The present paper deals with the problem of nonparametric kernel density estimation of the trend function for stochastic processes driven by fractional Brownian motion of the second kind.The consistency,the rate of co...The present paper deals with the problem of nonparametric kernel density estimation of the trend function for stochastic processes driven by fractional Brownian motion of the second kind.The consistency,the rate of convergence,and the asymptotic normality of the kernel-type estimator are discussed.Besides,we prove that the rate of convergence of the kernel-type estimator depends on the smoothness of the trend of the nonperturbed system.展开更多
A nonlinear lateral-torsional coupled vibration model of a planetary gear system was established by taking transmission errors,time varying meshing stiffness and multiple gear backlashes into account.The bifurcation d...A nonlinear lateral-torsional coupled vibration model of a planetary gear system was established by taking transmission errors,time varying meshing stiffness and multiple gear backlashes into account.The bifurcation diagram of the system's motion state with rotational speed of sun gear was conducted through four steps.As a bifurcation parameter,the effect of rotational speed on the bifurcation properties of the system was assessed.The study results reveal that periodic motion is the main motion state of planetary gear train in low speed region when ns<2 350 r/min,but chaos motion state is dominant in high speed region when ns>2 350 r/min,The way of periodic motion to chaos is doubling bifurcation.There are two kinds of unstable modes and nine unstable regions in the speed region when 1 000 r/min<ns<3 000 r/min.展开更多
The design and fabrication processes of a novel scanner with minimized coupling motions for a high-speed atomic force microscope （AFM） were addressed. An appropriate design modification was proposed through the anal...The design and fabrication processes of a novel scanner with minimized coupling motions for a high-speed atomic force microscope （AFM） were addressed. An appropriate design modification was proposed through the analyses of the dynamic characteristics of existing linear motion stages using a dynamic analysis program, Recurdyn. Because the scanning speed of each direction may differ, the linear motion stage for a high-speed scanner was designed to have different resonance frequencies for the modes, with one dominant displacement in the desired directions. This objective was achieved by using one-direction flexure mechanisms for each direction and mounting one stage for fast motion on the other stage for slow motion. This unsymmetrical configuration separated the frequencies of two vibration modes with one dominant displacement in each desired direction, and hence suppressed the coupling between motions in two directions. A pair of actuators was used for each axis to decrease the crosstalk between the two motions and give a sufficient force to actuate the slow motion stage, which carried the fast motion stage, A lossy material, such as grease, was inserted into the flexure hinge to suppress vibration problems that occurred when using an input triangular waveforrn. With these design modifications and the vibration suppression method, a novel scanner with a scanning speed greater than 20 Hz is achieved.展开更多
基金Supported by the National Natural Science Foundation of China(12101004)the Natural Science Research Project of Anhui Educational Committee(2023AH030021)the Research Startup Foundation for Introducing Talent of Anhui Polytechnic University(2020YQQ064)。
文摘The present paper deals with the problem of nonparametric kernel density estimation of the trend function for stochastic processes driven by fractional Brownian motion of the second kind.The consistency,the rate of convergence,and the asymptotic normality of the kernel-type estimator are discussed.Besides,we prove that the rate of convergence of the kernel-type estimator depends on the smoothness of the trend of the nonperturbed system.
基金Project(50775108) supported by the National Natural Science Foundation of China
文摘A nonlinear lateral-torsional coupled vibration model of a planetary gear system was established by taking transmission errors,time varying meshing stiffness and multiple gear backlashes into account.The bifurcation diagram of the system's motion state with rotational speed of sun gear was conducted through four steps.As a bifurcation parameter,the effect of rotational speed on the bifurcation properties of the system was assessed.The study results reveal that periodic motion is the main motion state of planetary gear train in low speed region when ns<2 350 r/min,but chaos motion state is dominant in high speed region when ns>2 350 r/min,The way of periodic motion to chaos is doubling bifurcation.There are two kinds of unstable modes and nine unstable regions in the speed region when 1 000 r/min<ns<3 000 r/min.
基金Work(R0A-2007-000-20042-0) partly supported by the Second Stage of Brain Korea 21 Projectspartly by the Korea Science and Engineering Foundation (KOSEF) through the National Research Laboratory Program funded by the Ministry of Science and Technology of Korea
文摘The design and fabrication processes of a novel scanner with minimized coupling motions for a high-speed atomic force microscope （AFM） were addressed. An appropriate design modification was proposed through the analyses of the dynamic characteristics of existing linear motion stages using a dynamic analysis program, Recurdyn. Because the scanning speed of each direction may differ, the linear motion stage for a high-speed scanner was designed to have different resonance frequencies for the modes, with one dominant displacement in the desired directions. This objective was achieved by using one-direction flexure mechanisms for each direction and mounting one stage for fast motion on the other stage for slow motion. This unsymmetrical configuration separated the frequencies of two vibration modes with one dominant displacement in each desired direction, and hence suppressed the coupling between motions in two directions. A pair of actuators was used for each axis to decrease the crosstalk between the two motions and give a sufficient force to actuate the slow motion stage, which carried the fast motion stage, A lossy material, such as grease, was inserted into the flexure hinge to suppress vibration problems that occurred when using an input triangular waveforrn. With these design modifications and the vibration suppression method, a novel scanner with a scanning speed greater than 20 Hz is achieved.
