Molecular Dynamics Characterization of a Force Sensor Integrated Fast Tool Servo for On-Machine Surface Metrology
Establishment of the tool-workpiece contact, in which the diamond tool is set on the workpiece surface with a small contact force, determines the depth of cut accuracy in a force sensor-integrated fast tool servo (FS-FTS) for single point diamond microcutting and the scan force and scan depth in the following step of on-machine surface metrology. Molecular dynamics (MD) simulations are carried out to characterize the tool-workpiece contact process. It is clarified that even a small instability induced by the vibration of the workpiece atoms can generate large uncertainties in the subnanometric MD simulation results. Based on the vibration of the workpiece, atoms have a certain period determined by the MD model size; a multi-relaxation time method is proposed for reduction of the atom vibrations and stabilization of the MD model. It is confirmed that the proposed multi-relaxation time method is effective to eliminate the instability over a wide temperature range up to room temperature under which a practical microcutting or surface metrology process is carried out. An accurate elastic-plastic transition contact depth is then evaluated by observing the residual defects on the workpiece surface after the diamond tool is retracted back to its initial position.
KeywordsMolecular dynamics Diamond tool Microcutting Surface metrology Contact depth Contact force Elastic-plastic transition Fast tool servo Surface damage Multi-relaxation time method Temperature
Ultraprecision diamond microcutting is widely employed for fabrication of high accuracy microstructures over large areas of diamond machinable materials (Gao et al. 2003; Brinksmeier et al. 2012; Mellor et al. 2013; Fang et al. 2013; Chen et al. 2014) by using a single point diamond tool on a diamond turning machine (Gao et al. 2007; Lee et al. 2011) or an ultraprecision lathe (Cheung and Lee 2003; Chen et al. 2015b, 2016). The increasing demand for devices and systems with nanometric size and nanometric or subnanometric accuracy has pushed the machining accuracy of the ultraprecision diamond microcutting and its following step of surface metrology to the subnanometric range (Sun et al. 2012; Cheng and Huo 2013).
In the conventional FTS-based microcutting, in order to generate the complicated tool paths corresponding to the designed microstructured surface forms, the fast in-feed motion of the diamond tool is controlled by a PZT actuator of the FTS in association with the slow cross-feed motions of the machine axes. The tool path can be generated with nanometric accuracies by the well-developed PZT and the ultraprecision machine tool technologies. However, the accuracy of the machined microstructured surface is significantly affected by the cutting conditions. Therefore, a force sensor-integrated FTS, which is referred to as the FS-FTS, has been developed to assure and improve the machining accuracy of the FTS-based microcutting (Noh et al. 2008; Gao et al. 2015). The developed FS-FTS also has a unique function of in-process measurement of microstructured surface form. After microstructured surface is fabricated by a diamond tool, which is controlled by the FS-FTS and the machine tool slide, the fabricated microstructured surface can be scanned with the same diamond tool by using the FS-FTS and the machine tool slide to generate the scanning motions. The position of the diamond tool tip along the depth of cut direction is servo-controlled by the PZT actuator of the FS-FTS, so that the contact force between the diamond tool and the workpiece surface is kept constant. The contact force is monitored by a force sensor of the FS-FTS. A displacement sensor of the FS-FTS is employed to measure the servo-controlled PZT motion. The microstructured surface form of the workpiece is then accurately reconstructed from a combination of the PZT motion and the machine axes during the scanning motion. This function has been employed for a set of on-machine surface metrology, including on-machine measurement of diamond cutting tool edge contour (Chen et al. 2015a), relay fabrication of microstructure array (Chen et al. 2014), and in-press detection and repair of micro-defects (Chen et al. 2015b).
Establishment of the tool-workpiece contact, in which the diamond tool tip is set on the workpiece surface with a small contact force, is the first step for microcutting and on-machine form measurement based on the FS-FTS. The tool-workpiece contact determines the depth of cut accuracy, which significantly influences the achievable machining accuracy of the ultraprecision diamond microcutting and the scan accuracy of the on-machine surface metrology. For establishment of the tool-workpiece contact, the diamond tool is brought toward the workpiece surface by controlling the machine tool slide or the PZT actuator of the FS-FTS, while the output of the force sensor of the FS-FTS is monitored simultaneously. The tool-workpiece contact is established when the output of the force sensor reaches a threshold value. Ideally, it is desired to establish the tool-workpiece contact within the purely elastic region of the workpiece surface so that the accuracy of the ultraprecision diamond microcutting and the integrity of the scanned microstructured surface can be maintained. In responding to these requirements, it is necessary to physically understand the elastic and plastic deformation behaviors of the workpiece material in a subnanometric range when the workpiece surface is contacted with the diamond tool with specific cutting edge geometry and make clear the threshold contact depth and the corresponding contact force of the subnanometric tool-workpiece contact.
Elastic contact is a traditional problem, which can be investigated by the classical contact mechanics based on the Hertz theory (Johnson 1985; Oliver 1992). However, as the contact depth goes down to the nanometer-scale and the contact phenomenon takes place in a limited region, the conventional continuum theory cannot provide a reasonable explanation in such a small scale because of the nonlinear constitutive equations and the complicated material parameters (Oliver 1992). The instrumented nanoindentation systems have a capacity of measuring the mechanical property of thin surface layers such as coatings and thin films (Page et al. 1992; Gao et al. 2000; Motoki et al. 2006; Huang and Zhao 2015). Typically, a Berkovich-type diamond indenter with a large tip diameter of several micrometers is used in the nanoindentation system. A diamond tool, with a nanometric cutting edge formed by a flat rake face and a conical or cylindrical clearance face, is not compatible with the nanoindentation system. Therefore, the diamond tool is not compatible with the indenter in a nanoindention instrument. The current version of the FS-FTS instrument is also difficult to be employed for the subnanometric indentation experiment due to the insufficient performances of the machining instrument. On the other hand, simulations on the different time scale and length scale have become powerful approaches to analyze the deformation mechanisms of various materials, such as finite element method (FEM) (Özel and Zeren 2004; Farzad and Abdolreza 2015), multiscale simulations using quasicontinuum (QC) method (Wang et al. 2008), and molecular dynamics (MD) simulations (Goel et al. 2011, 2015). In spite of MD, simulation suffers from the limitation on both time scale and length scale; yet, it has become a powerful approach because it enables to predict and analyze the nanoscale machining in theory, which provides a shortcut from micro phenomena to macro characteristics. On the other hand, the purpose of carrying out an MD simulation in many researches is not to replicate the experiment but to develop a theoretical understanding of the deformation and machining mechanisms (Faisal et al. 2014). Therefore, MD simulation has the potential for investigation of the deformation behavior of the workpiece of the subnanometric tool-workpiece contact in surface metrology.
In this research, cost-effective MD simulations are carried out to characterize the subnanometric tool-workpiece contact process in the single point diamond microcutting and in-process surface metrology for the purpose of optimization of the FS-FTS. Based on the investigations of workpiece atom vibrations, a multi-relaxation time method is then proposed to reduce the influence of the atom vibrations. After confirmation of the feasibility of the multi-relaxation method for MD model stabilization, identification of the elastic-plastic transition contact depth of the workpiece is carried out.
Molecular Dynamics Model
Model for Subnanometric Tool-Workpiece Contact
Computational parameters of MD simulations
Workpiece copper (FFC)
Tool diamond (rigid)
Cu-Cu: EAM potential
Cu-C: Morse potention
D = 0.087 eV; α = 51.40 nm−1; r0 = 0.2050 nm,
rcut-off = 0.9025 nm
From 0.1 nm to 0.5 nm with a step of 0.01 nm
 direction on the (001) surface
A personal computer (PC) with an Intel (R) Core (TM) CPU of 3.5 GHz and a RAM of 16 GB is employed for saving the computation cost. A public domain computer code “Large-scale atomic/molecular massively parallel simulator” (LAMMPS) (Plimpton 1995) is implemented for the MD simulations of the subnanometric tool-workpiece contact. The Visual Molecular Dynamics (VMD) (Humphrey et al. 1996) is employed to visualize the positions of the workpiece atoms calculated by LAMMPS during the simulation. The type of defects on the workpiece is identified by using the Open Visualization Tool (OVITO) (Stukowski 2010).
Subnanometric Tool-Workpiece Contact Process
In the relaxation step, the MD model is relaxed in a canonical ensemble (Wang et al. 1991), in which the number of atoms, N; the volume of the model, V; and the specified temperature, T, are kept constant, from the initial state with the artificially assigned initial conditions to its natural, dynamically equilibrium condition by running the MD program over a relaxation time of Δtrelax. After running the MD program over Δtrelax in the canonical ensemble, the internal potential energy of the MD model will gradually reach equilibrium around the initial temperature based on the thermal dynamic theory (Cheong et al. 2001).
After the system has reached its equilibrium state, the tool is approached to the workpiece surface z = 0 (point S) with a constant velocity of vtool. The diamond tool is penetrated into the workpiece surface until it reaches a command contact depth ztool_M at point M. This process is referred to as the contacting step. Then the diamond tool is retracted back to its original position (point A) with the same velocity vtool, which is referred to as the retracting step. The time of contacting step and retracting step for the diamond tool that travels from point A to point M and from point M to point A are ΔtAM and ΔtMA, respectively. Since the contact velocity is equal to the retract velocity, ΔtAM is equal to ΔtMA. The interaction force ft−w between the diamond tool atoms and the copper workpiece atoms is calculated by the Morse potential between the copper atoms and the diamond atoms for investigation of the subnanometric tool-workpiece contact.
Stabilization of the MD Model
The interaction force ft−w with respect to the tool position ztool is the summation of all the interatomic force components applied on the diamond tool atoms with a positive direction along the contact direction. Since the primary motivation of this simulation is to obtain the elastic-plastic transition contact depth and the corresponding contact force of the subnanometric tool-workpiece contact, the investigation of the relationship between ft−w and ztool is necessary. Taking into consideration that the tool-workpiece contact is in the subnanometric range, even a small instability induced by the vibrations of the workpiece atoms can generate large uncertainties in the MD simulation results. None of the researches has focused on the investigations of the stabilization of the MD model.
Vibration of Workpiece Atoms
Since the vibration period is on the same order as the contacting operation time and/or the retracting operation time, a simple low-pass filtering or moving average method of the data, which is often used to remove the periodic component in data handling process, cannot be employed for ft−w-ztool curve. Thus, it is necessary to propose an effective method to reduce the instability and stabilize the MD model.
Multi-relaxation Time Method at Low and Room Temperatures
However, in real situation, the FS-FTS-based microcutting and on-machine surface form measurement are performed at a room temperature around 293 K. In order to make the simulation results more practically useful, the effectiveness of the multi-relaxation time method for reduction of the atom vibrations and stabilization of the MD model should be verified under the condition of room temperature.
Characterization of the Subnanometric Tool-Workpiece Contact
After stabilization of the MD model, the identifications of the elastic-plastic transition contact depth of the copper workpiece under the diamond tool are carried out. In order to avoid the effect of thermal vibration on simulation results, the simulation temperature is set to be 0.1 K.
The ft−w-ztool Curve
The workpiece material, copper, is a typical elastoplastic material (Aliofkhazrae 2014). If the tool-workpiece contacts with a small command contact depth ztool_M, the deformed copper workpiece returns to its original state without any contact marks on the workpiece surface after the diamond tool is retracted back from the workpiece surface in the retracting step. However, when ztool_M is larger than a threshold value, which is referred to as ztool_transition, the shear stress caused by the contact force between the diamond tool and the workpiece will be larger than the yield stress of the copper. Consequently, the copper atoms are dislocated and the plastic deformation is generated on the workpiece (Müller et al. 2007). Thus, a contact mark will then generate on the workpiece surface after the contact force is released in the retracting step. The threshold ztool_transition and the corresponding ft−w_transition are referred to as the elastic-plastic transition contact depth and the elastic-plastic transition contact force, respectively. A rough ztool_transition is firstly identified from the ft−w-ztool curves during the contacting and retracting steps under various command contact depths ztool_M, which is set to be from 0.1 nm to 0.5 nm with a step of 0.1 nm.
Identification of the Elastic-Plastic Transition Contact Depth
A more reliable method is proposed for identification of an accurate ztool_transition of the subnanometric tool-workpiece contact, which is a threshold value of the plastic tool-workpiece contact. As introduced above, when ztool_M is larger than the elastic- plastic transition contact depth ztool_transition, the lattice structure of the workpiece atoms on the free surface will be distorted from its original position after the removal of the diamond tool from the workpiece surface. Based on the fact that the defects remain in the lattice structures after the retracting step, a more accurate approximation of ztool_transition is thus identified to be ztool_M, in which the occurrence of the defects on the workpiece is confirmed. Thus, the defects in the lattice structure of the workpiece atoms on the free surface after the removal of the diamond tool are observed by increasing ztool_M from ztool_G of 0.17 nm, which is taken as the initial approximation of ztool_transition and is denoted by ztool_transition_ini. In the simulation, ztool increases with a step of 0.01 nm from ztool_transition_ini. The 0.01 nm is fine enough from the viewpoint of practical applications of the tool-workpiece contact.
Based on the above simulation results, it should be noted that the evaluated ztool_transition of 0.34 nm and ft−w_transition of 93 nN are corresponding to the diamond tool with an arc AB length of 2.5 nm and a sharpness of 3.0 nm in the MD model. Therefore, the evaluated value of 0.34 nm for ztool_transition cannot be directly treated as the threshold value of the plastic tool-workpiece contact. The actual length C’ab of arc AB is approximately eliminated to be 2.3 μm for a command contact depth of 0.34 nm for a diamond tool with a nose radius of 2 mm in actual applications. In order to estimate the corresponding contact force applied to the actual tool cutting edge over C’ab – which is referred to as the transition contact force, ft−w_transition, for the actual diamond tool – the transition contact force ft−w_transition over Cab should be expanded based on the geometrical of the diamond tool shown in Fig. 2a. f′t-w_transition is then calculated to be approximately 0.09 mN. It should be noted that f′t-w_transition is only a rough estimation of the transition contact force. The resolution of the force sensor used in the previously designed FS-FTS is 0.06 mN (Chen et al. 2015a). Therefore, the force sensor can be employed in the next generation FS- FTS with an optimization of the force sensor electronics for a reduced noise level. On the other hand, the above simulations are carried out at a low temperature of 0.1 K, which are different from the practical tool-workpiece contact. In order to obtain a more reliable estimation of the elastic-plastic transition contact depth of the copper workpiece for practical application of the tool-workpiece contact, large-scale simulations with an extended sharpness of the tool at the room temperature, which is the practical experiment condition of the microcutting/form measurement, should be carried out.
Summary and Outlook
MD simulations have been performed to investigate the tool-workpiece contact in a force sensor-integrated fast tool servo (FS-FTS) for single point diamond microcutting and on-machine surface metrology.
A periodic component, which was determined by the size of the MD model, with a dominant period has been observed even after the simulation system has been relaxed to its equilibrium state at a low temperature of 0.1 K. It has been verified that periodical component was induced by the subnanometric vibrations of the workpiece atoms. The period of the workpiece atom vibrations was influenced by the volume of the MD model size, and the simulation temperature only affected the amplitude of the workpiece atom vibrations. Based on the fact that the dominant vibration component had a certain period, a multi-relaxation time method has been proposed for reduction of the atom vibrations and stabilization of the MD simulation model. The accurate interaction force in the tool-workpiece contact is evaluated from the average of the ft−w-ztool data sets obtained in a group of MD simulations of tool-workpiece contact with identical simulation parameters except relaxation times in the relaxation step. The uncertainty of the ft−w-ztool curves at the temperature of 0.1 K and 293 K is reduced from 17 nN and 23 nN to 0.1 nN and 2 nN by using the proposed multi-relaxation time method, from which the effectiveness of the proposed multi-relaxation time method has been confirmed over a wide temperature range up to the room temperature.
The identification of an accurate elastic-plastic transition contact depth of the workpiece of the subnanometric tool-workpiece contact in diamond microcutting and on-machine surface metrology has been carried out. According to the contact force and tool displacement curve, a rough elastic-plastic transition contact depth of the workpiece is firstly calculated. Then a method has been proposed for evaluating an accurate elastic-plastic transition contact depth by observing the occurrence of the defects induced on the workpiece surface after the diamond tool was retracted from the workpiece surface. As a result, for the diamond tool with the specified geometry in this research, the transition contact depth was identified to be 0.34 nm where the featured point defects were observed on the workpiece surface.
Identification of the elastic-plastic transition contact depth of the subnanometric tool-workpiece contact at the room temperature of 293 K when a diamond tool with a practical edge sharpness of up to 30 nm – under which a practical microcutting and on-machine surface metrology are conducted – will be carried out in the next step of the research for the purpose of the optimization of the FS-FTS.
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