temperature was assessed, leading to an optimal hot filament arrangement. A deposition experiment was carried out using the optimized parameters, and the results showed that the substrate surface temperature obtained by numerical simulation is highly consistent with the temperature measured by the infrared thermometer. The optimized deposition parameters contributed to a more suitable temperature range and more uniform temperature distribution on the Si _3 N _4 ceramic substrate. The deposited diamond film exhibited uniform crystal quality and grain morphology, thus verifying the validity of the simulation results.

In order to reveal the friction properties and improve the wear resistance of silicon nitride ceramic materials, a calculation model of static friction coefficient of silicon nitride ceramic is established. The influence law of contact surface roughness on friction coefficient under different contact load and friction speed is analyzed. The test and the results verification are carried out by using Friction Wear Testing Machine. Then the dry friction process of silicon nitride ceramic is simulated based on UDEC, and the wear failure form is analyzed. In the dry friction process of silicon nitride ceramics, the coefficient of friction is directly proportional to the contact surface roughness, inversely proportional to the contact load, and directly proportional to the friction speed. There is a critical value for the roughness of friction sub-contact surface. Silicon nitride ceramics can self-lubricate by friction when the contact surface roughness is less than this critical value. In the dry friction process, the oxidation of SiO2 has little effect on the friction. The wear surface of silicon nitride ceramics consists of shear failure units and tensile failure units, and their formation is related to the surface roughness. The results play an important role in revealing the frictional properties of engineering ceramics such as silicon nitride, as well as helpful to improve the wear resistance and service life of ceramic materials.

Recently, the engineering structural ceramics as friction and wear components in manufacturing technology and devices have attracted much attention due to their high strength and corrosion resistance. In this study, the tribological properties of Si3N4/Si3N4 sliding pairs were investigated by adding few-layer graphene to base lubricating oil on the lubrication and cooling under different experimental conditions. Test results showed that lubrication and cooling performance was obviously improved with the addition of graphene at high rotational speeds and low loads. For oil containing 0.1 wt% graphene at a rotational speed of 3000 r·min−1 and 40 N loads, the average friction coefficient was reduced by 76.33%. The cooling effect on Si3N4/Si3N4 sliding pairs, however, was optimal at low rotational speeds and high loads. For oil containing 0.05 wt% graphene at a lower rotational speed of 500 r·min−1 and a higher load of 140 N, the temperature rise was reduced by 19.76%. In addition, the wear mark depth would decrease when adding appropriate graphene. The mechanism behind the reduction in friction and anti-wear properties was related to the formation of a lubricating protective film.

Tooth wear is one of the main reasons that lead to gear failure. The amount of wear is nonlinearly related to temperature, lubrication, load, and various random factors of materials, with obvious randomness and slow time-varying characteristics. Wear is a nonstationary random process, which has no accurate mathematical model or accurate reliability estimation method. This article proposes a reliability model of spur gears which works under a nonstationary random process that exceeds the limit, and the time-varying wear reliability is studied based on the level crossing analysis method. The wear at tooth root is revised in the calculation under the nonstationary random process, and the reliability curves are obtained afterwards. An experiment is carried out on the spur gear meshing test rig, and the reliability model and wear performance are verified and analyzed. Results obtained with the proposed tooth surface wear reliability model match well with the experimental results. Therefore, this model is applicable for situations under a nonstationary random process. The new method makes contribution to the assessment of gear running status and is of great significance in the prediction of wear life under a nonstationary random process.

Ceramic angular contact ball bearing is widely used in a high-speed motorised spindle because of their excellent properties such as wear resistance, high temperature resistance, and corrosion resistance. In this study, the characteristics and influencing factors of the radiation noise for a full ceramic angular contact ball bearing applied in the motorised spindle are investigated. Based on a single factor test method, the variations of bearing noise with preload, oil supply, and rotation speed were investigated, and then, the optimal preload and oil supply under the specific speed were obtained. The sound field directivity in the circumferential distribution of the bearing noise was discussed, and the reasons for the uneven distribution of the sound field were elucidated. According to the experimental results, a prediction model on the radiation noise of a full ceramic angular contact ball bearing under certain conditions was proposed. The conclusions will provide a reference for reducing the radiation noise of full ceramic angular contact ball bearings in high-speed operation and improving the bearing performance.

The removal mechanism of silicon nitride ceramic under high-speed grinding is studied in this article, and grinding parameters are optimized. The efficiency of grinding is improved. The diamond grains of grinding wheel are simplified into the truncated octahedron and cone to simulate the grinding process. When the ceramic workpiece is grinded by single-diamond grain and continuously grinded by multi-diamond grains, the effects of grinding depth and grinding speed on grinding force and surface morphology are analyzed. Through the grinding experiment of the inner surface of silicon nitride ceramic, the grinding force data and surface morphology images were obtained. It proves that at the process of studying the effect of grinding speed on the grinding force and machining surface quality, the results of simulation using multi-diamond grains are closer to the experimental results. The results prove that by increasing wheel speed or lowering grinding depth, the grinding force would be reduced and the quality of grinding surface would be improved. Between grinding depth and grinding speed, the latter factor has a greater impact on grinding force and the quality of grinding surface.

This paper solves the leader-following consensus problem for a class of second-order multi-agent systems with input quantized by a newly proposed adaptive dynamic quantizer. The novel dynamic quantizer is an adaptive quantizer that combines the logarithmic quantizer and the uniform quantizer by introducing dynamic gain parameters to achieve quantizer adaptive adjustment. It has advantages of logarithmic, uniform, and adaptive dynamic quantizers in ensuring reducible communication expenses and acceptable quantizer errors for better system performance. On this basis, we transform the guide way climbing frame (GWCF) under ideal conditions into a second-order multi-agent system and solve the motion synchronization problem of GWCF. Finally, we illustrate our approach by numerical examples.

For full ceramic ball bearings, cracks occur frequently in the spalling on the rings, which leads to impacts on the bearing dynamic characteristics. In this paper, the spalling is set on the outer ring, and the dynamic model considering the effect of crack is proposed. The crack is considered to be related to the strain energy, and the effect on the stiffness of the outer ring is also analyzed. Results show that the appearance of cracks leads to the reduction of the full ceramic bearing stiffness, and the vibration amplitude of bearing increases. The effect of a crack depends on its size, and the vibration of the bearing with cracks of different widths and depths vary greatly. This study provides theoretical basis for the calculation of full ceramic bearing and is of great significance for the state monitoring and fault diagnosis.

The thermal characteristics of a motorized spindle are the main determinants of its performance, and influence the machining accuracy of computer numerical control machine tools. It is important to accurately predict the thermal field of a motorized spindle during its operation to improve its thermal characteristics. This paper proposes a model to predict the temperature field of a high-speed and high-precision motorized spindle under different working conditions using a finite element model and test data. The finite element model considers the influence of the parameters of the cooling system and the lubrication system, and that of environmental conditions on the coefficient of heat transfer based on test data for the surface temperature of the motorized spindle. A genetic algorithm is used to optimize the coefficient of heat transfer of the spindle, and its temperature field is predicted using a three-dimensional model that employs this optimal coefficient. A prediction model of the 170MD30 temperature field of the motorized spindle is created and simulation data for the temperature field are compared with the test data. The results show that when the speed of the spindle is 10,000 rpm, the relative mean prediction error is 1.5%, and when its speed is 15,000 rpm, the prediction error is 3.6%. Therefore, the proposed prediction model can predict the temperature field of the motorized spindle with high accuracy.