Influence of bit design on the stability of a rotary drilling system

Nonlinear Dynamics - This paper extends the RGD model originally proposed by Richard et al. (J Sound Vib 305(3):432–456, 2007, https://doi.org/10.1016/j.jsv.2007.04.015) to investigate...     

Finite-time stability of nonlinear systems with state-dependent delayed impulses

Nonlinear Dynamics - This paper addresses the issue of finite-time stability (FTS) and finite-time contractive stability (FTCS) of nonlinear systems involving state-dependent delayed impulsive...     

Leader-following formation control for second-order multiagent systems with time-varying delay and nonlinear dynamics

In this paper, the leader-following formation control problem for second-order multiagent systems with time-varying delay and nonlinear dynamics is considered. Two different cases of coupling topologies, fixed topology and switching topology, are analyzed. Based on the Lyapunov theory combined with the linear matrix inequality (LMI) method, sufficient conditions in terms of LMIs are given to ensure the multiagent systems can reach and maintain the desired formation. The simulation results are provided to demonstrate the effectiveness of the obtained theory results.     

Criticality of Hopf bifurcation in state-dependent delay model of turning processes

In this paper the non-linear dynamics of a state-dependent delay model of the turning process is analyzed. The size of the regenerative delay is determined not only by the rotation of the workpiece, but also by the vibrations of the tool. A numerical continuation technique is developed that can be used to follow the periodic orbits of a system with implicitly defined state-dependent delays. The numerical analysis of the model reveals that the criticality of the Hopf bifurcation depends on the feed rate. This is in contrast to simpler constant delay models where the criticality does not change. For small feed rates, subcritical Hopf bifurcations are found, similar to the constant delay models. In this case, periodic orbits coexist with the stable stationary cutting state and so there is the potential for large amplitude chatter and bistability. For large feed rates, the Hopf bifurcation becomes supercritical for a range of spindle speeds. In this case, stable periodic orbits instead coexist with the unstable stationary cutting state, removing the possibility of large amplitude chatter. Thus, the state-dependent delay in the model has a kind of stabilizing effect, since the supercritical case is more favorable from a practical viewpoint than the subcritical one.     

Bifurcation analyses on the chatter vibrations of a turning process with state-dependent delay

Bifurcation analyses are performed using the methods of multiple scales and harmonic balance in order to investigate the chatter vibration characteristics of a nonlinear turning system with state-dependent delay. In this study, the tool of the turning system is modeled as a two degrees of freedom oscillator and both the nonlinear stiffness and the nonlinear cutting force are considered. Prior to performing the bifurcation analyses, the nonlinear cutting force is appropriately expanded using a Taylor series, and an eigenanalysis is performed on the linearized system to obtain the linear stability boundaries. The bifurcation analyses are then performed and examined to explain the effect of state-dependent delay on the small- and large-amplitude behavior of the turning system. Analytic results derived from this study are validated through direct comparison with numerical results.     

含时滞反馈的楔式制动系统动力学分析

考虑含时滞反馈的影响,建立楔式制动系统动力学模型,运用多尺度方法对黏滑界面附近区域进行受迫主共振求解,分析时滞量、楔角与系统刚度对系统幅频响应的影响,应用Routh-Hurwitz判据分析系统稳定性的影响因素。基于解析解的分析表明:稳态幅值和稳定性边界都随时滞量发生周期性变化,周期内较大的时滞量引起鞍结分岔,并发展至不稳定多解;楔角和系统刚度增加引起主共振振幅增大,并扩大了不稳定区域。     

Soil-blade dynamics in reverse-rotational rotary tillage

Soil cutting and the clod crack formation process during reverse-rotational rotary tillage in a heavy clay soil were investigated. Of particular interest was the relationship between clod crack formation and tillage resistance during sequential rotations of the tillage blade. Investigation of the crack formation process is helpful to develop and to design more effective and high performance tillage methods. This paper describes two new discoveries. The first is that the tillage resistance showed a higher cross-correlation between sequential rotations within a certain distance of tilling, while there was little or no cross-correlation between different tillage plots that were separated more than 0.4 m. The forward distance of untilled soil that was disturbed by the tillage blade was estimated to be 36.4 mm. This is the distance of two tillage pitches. The second discovery involved the blade frequencies during tilling. Fluctuation in tillage resistance frequencies of a single blade was nearly equal to the predicted occurrence of crack intervals on the tilled clod's surface. This frequency was 120 Hz. When these frequencies were translated into the distance along the trochoid trajectory of the blade cutting edge, they were the same as the length of the clods tilled by the reverse-rotational rotary tiller. These minute vibrations in the tillage resistance were considered the important indexes for recognizing the tilled soil conditions and the tilled clod failure on the reverse-rotational rotary tiller. The analytical results of this paper will be utilized for the active occurrence of the cracks regarding with natural frequency of the blade and the operation condition of the reverse-rotational rotary tiller.     

On approximation of systems with delay and their stability

We study the problem of the approximation of differential equations with delay by a system of ordinary differential equations. We analyze the qualitative behavior of solutions of the original system and the approximating system and construct an algorithm for the investigation of the stability of solutions of systems with delay.Translated from Neliniini Kolyvannya, Vol. 7, No. 2, pp. 208–216, April–June, 2004.     

Fault estimation for rotary steerable drilling tool systems with strong vibrations and unknown terms

Nonlinear Dynamics - In this paper, the problem of gyro fault estimation is studied for the dynamic point-the-bit rotary steerable drilling tool system (DPRSDTS), and it is essentially the fault...     

Noise and stability in differential delay equations

We study the stability of linear stochastic differential delay equations in the presence of additive or multiplicative white and colored noise. Using a stochastic analog of the second Liapunov method, sufficient conditions for mean square and stochastic stability are derived.     

灌浆压力稳定性控制的流体力学模型研究

根据水泥浆液的Navier-Stokes方程及连续性方程,采用特征线法建立了灌浆管道非定常流动的动态流体力学模型.其中包括划分网格,单管混合问题的特征线差分法等,将整个灌浆管路简化为一系列描述管道、设备、灌浆孔、调节阀的非线性代数方程组,并采用 Newton-Raphson法进行了求解.基于该模型的 GYPC 控制系统可将波动的灌浆压力在短时间内调节控制在±0.02MPa范围内,表明该流体力学模型是合理与实用的.     

Consensus of second-order multi-agent systems with nonlinear dynamics and time delay

This paper aims at investigating the second-order consensus problem of the multi-agent systems with nonlinear dynamics. Since it is more difficult to obtain the velocity information compared with the position information in practical application, a very simple sufficient condition for updating the coupling gain of the velocity information exchange between each agent is firstly derived to achieve asymptotic consensus. Furthermore, communication delay of each agent is considered for velocity information exchange. The velocity signal from a virtual leader is introduced to reach the second-order consensus. All the above fundamental consensus criteria are guaranteed base on algebraic graph theory, matrix theory, and Lyapunov stability method. Two simulation examples are provided to demonstrate the effectiveness of the analytical results. The results obtained in this paper can be easily applied to various cases, which can facilitate practical designs for the second-order consensus.     

时滞线性系统振动主动控制的滑移模态方法

直接从时滞微分方程求解控制律，对时滞线性系统振动主动控制的滑移模态方法进行了研究，并给出了控制具体实现过程。推导出的切换面和控制律表达式中，除了包含有当前的状态反馈外，还包含有前若干步控制的线性组合。算例结果显示，所提控制方法能够较好地控制系统的峰值响应。且能够保证控制系统的稳定性；若按无时滞控制设计对地滞系统进行振动控制，系统响应有可能出现发散。     

Chaos RBF dynamics surface control of brushless DC motor with time delay based on tangent barrier Lyapunov function

Non-dimensional mathematical model of brushless DC motor (BLDCM) system is presented here. BLDCM is known to produce chaotic phenomenon under certain conditions. This paper fuses dynamic surface control, radial basis function neural network, and adaptive technology to control the BLDCM, which overcomes the repetitive differentiation of the nonlinear terms of backstepping and the boundedness hypothesis of control gain pre-determined. The tangent barrier Lyapunov function is also used for time-delay nonlinear system with parametric uncertainties. Simulation results under different conditions indicate that the proposed method works well to suppress chaos and effects of parameter variation.     

Nonlinear dynamics, stability and control of the scan process in noncontacting atomic force microscopy

The nonlinear equations of motion for the scan process in noncontacting atomic force microscopy are consistently derived using the extended Hamilton’s principle. A modal dynamical system obtained from the continuum model reveals that scan control appears in the form of parametric excitation. The system is analyzed asymptotically and numerically to yield escape bounds limiting the noncontacting mode of operation. Approximate stability bounds are deduced from both a global Melnikov integral and a local Moon–Chirikov overlap criterion. The Melnikov–Holmes stability curve and the overlap criterion are found to be similar for small damping. However, for very small damping, typical of ultra-high vacuum conditions, where the Melnikov bound becomes trivial, the Moon–Chirikov criterion yields an improved stability threshold.