So the feedback control force is (11)Formula (11) being put into Formula (4),Its result is (12)It can be seen from Formula (12) that under a constant gain negative velocity feedback control law, the system damping is composed of two parts: the damping of the structure itself, the equivalent damping from the feedback force.

Response analysis in the frequency domain is also studied by using random vibration theory,from two aspects of vibrartion-absorbing coefficient and equivalent damping ratio to study the effect of μ_d 、 λ_d 、ζ_d and φ_(k_1) to vibration control.

So the feedback control force is (11)Formula (11) being put into Formula (4),Its result is (12)It can be seen from Formula (12) that under a constant gain negative velocity feedback control law, the system damping is composed of two parts: the damping of the structure itself, the equivalent damping from the feedback force.

Response analysis in the frequency domain is also studied by using random vibration theory,from two aspects of vibrartion-absorbing coefficient and equivalent damping ratio to study the effect of μ_d 、 λ_d 、ζ_d and φ_(k_1) to vibration control.

The effects of a small "artificial" damping on the response, and the possibilities of an "equivalent" damping for the friction-affected constraints are also examined.

An increase in the kinematic viscosity of the filling liquid, or a decrease in the size of the particles of the filling solid, will result in a corresponding increase in the equivalent damping factor of the system.

This was evidenced by the measurements of the energy absorbed in the hysteresis loops, equivalent damping, and the stiffness and damping obtained from the free-vibration test.

It is shown that the equivalent damping ratio increases inproportion to the square of frequency.

The concept of an equivalent damping related to the delay feedback is proposed and the appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control.

A theory for describing deformation behaviour of sands under cyclic loading is proposed on the basis of the assumption that the permanent deformation of sands after each cycle of loading is mainly determined by the effctive stress states at the peak and the valley of that cycle of loading and a loading history parameter named as effective number of cycles. A series of cyclic triaxialtests on a medium sand has been per- formed in order to estabilish two sets of empirical relationships required in this theory....

A theory for describing deformation behaviour of sands under cyclic loading is proposed on the basis of the assumption that the permanent deformation of sands after each cycle of loading is mainly determined by the effctive stress states at the peak and the valley of that cycle of loading and a loading history parameter named as effective number of cycles. A series of cyclic triaxialtests on a medium sand has been per- formed in order to estabilish two sets of empirical relationships required in this theory. The first one, giving the expressions for mean shear modulus and equivalent damping ratio, is derived from the model proposed by Hardin and Drnevich with a revision to consider the coaction of cyclic normal stress and cyclic shear stress. The second one gives the expression for increments of permanent volumetric strain and deviatorie strain, taking account of the influence of assymetry of stress levels at the peak and the valley of loading in each cycle. The theory may be used to predict the liquefaction potential and deformation of sands subjected to repeated loading under plane strain condition.

文中探讨了建立砂土动力应变关系的途径,并根据砂土的动力变形主要取决于每个荷载循环中动应力达到峰值和谷值时的有效应力状态的假设,提出一个计算动力变形的平均发展过程的理论。从这一理论出发,根据一种砂料的三轴反复荷载试验结果,建议了一组计算残余体应变和残余剪应变的经验公式,并对哈定和达尼维奇(Hardin and Drnevich)的动剪切横量公式进行了修改。这些公式可以用于计算低频动荷载作用下砂土的液化和变形。

In this paper, based on the detailed analysis of the dynamic cutting force of the helical tooth end milling cutters and its direction coefficients, a method of analysing the behaviour of regenarative chatter for helical tooth end milling cutters with waved cutting edges is proposed.The cutting tests are carried out to check the theoretical analysis on validity and they have proved to be in good agreement with the results calculated from the theoretical analysis. The results obtained are summarized as follows:...

In this paper, based on the detailed analysis of the dynamic cutting force of the helical tooth end milling cutters and its direction coefficients, a method of analysing the behaviour of regenarative chatter for helical tooth end milling cutters with waved cutting edges is proposed.The cutting tests are carried out to check the theoretical analysis on validity and they have proved to be in good agreement with the results calculated from the theoretical analysis. The results obtained are summarized as follows: 1. The proposed theoretical formulae for the calculations of instantane -ous and mean direction coefficients can be applied to up- and down- milling operations with helical tooth end milling cutters. By using these formulae the relations between the chatter and cutting conditions can be found, which enables us to select the optimum cutting conditions easily. 2. The equation which can be applied to the determination of the critical width of cut for helical tooth end milling cutters with waved cutting edges is given below: Where: Kd is the coefficient of chip thickness, b is the critical width of cut, D is the equivalent damping ratio, K is the equivalent static stiffness, Rm is the mean direction coefficient, Z is the number of teeth, ψ is the phase shift between the two vibration waves in successive cutting teeth, ξ is the ratio between the length of the chip and the lead of the waved cutting edges, ηi, η2, ……,ηz are the ratio between the partial length on the underside of the chip and the length of the chip respectively. 3. It is dear from the theoretical analysis and the experimental results th at the critical width of cut for the helical tooth end milling cutters with waved cutting edges is considerably larger than that of the conventional milling cutters. Practically, this method of analysis can also be applied to the determination of the chatter behaviour for the helical tooth end milling cutters with any kinds of grooves on the cutting edges and it may be expected o obtain the similar results mentioned above.

This paper describes the method and process by which dynamic parameters of the spindle-case system of lathe are identified. An experiment on unconstrained (free) steady-state excitation has been made for the system mentioned by means of a transfer function analysis instrument, and impedance figure has been plotted. According to the impedance figure, mechanical and mathematical models of the structural system are established, and the accuracy of the mathematical model is verified. Based on the experimental-results,...

This paper describes the method and process by which dynamic parameters of the spindle-case system of lathe are identified. An experiment on unconstrained (free) steady-state excitation has been made for the system mentioned by means of a transfer function analysis instrument, and impedance figure has been plotted. According to the impedance figure, mechanical and mathematical models of the structural system are established, and the accuracy of the mathematical model is verified. Based on the experimental-results, the structural system is simlified as a mechanical model involving three masses, three springs and two dashpots. In this paper the contact stiffnesses and impedances between the rotors of the front and the rear bearings of the spindle, the inner and the outer rings, as well as the contact stiffnesses and impedances between the inner and the outer rings of the bearings and the spindle-case are simplified to equivalent spring stiffnesses and equivalent dampings. The equivalent stiffness coefficients and the equivalent damping coefficients of their supports are determined quantitatively.