Numerical and Experimental Study of Clearance Nonlinearities Based on Nonlinear Response Reconstruction

With the growing structural complexity and growing demands on structural reliability, nonlinear parameters identification is an efficient approach to provide better understanding of dynamic behaviors of the nonlinear system and contribute significantly to improve system performance. However, the dynamic response at nonlinear location, which cannot always be measured by the sensor, is the basis for most of these identification algorithms, and the clearance nonlinearity, which always exists to degrade the dynamic performance of mechanical structures, is rarely identified in previous studies. In this paper, based on the thought of output feedback which the nonlinear force is viewed as the internal feedback force of the nonlinear system acting on the underlying linear model, a frequency-domain nonlinear response reconstruction method is proposed to reconstruct the dynamic response at the nonlinear location from the arbitrary location where the sensor can be installed. For the clearance nonlinear system, the force graph method which is based on the reconstructed displacement response and nonlinear force is presented to identify the clearance value. The feasibility of the reconstruction method and identification method is verified by simulation data from a cantilever beam model with clearance nonlinearity. A clearance test-bed, which is a continuum structure with adjustable clearance nonlinearity, is designed to verify the effectiveness of proposed methods. The experimental results show that the reconstruction method can precisely reconstruct the displacement response at the clearance location from measured responses at reference locations, and based on the reconstructed response, the force graph method can also precisely identify the clearance parameter.

Vibration Analysis of Pipes Supported by a Flexible Tank Wall Considering the Support Clearances

The vibration of pipes supported by a flexible tank wall is analyzed taking into account the hydroelastic vibration of the tank and the nonlinearity caused by the support clearances. Because the support clearances increase the pipe displacement, it is important to examine whether the support clearances augment the pipe stress. We illustrate that the support clearances can cause an increase in the pipe stress not only due to the increase in pipe displacement but also to the difference between elastic behaviors of the tank wall and pipes. The tank wall and pipes are dominated by membrane and bending deformations, respectively. Furthermore, we illustrate that the support clearances render a stress reduction method ineffective. In this study, a semi-analytical method is applied, rather than a full finite element analysis. The semianalytical method is helpful not only for computationally efficient analysis but also for gaining physical insight into the clearance-nonlinearity-induced stress behaviors noted above.

A Comparison of Several SDOF Models of Gear Dynamics

It is commonly believed that a complete understanding of gear dynamics is essential for the design of gear transmission systems capable of running at low noise and vibration levels with prolonged service life. Several single degree of freedom (SDOF) models of gear dynamics with clearance nonlinearity are generalized based on previous research, while a constant damping ratio is assumed and the friction is neglected. These models include the effects of time-varying mesh stiffness, gear manufacturing errors, profile modifications and backlash. Comparisons of the steady responses predicted by these SDOF models are intensively studied and the relationships between these models are discussed. Even though, different types of mesh stiffness and different treatments of the gear error functions in the analysis are used in these models, the steady-state responses predicted by these models are generally consistent with each other and agree well with experimental results. However, some discrepancies and relationships do exist among these models. The advantages and disadvantages of each model are highlighted.

Experiments on clearance identification in cantilever beams reduced from artillery mechanism

Clearances existing in artillery mechanism cause the muzzle disturbance and reduce the artillery firing accuracy. If the parameters of the clearance nonlinearity can be identified by taking advantage of the dynamic information, the quantitative relation between the clearance and muzzle disturbance can be established, and then the clearances of such nonlinear system can be controlled in a reasonable range to improve the artillery firing accuracy. This paper proposed a nonlinear identification method for the cantilever beam with clearances reduced from barrel-cradle structure. A modified restoring force surface method is proposed to identify the clearance value of the cantilever beam in time domain, and then a modified nonlinear identification through feedback of outputs method, i.e., reduced-order nonlinear identification through feedback of the output method, is proposed to recognize the related contact stiffness in frequency domain. The feasibility of the combined identification process is verified by a cantilever beam with two clearances in simulation, and a test-bed with adjusted clearance and contact stiffness which is regardless of other nonlinear factors by adjusting the position of the clearance and excitation method was designed to verify the effectiveness of this method. In the end, some influence factors of this identification process are discussed in detail. The results show that the proposed methods can identify clearance-nonlinearity parameters with high precision.

Theoretical and Experimental Identification of Cantilever Beam With Clearances Using Statistical and Subspace-Based Methods

Clearance turns up in a large number of engineering structures because of the errors during assembling, manufacturing, and wearing. The presence of clearance in engineering structures changes the normal dynamic response and will result in low precision and short lifetime. The clearance parameter identification of such nonlinear system is the prerequisite to control and eliminate the effect of clearance nonlinearity. In this paper, a derivative plot of probability density function (DPPDF) for displacement response is proposed to precisely identify the clearance value of continuous system, and the nonlinear subspace identification (NSI) method is modified to recognize the related contact stiffness based on the frequency response function (FRF) equations of continuous system. The DPPDF method is carried out by analyzing the distribution characteristic of displacement response, and the clearance value is derived through inspecting the probability density function (PDF) plot and the second derivative plot of the PDF. Based on the identified clearance, the clearance nonlinearity is regarded as external force, and the relationship between the dynamic responses and the external forces in frequency domain can be expressed as the form of FRF equations. Based on the FRF equations, the contact stiffness in continuous system is obtained with modified NSI method. This combined identification process is verified by a single-degree-of-freedom (SDOF) system and a cantilever beam system with clearances, and some influence factors of this identification process, including noise, transfer error, and force level, are discussed in detail. In the end, an experiment device with changeable clearance and contact stiffness was designed to conduct identification experiments, and the results show that the proposed methods perform effectively in identifying the clearance parameters.

Non-Linear Dynamic Modeling and Experiment of Harmonic Gear Drive

A non-linear torsional vibration model of harmonic gear drive is proposed in the current study. The model includes clearance, nonlinearity torsional stiffness and nonlinearity damping. The clearance model is developed by introducing the piecewise-linear displacement functions. The function of nonlinearity torsional stiffness is obtained by torsional stiffness experimental. The model of nonlinearity damping is used to describe the process of transmission. The non-linear differential equations are solved using Runge-Kutta method. The numerical simulation results show that the influence of nonlinear factors on dynamic behavior, which has chaotic characteristics, is remarkable.