Experimental and modeling study of surface topography generation considering tool-workpiece vibration in high-precision turning

Xingying ZHOU, Henan LIU, Tianyu YUa,, Ruiyang GUO,Guangzhou WANG, Yazhou SUN, Mingjun CHENa,,*

a State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001, China

b School of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150001, China

KEYWORDS High-precision turning;Machining vibration;Modeling;Surface roughness;Surface topography

Abstract High-precision turning (HPT) is a main processing method for manufacturing rotary high-precision components, especially for metallic parts.However, the generated vibration between tool tip and workpiece during turning may seriously deteriorate the surface integrity.Therefore,exploring the effect of vibration on turning surface morphology and quality of copper parts using 3D surface topography regeneration model is crucial for predicting HPT performance.This developed model can update the machined surface topology in real time.In this study, the effects of tool arc radius, feed rate, radial vibration, axial vibration and tangential vibration on the surface topography and surface roughness were explored.The results show that the effect of radial vibration on surface topography is greater than that of axial vibration and tangential vibration.The radial vibration frequency is also critical.When vibration frequency changes, the surface topography profile presents three different types: the standard sinusoidal curve, the sinusoidal curve whose lowfrequency signal envelopes high-frequency signal, and the oscillation curve whose low-frequency signal superimposes high-frequency signal.In addition, HPT experiment was carried out to validate the developed model.The surface roughness obtained in the experiment was Ra=53 nm, while the roughness obtained by the simulation was Ra = 46 nm, achieving a prediction accuracy of 86.7 %.

1.Introduction

High-accuracy precision or micro components are increasingly in demand for various industries in recent years, such as biomedical engineering, MEMS, electro-optics, aerospace and communication.1–3These high-precision components often require sub-micro-level shape accuracy and surface finish.4–6Among the many processing methods, highprecision turning (HPT) is a promising way to generate surfaces with sub-micrometric form accuracy and nanometric roughness.7,8Compared with non-traditional machining methods such as electrical discharge machining (EDM), electrochemical machining (ECM), laser machining, ion beam machining,etc.,HPT has the advantages such as high machining efficiency, low machining cost, and no special machining environment requirements,and thus it is suitable for most processing materials.

A variety of factors during the machining process affect the shape accuracy and surface finish of the workpiece,such as the geometric error of the machine tool,the runout of the spindle,the processing flutter and tool wear.9,10Among them, the relative vibration between the tool and workpiece is considered as the most important factor affecting the surface morphology and surface finish of the workpiece.11–14Although the turning spindle bearing adopts aerostatic pressure technology, due to the existence of manufacturing and assembly errors, the spindle would inevitably cause eccentricity and unbalanced mass,and eventually lead to periodic vibrations.15–18In addition,since the cutting depth in HPT is at the micrometer level, the tiny vibration amplitude in the machining cannot be ignored.Conventionally,the set-up parameters for the HPT are usually selected with the aid of trial cutting experiments, which are both time-consuming and costly.19,20Moreover, the surface finish of the workpiece usually depends on the operator’s experience and machine equipment.Therefore, it is necessary to develop a simulation system that can predict the 3D topography and surface roughness of the workpiece.

In terms of ultra/high-precision turning, many researchers have proposed corresponding simulation models.Cheung and Lee presented a model-based simulation system to analyze the surface roughness generation in ultra-precision diamond turning, and a multi-spectrum analysis method was developed to investigate the surface micro-topography.21–23However,the effect of vibration frequency on surface topography and roughness was not presented in their study.Qu et al.developed a 3D simulation model for simulating optical surface morphology in ultra-precision roll die turning and investigated the impact of the relative vibration between tool and workpiece on surface roughness.24This model only discusses the modeling situation of cylindrical turning and does not involve the process of planar turning.Kim et al.proposed a metrological model of the relative vibration between the tool and the workpiece to simulate and analyze the surface microtopography of plane turning.25In this model, the cutting depth at different radial positions is represented by a functional expression.However,it is not accurate to express the cutting depth of different radial positions by function for complex tool-workpiece vibration.Sun et al.proposed a surface topography model considering the influence of the unbalanced electromagnetic force caused by the eccentricity of the motor rotor and the air pressure fluctuation.15.

Although there are many models for surface topography simulation of ultra/high-precision turning process, few literatures summarize and discuss the 3D topography simulation models of cylindrical surface turning and planar turning at the same time.In addition,the effect of processing parameters on the microstructure of materials is rarely reported.This paper attempts to fill this gap through the systematic study of ultra/high precision turning, involving the study of surface topography, surface roughness and dynamic recrystallization behavior.By introducing a dynamic cutting depth equation,the surface morphology model considering the influence of the tool nose, the feed rate and the tool-workpiece vibration is established.Different from other simulation models, the model developed in this paper determines which areas of material are removed by comparing the coordinates of machining surface points and cutting edges.In terms of microstructure prediction, the effect of feed rate on dynamic recrystallization process of polycrystalline copper is investigated.First,the temperature and strain rate data in the turning process of polycrystalline copper are obtained by FEA simulation.Then,the dynamic recrystallization phenomenon that may exist in the HPT process is simulated by a cellular automaton method.

The remainder of this article is organized as follows: Section 2 introduces the modeling flow of the surface topography model and the simulation method of dynamic recrystallization in HPT.In Section 3, the influence of process parameters (radius of tool nose, feed rate) and tool-workpiece vibration on the surface topography and surface roughness in HPT is studied.The influence of feed rate on the dynamic recrystallization of polycrystalline copper is also investigated.At the end of Section 3, a turning experiment of copper bar is carried out on a high-precision lathe to validate the proposed surface topography predictive model.Section 4 draws the conclusions.

2.Simulation model

2.1.Surface topography simulation model of the machined surface

According to the surface type, HPT can be divided into cylindrical and plane HPT,as shown in Fig.1(a).Direction 1 and 2 are the corresponding feed directions.The machining trajectories of these two turning types are shown in Fig.1(b)and Fig.1(c), which are cylindrical spiral and planar spiral respectively.Rwrepresents the radius of the workpiece and F represents the feed rate.When modeling the surface topography of the two turning types, the cutting edges should be discretized in the axial direction of the cylinder and the radial direction of the planar surface respectively.Cylindrical HPT usually needs to unfold into plane cutting in rectangular coordinate system,while plane turning can be carried out directly in cylindrical coordinate system.The modeling process of the surface topography evolution in cylindrical HPT is shown below.

Fig.2(a) shows the schematic of the cylindrical HPT.The radius of the tool nose is Rn, with an end-cutting edge angle of Ceand a side-cutting edge angle of Cs.The turning tool feeds along the axial direction.The nominal cutting depth is Dcand the residual height left on the machined surface is Rh.The schematic of the tool-workpiece vibration during turning is shown in Fig.2(b).The vibration consists of three components, namely radial, axial and tangential vibration.The time function of these three components are represented by Rcut(t）,Acut(t）and Tcut(t）respectively.Cylindrical HPT is usually developed into plane cutting.Fig.2(c) shows the schematic of plane cutting.The cutter is fed along the X axis and cuts along the Y axis, and the cutting depth occurs in the Z axis.Radial,axial and tangential vibrations could be transformed into Z,X and Y vibrations, respectively.

Fig.1 Two turning types and corresponding tool relative paths for cylindrical and planar spiral lines.

Fig.2 Conversion between cylindrical turning and planar cutting.

Owing to the vibration during HPT, the actual cutting depth varies from a nominal value.Fig.3(a) is the schematic of the cross-section of cylindrical workpiece.Due to the exis-tence of time-varying tangential vibration Tcut(t）and radial vibration Rcut(t）, the tool tip moves to a position with a distance Zrfrom the center of rotation at timet.The actual cutting depth can be calculated by Eq.(1) below.Dacon the left side of the equation indicates the actual cutting depth.As mentioned before, cylindrical HPT is usually converted to plane cutting for modeling.Fig.3(b) is a schematic of the contact between the tool nose and the workpiece surface in the XZ rectangular coordinate system in Fig.2(c).The meanings of Rn, Cs, Ceare consistent with the description in Fig.2(c).The reference plane represents the plane on which the surface of the unmachined workpiece lies.The Plstpoint represents the lowest point of the tool nose, and Pcrepresents any point on the tool nose contour involved in cutting.Ptland Ptrrepresent the tangent points of the straight segment and the arc segment on the left and right side of the tool nose, respectively.Points Pnland Pnrrepresent the intersection of the reference plane with the left and right side profile of the tool nose.The coordinates of the tool nose Plstpoint in the XYZ directions can be obtained from the number of feeds and processing time, and the specific calculation details are shown in Eqs.(2)-(4).xlst,ylstand zlstrepresent the coordinates of Plstin three directions, x0and y0represent the initial position coordinates of point Plstin the X and Y directions,F represents the feed rate,and ω is the rotation speed of the workpiece.

When the Z coordinate of the material point is greater than the Z coordinate of the corresponding cutting edge element,the material point is removed.Then, the Z coordinate of the material point is updated to that of the corresponding element of the cutting edge.It is necessary to discretize the cutting edge between PnlandPnr, which is determined by the cutting depth and the geometry of the tool nose.h1and h2represent the height differences between points Plstand point Ptland Ptrin the Z direction respectively.The values of h1and h2can be obtained from Eq.(5) and Eq.(6).Here Cetakes the value of 32 degrees and Cstakes the value of 10 degrees.When Ceand Cstake other values, the processing method is the same.

Fig.3 Schematic of tool tip contact with workpiece.

The discrete details of the cutting edges between Pnland Pnrare described below.First, the range between Pnland Pnris obtained by discussing three relationships of actual cutting depth Dacwith respect to h1and h2.Then, the Z coordinate of Pccan be obtained by discussing the four positions relationships between PcandPlst.Let xnland xnrdenote the X coordinates of point Pnland pointPnr.

Fig.4 Calculation flowchart of surface topology regeneration model.

when Dac≤h1,

When the range between Pnland Pnris determined,the cutting edges within this range need to be discretized.Let Pcbe any point in this range, and xcis the coordinate value in the X direction.When the position relationship between xcand xlstis determined,the coordinate value of Pcin the Z direction can be determined.

Fig.5 3D FEA model of HPT of a copper cylinder.

when xc-xlst≤-Rnsin(Ce）,

Fig.4 introduces the details of the calculation process.First, some additional conditions need to be provided, such as workpiece geometry, tool geometry, machining condition parameters and three vibration components.Then,set the size of the simulation area and initialize the Z coordinate of the workpiece surface.The X coordinate range of this simulationarea is represented by the vector X.The lower limit of X is Xmin, the upper limit is Xmax, and the discrete interval is ΔX.Similarly,the Y coordinate range of this simulation area is represented by the vector Y.The lower limit of Y is Ymin, the upper limit is Ymax,and the discrete interval is ΔY.The Z coordinates of discrete points in this area are represented by vector Z, which needs to be initialized to zero before iterative calculation.Next, the simulation duration and time steps are set to improve the convergence and computational efficiency.t is used to represent the machining time, whose starting value is tmin,ending value is tmax,and step size is Δt.Then the circular calculation is carried out to update the Z coordinate of the workpiece surface.The first step of the cyclic calculation is to find the coordinates of Plstby Eqs.(2)-(4).The second step is to find the range on the cutting edge that needs to be discretized by Eqs.(7)-(12).The third step is to update the Z coordinates of the machined surface.The Z coordinate of any point Pcon the cutting edge can be obtained by Eqs.(13)-(16).Finally, the three-dimensional coordinates of the workpiece surface are obtained as the surface topography of the workpiece.

Table 1 Parameters for copper used in Johnson-Cook constitutive equation28.

Fig.6 Flowchart of dynamic recrystallization process simulation by cellular automaton method.

Table 2 Material parameters for copper used in CA simulation39.

2.2.Dynamic recrystallization model in HPT

2.2.1.Description of thermo-mechanical model and cellular automaton model

Fig.7 Schematic diagram of material removal during turning.

The feed rate of HPT does not only affect the surface topography of the machined surface through the residual height, but also affect the microstructure of the material by changing the strain rate and temperature.Therefore,the evolution of grain structure of the polycrystalline copper under different feed rates was studied by using thermomechanical models and cellular automation (CA) models.For numerical analysis of dynamic recrystallization in the HPT process, the strain rate and temperature need to be determined first.26A thermo-mechanical model has been built in Abaqus to calculate the temperature and strain evolution during HPT.27Fig.5 shows the FEA mesh and schematic of the numeric model.The radius of the workpiece is 3 mm, and the radius of tool nose is 400 μm.Sweep method was used for meshing.For workpiece, mesh is finer around the surface area and coarser around the central area.The element shape of both cutter and workpiece is hexagonal.The element type is explicit coupled temperaturedisplacement.The number of cutter elements is 1600, and the number of workpiece elements is 265200.The material of the cylindrical workpiece is pure copper, and plasticity rule used is Johnson-Cook constitutive equation, as shown in28.

where σ is the shear flow stress,A is the initial yield stress,B is the hardening constant,C is the sensitivity coefficient of strain rate, mh is the heat softening coefficient, nh is the hardening index,ε is the equivalent plastic strain, ˙ε is the equivalent plastic strain rate, ˙ε0is the reference strain rate, T is the material deformation temperature, Tmis the melting temperature, and Tris the room temperature.The specific parameters are listed in Table 1.The initial temperature of the tool and workpiece was set to 300 K, and the cutting was carried out at a room temperature.

Table 3 Cutting condition used in simulation.

Fig.8 3D topography simulation results of cylindrical turning and plane turning.

The strain rate and temperature history can be obtained from the thermo-mechanical model.Then, a two-dimensional cellular automaton model with a simulation area of 150 μm×150 μm was established to simulate the evolution of dynamic recrystallization of the machined copper.The von Neumann’s neighboring rule was used in the CA model and the periodic boundary conditions were defined at the boundaries.The basic idea of the CA method is to describe the evolution of complex systems in discrete time and space by establishing deterministic or probabilistic transformation rules for adjacent cells.In the CA model,a complex system is decomposed into a finite number of cells.The possible states of each cell are then divided into a finite number of independent states.

2.2.2.Evolution of dislocation density

As mentioned before,dislocation density is an important grain boundary driving force to the dynamic recrystallization process.The accumulation of dislocations due to plastic deformation and dynamic recovery is expressed by KM model as a relationship between dislocation density and true strain which is shown as29.

Fig.9 Effect of tool nose arc radius on surface topography.

where ρi,jis the dislocation density for the cell with coordinates(i,j).The value of dislocation density can be obtained according to the relationshipσ=αμb √ρ.30The meaning of σ is the same as that in Eq.(17),and α is a dislocation interaction coefficient of approximately 0.5.31μ is the shear modulus,and b is the magnitude of the Burger’s vector.In Eq.(18), k1is a constant that represents hardening,and k2is a function of temperature and strain rate.32.

2.2.3.Grain nucleation and growth

For dynamic recrystallization,the critical dislocation density is set to be ρc,and the nucleation rate ˙n at the grain boundary is determined by33.

where c and m are material constants,and m is taken as 1;Qactis the activation energy.Adopting the method of Lin et al.,34the value of c can be obtained.The critical dislocation density used to determine dynamic recrystallization process can be calculated by35.

where γiis the grain boundary energy, M is the velocity of grain boundary movement, τ is the dislocation line energy,and l is the free path of dislocation.The grain boundary energy γican be obtained by36.

where θiis the grain boundary misorientation between the two adjacent grains, γmand θmare the boundary energy and the critical misorientation for high angle grain boundary, respectively.The grain boundary movement velocity viof the ith grain can be expressed as37.

Fig.10 Effect of feed rate on surface topography.

In the formula, fiis the driving pressure applied to the ith grain boundary, and the meaning of M is the same as that in Eq.(20).M can be expressed as33.

where D0bis the boundary self-diffusion, Qbis the recrystallization boundary activation energy, δ is the grain boundary thickness, and k is the Boltzmann parameter.

In two-dimensional simulation, the newly generated crystal nucleus can usually be equivalent to a circle, so fican be expressed as38.

where ρiand riare the dislocation density and radius of the ith recrystallized grain respectively,and ρmis the dislocation density of the base material.

2.2.4.Dynamic recrystallization simulation procedure

The flowchart of the calculation process is shown in Fig.6.The CA simulation program was realized by C++high-level programming language.The information of strain rate and temperature in CA method is obtained by FEA simulation of HPT.After the completion of each iteration step, decide whether the time reaches the end time of simulation.Then,the iteration ends otherwise the state variables and grain morphology are updated.The material parameters used in the CA simulation are shown in Table 239.

3.Results and discussion

3.1.Effects of tool nose arc radius and feed rate on surface topography

The radius of the tool nose and the feed rate are the important factors affecting the machined surface morphology.They affect the surface topography by residual height.The specific calculation equation is shown in Eq.(25).Rhrepresents the residual height, Rnrepresents the radius of the tool nose,and F represents the feed rate.The schematic of the material removal process is shown in Fig.7.The machined surface exhibits undulations due to the presence of the residual height.Furthermore,the amount of material removed per cut is determined by the cutting depth and the feed rate.

Fig.11 Influence of radial vibration frequency on 2D topography profiles.

Fig.12 3D Surface topography at several typical radial vibration frequencies.

Fig.13 Influence of radial vibration frequency and amplitude on machined surface roughness.

Fig.8 shows the simulation results of cylindrical HPT and planar HPT.Fig.8(a) is an unfolded view of the cylindrical surface morphology and Fig.8(b) is a plane turning topography.Fig.8(a) and Fig.8(b) show the simulated topography of a small region.Due to the existence of residual height, the surface is undulating.These results are consistent with the previous findings.The cutting conditions used in the simulation are shown in Table 3.The tool nose arc radius Rnis 100 μm,the end-cutting edge angle Ceis 32°, and the side-cutting edge angle Csis 10°.The cutting depth Dcis 5 μm and the feed rate F is 5 μm/r.The simulation was carried out to the workpiece with a radius Rwof 3 mm.

The results shown in Fig.8 proved that the established model is suitable for both cylindrical HPT and planar HPT.To explore the quantitative effects of tool nose radius and feed rate on the surface topography and roughness, a singlevariable simulation study is required.Fig.9 shows the influence of tool nose radius on the machined surface topography.The values of nose arc radius corresponding to Fig.9(a)-9(g)are 50 μm, 100 μm, 200 μm, 400 μm, 600 μm, 800 μm and 1000 μm respectively.As shown in the Fig.9(a)-9(g), when the radius of the tool nose increases from 50 μm to 400 μm,the topography fluctuation caused by the residual height is effectively suppressed.But further increasing the radius of the tool nose has little effect on

the surface topography.Specifically,when the tool nose arc radius is 50 μm,the residual height left is 62 nm,and when the tool nose arc radius increases to 400 μm, the residual height rapidly decreases to 7.8 nm.When the value continues to increase, the residual height decreases slowly.The blue curve in Fig.9(h) shows the change of surface roughness with the radius of tool nose arc.When the arc radius is 50 μm, the roughness Rais 16.2 nm; when the arc radius increases to 400 μm, the roughness Radecreases to 2.1 nm.When the arc radius continues to increase, the roughness does not decrease significantly.

Fig.14 Influence of axial vibration frequency on 2D topography profile.

The effect of the nose radius on the surface topography and roughness has been given.Seven groups of different feed rates are selected for simulation when the radius of the tool nose is 100 μm, as shown in Fig.10.Fig.10(a)-10(g) correspond to feed rates from 1 μm/r to 7 μm/r.The surface residual height and roughness Raincrease approximately linearly with the increase of feed rate, as shown in Fig.10(h).The residual height increases from 1.25 nm to 61.3 nm and the roughness Raincreases from 0.32 nm to 18.5 nm when the feed rate increases from 1 μm/r to 7 μm/r.

3.2.Effects of radial direction vibration on surface topography

The vibration between the tool and workpiece during the HPT process can seriously deteriorate the quality of the machined surface.Therefore, the radial vibration is first explored.Assuming that the radial vibration is a sine wave function with an amplitude of 4 μm.The process parameters are shown in Table 3.The workpiece rotation speed is 1000 r/min (frequency:16.6 Hz).In the range less than twice the rotation frequency, 16 different frequencies were selected to study the effect of the radial vibration frequency on the surface topography.The results are shown in Fig.11.

Fig.15 3D surface topography at several typical axial vibration frequencies.

Fig.16 Influence of axial vibration frequency and amplitude on surface roughness.

In the frequency range less than the rotation frequency,with the increase of vibration frequency, the topography contour waveform becomes more irregular, and the highfrequency signal component becomes stronger, as shown in Fig.11(a)-11(f).When the vibration frequency is close to the rotation frequency, the waveform of the topography contour shows a standard sinusoidal waveform,and the waveform period increases with the increase of vibration frequency, as shown in Fig.11(g)-11(i).When the frequency is greater than the rotation frequency, with the increase of the vibration frequency,the contour waveform of the topography becomes disordered at first and then gradually shows an ordered sine wave,as shown in Fig.11(j)-11(p).

The 3D topographies of eight representative typical topographies are shown in Fig.12.A dovetail groove will be left at the trough of the machined surface under the vibration with the frequency of 5 Hz and 8 Hz.The dovetail groove of 5 Hz is deeper than that of 8 Hz.Although the 2D topography profiles at 10 Hz and 12 Hz are both obtained by mixing highfrequency and low-frequency signals, the 3D topography presented is quite different.The topography at 10 Hz presents more regular shape, while at 12 Hz fluctuates more obviously.The surface presents the effect of superposition of grooves of different depths when the vibration frequency is 21 Hz.When the vibration frequency is 24 Hz,the surface is relatively regular, due to the decrease of the high-frequency signal composition.When it is 28 Hz, many shallow micro grooves are attached to the surface of the macro grooves.The surface is relatively normal when the vibration frequency is 31 Hz.The reason may be that the surface topography is formed by the high-frequency signal enveloped by the low-frequency signal.

Fig.17 Influence of tangential vibration frequency on 2D topography profile.

To evaluate the surface finish, it is necessary to explore the surface roughness evolution.Fig.13 shows the effect of radial vibration frequencies and amplitudes on the surface roughness.When the radial vibration frequency is low or close to an integer multiple of the rotation frequency, the surface roughness(greater than 800 nm) is larger than other frequency bands.In other cases, the surface roughness is between Ra200 and 400 nm.Fig.13(b) shows the influence of radial vibration on the surface roughness at different frequency.When the vibration frequency is 16 Hz, increasing the radial vibration amplitude will significantly increase the surface roughness.In other cases, increasing the amplitude has no obvious effect, because the effect of amplitude on surface roughness can be significantly enhanced when the vibration frequency is close to the workpiece rotary frequency.

3.3.Effect of axial vibration on surface topography

The effect of axial tool-workpiece vibration is discussed.The influence of axial vibration on surface topography at 16 frequencies was investigated, as shown in Fig.14.As seen from Fig.14(a)-14(c), if the vibration frequency is less than 8 Hz,the fluctuation of the surface topography gradually increases with the increase of vibration frequency.When it is near half of the rotation frequency, the surface topography contour shows the standard sinusoidal waveform, which is different form the radial vibration.If it is located between half and one rotation frequency,such as 12 Hz,the surface topography contour fluctuates greatly and is mixed with many highfrequency signal components, as shown in Fig.14(f).When it is close to the rotation frequency,the waveform of the topography contour shows a standard sinusoidal waveform,and the waveform period increases with the gradual increase of vibration frequency.The waveform envelope phenomenon of the surface topography contour is particularly obvious under the vibration frequency of 21 Hz.If the vibration frequency gradually approaches two times the rotation frequency, the waveform of the surface topography contour gradually approaches the standard sinusoidal waveform, which can be seen in Fig.14(n)-14(p).Several typical 3D morphologies are shown in Fig.15.When the vibration frequencies are 2 Hz and 12 Hz, the surface topography shows the characteristics of a waveform envelope.When it is 5 Hz,the surface topography shows the characteristic of half wave and full wave alternating.It is observed that if the vibration frequencies are 12 Hz, 28 Hz and 31 Hz, there is no significant difference in the 3D topography of the surface, although their 2D topography contour are quite different.

The evolution of surface roughness under axial vibration is shown in Fig.16.The surface roughness and frequency of radial vibration are almost independent, as shown in Fig.16(a).Compared to the surface roughness Raof 8 nm in the absence of any vibration, the axial vibration reduces the surface roughness to a certain extent because the residual height is reduced by the axial vibration.Fig.16(b) shows the evolution of surface roughness with vibration amplitude under four different vibration frequencies.The increase trend of surface roughness with amplitude is the most obvious at 12 Hz, followed by 10 Hz and 15 Hz,and the minimum is 16 Hz.In addition, it can be seen that the surface roughness is insensitive to the vibration frequency when the vibration amplitude is less than 6 μm.

3.4.Effect of tangential vibration on surface topography

Whether the surface topography is sensitive to vibration frequency can be revealed by simulating the surface topography under several groups of characteristic vibration frequencies.Six groups of surface topography under different tangential vibration frequencies with the vibration amplitude of 4 μm were studied, as shown in Fig.17.The contour waveforms of surface topography under different vibration frequencies show the characteristics of waveform envelope.The only difference is the period of envelope wave.Fig.18(a)shows the 3D surface topography at a vibration frequency of 16 Hz with a moderate envelope wave period.It can be seen that the slight contour fluctuations can be basically ignored in the 3D surface topography.

The surface roughness evolution with tangential vibration is investigated below.Fig.18(b)shows the variation of surface roughness with tangential vibration frequency when the amplitude is 4 and 14 μm.It can be seen that when the vibration amplitude is 4 μm, the surface roughness Rais about 8.1 nm,and the change of surface roughness Rais less than 0.2 nm with the change of vibration frequency.When the vibration amplitude increases from 4 μm to 14 μm, although the surface roughness Raat all vibration frequencies increases,the increase is still small and less than 0.5 nm.Compared with the previous research on radial vibration and axial vibration, it can be found that the tangential vibration has the least influence on the surface topography and surface roughness.

Fig.18 Surface topography and surface roughness under tangential vibration.

Table 4 Machining parameters used in simulation.

3.5.Effect of feed rate on dynamic recrystallization of the machined surface

During HPT process, dynamic recrystallization process may occur under a large strain and a high strain rate, resulting in grain refinement of the machined surface.Since mechanical properties of alloys are strongly dependent on their microstructure, investigating the microstructural evolution,especially the crystal structure evolution in HPT is of prime importance.The influence of the feed rate on the copper dynamic recrystallization process under large a feed rate was investigated using simulation.The specific process parameters are shown in Table 4.

Fig.19 and Fig.20 show the influence of different feed rates on dynamic recrystallization process at 1000 r/min rotation rate.It can be seen from the thermo-mechanical process curves of the two figures that the peak temperature in the turning process is about 800 K and the peak strain rate is about 100 s-1.When the feed rate is 0.2 mm/r, the duration of the process is about 0.7 s,while when the feed rate is 0.4 mm/r,the duration of the process is about 0.35 s.Therefore, at the same rotating speed,the higher the feeding rate,the lower the heat input per unit time and the lower the peak temperature.From Fig.19(f)and Fig.20(f), it can be found that dynamic recrystallization occurs in a larger area at the high feed rate (0.4 mm/r) than at the low feed rate(0.2 mm/r).Therefore,it can be considered that even though the high feed rate may reduce the peak temperature and thus slow down the dynamic recrystallization process, the positive promotion effect of the high strain rate brought by the high feed rate on dynamic recrystallization is more significant.

As shown in Fig.19(a) and Fig.20(a), five moments in the thermo-mechanical process were selected to display the dynamic recrystallization results.These moments include b)deformation occurs, c) dynamic recrystallization begins, d)strain rate reaches its peak, e) dynamic recrystallization ends and f) deformation ends.It can be seen from Fig.19(b) and Fig.20(b) that no new grains were generated when the plastic deformation just occurred because the dislocation density of grain boundary did not reach the critical nucleation dislocation density.Thus, there are only parent metal crystal grains that grow slightly during the process of temperature rising.Later, the strain rate begins to rise gradually, dislocation begins to accumulate, and dynamic recrystallization occurs,as shown in Fig.19(c) and Fig.20(c).At this point, sparse grains begin to form at the grain boundaries.When the strain rate reaches the peak, new grains are formed at all grain boundaries of the initial parent crystal, which can be seen in Fig.19(d)and Fig.20(d).The whole dynamic recrystallization process continues until the end of deformation.When the feed rate is 0.2 mm/r and 0.4 mm/r, the dynamic recrystallization ends at 0.6643 s and 0.3312 s, respectively.Compared with the previous characteristic moments,the number of new grains at the end of dynamic recrystallization increased multiply.Because the duration between the end of deformation and the end of dynamic recrystallization is very short, there is almost no change in the grain morphology during this process.The grain morphology at the end of deformation at two different feeding rates is shown in Fig.19(f) and Fig.20(f).Compared with low strain rate, high strain rate case can induce a larger area of dynamic recrystallization.

Fig.19 Results of dynamic recrystallization at a low feed rate during HPT (0.2 mm/r).

Fig.20 Results of dynamic recrystallization at a high feed rate during HPT (0.4 mm/r).

Fig.21 High-precision turning experimental setup.

3.6.Experimental validation of the developed topography prediction model

The accuracy of the model was verified through experiment.Fig.21(a) shows the experimental setup.The turning tool is fixed on the holder by means of bolts.The workpiece is a brass rod with a diameter of 6 mm fixing on the aerostatic rotary shaft (Nakanishi Spindle E3000).Brass rod rotates together with the rotary shaft during the HPT.A high-resolution CCD camera (DH-HV5051UM-ML) is placed on the left side of the workpiece to assist tool setting and monitoring.A highaccuracy laser displacement sensor(KEYENCE LK-G5000)is placed in front of the workpiece to measure its vibration during HPT,as shown in Fig.21(b).The micro-displacement platform connected with the laser displacement sensor can realize three mutually vertical position adjustment.The measured vibration is input into the simulation model as the toolworkpiece vibration data for calculation.Fig.21(c) shows the presentation results of CCD camera software and laser displacement sensor software in the interface of laptop computer.The vibration video image information and numerical information can be easily captured by corresponding software.The tool used for turning is a carbide arc turning tool with nose radius of 500.37 μm, as shown in Fig.21(d).

In the experiment,the rotation rate of the workpiece is 1000 r/min, the cutting depth is 1 μm, and the feed rate is 2 μm/r.After HPT, a white light interferometer (Zygo NewViewTM7300)was used to observe the topography of the machined surface.Fig.22(a)shows the 3D surface topography of brass bar measured after machining, which is full of scratches.A horizontal line was selected in the center region of the topography to obtain its contour line, as shown in Fig.22(b).The roughness Raof the contour line is 53 nm, and the fluctuation of the contour line is about 0.1 μm in the range of 300 μm.Fig.22(c) shows the radial vibration of the workpiece measured by laser displacement sensor in the turning process.The sampling frequency was set to 10000 Hz, and the radial vibration of the workpiece was recorded within 10 s after entering the stable cutting stage.Because the tool is fixed during HPT, the vibration of workpiece here is equivalent to the tool-workpiece vibration.The amplitude of workpiece during HPT is about 2 μm.Through Fourier transform of the vibration displacement versus time curve of the workpiece, it is found that the main frequency of vibration is 17.8 Hz, as shown in Fig.22(d).

Fig.22 Surface topography of workpiece after turning and vibration of workpiece during turning.

Fig.23 Comparison of topographic profiles between experiment and simulation.

Considering the calculation cost,the radial vibration of the tool relative to the workpiece in this experiment can be equivalent to a sine wave with a frequency of 17.8 Hz and an amplitude of 2 μm.By substituting the simplified sinusoidal vibration waveform,tool arc radius parameters and machining parameters into the simulation model, the simulation results corresponding to the experiments can be obtained.Fig.23 shows the comparison of the surface topography contour obtained by simulation and experiment.It can be found that the two contours are in good agreement in terms of peak-tovalley distance and fluctuation period.The roughness Raof the simulated surface topography contour line is 46 nm,which is 86.7 % of the experimental roughness Ra53 nm.The existence of high-frequency vibration signal, which is ignored in the simulation causes the difference.

4.Conclusions

In this study, a surface topography model considering toolworkpiece vibration is presented.The effects of tool arc radius,feed rate and three vibrations components on the surface topography were studied, respectively.In addition, the FEA and cellular automaton method were combined to investigate the effect of feed rate on the dynamic recrystallization behavior of polycrystalline copper.From this study, the following conclusions can be drawn:

(1) The radial vibration has the greatest influence on the surface topography, the axial vibration is secondary, and the tangential vibration is the smallest.When the vibration frequency changes, the surface topography profile presents three types: the standard sinusoidal curve, the sinusoidal curve in which the low-frequency signal envelopes the high-frequency signal, and the oscillation curve in which the low-frequency signal superimposes the high-frequency signal.

(2) The surface roughness Rais the largest when the radial vibration is close to the rotation frequency, which is greater than 1.2 μm.However, the axial and tangential vibrations are frequency-insensitive and the surface roughness is at the level of Ra6.4 nm and Ra8.3 nm, respectively.

(3) When the radial vibration is close to the rotation frequency,its amplitude has great influence on the surface roughness,but when it is in other frequency range,its amplitude has little influence.When the axial vibration frequency is 12 Hz,the amplitude has a large effect on the surface roughness,while when it is 16 Hz,the amplitude has a small effect.The tangential vibration amplitude has little effect on the surface roughness in all vibration frequency bands.

(4)At the same rotation rate,a higher feed rate produces a higher strain rate and lower peak temperature.Higher strain rates lead to faster dynamic recrystallization process during machining, so more recrystallized grains are formed on the machine surface at higher feed rates, resulting in smaller average grain size.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (Nos.51775147 and 52005133).