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Governments all over the world usually establish the policy of subsidies to stimulate firms’ technology innovation behaviors. The participating firms may share the high risk of expense through cooperative technology innovation. Different forms of governmental subsidies may have a significant impact on the choice of firms’ cooperative innovation strategies. This paper investigates the effect of government subsidies on firms’ technology innovation strategies. We consider two modes of cooperative technology innovation (technology transfer or joint innovation) in a two-level supply chain including an upstream manufacturer (UM) and a downstream manufacturer (DM) in the presence of two forms of governmental subsidies (a per-unit production subsidy or an innovation subsidy). We find that in the presence of either form of governmental subsidy, technology transfer mode is better off for the UM than joint innovation mode when the UM’s distribution power is greater than a threshold, otherwise joint innovation mode is better off. In the presence of a given form of governmental subsidy, the DM’s response strategy is influenced by the interaction of different values of the proportion of revenue and the fraction of innovation cost. In the presence of a per-unit production subsidy, the social welfare is always more under technology transfer mode than under joint innovation mode, while in the presence of an innovation subsidy, the opposite is true. We also show that under a given cooperative innovation mode, both the UM and DM expect a per-unit production subsidy if the per-unit tax credit is high, and they expect an innovation subsidy if the proportion of governmental subsidy is high. Finally, we discuss the robustness of the theoretical results.

Chatter will cause a series of changes in machining state during the boring process. Due to the difference in the sensitivity and ability of various sensors to resist external interference, the change of machining environment can lead to variation in response and make difference to the characteristics of signal. Therefore, it is essential to extract the features related to chatter from the machining signals. In this study, the dynamic model considering the regenerative effect is constructed, based on which the relationship between the limited cutting width and the spindle speed is determined. In addition, eddy current displacement sensor, vibration acceleration sensor, and acoustic pressure sensor are applied to propose a feasible boring chatter monitoring scheme and collect the machining signals. The time and frequency domain of the collected signals are analyzed to determine the pattern of time–frequency variation for three kinds of sensor signals generated with chatter.

In the boring process, chatter is easy to occur because of the large overhang of the boring bar and the poor structural stiffness of the system. The key technique to reduce the chatter effect in boring process is to identify the chatter state accurately. In this paper, a method of chatter identification based on multi-sensor feature fusion and manifold learning is proposed. Displacement sensor, acceleration sensor, and acoustic pressure sensor are used to acquire processing signals synchronously, and then triple signals are decomposed by empirical mode decomposition (EMD). The multi-indicators are used to construct high-dimensional space, and then different manifold learning algorithms are used to reduce feature dimensionality. Support vector machine chatter identification models are obtained to verify the effect of boring chatter identification. Multi-sensor feature fusion realizes the complementary of different features and achieves better recognition results. The results show that the proposed method can identify boring chatter effectively. And the best result is obtained by the combination of the displacement sensor and acceleration sensor.

Chatter is one of the challenging topics in the field of metal cutting. The dynamic characteristics of five-axis milling system are complex and variable. Especially in high-speed milling process, the influence of the tool-workpiece interactions and speed effect on milling stability is more obvious. It is necessary to investigate the influence of various interaction effects on milling stability. In this paper, the dynamical model of spindle system was established, and then the model was applied to investigate the influence of gyroscopic effect and centrifugal force on the dynamical characteristics of the tool tip. In order to solve the chatter problem of five-axis flank milling, the extended dynamical model of five-axis flank milling which considers the tool-workpiece interactions and speed effect was established. Based on the established milling dynamical model, the influence mechanism of the spindle system-tool-workpiece interaction effects on five-axis flank milling stability was investigated. The stability lobe diagrams of five-axis flank milling which contains the tool-workpiece interactions and speed effect can be obtained. Experimental results show that the proposed five-axis flank milling dynamical model can predict the milling state more reliable than the traditional ones. The research results are of great significance in preventing five-axis flank milling chatter.

The main reason why supply uncertainty reduces supply chain performance is that it is difficult to estimate whether uncertain supply matches demand. Seldom do papers study retailers’ decision-selection problems according to the reliability of uncertain supply in satisfying demand. This paper considers the optimal decision selection of a retailer working with a main supplier facing supply uncertainty and a backup supplier whose yield is infinite or uncertain. The retailer can enforce demand management by adjusting prices, seeking the backup supplier to make up for the lack of products or mixing the two decisions. We provide the definition called the reliability level of serving the market (RLSM) to characterize the reliability of uncertain supply in satisfying market demand. Under different RLSMs, the participants maximize their profits based on a confidence level in three scenarios: benchmark, infinite backup supply and uncertain backup supply. Whether the main supplier determines the wholesale price or not, we find that in the benchmark, the retailer orders from the main supplier if the RLSM is low; otherwise, the retailer gives up purchasing the product. In the latter two scenarios, our results show that the particular order strategy chosen by the retailer depends on the values of the RLSM and that the retailer’s order quantity follows threshold rules. It is interesting that for different RLSMs, the retailer chooses either a price adjustment strategy, a backup supply strategy or neither of them but does not choose the mixed one, which is counterintuitive. We also derive the particular scenario that is good for the retailer by comparing the results in the three scenarios. Finally, a proper RLSM is suggested for the retailer to balance the reliability of serving the market and her profit.

Carbon-fiber reinforced silicon carbide matrix (C/SiC) composites are typical difficult-to-cut materials due to high hardness and brittleness. Aiming at the problem of the serious tool wear in conventional milling (CM) C/SiC composite process, ultrasonic vibration–assisted milling (UVAM) and conventional milling tests with a diamond-coated milling cutter were conducted. Theoretical and experimental research on the cutting force during the ultrasonic vibration milling process of C/SiC composites is carried out. Based on the kinematics analysis of tool path during ultrasonic vibration milling process, the cutting force model of ultrasonic vibration milling is established, and the influence mechanism of ultrasonic vibration on the cutting force is revealed. Based on the analysis of the evolution law of tool wear profile and wear curve during the traditional milling and ultrasonic vibration milling of C/SiC, the tool wear forms and mechanism of diamond-coated milling cutters in two processing modes and the influence mechanism of ultrasonic vibration on tool wear are revealed. It is found that the main wear mechanism of the diamond-coated milling cutter is abrasive wear, and the main wear form is the coating peeling. Compared with the traditional milling, the tool wear can be reduced by the ultrasonic vibration milling in machining process. In the range of test parameters, the tool wear decreases first and then increases with the increase of ultrasonic amplitude.

In five-axis ball-end machining, stability of the milling process is not only determined by the combination of depth of cut and the spindle speed, but also determined by the lead and tilt angles of the milling tool (i.e., the tool orientations). As the degree of freedom increases, five-axis machining machines have more complex dynamic characteristics. Therefore, the influence of the tool-workpiece interactions on the machining performance is more obvious. In this paper, a new five-axis ball-end milling dynamical model which considers the multiple interactions between the tool and workpiece is established for the first time. Based on the established dynamical model, the effects of regenerative effect, structural mode coupling and process damping on the dynamic characteristics of five-axis milling are investigated. In addition, the effects of lead angle and tilt angle on the stability prediction of five-axis milling are investigated. The experimental results show that the proposed five-axis milling dynamical model is more reliable than the traditional one in predicting the stability of five-axis milling.

Assembly clearance has a great influence on the performance of precision parts. Improper assembly clearance affects the working state and induces failure of parts. A method to analyze the assembly clearance of the precision spherical coupling parts by analyzing the points cloud was proposed. The least square center was used to find a rough center. Accurate center was searched near the least square center by the particle swarm optimization (PSO) algorithm based on the minimum zone method. Radical clearance and Z clearance of precision spherical coupling parts were calculated. Furthermore, the dynamic change of assembly clearance was also calculated by rotating the parts. The sphericity error evaluation results were improved obviously compared with other results. The accuracy of the evaluation results improved 4.51%∼28.97%.

Cross-shaped chisel edge thinning is an effective method to improve the drilling performance of non-coaxial helical flank micro-drill. In order to study the effect of the cross-shaped chisel edge on drilling performance, the mathematical model of cross-shaped chisel edge is proposed. The rake angle, lip inclination angle, uncut chip thickness, and uncut chip width are calculated by MATLAB software. Finite element models of four kinds of micro-drills with a different thinned chisel edge are established using DEFORM-3D software, and micro-drilling simulations on 304 austenitic stainless steel are carried out. The simulation results show that with a decrease in chisel edge length, the drilling force, tool temperature, tool wear, and curl degree of the chip are clearly reduced. However, for micro-drill without chisel edge, the torque and tool temperature are larger than other micro-drills, and string chips are generated during the drilling process. Furthermore, the non-coaxial helical flank micro-drill with an optimal cross-shaped chisel edge is manufactured by a six-axis CNC grinding machine, and the measurement results indicate that the geometrical parameters meet the designed values. At last, the micro-drill with an optimal cross-shaped chisel edge has a satisfactory drilling performance by the micro-drilling experiment.

The stability of micro-milling has an important influence on the machined surface, and choosing proper machining parameters can effectively avoid machining process instability and dynamic error. The frequency response function (FRF) of micro-milling tool point varies with tool overhang lengths, and it affects stability lobe diagram (SLD) of the machining system. During the micro-milling process, the cutting thickness was divided into the shearing zone and the plowing zone. In the shearing zone, the cutting thickness was calculated with considering cycloidal tool path and dynamic cutting thickness. After the micro-milling force model was established, the receptance coupling substructure analysis (RCSA) and experimental modal analysis (EMA) were used to obtain the FRFs at the micro-milling tool point. The 2 three-dimensional diagrams, SLD and surface location error (SLE), were developed comprehensively by means of frequency domain method, and the flank micro-milling experiments were carried out. The validity of the three-dimensional SLD containing tool overhang length and the prediction model of SLE was verified by the experimental results, and surface topography was characterized to show the actual machining state. The experimental results show that, compared with SLE, the change of tool overhang length had more significant influence on SLD, and the chatter remarks were not very obvious on the bottom of the workpiece no matter whether the machining process was stable or not. In unstable region, chatter caused by cutting tool left marks on the machined surface. Under the condition of stable milling, a machined surface with smaller SLE and better topography was obtained. The 2 three-dimensional diagrams can provide good references for the selection of optimal tool overhang length and machining parameters comprehensively.

Chatter is a kind of self-excited vibrations which is related to regenerative effect, mode coupling effect, and process damping, etc. To predict milling chatter more accurately, a suitable dynamical model of milling process which can reflect the practical chatter mechanism should be obtained firstly. In this paper, a new milling dynamical model which simultaneously considers the regenerative effect, mode coupling effect, and process damping is established. Based on the new dynamical model and the updated full-discretization method (FDM), the coupling influences of regenerative effect, mode coupling effect, and process damping on the accurate of the stability lobe diagrams (SLDs) for up-milling and down-milling operations are investigated. A series of numerical simulation and experiments are carried out to verify the accuracy of the proposed milling dynamical model. The experiment results show that the mode coupling effect and process damping have great influences on the prediction of milling stability. The SLD which obtained by the new milling dynamical equation (considering the regenerative effect, mode coupling, and process damping) is more accurate than that which obtained by only considering the regenerative effect.

In this paper, a method is given to predict the surface topography in flank milling based on the experiment data of Al7075. First, the kinematic topography of the machined surface is analyzed with dexel model by CutS. Then, the measured stochastic topography is described by four-distribution-moment Gaussian distribution and quadratic regression is used to fit the values. Abbott curve is applied in pseudo random number generation to create the simulated stochastic topography. Finally, the combination of the kinematic and stochastic topography is calculated by material removal simulations (MRS) and is used to predict the real measured topography. The results show that the roughness of the stochastic topography increases with an increased feed per tooth and depth of cut, and the combined topography mostly matches to the measured one within the proposed method.

Chatter is undesirable self-excited vibrations, which always lead to adverse effects during milling process. Selecting a reasonable combination of cutting parameters is an effective way to avoid chatter. Based on the mathematical model of milling process and the Floquet theory, the stable cutting area can be determined. The stability lobe diagrams (SLD) could be obtained by different interpolation methods. To study the effect of higher order interpolation methods on the accuracy and efficiency of milling stability prediction, the state item, the time-delayed item, and the periodic-coefficient item of the state-space equation are approximated by different higher order interpolation methods, respectively. The calculations show that when the state item is approximated by the third-order Hermite interpolation polynomial, third-order Newton interpolation of the time-delayed item can improve the accuracy of SLD, while higher order interpolation of periodic-coefficient item has negative effect on improving effectiveness and efficiency compared to high-order interpolation of the state item and the time-delayed item. In order to obtain the SLD of milling process more accurately, an updated full-discretization milling stability prediction method which based on the third-order Hermite-Newton interpolation polynomial approximation is proposed in this paper. By dividing the tooth passing period equally into a finite set of time intervals, the third-order Hermite interpolation polynomial and the third-order Newton interpolation polynomial are utilized in each time interval to estimate the state item and the time-delayed item, respectively. The comparison of convergence rate of the critical eigenvalues and the SLD of the proposed method between the existing methods is carried out. The results indicate that the proposed method show a faster convergence rate than that of other methods, and its SLD is more close to the ideal ones with small number of time intervals.

Based on third-order Newton interpolation polynomial and direct integration scheme (DIS), this paper proposes a method to generate stability lobe diagram in milling process. The dynamic model of milling process with consideration of regeneration effect is described by time periodic delay-differential equation (DDE). Then, the DDE is rewritten as state space equation by a transformation. After equally discretizing the time delay into a series of small time intervals, the state space equation of milling system is integrated on the small time interval. Both the state term and delayed term are interpolated by third-order Newton interpolation polynomial, and the periodic-coefficient matrix is interpolated by first-order Newton interpolation polynomial. The state transition matrix which reflects the discrete mapping relation of dynamic responses for current tooth pass period and immediate previous tooth pass period is obtained directly. The accuracy of the proposed method is evaluated by comparing with benchmark methods in terms of the rate of convergence. The efficiency of the proposed method is verified through the comparison of computational time with existing methods. The proposed method is proved to be an accurate and efficient method by the comparison results. The distinction between up-milling and down-milling operations is also analyzed by comparing the stability lobe diagrams for these two operations. Besides, according to the analysis of rate of convergence, the number of substitutions, which are used to convert the variables located out of the required range into the required range, may affect the results of stability lobe diagrams. Moreover, the stability lobe diagram cannot be generated by using fourth-order updated full-discretization method.

Chatter is a kind of self-excited unstable vibration during machining process, which always leads to multiple negative effects such as poor surface quality, dimension accuracy error, excessive noise, and tool wear. For purposes of monitoring the processing state of milling process and detecting chatter timely, a novel online chatter detection method was proposed. In the proposed method, the acceleration signals acquired by sensor were decomposed into a series of intrinsic mode functions (IMFs) by the adaptive analysis method named ensemble empirical mode decomposition (EEMD), and the IMFs which contain the feature information of milling process were selected as the analyzed signals. The two indicators power spectral entropy and fractal dimension which is obtained by morphological covering method are introduced to detect the chatter features. Then, both the frequency characteristic and morphological feature of the extracted signals can be reflected by the two indicators. To verify the approach, milling experiments were performed; the experiment results show that the proposed method can detect chatter timely and effectively, which is important in the aspect of improving the milling quality. And finally, in order to detect milling chatter timely, an online milling chatter monitoring system was developed.

Based on orthogonal polynomial approximation scheme, this paper presents several stability prediction methods using different kinds of orthogonal polynomials. The milling dynamics with consideration of the regenerative effect is described by time periodic delay-differential equations (DDEs). Firstly, this work employs the classical Legendre and Chebyshev polynomials to approximate the state term, delayed term, and periodic-coefficient matrix. With the help of direct integration scheme (DIS), the state transition matrixes which indicate the mapping relations of the dynamic response between the current tooth pass and the previous tooth pass are obtained. The stability lobe diagrams for single degree of freedom (DOF) and two DOF milling models are generated by using the Legendre and Chebyshev polynomial approximation-based methods. The rate of convergence of the Legendre and Chebyshev polynomial-based methods is compared with that of the benchmark first-order semi-discretization method (1stSDM). The comparison results indicate that the rate of convergence and the numerical stability of the Legendre and Chebyshev polynomial-based methods are both need to be improved. In order to develop new methods with high rate of convergence and numerical stability base on DIS, the monic orthogonal polynomial sequences are constructed by using Gram-Schmidt orthogonalization to approximate the state term, delayed term, and periodic-coefficient matrix. The rate of convergence and the computational efficiency of the monic orthogonal polynomial-based methods are evaluated by comparing with those of the benchmark 1stSDM. The results turn out that the monic orthogonal polynomial-based methods are advantageous in terms of the rate of convergence and numerical stability. The stability lobe diagrams for single DOF and two DOF milling models obtained by the monic orthogonal polynomial-based methods are compared with those obtained by the 1stSDM. Finally, the monic orthogonal polynomial-based methods are proved to be the effective and efficient methods to predict the milling stability.

This paper presents a study of the Taguchi application to optimize surface quality based on fractal theory in meso-scale end-milling operation. Usually, the surface quality is characterized by roughness, but in the meso-scale area, the size of the workpiece will be difficult to meet the requirements of the sampling length, which will have a huge influence on the characterization results. Although there are many algorithms for adjusting, the operation process is very cumbersome; for this reason, characterization method based on fractal theory is introduced and applied to evaluate the machined surface in the research. Also, the Taguchi method is applied to search the optimal parameters combination, during which spindle speed, depth of cut, and feed rate are considered as the control factors. Specifically, firstly, the machining surface characterization method based on fractal theory is introduced in details; then, an orthogonal array of L25(53) is used for the experimental study; through ANOVA analyses, the significant factors which affect surface quality are established, and the optimal cutting parameter combination is determined; later, confirmation tests are carried out to verify the applicability of the characterization methods for the meso-scale cutting surface. Research shows that fractal characterization method is better to evaluate the surface quality in the meso-scale.

With the rapid development of aerospace technology, Al7075 has been widely used for structural components. High-speed milling is one of the most effective ways to improve machining efficiency of Al7075. During the milling process, regenerative chatter which restricts the milling quality and productivity often occurs. With the aim of avoiding regenerative chatter, stability lobe diagram (SLD) is widely used to obtain chatter-free parameters. This work presents a stability prediction method by using shifted Chebyshev polynomials. The milling dynamics with consideration of the regenerative effect is described by time periodic delay-differential equations (DDEs). The transition matrix of the milling system is constructed with the help of Chebyshev–Gauss–Lobatto (CGL) points. In order to demonstrate the accuracy of the proposed method, the rate of convergence of the proposed method is compared with that of the classical benchmark methods. On the other hand, in the process of thin-walled workpiece milling, the dynamic behavior of the workpiece depends on the tool position. To study the influence of the tool position dependent dynamics on the chatter stability of the thin-walled workpiece, a three-dimensional SLD is obtained. The verification experiments are conducted to verify the reliability of the proposed method. The results show that the experimental results are consistent with the predicted results.

In precision manufacturing industry, requirements for surface quality are very high. It is important to accurately predict the machined surface errors to reduce manufacturing costs and lead times as well as develop fixturing scheme to optimize machining quality. This paper presents a contribution for predicting the machined surface errors where fixture-workpiece system dynamic effects during milling process are considered. The combined effect of clamping and milling on machined surface errors prediction is taken into account, and finite element analysis is developed to analyze the workpiece deformation. In finite element analysis environment, the static analysis and explicit dynamic analysis are used to calculate the static deformation due to clamping force and the dynamic deformation due to milling force. Milling forces are applied to the manufacturing points step by step. The chip removal effect is taken into account based on element death technique, and every fixture locator is modeled as a virtual spring-damper system to emulate the fixture-workpiece contact points. The developed methodology has been verified by a set of end milling experiments for ten fixture layouts. The measured and predicted results are in good agreement, and the results also illustrate that the closer the triangle formed by the three locators in the primary datum is to an equilateral triangle, the smaller machined surface errors will be.

In the face milling of large low-rigidity aluminium alloy parts, the heat generated is one of the most important issues and leads to thermal expansion of the workpiece and the serious reduction of dimensional and geometrical precision. In this paper, a new heat transfer analytical model for face milling was established based on the heat source method, in which the cutting edge of the machine tool was considered as a finite-length rotating line heat source. Then, a transient numerical simulation was also conducted to predict the temperature field on the machined surface in single-tooth and multi-tooth milling by using the finite-element method (FEM). Finally, experiments involving the measurement of the aluminium alloy milling temperature were performed using a semi-artificial thermocouple, in which the hot end of the thermocouple was embedded into the machined surface to obtain the instantaneous face milling temperature. Those experimental results exhibited good agreement with the results from the theoretical analytical model and numerical simulation.

An investigation is carried out to analyze and quantify the wear mechanisms of resin-bonded diamond wheel in Elliptical Ultrasonic Assisted Grinding (EUAG) of monocrystal sapphire. The EUAG is a new grinding method proposed by the present authors in which an elliptical ultrasonic vibration is imposed on the workpiece by using an elliptical ultrasonic vibrator. In this paper, a series of grinding experiments under the presence/absence of ultrasonic vibration assistance are performed. The grinding forces and work-surface roughness are measured, and the wheel surface is examined too. The experimental results indicate that during grinding, the steady process region performed in EUAG is longer than that in Conventional Grinding (CG) by 20%, meaning that the grinding wheel has a longer sharp cutting period in EUAG. It is validated that the main wear mechanisms in EUAG is micro-fracture and cleavage of abrasive grains, which has a positive effect on the better grinding performance, such as lower grinding forces, force ratio Fn/Ft, wheel loading, and smoother work-surface. This study demonstrates that the improved grinding performance of diamond wheel can be realized by using EUAG method.