Surface Topography Model Research Articles

Freeform surface topography model for ultraprecision turning under the influence of various errors

This work establishes an accurate freeform surface topography model considering geometric errors, tracking errors, and cutting forces. Regarding geometric errors, based on the theory of multibody systems and homogeneous coordinate transformation, the transfer relationship between various geometric errors and the tool error in the workpiece coordinate system is described. Using the continuous acceleration Position-Velocity-Time (PVT) interpolation method, the offset discrete points caused by geometric errors are interpolated and rediscretized, and the accurate mathematical model between the tool errors (position and posture) in the workpiece coordinate system and the topography of the freeform surface is established. Based on the model, the influence of geometric errors on the contour errors of freeform surfaces is accurately calculated, and the contribution and similarity of the effects of various geometric errors on the contour errors of freeform surfaces are analyzed. For dynamic-dependent factors, a second-order system with two degrees of freedom on the X or Z axis is established. According to the simplified result of the equivalent system, the contour error of the freeform surface caused by the tracking error and cutting force is analyzed. For the tracking error, under the condition of constant rotation velocity of the spindle, the change of the slope of the freeform surface along the circumferential direction causes the change in the velocity and acceleration of the motion axis; thus, the corresponding area of the surface has a larger contour error. For cutting force, the change of the slope of the freeform surface along the circumferential direction changes the tool working rake angle, the tool working clearance angle, and the shearing angle, resulting in a change in the cutting force. Moreover, the change of cutting speed is accompanied by the change of cutting force. An experiment verifies the effectiveness of the proposed modeling method. In addition, the modeling method provides an effective solution for the calculation of the contribution rate of different error sources to the contour error of the freeform surface.

Surface Topography Prediction Model for Free-form Surface Milling under a Dynamic System Response

At present, numerous studies on surface topography prediction models for plane workpieces have been performed at home and abroad. Given the complexity of curved surface models (especially free-form surfaces that cannot be expressed in analytic formulas), prediction models for the surface topography of free-form surfaces are rarely studied. This paper aims to establish and simulate a 3D surface topography model of ball-end milling for all types of curved surfaces, including simple surfaces and free-form surfaces. The dynamic factors influencing the surface topography, such as the spindle runout initial phase angle, runout amplitude, axial drift initial phase angle, and axial drift amplitude are considered in this model. Moreover, some processing parameters influencing the surface topography, such as cutter tooth number, machining inclination, radial cutting depth, feeding frequency and feed per tooth are also considered in this model. The simulation results can be used to optimize the milling process of the actual free-form surface to improve workpiece surface quality or to predict the surface topography of the given machining parameters.

Modeling and Analysis of Micro Surface Topography from Ball-End Milling in a Trochoidal Milling Mode.

The trochoidal milling mode is widely used in high-speed machining, and due to good adaptability and flexible posture adjustment, ball-end milling cutters are conducive to complex surface machining with this mode. However, the processes of material removal and formation of machined micro surfaces are very difficult to describe as the profile of cutter teeth is complex and the trajectory direction changes continuously during the trochoidal milling process. A modeling method for the generation of micro surface topography of ball-end milling in the trochoidal milling mode is put forward. In this method, the locus equation of each cutter tooth is established based on the principle of homogeneous coordinate transformation, after which a Z-MAP algorithm is designed to simulate the micro surface topography. The Z-MAP algorithm can quickly obtain the part grid nodes potentially swept by the cutter tooth within a unit time step through the establishment of servo rectangular encirclement and instantaneous sweeping quadrilateral of the element of cutter teeth; the part grid nodes actually swept are further determined through an angle summation method, and the height coordinate is calculated with the method of linear interpolation according to Taylor’s formula of multivariate functions. Experiments showed that the micro surface topography resulting from ball-end milling in the trochoidal milling mode had high consistency with the simulation, which indicates that the proposed method can predict micro surface topography in practical manufacturing. In addition, a comparison of micro surface topography between trochoidal milling and ordinary straight-linear milling was conducted, and the results showed that the former was overall superior to the latter in resulting characteristics. Based on this conclusion, the influences of cutting parameters of ball-end trochoidal milling on surface characteristics, particularly amplitude and function, were analyzed according to the simulated micro surface topography data.

Regional Mean Sea Surface and Mean Dynamic Topography Models Around Malaysian Seas Developed From 27 Years of Along-Track Multi-Mission Satellite Altimetry Data

Contemporary Universiti Teknologi Malaysia 2020 Mean Sea Surface (UTM20 MSS) and Mean Dynamic Topography (UTM20 MDT) models around Malaysian seas are introduced in this study. These regional models are computed via scrutinizing along-track sea surface height (SSH) points and specific interpolation methods. A 1.5-min resolution of UTM20 MSS is established by integrating 27 years of along-track multi-mission satellite altimetry covering 1993–2019 and considering the 19-year moving average technique. The Exact Repeat Mission (ERM) collinear analysis, reduction of sea level variability of geodetic mission (GM) data, crossover adjustment, and data gridding are presented as part of the MSS computation. The UTM20 MDT is derived using a pointwise approach from the differences between UTM20 MSS and the local gravimetric geoid. UTM20 MSS and MDT reliability are validated with the latest Technical University of Denmark (DTU) and Collecte Localisation Services (CLS) models along with coastal tide gauges. The findings presented that the UTM20, CLS15, and DTU18 MSS models exhibit good agreement. Besides, UTM20 MDT is also in good agreement with CLS18 and DTU15 MDT models with an accuracy of 5.1 and 5.5 cm, respectively. The results also indicate that UTM20 MDT statistically achieves better accuracy than global models compared to tide gauges. Meanwhile, the UTM20 MSS accuracy is within 7.5 cm. These outcomes prove that UTM20 MSS and MDT models yield significant improvement compared to the previous regional models developed by UTM, denoted as MSS1 and MSS2 in this study.

Generation mechanism modeling of surface topography in tangential ultrasonic vibration-assisted grinding with green silicon carbide abrasive wheel

Tangential ultrasonic vibration-assisted grinding (TUAG) has a wide prospect in machining difficult-to-machine materials. However, the surface generation mechanism in TUAG is not fully recovered. This study proposes an analytical model of the surface topography produced by TUAG. Based on the model, the surface topography and roughness are predicted and experimentally verified. In addition, the influence of the grinding parameters on the surface topography is analyzed. The predicted surface topography well coincides with experimental measurements, and the prediction error in surface roughness Ra by the proposed model is less than 5%. Compared with conventional grinding, TUAG produces a surface with more uniform scratches and surface roughness Ra was reduced by up to 27% with the proper parameters. However, the improvement of surface roughness in TUAG is weakened when grinding speed or depth of cut increases. Moreover, the influence of the ultrasonic vibration amplitude on the surface roughness is not monotonous. With the grinding parameters selected in this study, TUAG with an ultrasonic amplitude of 7.5 μm produces the minimum surface roughness.

An analytical prediction model of surface topography generated in 4-axis milling process

An analytical prediction model of surface topography generated in 4-axis milling process

Modeling and simulation of surface topography in five-axis ball end milling

Computer simulation can be used to predict the machined surface topography and roughness, which can provide a basis for the reasonable selection of cutting parameters and tools. To do so, the motion trajectory equation of ball end milling cutter was established based on homogeneous coordinate transformation matrix. On this basis, a 3D surface topography simulation algorithm based on workpiece meshing is constructed. Finally, the influence laws of feed rate per tooth, path internal and initial phase angle on surface topography were analyzed by simulation. The conclusion has a good guiding significance for the surface quality control and adjustment of machining parameters in actual production.

Characterization of Machined Surface Topography Based on the Normal Declination Angle of Microfacets.

It is important to characterize surface topography in order to study machined surface characteristics. Due to the features of periodicity and randomness of machined surface topography, the existing topographical parameters may not describe its features accurately. A novel characterization method called the normal declination angle of microfacet-based surface topography is thus proposed for this task. The topography of machined surfaces is measured and the data on the normal declination angle are obtained. Then, surface topography is analyzed via the distribution of the normal declination angle. The lognormal distribution characterization model of machined surface topography is established, and the accuracy of the model is verified by error analysis. The results show that the calculated results of the present characterization model are generally consistent with the distribution of the normal declination angle, where the maximal root mean square errors (RMSE) is 4.5%. Therefore, this study may serve as an effective and novel way to describe the characteristics of the machined surface topography.

Simulation and experiment on surface topography of complex surface in single point diamond turning based on determined tool path

Surface topography is an important element that reflects the machining quality of workpieces and the functional performance of components. To avoid expensive cutting experiments, forecasting the surface topography before actual machining is necessary. Surface topography of diamond turned surfaces is directly affected by generated tool path in ultraprecision single point diamond turning (SPDT). In this study, a novel surface topography modeling method was presented. The planned tool path based on active machining precision control was considered in this method. Simulation and experiment of an umbrella surface diamond turning were conducted to testify the usability of the proposed model. Through comparing the simulation and experimental data of surface topography and machining error, the results showed that the proposed model can be applied to forecast the surface topography and machining error in SPDT using the generated tool path.

A dissolution model of alite coupling surface topography and ions transport under different hydrodynamics conditions at microscale

Portland cement is the most produced material in the world. The hydration process of cement consists of a group of complex chemical reactions. In order to investigate the mechanism of cement hydration, it is vital to study the hydration of each phase separately. An integrated model is proposed in this paper to simulate the dissolution of alite under different hydrodynamic conditions at microscale, coupling Kinetic Monte Carlo model (KMC), Lattice Boltzmann method (LBM) and diffusion boundary layer (DBL). The dissolution of alite is initialised with KMC. Two Multiple-relaxation-time (MRT) LB models are used to simulate the fluid flow and transport of ions, respectively. For solid-liquid interface, DBL is adapted to calculate the concentration gradient and dissolution flux. The model is validated with experiment from literature. The simulation results show good agreements with the results published in the literature.

Modeling, simulation, and prediction of surface topography in two-dimensional ultrasonic rolling 7075 Al-alloy

Two-dimensional ultrasonic rolling (TDUR) is a kind of surface finishing and deformation strengthening technology, which can improve the surface quality and reduce the surface roughness of the workpiece so as to improve its fatigue resistance. In order to study the formation process of the surface topography of 7075 Al-alloy treated by TDUR, a dynamic model of the rolling system was established based on the principle of TDUR to obtain the dynamic force of the roller on the workpiece during the rolling process. The penetration depth model of the workpiece surface under the action of the static load and longitudinal ultrasonic impact was constructed based on the Hertz contact theory and the metal elastic-plastic deformation theory. Then, the simulation model of surface topography was established using the space transformation theory based on the penetration depth model and the trajectory of the roller. Sequentially, the surface topography was reconstructed with the Z-map method. Using the simulation results, the axial profile curve data was extracted, and the surface roughness was calculated by the surface roughness calculation model. Finally, a designed TDUR experiment was carried out to verify the theoretical surface topography and roughness models. And it shows that the simulated surface topography and predicted roughness are in good agreement with the experimental results. The maximum relative error between the predicted roughness and the experimental results is no more than 9%. Under the experimental conditions, the turning marks can be almost eliminated when the static load Fs is 215 N. At this time, the surface profile height was about 1.5 μm, and the roughness Ra is 0.413 μm, which is 78% lower than that of turning. Therefore, the surface topography and surface roughness models proposed in this work can be used to effectively predict the surface topography and surface roughness of 7075 Al-alloy treated by TDUR.

Modelling of machined surface topography and anisotropic texture direction considering stochastic tool grinding error and wear in peripheral milling

This paper establishes a new model for predicting machined surface topography and anisotropic texture direction in peripheral milling. Unlike previous models, this model takes into account the largest number of influential factors, i.e., tool setting error (radial offset and axial tilt), static tool deflection, forced vibration, chatter vibration, and stochastic tool grinding error and wear (STGEW). STGEW, quantified by the normal distribution (μ, σ2), is incorporated into the model for the first time. The model predictions for 3D surface topography, anisotropic texture direction, 2D surface profile or roughness agree remarkably well with experimental or published results, under both stable and unstable milling conditions. It is found that static deflection slightly attenuates the effect of tool setting error on roughness. Even machining with fresh tools or tools with very small cutting length (<15 mm) and wear (VB∼5 μm), inherent STGEW creates random scratches with different geometries parallel to feed direction on the milled surface. STGEW expands the difference of roughness in axial direction. STGEW induces an additional surface texture in feed direction, which co-exist with axial texture contributed by feed marks when standard deviation σ to feed rate ft ratio is small. As σ increases, (1) feed marks are gradually obliterated by scratches, and surface texture is only oriented in feed direction; (2) the mean and variance of roughness in both directions increase, and axial roughness prevails transverse toughness at high σ. The study discovers that, STGEW, even with small σ (e.g., σ=[0.01 μm, 0.1 μm]), is an important factor affecting surface topography, anisotropic surface texture direction and roughness that cannot be ignored, especially in the case of low-feed machining, e.g., ft = 0.05 mm, which is commonly adopted in finish-milling of difficult-to-cut materials. The proposed model can be used to reliably and accurately predict surface topography, surface roughness and surface texture direction in peripheral milling operation.

Establishment of Seamless Chart Datum and Vertical Datum Transformation for Hydrography with a Combining Geoid, Sea Surface Topography, and Ocean Tide Model in Prydz Bay, Antarctica

Ke, H.; Wang, A.; Lei, J.; Wu, J.; Wang, Z., and Zhang, S., 2020. Establishment of seamless chart datum and vertical datum transformation for hydrography with a combining geoid, sea surface topography, and ocean tide model in Prydz Bay, Antarctica. In: Hu, C. and Cai, M. (eds.), Geo-informatics and Oceanography. Journal of Coastal Research, Special Issue No. 105, pp. 204–209. Coconut Creek (Florida), ISSN 0749-0208.The establishment of a seamless chart datum and a transformation model with other vertical datums are the key to unifying sea–land measurement achievements. Since construction of the Chinese Antarctic Zhongshan scientific research station, nearby Prydz Bay has become a significant investigation area. However, it is still difficult to unify bathymetric measurements in Prydz Bay and topographic measurements in the station to the same vertical datum. In response to this problem, the Earth Gravitational Model 2008 geoid model, the Indian Ocean 2010 tide model, and sea surface topography model product of a satellite altimeter were used to establish a seamless chart datum and a transformation model between the WGS84 ellipsoidal reference and the chart datum through the fusion method, with a scope of –69°48′ to –66°24′ S and 70°00′ to 82°00′ E. The accuracy of the transformation model had been evaluated to be 10.7 cm on the basis of the error of each model and the law of error propagation. Meanwhile, the difference between the transformation model estimation and the field-measured value derived from a GPS tide was 8.8 cm. To some extent, this comparison result can reflect the accuracy of the model, but more field-measured data still needed to verify it.

Study on Modeling and Simulation of Surface Topography of Spherical Milling with Ball-end Milling Cutters

Study on Modeling and Simulation of Surface Topography of Spherical Milling with Ball-end Milling Cutters

Influence of Unbalanced Electromagnetic Force and Air Supply Pressure Fluctuation in Air Bearing Spindles on Machining Surface Topography

Air bearing spindles (ABS) can meet high accuracy demands for the precise rotation motion, which adopt air bearings to support spindle shaft, and the spindle shaft directly connects the motor rotor. The unbalanced electromagnetic force caused by motor rotor eccentricity (MRE) and air pressure fluctuation (APF) are two important influential factors to the dynamic performance of the spindle system and machining surface quality. This paper addresses the problems of measuring the MRE and APF in an ABS through testing machining surface topography. A permanent magnet synchronous motor (PMSM) was modelled by finite element simulation (FES). Through FES it found that the MRE between the motor rotor and stator hole produced a radial magnetic force (RMF), which could cause ABS to periodically vibrate in the axial direction. Besides, the change of the air supply caused the stiffness variation of ABS and result in the tilt error motions of the spindle shaft. A theoretical model of machining surface topography considering MRE and APF was then proposed for the first time, which revealed that the MRE and APF resulted in the periodic fluctuations of the machining surface topography. The overall surface topography then became grooved surfaces. The above findings were finally validated by measurement results of ultraprecision diamond turning experiments.

Influence of defects in the aluminium alloy Al6061 on the diffraction effect of diamond turned optics

Aluminium alloy Al6061 is one of the most popular materials for the fabrication of reflective optics. To reveal the influence of material defects in Al6061 on the diffraction effect of diamond turned optics, simulations are performed on a well-established surface topography model. The results indicate that for the defects with similar size parameters in the x- and y-axis direction, e.g. grain boundary, hard inclusion protrusion and void, they are responsible for the diffracted light spots on the whole receiving screen. The scratch on the machined surface mainly affects the diffracted light spots in the horizontal direction; and its influencing pattern is similar to the turning mark. The influence of oxide film on the diffracted light distribution is rather limited due to its uniform property and small thickness on the ambient environment. The simulation and experiment results indicate that the diffraction efficiency of the specular light obviously decreases with the increase of the defect size in the work material matrix.

Modeling of Convex Surface Topography in Milling Process

Cr12MoV die steel is a typical high-strength and high-hardness material. Because of the high hardness of Cr12MoV die steel, which is approximately 50–65 HRC after quenching, and the tool’s weak rigidity, cutting vibration, and tool deformation are inevitable during the cutting process. In this paper, a model for predicting the surface topography of a convex curved die steel machined by a ball-end milling cutter was established. In addition, the surface springback of the workpiece is considered. According to the surface characteristics of the convex curved workpiece, the vector algorithm and transformation matrix are applied to calculate the milling cutter motion trajectory equation. Then, the influence of dynamic factors on the tool path is calculated, and finally the surface topography of the workpiece is simulated through the Z-map model. The simulation error of three-dimensional surface roughness Sa at different positions of the curved surface is between 10% and 16%. After considering the dynamic factors, the simulation error is reduced by about 50%.

Prediction model of peripheral milling surface geometry considering cutting force and vibration

Milling surface quality is an important factor to assess the performance of a product, which is usually affected by cutting parameters. This paper presents a novel model of peripheral milling surface topography considering tool vibration. The model used the idea of discretization by introducing the milling dynamics and ignored the effect of tool wear, tilting, and thermal deformation. The simulation results were verified and showed good consistence with experimental results. Afterwards, parametric analysis was conducted to investigate the impact of process parameters and showed that feed per tooth impacts most on the surface roughness while axial depth of cut has the least impact. The presented method enables researchers to predict the peripheral milling surface before processing. Moreover, the method helps to build the formula of surface roughness to conduct the parameter optimization.

Online reconstruction of surface topography along the entire cutting path in peripheral milling

This paper presents a novel method for online reconstruction of 3D surface topography in peripheral milling. Compared with the traditional surface topography modeling only focusing on local features as well as losing the time and location information, the presented method can accurately depict not only the variation of dynamic characteristics and the topography features within the local scope, but also along the entire cutting path. Meanwhile, the actual machining time and workpiece location information are introduced in surface topography modeling by using sensor information. The multi-sensor information, including cutting force signals and the eddy current sensor information in multiple directions, is employed to model dynamic factors, namely the vibration relating to deflection of cutting tool and the machining system characteristics, respectively. Two parts of work are carried out on modeling the vibration relating to deflection along the entire cutting path. First, a method based on the Kolmogorov-Smirnov test is applied to the real-time force signals, where the force signals between the entrance and exit points of the cutting teeth along the entire cutting path can be automatically extracted. Second, combining with an axial weight distribution model of the instantaneous cutting thickness, the extracted force signals can be transformed into the required force factors and correspondingly nonlinearly distributed along the instantaneous cutting depth. A piecewise cubic Hermite algorithm is then introduced to create the discrete values of the dynamic factors as continuous models without losing original precision. The continuous models are successfully coupled into ideal cutting edge trajectory equation to form a surface topography model. Further, a numerical algorithm with the characteristics of self-searching function is performed to solve the surface topography model, any point on the workpiece surface can be precisely reconstructed and thus formed the reconstructed surface topography. Eventually, cutting experiments were conducted to validate the effectiveness of the proposed method by comparing the measured and reconstructed results. A good agreement on all the quantitative and qualitative indicators is found. The results demonstrate that the proposed method can accurately realize an online reconstruction of the surface topography along the entire cutting path, and is also an appropriate monitoring approach for a number of features on surface topography (e.g., surface roughness, form deviation).

3D surface topography simulation and experiments for ball-end NC milling considering dynamic feedrate

Dynamic change of feedrate is almost inevitable in high speed milling along a curved path due to the drive limits of the machine tools. The surface topography caused by the change of feedrate, which has a significant influence on mechanical prosperities and performances of the machined part, cannot be predicted using the existing methods that only consider constant feedrate. To better understand the surface topography formation process in high speed milling and also to more effectively control the machining parameters, in this paper we present a surface topography model for a ball-end cutter, which takes varying feedrate into full consideration. Our model considers the affecting elements including the surface's local geometry, the cutting edge shape, the path interval, as well as the relative motion of tool-workpiece (especially the changes of the tool orientation and feedrate). 3- and 5-axis ball-end milling experiments, in computer simulation and physical cutting, are performed to validate the developed model. The simulation results exhibit good agreement with that of the actual cutting, thereby showing the potential of the developed model for controlling the surface topography and roughness in real NC ball-end milling.