Research on the Influence of Raceway Waviness on the Vibration Characteristics of Deep Groove Ball Bearings

The dynamics model of a 2-degree-of-freedom deep groove ball bearing is established by incorporating the raceway surface waviness model comprising multiple sinusoidal functions superposition.The model is solved using the fourth-order Runge-Kutta method to obtain the vibration characteristics including displacement,velocity,acceleration,and frequency of the bearing.Validation of the model is accomplished through comparison with theoretical vibration frequencies.The influence of the amplitude of waviness of the inner and outer ring raceway surfaces of deep groove ball bearings on the vibration displacement,peak-to-peak vibration displacement and root-mean-square vibration acceleration is analyzed,and the results show that as the amplitude of the inner and outer ring raceway surfaces waviness increases,all the vibration characteristic indexes increase,indicating that the vibration amplitude of the bearings as well as the energy of the waviness-induced shock waveforms increase with the increase of the amplitude of the waviness.

Dynamic analysis of traction motor in a locomotive considering surface waviness on races of a motor bearing

The traction motor is the power source of the locomotive.If the surface waviness occurs on the races of the motor bearing,it will cause abnormal vibration and noise,accelerate fatigue and wear,and seriously affect the stability and safety of the traction power transmission.In this paper,an excitation model coupling the time-varying displacement and contact stiffness excitations is adopted to investigate the effect of the surface waviness of the motor bearing on the traction motor under the excitation from the locomotive-track coupled system.The detailed mechanical power transmission path and the internal/external excitations(e.g.,wheel–rail interaction,gear mesh,and internal interactions of the rolling bearing)of the locomotive are comprehensively considered to provide accurate dynamic loads for the traction motor.Effects of the wavenumber and amplitude of the surface waviness on the traction motor and its neighbor components of the locomotive are investigated.The results indicate that controlling the amplitude of the waviness and avoiding the wavenumber being an integer multiple of the number of the rollers are helpful for reducing the abnormal vibration and noise of the traction motor.

Investigation of Surface Micro Waviness in Single Point Diamond Fly Cutting

Single point diamond fly cutting is widely used in the manufacture of large-aperture ultra-precision optical elements. However,some micro waviness( amplitude about 30 nm,wavelength about 15 mm) along the cutting direction which will decrease the quality of the optical elements can always be found in the processed surface,and the axial vibration of the spindle caused by the cut-in process is speculated as the immediate cause of this waviness. In this paper,the analytical method of dynamic mesh is applied for simulating the dynamic behavior of the vertical spindle. The consequence is then exerted to the fly cutter and the processed surface profile is simulated. The wavelength of the simulation result coincides well with the experimental result which proves the importance of the cut-in process during the single point diamond fly cutting.

Surface Waviness in Grinding of Thin Mould Insert Using Chilled Air as Coolant

On going trend of miniaturization in electronic rel at ed parts, which is an average of two times in every 5～7 years introduce grindin g challenges. In grinding process, the surface waviness control of thin parts is an ardent task due to its warpage, induced by the high specific grinding energy (2～10 J/mm 3). Therefore, coolant is often used to avoid thermal damage, obtai n better surface integrity and to prolong wheel life. However coolant, the incomp ressibility media introduce high forces at the grinding zone creating dimensiona l as well as shape instability. In view of these situations chilled air was ap plied in place of conventional coolant. The chilled air is produced using a two -stage vapor compression refrigeration cycle with characteristics of: temperatu re -35 ℃, pressure 0.2～0.3 MPa and flow rate 0.4 m 3/min. Also traces of eco - oil mist that encompass the chilled air are supplied to the grinding zone. B oth chilled air and eco-oil mist are applied through two independent paths of a specially designed twin compartment nozzle for maximizing the penetration. This paper investigates the grinding characteristics of mold insert which is closer to M2 tool steel (component widely used in connector industries) when using chil led air as coolant media. Grinding experiments were conducted using a vitrified bond CBN wheel (B91N100V) and a surface grinder. Initial study was focussed on establishing the most suita ble clamping method for the thin mold insert. FEM analysis and grinding experime nt studies were performed to quantitatively analyze the clamping induced deflect ion. Waviness value (W t) of (24～62) μm was achieved for resin clampi n g whereas (4～8) μm, (4～6) μm were achieved for magnetic and wax clamping res pe ctively. Wax clamping is predominantly used in all the grinding experiments that characterize the grinding process, which use chilled air as the coolant media. Between 0.15 to 0.9 mm 3/mm.s of specific material removal rate, ground sur face temperature of mold insert was increased from 0.3 ℃ to 59.7 ℃ for chi lled air. For the similar grinding conditions with the coolant fluid an increase from 0.9 ℃ to 14.4 ℃ was recorded. With increase of specific material removal rate from 0.15 to 0.65 mm 3/mm.s, F t/F n ratio was increased from (0.2 to 0.4), (0.6 to 1.67) for wet coolant and chilled air respectively. Despite of high F t/F n ratio and ground surface temperature, chilled air method has shown a surface waviness, W t from (2 to 5.6) μm. Microstructure examination of chilled air produced ground surface was comparable to those of using coolant fluids. Surface finish, R a of (0.45～0.7) μm was achieved for mold insert . This work will enable to have clear understanding about the quantitative influe nce of chilled air as well as the clamping method against the surface waviness o f thin mold insert.

Vibration analysis of a single row angular contact ball bearing with the coupling errors including the surface roundness and waviness

Roundness and surface waviness are main manufacturing errors on the components of single row angular contact ball bearings(ACBBs).An analytical study for vibrations of the ACBBs with coupling errors including the roundness and waviness can be useful for the vibration control of the rotating machinery.However,most previous works only focused on the single error modelling method.In this paper,an improved time dependent displacement excitation(TDDE)model is proposed to consider the coupling errors including the roundness and waviness on the inner and outer races of an ACBB.The TDDE model for the roundness and waviness is established by using a combination of several sinusoidal functions.A dynamic model in the previous study is improved to consider the influences of coupling errors including the roundness and waviness.The Hertzian contact theory and Dowson’s method are adopted to calculate the bearing contact stiffness.The time-and frequency-domain vibrations for the experimental and simulation results are compared to show some model validation.The influences of roundness orders and waviness amplitudes on the vibrations of the ACBB are analysed.The obtained results show that the coupling errors including the roundness and waviness have some influence on the time-domain impulse waveform and frequency-domain spectrum characteristics of the bearing accelerations.The differences of the vibrations between the coupling errors and sing error are from 4%to 42%.This paper can provide a useful guidance for the accurate diagnosis of surface imperfections in the ACBBs.

A comparative study of surface waviness models for predicting vibrations of a ball bearing

Surface waviness models utilized to describe the excitation events in the ball bearings(BABs) play an important role in predicting the vibrations of the ball bearing systems. This work proposes a comparative study on the most relevant existing surface waviness models. One model is named as time-varying displacement(TVD) model, which can only describe the time-varying displacement excitation(TDIE). Another model is named as TVDS model, which can describe the TDIE and time-varying contact stiffness coefficient excitation(TCSE). The influences of the wave number, maximum amplitude, nonuniform distribution on the contact stiffness coefficients are studied, as well as vibrations of the BAB. The comparative results demonstrate that the time-varying displacement and stiffness(TVDS) model can provide a more accurate impulses caused by the uniform and nonuniform surface waviness on the races of the BABs. It also seems that the surface waviness distribution has a significantly influence on vibrations of the BABs.

Frictional contact analysis of a rigid solid with periodic surface sliding on the thermoelectric material

Understanding and characterizing rough contact and wavy surfaces are essential for developing effective strategies to mitigate wear,optimize lubrication,and enhance the overall performance and durability of mechanical systems.The sliding friction contact problem between a thermoelectric(TE)half-plane and a rigid solid with a periodic wavy surface is the focus of this investigation.To simplify the problem,we utilize mixed boundary conditions,leading to a set of singular integral equations(SIEs)with the Hilbert kernels.The analytical solutions for the energy flux and electric current density are obtained by the variable transform method in the context of the electric and temperature field.The contact problem for the elastic field is transformed into the second-kind SIE and solved by the Jacobi polynomials.Notably,the smoothness of the wavy contact surface ensures that there are no singularities in the surface contact stress,and ensures that it remains free at the contact edge.Based on the plane strain theory of elasticity,the analysis primarily examines the correlation between the applied load and the effective contact area.The distribution of the normal stress on the surface with or without TE loads is discussed in detail for various friction coefficients.Furthermore,the obtained results indicate that the in-plane stress decreases behind the trailing edge,while it increases ahead of the trailing edge when subjected to TE loads.

Formation mechanism and modeling of surface waviness in incremental sheet forming

mproving and controlling surface quality has always been a challenge for incremental sheet forming (ISF), whereas the generation mechanism of waviness surface is still unknown, which impedes the widely application of ISF in the industrial field. In this paper, the formation mechanism and the prediction of waviness are both investigated through experiments, numerical simulation, and theoretical analysis. Based on a verified finite element model, the waviness topography is predicted numerically for the first time, and its generation is attributed to the residual bending deformation through deformation history analysis. For more efficient engineering application, a theoretical model for waviness height is proposed based on the generation mechanism, using a modified strain function considering deformation modes. This work is favorable for the perfection of formation mechanism and control of surface quality in ISF.

Quantification methodologies on organization and morphology features of fiber-like structures:A review

Among all the structural formations,fiber-like structure is one of the most common modalities in organisms that undertake essential functions.Alterations in spatial organization of fibrous structures can refiect information of physiological and pathological activities,which is of significance in both researches and clinical applications.Hence,the quantification of subtle changes in fiber-like structures is potentiallymeaningful in studying structure-function relationships,disease progression,carcinoma staging and engineered tissue remodeling.In this study,we examined a wide range of methodologies that quantify organizational and morphological features of fibrous structures,including orientation,alignment,waviness and thickness.Each method was demonstrated with specific applications.Finally,perspectives of future quantification analysis techniques were explored.

Dilution characteristics of dual buoyant jets in wavy cross-flow environment

Due to the difference in density between the discharge effluent and coastal water,partially treated wastewater is often discharged into the marine environment as a buoyant jet via submarine outfalls with multiport diffusers.The dilution characteristics of effluent discharge(dual buoyant jets)in a wavy cross-flow environment were studied in a laboratory.The planar laser-induced fluorescence technique was used to obtain the concentration data of the jets.The effects of different environmental variables on the diffusion and dilution characteristics of the jets were examined through physical experiments,dimensional analysis,and empirical formulations.It was found that the dilution process of the dual jets could be divided into two components:the original jet component and the effluent cloud component.The jet-to-current velocity ratio was the main parameter affecting the concentration levels of the effluent cloud.The merging of the two jets increased the jet concentration in the flow field.When the jets traveled further downstream,the axial dilution increased gradually and then increased significantly along the axis.Under the effects of strong waves,the concentration contours branched into two peaks,and the mean dilution became more significant than under the effects of weak waves.Therefore,the dilution of the effluent discharge was expected to be significant under strong wave effects because the hydrodynamic force increased.A dilution equation was derived to improve our understanding of the dilution process of buoyant jets in a wavy cross-flow environment.This equation was used to determine the influences of the jet-to-current velocity ratio,wave-to-current velocity ratio,and Strouhal number on the minimum jet dilution.It revealed that the wave and buoyancy effects in effluent discharges were significant.

Magnetic Field Effect and Heat Transfer of Nanofluids within Waveform Microchannel

In this research,a numerical study of mixed convection of non-Newtonian fluid and magnetic field effect along a vertical wavy surface was investigated.A simple coordinate transformation to transform wavy surface to a flat surface is employed.A cubic spline collocation numerical method is employed to analyze transformed equations.The effect of various parameters such as Reynolds number,volume fraction 0-,Hartmann number,and amplitude of wave length was evaluated in improving the performance of a wavy microchannel.According to the presented results,the sinusoidal shape of the microchannel has a direct impact on heat transfer.By increasing the microchannel wave amplitude,the Nusselt number has risen.On the other hand,increasing the heat transfer in the higher wavelength ratio corrugated channel is seen as an effective method of increasing the heat transfer,especially at higher Reynolds numbers.The results showed that with increasing Hartmann numbers,the flow line near thewall becomesmore regular and,according to the temperature gradient created,theNusselt number growth.

Fluid Flow and Mixed Heat Transfer in a Horizontal Channel with an Open Cavity and Wavy Wall

Heat exchangers are utilized extensively in different industries and technologies.Consequently,optimizing heat exchangers has been a major concern among researchers.Although various studies have been conducted to improve the heat transfer rate,the use of a wavy wall in the presence of different types of heat transfer mechanisms has not been investigated.This study thus investigates the mixed heat transmission behavior of fluid in a horizontal channel with a cavity and a hot,wavy wall.The fluid flow in the channel is considered laminar,and the governing equations including continuity,momentum,and energy are all solved numerically.The numerical solution is stabilized by using a first-order multi-dimensional characteristic-based scheme in combination with a fifth-order Runge-Kutta method.The flow and heat transfer effects of varying Richardson numbers,Reynolds numbers,wave amplitude,wavelength,channel height,and cavity width are examined.The results indicate that the mean Nusselt number increases with an increase in Reynolds number,wave amplitude,and cavity width,while it decreases with an increase in Richardson number,wavelength,and channel height.The minimum Nusselt number is calculated to be 0.7,whereas the maximum Nusselt number is 27.09.The Nusselt number has only increased by 40%in the higher depths of the cavity,despite the Richardson number being 10,000 times larger.But this figure increases to 130%at lower depths.The mean Nusselt number is thus significantly influenced by channel height and cavity width.The influence of wave amplitude on the mean Nusselt number is twice that of wavelength.

Modeling of Mixed Convection in a Lid Driven Wavy Enclosure with Two Square Blocks Placed at Different Positions

The purpose of this paper is to investigate the simulation of mixed convection in a lid-driven wavy enclosure with blocks positioned at various positions. This study also examined the impact of the longitudinal position of the heated block on heat transfer enhancement. The Galerkin weighted residual finite element method is employed to computationally solve the governing equations of Navier-Stokes, thermal energy, and mass conservation. The enclosure consists of two square heated blocks strategically placed at different heights—firstly, one set is closer to the bottom surface;secondly, one set is nearer to the middle area and finally, one set is closer to the upper undulating surface of the enclosure. The wavy top wall’s thermal insulation, along with active heating of the bottom wall and blocks, generates a dynamic convective atmosphere. In addition, the left wall ascends as the right wall falls, causing the flow formed by the lid. The study investigates the impact of the Richardson number on many factors, such as streamlines, isotherms, dimensionless temperature, velocity profiles, and average Nusselt numbers. These impacts are depicted through graphical illustrations. In all instances, two counter-rotating eddies were generated within the cage. Higher rotating speed consistently leads to improved performance, irrespective of other characteristics. Furthermore, an ideal amalgamation of the regulating factors would lead to increased heat transmission.

Simulation of Natural Convection Flow with Magneto-Hydrodynamics in a Wavy Top Enclosure with a Semi-Circular Heater

Natural convection flow in enclosure has different applications such as room ventilation, heat exchangers, the cooling system of a building etc. The Finite-Element method based on the Galerkin weighted residual approach is used to solve two-dimensional governing mass, momentum and energy-equations for natural convection flow in the presence of a magnetic field on a roof top with semi-circular heater. In the enclosure the horizontal lower wall was heated, the vertical two walls were adiabatic, inside the semi-circular heater, the wavy top wall cooled. The parameters Rayleigh number, Hartmann number and Prandtl number are considered. The effects of the Hartmann number and Rayleigh number on the streamlines, isotherms, velocity profiles and average Nusselt number are examined graphically. The local Nusselt number and the average Nusselt number of the heated portion of the enclosure with the semi-circular heater are presented in this paper. Finally, for the validation of the existing work, the current results are compared with published results and the auspicious agreement is achieved.

Surface Roughness Quality and Dimensional Accuracy—A Comprehensive Analysis of 100% Infill Printed Parts Fabricated by a Personal/Desktop Cost-Effective FDM 3D Printer

Fused deposition modeling (FDM) has become widely used for personal/ desktop cost-effective printers. This work presents an investigational platform, which is used to study the surface roughness quality, and dimensional accuracy of 100% infill density printed parts fabricated by a personal/desktop cost-effective FDM 3D printer using different types of thermoplastic filament materials namely, PLA, PLA+, ABS and ABS+. Varieties of experiments were conducted after the fabricated parts were naturally cooled down for at least three hours to room temperature. During printing work, the nozzle diameter, layer height, nozzle temperature and printing speed were set at 0.3 mm, 0.1 mm, 220°C and 30 mm/s, respectively. According to the experimentally obtained data results over 10 mm scanned profile and 90°measuring direction (perpendicular to building direction), PLA+ thermoplastic filament material shows an excellent surface behaviour and is found to be more accurate while ABS does exhibit high surface roughness, waviness and primary behaviour. Both PLA and ABS+ show good surface performance.

Effect of Cutting Speed on Surface Quality by Bandsawing

The surface profile behavior of workpieces sawn has been investigated. Six species were sawn under the condi-tion of four different kinds of cutting speed by the band saw. The real surface profile of a sawn workpiecc is composed of twosections, which arc the additivity of the waviness of filtered wave and roughness curve. The roughness of center line avernge aswell as amplitude decrease with the increasing of cutting speed for different kinds of species used in the experiment.

Finite Element Analysis for Grinding and Lapping of Wire-sawn Silicon Wafers

Silicon wafers are the most widely used substrates for semiconductors. The falling price of silicon wafers has created tremendous pressure on silicon wafer manufacturers to develop cost-effective manufacturing processes. A critical issue in wafer production is the waviness induced by wire sawing. If this waviness is not removed, it will affect wafer flatness and semiconductor performance. In practice, both lapping and grinding have been used to flatten wire-sawn wafers. Although grinding is not as effective as lapping in removing waviness, it has many other advantages over lapping (such as higher throughput, fully automatic, and more benign to environment) and has great potential to reduce manufacturing cost of silicon wafers. This paper presents a finite element analysis (FEA) study on grinding and lapping of wire-sawn silicon wafers. An FEA model is first developed to simulate the waviness deformation of wire-sawn wafers in grinding and lapping processes. It is then used to explain how the waviness is removed or reduced by lapping and grinding and why the effectiveness of grinding in removing waviness is different from that of lapping. Furthermore, the model is used to study the effects of various parameters including active-grinding-zone orientation, grinding force, waviness wavelength, and waviness height on the reduction and elimination of waviness. Finally, the results of pilot experiments to verify the model are discussed.

3D surface topography formation in ultra-precision turning

The generation process of 3D surface topography in ultra-precision turning is analyzed, as the result of superimposing between actual roughness surface,waviness surface and geometrical form texture surface. From the viewpoints of machine technical system and manufacturing process,factors influencing on roughness surface, waviness surface and geometrical form texture surface in ultra-precision turning are discussed further.The 3D topography of ideal roughness surface and actual surface affected by cutting vibration are simulated respectively.

Evolution of appearance profile of hot-dip galvanized car-body steel sheet during deformation process

In recent years, the waterborne free intermediate coating process has been widely used in the automotive industry. Because the baking times and coating thickness are decreased, the surface covering capability of the painting process is reduced, which directly affects the appearance quality（ long-and short-wave values） of the body paint. Thus, there are correspondingly higher requirements for the white body surface profile prior to painting. The surface profile of the white body is mainly affected by the plate material, the surface profile, and the deformation process. So,the change rule for the surface profile during deformation of the steel plate is a key factor in coating appearance optimization. In this paper, we first analyze the typical deformation of the outer cover of a car body. Then ,we examine the change tendency of the surface profile of steel plates with respect to different deformation rates, specifically for a steel plate comprising a hot-dip galvanized bake-hardened steel sheet. Based on our analysis of the influence of the deformation on the coating appearance,we selected 3% ,5% ,and 8% deformation rates in this research. We found the roughness （Ra） value in the typical deformation range （3% -8% ） of the car body to exhibit a decreasing trend at first and then an increasing trend. The Ra value of the 8% deformation is not more than the original plate test value. When the Pc value of the original plate is in the lower range （ about 60）, it exhibits a slight increasing trend in the deformation process （3 % -8 % ）. And when the Pc value of the original plate is in the higher range （ about 120 ）, it exhibits no increasing trend in the deformation process （ 3% -8% ）. In contrast,the waviness （WCA） value in the car body＇s typical deformation range （3%-8%） shows a significant growth trend.

Influence of Abrasive Waterjet Machining Parameters on the Surface Texture Quality of Carrara Marble

Abrasive waterjet (AWJ) cutting technology has been used extensively for the cutting and processing of almost all engineering materials because of its precise cutting technique and the lack of damage caused. Currently, the use of abrasive waterjet cutting in the natural stone industry is increasing. However, the effectiveness of abrasive waterjet cutting of natural stones is dependent on the rock properties and machine operating parameters. Consequently, this paper presents the influence of abrasive waterjet machining parameters on the surface texture quality of Carrara marble. The results have shown that the abrasive waterjet cutting process offers better cut surface texture quality of Carrara marble under certain parameter conditions as well as being more environmentally-friendly. The stand-off distance shows the opposite effect on both surface roughness and waviness. With a view to reducing the machining costs, every user tries to select the traverse rate of the cutting head to be as high as possible, but results show that increasing the traverse rate always causes a corresponding increase in terms of inaccuracy, surface roughness, Ra ≈ 93.7 μm, and waviness, Wa ≈ 92.6 μm. The abrasive mass flow rate is not a significant parameter during the cutting process. In all investigations, it was found that the machined surface of the marble is smoother near the jet entrance, Ra ≈ 4 μm, and waviness, Wa ≈ 5 μm, and increasingly becomes rougher towards the jet exit. The result also shows that the micro-hardness value of the Carrara marble was in the range of 122 HV to 124 HV.