Machined Surface Research Articles

Characteristics of a novel elliptical ultrasonic vibration-assisted turning device

ABSTRACT 2D Ultrasonic Vibration-Assisted Turning (2D-UVAT) is a proven method to improve the traditional turning process. This process utilises bi-axial vibrations to enhance the smoothness of the machined surface and to suppress cutting temperature and cutting force. This study investigates the effects of employing a novel non-resonant vibration module, called the RNO vibrator, on the surface roughness, cutting temperature, and cutting force of aluminium alloy 6061-T6 machined using 2D-UVAT technique. The RNO vibrator operates by harnessing flexural hinges to disseminate and amplify the actuated vibrations originating from two orthogonal piezo actuator stacks. This vibrator was designed from a simple bar concept, expecting minimal adjustment on the tool post during installation. The experimental evaluation of the RNO vibrator’s performance was conducted by varying key machining parameters, including spindle speed, depth of cut, feed rate, and vibrational frequency. The study reveals that the introduced RNO vibrator substantially enhances machining quality by diminishing surface roughness and cutting temperature, while concurrently reducing cutting forces. Under the given conditions, the machined workpieces had a surface roughness between 0.41 and 1.25 µm and a cutting temperature ranging from 153.36°C to 180.5°C, while the cutting force was low, typically between 35.3 N and 145.5 N. The vibrator works better at high frequency, particularly at 20 kHz. Eventually, the study suggests that the RNO vibrator has a promising performance as a vibration module for the 2D-UVAT process.

Comparative Evaluation of Bone–Implant Contact in Various Surface-Treated Dental Implants Using High-Resolution Micro-CT in Rabbits’ Bone

This study evaluated the bone-to-implant contact (BIC) of various surface-treated dental implants using high-resolution micro-CT in rabbit bone, focusing on the effects of different treatments on osseointegration and implant stability before and after bone demineralization. Six male New Zealand White rabbits were used. Four implant types were tested: machined surface with anodizing, only etching, sandblasting with Al2O3 + etching, and sandblasting with TiO2 + etching. Implants were scanned with high-resolution micro-CT before and after demineralization. Parameters like implant volume, surface area, and BIC were determined using specific software tools. During demineralization, the BIC changed about 6% for machined surface with anodizing, 5% for only etching, 4% for sandblasting with Al2O3 + etching, and 10% for sandblasting with TiO2 + etching. Demineralization reduced BIC percentages, notably in the machined surface with anodizing and sandblasting with TiO2 + etching groups. Etching and sandblasting combined with etching showed higher initial BIC compared to anodizing alone. Demineralization negatively impacted the BIC across all treatments. This study underscores the importance of surface modification in implant integration, especially in compromised bone. Further research with larger sample sizes and advanced techniques is recommended.

Mathematical Modeling and Generating Method of Hourglass Worm Gear Hob’s Rake Face Based on a Rotating Paraboloid Surface

The rake angles on both sides of the cutting edges of the hourglass worm gear hob significantly influence its cutting performance, which, in turn, plays a decisive role in the surface quality of the machined worm wheel. To balance the rake angles along the tooth height direction of each hob tooth and enhance the overall cutting performance of the hob, this paper proposes a method that utilizes a rotating paraboloid surface to generate the helical rake face of the hourglass worm gear hob. First, the conjugate condition equations for the rake face generated by the rotating paraboloid surface are derived. A mathematical model for the helical rake face of planar double-enveloping hourglass worm gear hob is established. This study explores the influence of two machining parameters on the rake angle, specifically the milling drive ratio coefficient k and the geometric parameter of a parabolic milling cutter p. Through a systematic analysis of the variations in rake angle at the dividing toroidal surface and along the tooth height direction, the optimal parameter values were identified as k = 0.9115 and p = 0.6834. The results show that, after optimization, the hob rake angle range is around ±4.7°, with a maximum rake angle difference of 6.3072° along the tooth height direction, and the rake angles on both sides of the teeth are more balanced. The structure of the rake face is more reasonable, reflecting the feasibility of rotating paraboloid tools for forming tools in the machining of complex surfaces.

Optimisation of parameters of a dual-axis soil remediation device based on response surface methodology and machine learning algorithm

To accelerate the recycling of black soil, it is necessary to develop a new type of soil remediation equipment to improve its working efficiency. The one-way test was used to determine the mean level value of the steepest climb test, and the combined equilibrium method was used to determine the upper and lower interval levels of the response surface test for parameter optimisation. Based on the results of the response surface indices, machine learning was performed and the optimal model was determined. The results show that the predictive ability and stability of the decision tree model for the two indicators are better than that of random forest and support vector machine. The optimal parameter combinations determined using the decision tree model are: speed 73 rpm, homogenisation pitch 183 mm, homogenisation time 1 s, descent speed 0.06 m/s. The error between the optimal value of the machine learning prediction model and the actual simulation is 1.1% and 5.72%, respectively. The results of the study show that the effect of optimising the parameters through machine learning achieves a satisfactory prediction accuracy.

Machining error compensation of free-form surfaces by combination of ordinary kriging method and mirror compensation method

ABSTRACT Improving the accuracy and efficiency of free-form surface machining is a common goal of modern manufacturing. In this study, a compensation method combining the ordinary kriging method based on sequential quadratic programming method optimization (SQP-OK) and the mirror compensation method for machining errors of free-form workpieces was applied, with the aim of significantly improving the workpiece machining accuracy. Machining errors on the surface of the workpiece were predicted utilizing the SQP-OK after the workpieces were completed with semi-finishing machining based on the on-machine measurement (OMM) results of the workpiece. Based on the prediction result, the mirror compensation method was applied to calculate the compensation points. Free-form workpieces were compensated for by modifying the NC code for semi-finishing. To verify the effectiveness of the proposed method, two free-form workpieces were machined with computer numerical control (CNC) compensation, applying the proposed method and the method modifying the overall machining allowance. The experimental results revealed that the compensation method proposed in this paper reduced the average value of the machining errors decreased by 28.6% in absolute value, 31.1% in maximum undercut, and 28.8% in maximum overcut for the free-form workpiece, respectively, compared with the compensation method of modifying the overall machining allowance.

Review of Image Processing Methods for Surface and Tool Condition Assessments in Machining

Review of Image Processing Methods for Surface and Tool Condition Assessments in Machining

Optimizing the surface quality of electrochemical machined Ni-based single crystal superalloy via manipulation of phase and dendrite dissolution

The transpassive dissolution behaviors of Ni-based single crystal superalloy in 10 %NaCl, 10 %NaNO3, and mixed solution are investigated by using potentiodynamic polarization, scanning electron microscopy, energy dispersive X-ray spectroscopy, and X-ray photoelectron spectroscopy. The alloy exhibits opposite yet complementary dissolution characteristics in NaCl and NaNO3 solutions. The different responses of γ/γ′ phases to Cl− and NO3− contribute to the opposite dissolution behaviors of dendrites and interdendritic regions. The surface flatness is noticeably enhanced in mixed solution due to the synchronous dissolution of the γ/γ′ phases. Our work paves the way for obtaining high-quality surface in electrochemical machining of single crystal superalloys.

Single Vesicle Surface Protein Profiling and Machine Learning-Based Dual Image Analysis for Breast Cancer Detection

Single-vesicle molecular profiling of cancer-associated extracellular vesicles (EVs) is increasingly being recognized as a powerful tool for cancer detection and monitoring. Mask and target dual imaging is a facile method to quantify the fraction of the molecularly targeted population of EVs in biofluids at the single-vesicle level. However, accurate and efficient dual imaging vesicle analysis has been challenging due to the interference of false signals on the mask images and the need to analyze a large number of images in clinical samples. In this work, we report a fully automatic dual imaging analysis method based on machine learning and use it with dual imaging single-vesicle technology (DISVT) to detect breast cancer at different stages. The convolutional neural network Resnet34 was used along with transfer learning to produce a suitable machine learning model that could accurately identify areas of interest in experimental data. A combination of experimental and synthetic data were used to train the model. Using DISVT and our machine learning-assisted image analysis platform, we determined the fractions of EpCAM-positive EVs and CD24-positive EVs over captured plasma EVs with CD81 marker in the blood plasma of pilot HER2-positive breast cancer patients and compared to those from healthy donors. The amount of both EpCAM-positive and CD24-positive EVs was found negligible for both healthy donors and Stage I patients. The amount of EpCAM-positive EVs (also CD81-positive) increased from 18% to 29% as the cancer progressed from Stage II to III. No significant increase was found with further progression to Stage IV. A similar trend was found for the CD24-positive EVs. Statistical analysis showed that both EpCAM and CD24 markers can detect HER2-positive breast cancer at Stages II, III, or IV. They can also differentiate individual cancer stages except those between Stage III and Stage IV. Due to the simplicity, high sensitivity, and high efficiency, the DISVT with the AI-assisted dual imaging analysis can be widely used for both basic research and clinical applications to quantitatively characterize molecularly targeted EV subtypes in biofluids.

Fundamental study on dielectric oil viscosity for high-performance wire EDM

AbstractDielectric oil has been recently used in wire electrical discharge machining (wire EDM) for achieving high-precision machining. However, the influence of dielectric oil properties on wire EDM characteristics has not been clarified sufficiently. This study fundamentally investigated the influence of dielectric oil viscosity on wire EDM characteristics. In this study, three types of dielectric oil differing only in viscosity were prepared and examined. Linear cutting experiment results showed that the removal rate and the machined surface roughness increase with dielectric oil viscosity. Then, the influence of viscosity on crater removal volume was investigated to discuss the cause of the change in removal rate, and it was found that crater removal volume increases with the viscosity. Furthermore, CFD (computational fluid dynamics) analysis results and discharge observation results showed that the debris exclusion becomes worse in higher viscosity oil, and the discharge concentration occurs frequently, resulting in the deterioration in machined surface roughness. Next, the difference in machining accuracy with dielectric oil viscosity was investigated. It was found that the corner shape accuracy deteriorates with the increase of viscosity while the machined surface waviness and straightness improve slightly. Structural analysis results showed that wire deflection increases with viscosity, resulting in the deterioration in corner shape accuracy. On the other hand, high-speed observation of wire vibration was carried out, and it was found that the wire vibration decreases in the case of higher viscosity, which leads to the improvement in machined surface waviness and straightness.

Machining mechanism of CoCrFeNiAlX high entropy alloys via ultrasonic elliptical vibration cutting

Abstract This study investigates the micro-cutting mechanism of CoCrFeNiAl X high entropy alloys, focusing on the impact of amplitude, vibration frequency, cutting depth, and the Al element content. The mechanical response of the material is analyzed using simulation methods for both conventional cutting and ultrasonic elliptical vibration assisted cutting (UEVAC). The results show that under different vibration parameters and cutting depth, the cutting temperature produced by UEVAC is significantly higher than that of conventional cutting temperature. When the Y-axis amplitude is reduced from 90 μm to 30 μm, the cutting temperature is reduced by 50%. In addition, the cutting temperature is positively correlated with the Al content, and when the molar ratio is 20%, the cutting temperature is about 2.1 times that of 13%. While keeping the cutting parameters unchanged, the cutting force generated by UEVAC is significantly reduced compared to conventional cutting. It is worth noting that when the X-axis amplitude is 40 μm, the Y-axis amplitude is 90 μm, and the vibration frequency is 25 KHz, the cutting force of UEVAC is the smallest, which is only about 13% of the conventional cutting force. With the increase of the mole ratio of aluminum in the high entropy alloy, when the mole ratio of aluminum increases from 0% to 13%, the cutting force begins to decrease by about 33%. However, when the molar ratio increases from 13% to 20%, the cutting force increases by about 214%. On the surface of the workpiece (within the range of 0–3 μm from the machining surface), the residual stress generated by UEVAC is mainly manifested as compressive stress or tensile stress, which is significantly less than the residual stress generated by conventional cutting. The relation of residual compressive stress of workpiece under different aluminum content is Al1 > Al0.6 > Al0.

Optimizing dry milling of stir-cast and heat-treated AZ80 magnesium alloy using multiple criteria optimization technique: an experimental study.

The primary aspects of this research are to evaluate surface roughness, cutting force, and material removal rate and optimize it with dry milling process parameters for heat-treated and stir-cast AZ80 magnesium alloy. Multiple methodologies are utilized in the research, which includes the Integration of design of experiments-response surface methodology for experimental design with the technique for order of preference by similarity to ideal solution for multi-criteria optimization. In order to evaluate the effect of process parameters on the response, the experimental design manipulates the depth of cut, feed rate, and cutting speed in a systematic manner. An evaluation of the machined surface's quality is conducted via surface roughness measurements. Likewise, insights into the forces exerted during milling can be obtained through continuous monitoring of cutting forces. The calculation of material removal rate is predicated on weight reduction. The interaction between the depth of cut and feed rate has a significant impact on the critical-to-quality characteristics of the alloy, which has contribution percentage greater than 25%. This finding validates that despite the heat-treated alloy having a similar composition to the as-cast alloy (where the closeness coefficient is 0.9843), the optimal process parameters of the former are not applicable to the latter. Nevertheless, the technique used to prepare the specimen has no bearing on the material removal rate, which is a process parameter-specific effect.

Taguchi optimization of Wire EDM process parameters for machining LM5 aluminium alloy.

LM5 alloy is suitable for metal castings for marine and aesthetic uses due to its admirable resistance to corrosion. In order to make intricate shapes in the LM5 alloy, this study intends to assess the impact of Wire Electric Discharge Machining process variables, like Pulse on Time (Ton), Pulse off Time (Toff), Gap Voltage (GV) and Wire Feed (WF) on responses like Material Removal Rate (MRR), Surface Roughness (SR), and Kerf Width (Kw). The LM5 aluminium alloy plate was produced through stir casting process. SEM, EDAX and XRD images confirm the LM5 Al alloy's microstructure and crystal structure. WEDM studies were conducted using design of experiments approach based on L9 orthogonal array and analysed using Taguchi's Signal to Noise Ratio (S/N) analysis. Pulse on Time has the greatest statistical effects on MRR (68.25%), SR (79.46%) and kerf (81.97%). In order to assess the surface integrity of the WEDM machined surfaces, the SEM study on the topography was conducted using the optimum surface roughness process variables: Ton 110 μs, Toff 50 μs, GV 40 V, and WF 9 m/min. SEM images show the recast layer and its thickness. The average absolute error for MRR is 1.69%, SR is 3.89% and kerf is 0.88%, based on mathematical (linear regression) models. The Taguchi's Signal to Noise ratio analysis is the most appropriate for single objective optimization of responses.

Research on microscopic fracture mechanism of glass-ceramics grinding surface based on progressive scratch test

Progressive scratch test was carried out on the glass-ceramics to study the continuous micro-fracture mechanism of its surface, which provided an important basis for the research on the grinding mechanism of glass-ceramics. By microimaging of scratch, the continuous material removal process of glass-ceramics from ductility to ductile brittleness to brittleness was observed in micro-view, confirming that there was a ductile brittleness between ductility and brittleness on the surface of glass-ceramics. The critical point for breaking from ductility to ductile brittleness and the critical point for breaking from ductile brittleness to brittleness were measured. The machined critical depth hc1 of the composite domain of ductility and ductile brittleness and the machined critical depth hc2 of the composite domain of ductile brittleness and brittleness for glass-ceramics were further obtained by computational analysis. This study provides valuable insights into the surface machining forming and surface microstructure generating of glass-ceramics material. The research results can also provide reference on determining the critical grinding parameters of glass-ceramics material.

Trajectory error compensation method for grinding robots based on kinematic calibration and joint variable prediction

Trajectory accuracy, a crucial metric in assessing the dynamic performance of grinding robots, is influenced by the uncertain movement of the tool center point, directly impacting the surface quality of processed workpieces. This article introduces an innovative method for compensating trajectory errors. Initially, a strategy for error compensation is derived using differential kinematics theory. Subsequently, a robot kinematic calibration method utilizing ring particle swarm optimization (RPSO) is proposed to address static errors in the grinding robot. Simultaneously, a method for predicting robot joint variables based on a dual-channel feedforward neural network (DCFNN) is designed to mitigate dynamic errors. Finally, a simulation platform is developed to validate the proposed method. Simulation analysis using extensive data demonstrates an 89.3% improvement in absolute position accuracy and a 74.2% reduction in error fluctuation range, outperforming sparrow search algorithm (SSA), improved mayfly algorithm (IMA), multi-representation integrated predictive neural network (MRIPNN), etc. Algorithmic comparison reveals that kinematic calibration significantly reduces the average trajectory error, while joint variable prediction notably minimizes error fluctuation. Validation through trajectory straightness testing and a 3D printing propeller grinding experiment achieves a trajectory straightness of 0.2425 mm. Implementing this method enables achieving 86.1% surface machining allowance within tolerance, making it an optimal solution for grinding robots.

To investigate the effect of discharge energy and addition of nano-powder on processing of micro slots using EDM assisted µ-milling operation

ABSTRACT Micro-electric Discharge-Milling (µ-ED-M) is a non-contact process that uses an electrical spark to remove the material from a submerged workpiece with an electrode in a dielectric. The present paper focuses on optimizing process energizing (Capacitor, Voltage) and process stabilizing (Tool Travel Speed, Nano-Powder) parameters for controlling the size and surface characteristics of micro-crater. The present work focuses on the effect of nano-powder concerning dimensional aspects and surface characteristics at high and low capacitance levels. A µ-slot has been generated on the copper material by a tungsten carbide electrode. The experimentation is performed with two capacitor levels and three voltage and tool travel speed levels using full factorial design technique using with and without mixing of nano-powder in dielectric. The desirability functional multi-objective optimization approach is used to analyze the MRR, TWR, Width, and Depth. Field emission scanning electron microscopy (FESEM), non-contact optical profilometer, and x-ray diffraction (XRD) techniques are used to analyze the surface morphology of machined surfaces. The ANOVA is used to optimize the results; at low discharge energy, tool travel speed contributes 41% and promotes a higher thickness of recast layer 12.7 µm, whereas high discharge energy and nano-powder concentration contribute approx.—36% with 8.56 µm of recast layer.

Wear Behavior of TiAlN/DLC Coating on Tools in Milling Copper–Beryllium Alloy AMPCOLOY® 83

In recent years, the exponential growth of the machining industry and its needs has driven the development of new manufacturing technologies, more advanced cutting tool types, and new types of coatings to extend tool lifespan. New coating solutions have been studied and implemented for machining tools, which provide a low friction coefficient and lubrication, thus increasing tool lifespan. Following this line of reasoning, it is relevant to develop scientific work aimed at studying the behavior of cutting tools coated with thin films that promote low friction and high lubrication, as is the case with DLC (diamond-like carbon) coatings. These coatings promote good resistance to oxidation and allow high machining speeds, properties also exhibited by TiAlN (titanium aluminum nitride) coatings. In fact, there is a gap in the literature studying the performance of cemented carbide tools provided with multilayered coatings in milling operations of Cu–Be alloys, commonly used in inserts of plastic injection molds. This study’s objective was to investigate the effect of a multilayer coating (TiAlN/DLC) on end-milling tools to analyze their cutting performance when milling a Cu–Be alloy known commercially as AMPCOLOY®83. The quality of the machined surface was evaluated, and the wear of the cutting tool was studied. A comparative analysis of milling parameters with respect to their effect on the condition of the surface after machining and the resulting wear on the tools, using coated and uncoated tools and different machining parameters, allowed us to verify a better quality of the machined surface and wear quantified in approximately half when used coated tools.

Influence of different wire materials on the machining of Albromet W130 by WEDM

Wire Electrical Discharge Machining (WEDM) is an unconventional machining technology, widely spread in different sectors of many industries. The machining uses periodically repeating electrical impulses, which allows all materials with at least a minimum electrical conductivity to be machined. The machining tool is a thin wire that can be made of many different materials. Wire electrode material requirements vary from industry to industry. This study aimed to increase the efficiency of WEDM through an analysis of the influence of the type of wire material on the machining of Albromet W130 copper alloy. The analysis comprised a molybdenum, brass and a copper wire of a 0.25 mm diameter and a Box-Behnken design of experiment totalling 42 rounds. The design of experiment results analysis covered cutting speed, machined surfaces’ topography and morphology, and the subsurface layer condition. Furthermore, an analysis of the wire electrodes used in the experiment was carried out. The highest cutting speed was achieved using a copper wire and the lowest R a values were achieved in samples machined with a molybdenum wire.

Cooling and Lubricating Strategies for INCONEL® Alloys Machining: A Comprehensive Review on Recent Advances

Abstract INCONEL® alloys are Ni-based superalloys with superior mechanical properties for extremely high temperature (T) applications. These alloys present significant challenges: they are difficult-to-cut materials due to the low thermal conductivity (k), severe work hardening and elevated surface hardness. They are widely used in applications that require good dimensional stability; however, built-up edge (BUE) followed by premature Tool Wear (TW) are the most common problems when applying conventional machining (CM) and hybrid machining processes, i.e. Additive Manufacturing (AM) followed by milling, resulting in a meagre final product finishing. Regarding cooling/lubricating environments, a miscellanea of methods can effectively be applied to INCONEL® alloys, depending on their advantages and disadvantages. It is imperative to refine the machining parameters to enhance the performance outcomes of the process, particularly concerning the quality and cost-effectiveness of the product. This current review intends to offer a systematic summary and analysis of the progress taken within the field of INCONEL® CM and the various cooling/lubricating methods over the past decade, filling a gap found in the literature in this field of knowledge. A Systematic Literature Review (SLR) approach was employed in this study, aiming to identify pertinent papers within the cooling and lubricating strategies for INCONEL® alloys machining. The most recent solutions found in the industry and the prospects from researchers will be presented, providing significant insights for academic researchers and industry professionals. It was found that selecting cooling methods for INCONEL® machining requires careful consideration of various factors. Each lubrication environment utilized in traditional INCONEL® machining methods offer unique advantages and challenges regarding the different outcomes: TW, Tool-Life (TL) and/or surface quality assessment; nevertheless, cryogenic cooling by CO2(l) and N2(l) highlights as the better cooling environment to improve the machined surface quality.

Comparative analysis of the wear behaviour of TiN/TiAlN, TiAlVN, and TiAlYN coated tools in milling operations of Inconel 718

Abstract Milling is widely used in the aeronautical and aerospace industries, due to the possibility of producing parts with good dimensional stability and surface quality. Because of its exceptional mechanical qualities and limited thermal conductivity, Inconel 718 is a nickel superalloy that is regarded as a challenging material to process. Due to the flexibility of milling, this is the most commonly used process for machining INCONEL alloys. However, high levels of tool wear can be observed. Coatings can be deposited on the cutting tools to improve process performance. Nonetheless, doping elements such as yttrium and vanadium when added to TiAlN-based coatings can increase the coating's resistance. Furthermore, multilayer coatings tend to be very promising resistance to crack propagation. Thus, this work intends to compare three coatings deposited via PVD, in terms of the quality of the machined surface and wear resulting from the process: TiAlVN, TiAlYN, and TiN/TiAlN. The cutting speed (Vc), feed per tooth (fz), and cutting length (Lcut) were varied. It was possible to verify that the multilayer coating had better results, in terms of average roughness (Ra) and in measuring wear (VB3) and its characterisation. On the other hand, the TiAlVN coating showed the worst results. It was concluded that due to the TiN layer, the TiN/TiAlN coating has better resistance to crack propagation, as its adhesion to the substrate is good and there is no delamination.

Investigation on the influence of mesoscale geometric features on the surface white layer characteristics in titanium alloy milling using ball end mills

A white layer will be generated on the machined surface when milling titanium alloy. Its existence will make the surface of the workpiece more brittle, and it is easy to produce cracks during the machining process, which greatly harms machining. Aiming at this problem, this paper takes the ball-end milling cutter with mesoscopic geometric characteristics as the research object, establishes the theoretical model of the white layer thickness of the workpiece under the micro-texture and cutting edge factors, analyzes the single factor of micro-texture parameters and cutting edge parameters, and the interaction between them and cutting parameters on the milling force-thermal characteristics and the white layer of the workpiece. The influence law reveals its mechanism from the macro and micro perspectives. It uses the white layer thickness as the evaluation index to optimize the mesoscopic geometric characteristic parameters by using the simulated annealing algorithm. The results demonstrate that the mesoscopic geometric feature of the ball-end milling cutter effectively reduces the thickness of the white layer, achieving a 38% reduction compared to that observed with a non-textured milling cutter. The thickness of the white layer exhibits a positive correlation with the distance L from the blade and a negative correlation with the edge radius R. The interaction between the cutting edge radius R and the cutting depth a p influences the milling force and heat, alters the micro-texture of the workpiece surface, induces the α + β phase transformation, and affects the white layer thickness. Based on the predictive model for white layer thickness, the optimization results for comprehensive milling performance are as follows: R is 59.39 μm, L is 110.01 μm, D is 58.68 μm, L1 is 130.59 μm, a p is 0.30 mm, V is 147.39 mm/min, f is 0.08 mm/z.