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Abstract
The tooth surface of the spur face gear is a kind of complex space curved surface, in order to solve the technical defects in traditional NC milling manufacturing. This paper utilizes the complex tooth surface grid planning principle to establish the cathode surface firstly; Secondly, the orthogonal test, linear regression analysis and weighted comprehensive scoring system is adopted to obtain the optimal processing parameters; And finally, the Lagrange interpolation method is used to realize the modification of the cathode surface. The verification test shows that this method compared with the traditional NC milling, reduces the cost by 70% and the cycle by 75%, can realizes the rapid high-precision batch manufacturing of complex structure products.
... The circular cutters were also applied by Guo et al. [10] to study the influence of the cutter parameters on the meshing performance of face gear drives. For the roughing purpose, CNC milling [11], electrochemical machining [12], forming [13], plunge milling [14] and planing [15] were also studied to manufacture face gears. Honing was also studied by Wang et al. [16] to improve the quality of the finishing process of face gears. ...
... The M fw e in Eq.(12) represents the actual homogeneous transformation matrix between S w to S f . It can be expressed asM fw e = M fC e ⋅ M CY e ⋅ M YO e ⋅ M OZ e ⋅ M ZX e ⋅ M Xm ⋅ M mA e ⋅ M AB e ⋅ M Bw e(14)Specially, there are three points worth to be mentioned to the derivation of Eq.(14).(I) ...
As one of the main error sources, the geometric errors are compensated in this work for the accurate worm grinding of spur face gears. The previous methods of the geometric error compensation are usually applied to the machining with rotary cutters, of which the error of cutter rotation angle is not compensated since it does not affect the machining result. These methods are inappropriate to the worm grinding of face gears, because the worm is a non-rotary cutter and the machining result is sensitive to the error of cutter rotation angle. In this work, an innovative geometric error compensation method is proposed to the machining with non-rotary cutters based on two main points. First, the cutter rotation angle is considered to both the modeling and compensation of the geometric errors. Second, the instantaneous ideal contact point, which is calculated according to the generation process of the worm grinding of face gears, is chosen as the reference point to the compensation algorithm rather than the cutter tip point used in the previous method. The proposed method is validated by the example with both the theoretical calculation and practical machining.
... It has the advantages of non-contact, free of cutting force, no concentrated heat affected zone, high machining efficiency and good machining surface quality. [6][7][8][9] Therefore, ECM is widely used to process hard-to-cut materials and complex structural parts. 10,11 There are many methods based on ECM available for manufacturing blade components, including numerical control ECM, [12][13][14] profile ECM, [15][16][17] and electrochemical trepanning. ...
In this work, a multi-physics field coupling model based on electric field, gas-liquid two-phase flow field ,and temperature field of forward flow electrochemical trepanning (FFECT) blades was established, and the distribution law of hydrogen bubble volume fraction, electrolyte temperature, and electrolyte conductivity in the machining gap was obtained. Based on the simulation results, the time-varying process of electrolyte flow velocity distribution was divided into three stages according to the change in machining gap corresponding to different blade machining heights H, and the effects of the machining voltage U and the cathode feed rate v on the side gap Δs and the end gap Δe were investigated. The simulation analysis and experimental results show that both side gap and end gap increase as machining voltage increases but decrease with the increase in cathode feed rate. The model predictions are in good agreement with the experimental results, and the maximum errors of side gap and end gap are 10.6% and 17.7%, respectively. In addition, the effects of machining voltage and cathode feed rate on the surface quality were studied experimentally. Results reveal that surface roughness can be reduced by appropriately decreasing the machining voltage and increasing the cathode feed rate.
... The main applications are based on the aerospace industry as a finishing process for turbine blades, including internal channels. 28 However, other applications were also investigated, such as combs for seal elements, 29 gears, 30 molds, and dies, as well as for the production of medical devices and other applications. 31 Additionally, Bao et al. 32 demonstrated the feasibility of ECM for aviation components using pure water as an electrolyte. ...
Electron beam melting (EBM) made feasible γ-titanium aluminide (TiAl) alloys. However, the surface roughness resulting from EBM is poor, and the high mechanical properties make γ-TiAl difficult to be machined. Electro-Chemical Machining (ECM) is gaining interest as a finishing process to achieve low surface roughness. Based on the anodic dissolution mechanism, ECM realises a contactless material removal and results particularly suitable for difficult-to-cut materials. The paper investigates the use of ECM for the finishing of Ti-48Al-2Nb-2Cr, a γ-TiAl alloy made by EBM. The effects of current, voltage, feed rate and duty ratio have been accounted for under pulsed machining conditions.
... Cui et al. has introduced machining principle for the continuous generative grinding face gear by a worm wheel [5]. Huang et al. has established the complex tooth surface principle to solve the technical defects for face gear in traditional CNC manufacturing [6]. Han et al. has presented a machining method as power skiving for face gear to improve machining efficiency [7]. ...
As a new manufacturing method of minimal metal loss, coherent metal streamline, and higher load-bearing capacity for straight face gears, hot rolling forming can effectively improve the forming quality and the fatigue strength of face gear. In this paper, the key technologies involved in hot rolling process are studied, and hot rolling forming simulation of straight face gears is realized by using Deform-3D. Orthogonal simulation experiments are carried out by introducing three evaluation indexes, such as proportion coefficient of lug, metal streamline defect, and rolling force. Combining with the multi-objective process parameter optimization method of improved DEMATEL (decision making trial and evaluation laboratory) and improved TOPSIS (technique for order preference by similarity to an ideal solution), the optimal combination of technological parameters for hot rolling of straight face gear is accurately determined. Based on the optimal combination of parameters, the hot rolling manufacturing experiment of straight face gear is realized. The rationality of the optimal technological parameters and the feasibility of the rolling forming manufacturing technology are verified by simulation results and experiment results, and the theoretical basis and practical value for the precision manufacturing of rolled face gear are provided.
... The main applications are based on the aerospace industry as a finishing process for turbine blades, including internal channels. 28 However, other applications were also investigated, such as combs for seal elements, 29 gears, 30 molds, and dies, as well as for the production of medical devices and other applications. 31 Additionally, Bao et al. 32 demonstrated the feasibility of ECM for aviation components using pure water as an electrolyte. ...
Ti-48Al-2Nb-2Cr is a challenging and difficult-to-cut titanium aluminide (TiAl) alloy with several manufacturing issues because of the high sensitivity to crack formation and oxygen picking up. Electron beam powder bed fusion (EB-PBF) made feasible TiAl near net shape components, but the surfaces are particularly rough and present complex surface topographies. In this present investigation, experimental analysis and optimization are proposed for electro-chemical machining (ECM) on as-built Ti-48Al-2Nb-2Cr surfaces manufactured using EB-PBF. Experimental runs are performed under pulsed machining conditions and varying specific process metrics to understand the machining effects on the process efficiency and removal phenomena. In particular, the morphology and isotropy of the surface are studied before and after the machining by scanning
electron and confocal microscopies. The results establish the optimal machining conditions and a range for the active machining time that produce, compared to the as-built surface, an extremely smooth and isotropy surface without any detrimental effect on the surface integrity and microstructure.
The contact ratio of face gear drive is hard to calculate precisely because it is point contact adjusted from line contact to avoid jamming. To obtain the calculation methods and improvement measures for the contact ratio of face gear drive, the line contact ratio (LCR) in shaping and the point contact ratio (PCR) in meshing are investigated in this paper. Tooth surface equations of face gear shaping are established based on its generation principle and the contact line midpoint tracks are obtained. Iterative equations to accurately calculate restrictive conditions (undercutting and pointing) for face gear tooth surface are constructed and verified, their approximate equations are given further. Meshing tracks of face gear drive are obtained by solving the established meshing equations. Calculation methods of the LCR and PCR are elaborated according to its definition and the fitting equations are given for engineering application. The results show that the PCR is markedly lower than the LCR. The advantage of high contact ratio of face gear drive is significantly affected because it is very sensitive to the realization of point contact. It is acceptable to use the LCR to approximate the PCR when the distribution range of the meshing track on the face gear tooth surface is determined. It provides a theoretical basis for the design and optimization of orthogonal spur-face gear drive.
Face gear drives have been widely applied in power transmission, but the finishing of continuous generation is a difficult problem. This is mainly because the teeth of face gears are on a plane, which leads to interference by worm grinding. Hence, a shaving method for face gears is proposed in this paper. This work studies the theory of face gear shaving, the causes of mid-concave phenomena based on load tooth contact analysis (LTCA), a solution for the modification coefficient of the shaving cutter and a control method for the cutter location point. The experimental results show that the maximum machining error is −12.7μm, that many generating lines appear and that the residual stress increases by 49.2% in comparison with that of the grinding tooth surface. The present study suggests that the shaving method for spur face gears can not only achieve the finishing of continuous generation but also improve the surface integrity of the gear.
This work describes the design and testing of an ultrasonic reactor suitable for processes which require agitation within a narrow gap in a tank geometry. A maskless microfabrication process was used to validate the ultrasonic reactor design. This mask-less electrodeposition method requires the inter-electrode distance between the anode tool and the cathode substrate to be maintained at 300 μm, and sufficient stirring of the electrolyte by ultrasound agitation. A design was proposed allowing 74 mm × 105 mm size substrates to be mounted into an electrode holder and loaded into an 18 L ultrasonic reactor. Experiments were carried out to test the uniformity of the mass transfer within the narrow electrode gap at different locations on the substrate, and to validate the feasibility of a mask-less metal plating technique by depositing features of μm-scale. When increasing ultrasonic powers from 30 to 60 W L⁻¹, increasing agitation was observed at the centre of the substrate, but not at its edges. A Sherwood number correlation showed developing turbulence within the narrow gap, even in the centre of the plate. Micron scale features were plated onto A7 substrates, but the deposited features were 2.5 times the original width. The work showed that sonic streaming can produce sufficient agitation in long sub millimetre channels which can be employed to overcome mass transfer limitations.
The proposed mechanism of face gear shaping is applied to develop the mathematical model of face gears. Based on the developed mathematical model of the face gear, computer graph of the face gear set is created. Then, the transmission errors of the face gear pairs under various assembly errors are investigated based on the constraints theory of six-degree-of-freedom rigid body motion. The assembly errors are finally obtained by applying the TCA (tooth contact analysis) method. Also, the developed computer simulation programs quantitatively evaluate the influence of assembly errors including offset and angular position errors on the position of contact path and TE (transmission error) in a complete mesh cycle. Besides, the loaded tooth contact characteristics are investigated by using the FEM (finite element method) to study the stick-slip trajectories of the surfaces. The results are illustrated with numerical examples.
To determine the error compensation for cutting forces with a machine tool, this paper proposes a comprehensive error compensation method that determines an equivalent cutting force. The loading system that applies this equivalent cutting force was designed to load a constant force that imitates the actual cutting force of a machine tool. The equivalent cutting force, when applied to the working table of the machine tool, induces an error that can be directly measured by a laser interferometer. Moreover, a stable measurement environment suitable for laser interferometer is configured. A comprehensive error compensation model of a three-axis computer numerical control (CNC) machine tool was developed using multi-body systems theory and homogeneous transformation matrices. Solutions for the error compensation model and parametric equation were automatically found using MATLAB, based on this model. The effectiveness of this compensation method has been confirmed by machining experiments. The experimental results show that this comprehensive error compensation of the equivalent cutting force can greatly improve machining accuracy.
In this paper, we use the quantum mutual entropy to measure the degree of entanglement in the time development of a two-level particle (atom or trapped ion). We find an exact solution of the Milburn equation for the system. The exact solution is then used to discuss the influence of intrinsic decoherence on degree of entanglement. The exact results are employed to perform a careful investigation of the temporal evolution of the entropy. It is shown that the degree of entanglement is very sensitive to the changes of the intrinsic decoherence. The results show that the effect of the intrinsic decoherence decreases the quasiperiod of the entanglement between the atom and the field. The general conclusions reached are illustrated by numerical results.
In the actual design and manufacturing of spiral bevel and hypoid gears, the real tooth flank form geometry inevitably deviate from their theoretical or master target one, due to machine tolerances and systematic flexibility, heat treatment distortions, variation of cuttings forces and other noise factors. This deviation in normal direction is tooth flank form error which can cause some detrimental effects on tooth contact performances. Particularly, once the edge contact or highly concentrated stresses occurs, it will result in noisy operation and premature failure. This paper presents an accurate systematic CMM measurement method to prescribe and data-driven control the tooth flank form error. Firstly, the accurate measurement positioning is developed as an important step in whole measurement. And then, a data-driven programming is performed to prescribe a flank grid in CMM measurement. Where, this programming includes: (i) UMC machine settings are used to establish a universal tooth flank model, (ii) NURBS fitting and stitching approach is employed to accurate explicit flank expression, and (iii) flank parameterization using the steepest descent method with Newton step is proposed to identify flank grid points. Moreover, to distinguish with the conventional methods, a high-order machine setting modification considering residual tooth flank form error is proposed to get a flexible compensation of tooth flank form error. Given numerical test can verify the proposed methods.
A cathode of zinc-air fuel cells (ZAFCs) comprises a catalyst layer and a diffusion layer. We propose a new type of cathode, which overcomes the disadvantages of a double-layer cathode used in ZAFCs. To improve the performance of the single-layer cathode, dispersing the particles and reducing their size in the cathode mixture were conducted. The single-layer cathode had the same hydrophobicity as with the diffusion layer of the double-layer cathode and showed better electrochemical properties than the catalyst layer of the double-layer cathode. The single-layer cathode had a dense microstructure and a flat surface. The electrochemical performance and mechanical strength of the single-layer cathode were superior to those of a double-layer cathode. We showed single-layer cathode cell had better electrochemical performance than the double-layer cathode cell through a newly designed flexible-tubular-type ZAFC.
This paper presents new results on some aspects of the properties of the entropy squeezing in the time development of a degenerate two-photon of a single-mode interacting with a two-level system with a nonlinear medium. A general analytic expression for the density matrix is obtained on the basis of a Hamiltonian generalized in that it includes nonlinear effects and Stark shifts, by means of which we identify and numerically demonstrate the region of parameters where significantly large squeezing can be obtained. The influence of various parameters on the entropy squeezing are explored. It is shown that features of the entropy squeezing were influenced significantly by changing the nonlinear medium, Stark shift and the detuning. The results show that, certain amounts of the nonlinear effect yield the superstructure of atomic Rabi oscillation and changes the quasiperiod of the entropy evolution and atomic inversion.
Electrochemical machining is a unique prevalent nonconventional manufacturing process used in different industries involving various process parameters, which greatly influence machining performance. Therefore, selection of proper and optimal parameters setting is a challenging issue. In this paper, differential evolution algorithm is applied to look for the optimum solution to this problem. Four parameters, i.e. voltage, tool feed rate, electrolyte flow rate, and electrolyte concentration; and two machining criteria, i.e. material removal rate and surface roughness (Ra) are considered as input variables and responses, respectively. The main purpose is to maximize material removal rate and minimize Ra to achieve better machining performance. In this way, comprehensive mathematical models have first been developed using response surface methodology through experimentation based on central composite design plan. Then, differential evolution algorithm has been utilized for optimizing the process parameters; both single- and multiobjective optimizations are considered, and optimal Pareto front is determined. Finally, optimization result of a trade-off design point in the Pareto front of Ra and material removal rate was also verified experimentally. This machined surface was examined with field-emission scanning electron microscope images. The results showed that the proposed approach is an effective and suitable strategy for optimization of the electrochemical machining process.
To improve the machining accuracy and production efficiency of face gears, this article presents a generating milling method for the spur face gear using a five-axis computer numerical control milling machine and proposes a milling principle of the spur face gear using a milling cutter. Based on the milling principle and theory of gearing, a mathematical model of the spur face gear milling cutter is established, and the design parameters of the cutter are determined. Considering the requirements of machine motion during the face gear milling process, a five-axis computer numerical control milling machine is developed to produce the face gear. Based on the structure of the milling machine, a mathematical model of the spur face gear is established, and a milling method is proposed. The spur face gear milling cutter is manufactured, and the face gear milling experiments are conducted on the self-developed milling machine. The measurement results of the tooth surface deviations indicate that the maximum deviation is 22.6 µm, and that the machined spur face gear accuracy can meet the requirements of roughing. The experimental results verify the validity of the proposed generating milling method and demonstrate that the generating milling method is an effective approach to improve the accuracy and efficiency of the spur face gear.
The conjugate meshing face-gear pairs are implemented to high shaft angle intersecting axis gears such as the pericyclic transmission system. The meshing face-gear pair tooth surfaces are generated with a mutually conjugate spur shaper. The established tooth geometry and the dimensions of the conjugate face-gear pairs are summarized in this article. Four different example face-gear pairs are generated at various shaft angles and numbers of tooth combinations. Tooth bending stresses of these face-gear pair teeth are investigated based on finite element analysis methods. In these analyses, only single pairs of teeth are investigated. These results are compared to analog the spur gear tooth bending stresses calculated by finite element analysis and standard spur gear stress formulas. Meshing face-gear pair single tooth bending stress levels show approximately 3% to 6% difference from same size spur gear tooth.
The face load factor is a common coefficient used in gear design standards that takes into account the uneven distribution of load across the face width of the gears caused by the mesh misalignment. In this paper, a finite element model that includes the gears and the corresponding shafts is proposed. The results obtained from the application of finite element analysis to this model are compared with those obtained from application of the ISO Standard 6336 coefficient-based method (Method C). The influence of the length of gear shafts, the face width of the gears, the relative position of the gears over their shafts, the ratio between the pitch radii of the gears and the radii of their shafts, and the relation between the mesh misalignment and the face load factor, have been investigated.
In the current study, differently from the conventional manufacturing methods, cutting of spur gear by the end mill in the
computer numerically controlled (CNC) vertical milling machine was purposed. For this aim, two different approaches, radial
and axial cutting methods, were introduced. However, the cutting process is performed by use of only the radial cutting method.
Parametric equations of tool paths for cutting the spur gear were derived. Regarding those equations, by using the macro-program
of the Dyna 2009 Myte type CNC milling machine, a CAM program is developed. By varying the parameters in the tool paths such
as module, number of teeth, face width of the spur gear, cutting depth, and cutting angle, spur gear was cut and the production
time was obtained. Furthermore, the dimensions of new manufactured spur gear were measured by gear tooth vernies. The dimensions
were also calculated by using mathematical expressions and it was concluded that the measured values are well agreeable with
the calculated values. It was observed that the production time increases with increasing the module value or number of teeth
and decreasing the cutting angle or the cutting depth.
KeywordsSpur gear cutting–End mill–CNC milling machine–Production times
We analyze a controllable generation of maximally entangled mixed states of a circuit containing two-coupled superconducting charge qubits. Each qubit is based on a Cooper pair box connected to a reservoir electrode through a Josephson junction. Illustrative variational calculations were performed to demonstrate the effect on the two-qubits entanglement. At sufficiently deviation between the Josephson energies of the qubits and/or strong coupling regime, maximally entangled mixed states at certain instances of time is synthesized. We show that entanglement has an interesting subsequent time evolution, including the sudden death effect. This enables us to completely characterize the phenomenon of entanglement sharing in the coupling of two superconducting charge qubits, a system of both theoretical and experimental interest. Comment: 11 pages, 7 figures
Face gear drive and its research developments in domestic
- Z Wang
- J W Liu
- R Liu
Wang Z, Liu JW, Liu R, et al. Face gear drive and its research developments in
domestic. Mach Des Manuf 2012;3:217-21.
The technology and development trend of electrochemical machining
- F H Yin
- L W Jiang
- Y F He
Yin FH, Jiang LW, He YF, et al. The technology and development trend of electrochemical machining. Mach Des Manuf Eng 2018;47:13-17.
The tooth surface error measurement and evaluation of spiral bevel gear based on three-coordinate measurement
- H Zhao
Zhao H. The tooth surface error measurement and evaluation of spiral bevel
gear based on three-coordinate measurement. J Mech Transm. 2011;35:21-6.
Key technologies of spiral bevel gear examination based on three-coordinate measuring machine
- G H Wu
- H Zhao
- Z Y Wu
Wu GH, Zhao H, Wu ZY. Key technologies of spiral bevel gear examination based on three-coordinate measuring machine. J HeFei Univ Sci Technol
2015;38:438-40.
Digital correction model of cathode for aeroengine blade electrolytic machining
- D Zhu
- Z Y Xu
Zhu D, Xu ZY. Digital correction model of cathode for aeroengine blade electrolytic machining. J Mech Eng 2011;20:192-8.
A qualitative perspective on the dynamics of a single-cooper-pair box with a phase-damped cavity
Abdel-Aty M. A qualitative perspective on the dynamics of a single-cooper-pair
box with a phase-damped cavity. J Phys A 2008;41:15-30.
Entanglement degree of a three-level atom interacting with paircoherent states with a nonlinear medium
Abdel-Aty M. Entanglement degree of a three-level atom interacting with paircoherent states with a nonlinear medium. Laser Phys 2001;11:871-8.