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Improving the rigidity of machine tools for identifying the weak links of structural stiffness is one of the important issues in mechanical engineering. In this paper, a new weak index is proposed on a cantilever structure of the machine tool to identify the weak stiffness link. The weak index is a frequency parameter obtained via the vibration test method. In this method, the FRF coefficient of variation technique is proposed based on the FRF curvature method. The change of weak index is used to identify the weak link in the structural stiffness. The element stiffness weakening method that employs numerical examples of a cantilever beam and an elastic support beam is used to simulate the weak links of the stiffness. Compared with the FRF curvature ratio (FRF_CR) method, the FRF mutation coefficient is improved in the same frequency range. Moreover, the FRF_MCR indicator has more frequency points than the FRF_CR indicator in the same frequency range.

In practice, even the tiny relative reciprocating motion generated by external load or environmental vibration can cause interface wear. In this work, three-dimensional (3D) finite element analysis (FEA) is used to investigate the fretting wear between deformable crossed parabolic cylinders. Fretting is achieved by the application of a periodic displacement-controlled load, while the contact pair is defined as the same material, i.e., Carbon Steel/Carbon Steel, Copper Alloy/Copper Alloy, and Aluminum Alloy/Aluminum Alloy. Meanwhile, three different axis crossing angles are also studied, i.e., 45°, 60°, and 90°. Originally, a wide range of coefficients of friction (COFs) are applied to the interface without considering the damage. The results show that, when the COF is sufficiently large (µ = 1), the junction growth and the tangential load increase significantly in the first loading cycle, but then become gradually stable. Subsequently, the Archard wear model is applied to the frictional interface. Empirical equations for the initial gross slip distance and the wear volume at the end of the partial slip are established in turn. Furthermore, an empirical equation for the wear volume of a single fretting cycle is established, which is in good agreement with the FEA results. Lastly, the effect of relevant parameters on the wear volume for a single fretting cycle under elastic condition is discussed, but also the evolution of wear volume in the early stage of cyclic fretting. All the results are normalized, enabling their application to the 3D fretting wear of other material pairs.

Investigating weak parts of the structure is one of the most important issues for improving the stiffness of the machine tool. However, studies show that overcoming the static deformation is a challenging problem in practical structures. In the present study, the dynamic hammer testing approach is applied to analyze the cantilever structure of the machine tool with elastic support. Accordingly, a new weakness index (WI) is proposed to identify weak parts of the cantilever structure with an elastic support. Then the cantilever beam with the elastic support is numerically simulated and weak parts are modeled as stiffness reduction. In this regard, finite element (FE) simulations are carried out to evaluate the effectiveness of the WI method in several scenarios with single and multiple weaknesses, including the noise case. In the combined structure of the tailstock and the bed of the machine tool, sensors are utilized to collect vibration data. Furthermore, the dynamic characteristics are calculated through the modal state-space method to obtain the stiffness data at zero-frequency. Then, weak parts of the structural stiffness are identified based on the weakness index. It is found that the FE simulations are in an excellent agreement with the experiment. Therefore, it is proved that the WI can accurately identify the weak parts of the machine tool cantilever structure.

In practice, it is difficult to avoid the axis angle deviation when some regular surfaces are in micro-sliding, such as gears and machined surfaces. In order to better investigate the micro-motion contact characteristics, a crossed paraboloidal contact model under frictional condition is proposed to simulate both tangential displacement-controlled fretting and the evolution of the energy dissipation in a load cycle. By deriving the theoretical of the normal and tangential contact course of the model, the load–displacement curves during initial loading, unloading, and reloading stage are presented. On this basis, the hysteresis curve is then obtained by integrating the closed area surrounded by load–displacement during unloading and reloading, which also means that the empirical formulation for microslip in a load cycle is constructed. This study also reveals the plastic yield phenomenon under pure normal loading and plastic shakedown behavior caused by cyclic reciprocating displacement loads. In addition, the research on the junction growth, the evolution of tangential load, and hysteresis curve with different COFs under multiple-cycle load is also carried out. The implications of involved parameters, such as friction coefficient, axis intersection angle, normal load, and so on, are discussed with respect to hysteresis curve shape and energy dissipation. The difference in hysteresis and energy dissipation curves between the paraboloidal contact model and other classic contact models is then presented. It is discovered by comparison with other models that the paraboloidal contact model presents a relatively high energy dissipation in a load cycle.

In this paper, a cylinder contact model with different axis crossing angles is proposed, and the axis crossing angle is introduced into the normal and tangential constitutive equations. This paper uses the method of formula derivation to establish the analytical solution of the tangential elastic contact of the cylinder with different axis cross angles, and gives the relational expression of the tangential load and the tangential displacement. The finite element method (FEM) is used to verify the tangential displacement load curve and the tangential stiffness curve of the two cylinders. The influence of various factors on mechanical properties such as tangential stiffness, tangential displacement and contact area is explored, and the distribution of stress and strain on the contact surface is analyzed. The research results show that the tangential displacement and tangential stiffness of the cylindrical contact model correspond well to the simulation results.

Identifying the weak link of structural stiffness is one of the important issues in improving machine tool stiffness. Aiming at the cantilever structure in machine tool, this paper proposes a new weak index to identify the weak link of stiffness. The weak index is based on the modal parameters obtained by vibration test method. In this method, the weak parameter matrix is obtained by multiplying the difference between the reciprocal of the flexibility matrix of the overall structure and the stiffness matrix of the overall structure. The diagonal elements of the weak parameter matrix are extracted to obtain the weak index. And the change of weak index is adopted to identify the weak link of structural stiffness. The method of element stiffness reduction is used to simulate the weak link of stiffness, so as to verify the proposed method. Finite element simulation is used to verify different noises and single and multiple stiffness weak links. The method is verified by numerical examples of cantilever beam and elastic support beam structure. It has higher recognition accuracy under noise interference, which is more advantageous than the flexibility difference method. Finally, an experimental study on the elastic supported cantilever beam structure and the tailstock of machine tool are carried out to verify the effectiveness of the method.

A paraboloidal contact model with different axial crossing angles is established. The contact model is subjected to a combined action of normal and tangential loads. Based on the Hertzian theory, the contact states of the model under the action of the normal load are obtained by deriving the equations. The contact states include critical interference values of the elastic phase, elastoplastic phase, and plastic phase. Under the action of the normal preload, the tangential stiffness of the contact model is obtained and verified by finite element simulation. Simulation results indicate that tangential displacements of the contact model in the deformation phase correspond well with analytical solution equations. Stresses and strains on the contact surface are also investigated. By employing the proposed contact model, the effects of axial crossing angle, friction factor, focal length, and normal load on mechanical properties are investigated. The paraboloidal contact model is advantageous to contact analysis for paraboloidal gears and cams.

Identification of the vulnerabilities in the structural stiffness is one of the most crucial issues in improving this property of machine tools. In this paper, the Flexibility Matrix Diagonal element method, based on hammer testing, is proposed as an effective approach to identifying the stiffness weakness of cantilever structures. To verify the proposed method, the element stiffness weakening is used to simulate the weak parts regarding stiffness. Several scenarios, with single and multiple weakness points, including various noise levels, are studied, using finite element simulations. Next, a novel method, to measure the accuracy of the algorithm and quantify the weakness level, under noise conditions, is proposed. The advantage of this method, compared to the ones based on Flexibility Difference Method, is the higher identification accuracy under noise interference. Finally, the cantilever beam with elastic support is experimentally studied. The natural frequencies and modal shapes are obtained, according to the singular value decomposition method, to establish the flexibility matrix. In addition, using only the lowest three modes, a series of numerical examples and experiments are provided, to illustrate the validity and the considerable practical engineering value of the method.

Determining the weak parts of a structure is one of the key issues in the field of machine tool stiffness improvement. However, studies show that overcoming the static deformation with acquisition difficulty is a complex problem in practical structures. This study considers the machine tool cantilever structure, as a cantilever beam and bar structure, where the objective is to propose a weakness index, to identify the weak part, using system reconstruction to extract the measured static deformation data and the fitting data. Stiffness reduction is used to simulate weak parts, while the effectiveness of the method is evaluated, in the case of various weakness values and of different noise levels, using the finite element simulation approach. The validity of the proposed method is illustrated through comparison of the theoretical results to the experimental ones, using the cantilever structure of a test machine tool. The research content provides some means of improving the machining accuracy of machine tools.

Based on Hertz elastic contact theory, the contact mechanics model of two cosine wave is established. The mechanical characteristics of the model in the elastic, elastic-plastic, and plastic stages were studied. The influence of load on contact deformation and other characteristics is considered. The finite element method is used to analyze the deformation process of the model, and the results are compared with those of the mechanical model. The effects of amplitude and wavelength of cosine wave on its mechanical characteristics are discussed. The results show that the model reflects the relationship between the load and the mechanical characteristics of the model, and the difference of amplitude and wavelength will affect this characteristic.

To find the weak link of the structural stiffness is important to improve machine tool stiffness. However, how to overcome the static deformation with difficulty acquisition is a difficult problem in machine tool structure. The article takes the cantilever beam structure as a numerical example, the weak link is modeled as EA reduction in stiffness. Thorough finite element simulations are performed to assess the robustness and limitations of the method in several scenarios with single and multiple weaknesses. The sensors are used to acquire the acceleration data, the structural modal parameters are obtained by the singular value decomposition technique, and the dynamic characteristics are systematically reconstructed by using the modal state-space method to obtain static stiffness. Then, an identification method proposed by measured data and reconstructed data to identify the weak link of stiffness of the cantilever structure. Furthermore, the comparison of numerical and experimental results validate the correctness and effectiveness of this method. The research has certain practical engineering value and provides an accurate guidance for the optimization of machine tool stiffness.

Based on Hertz contact theory, an elastic-plastic contact mechanics model of outer cylinder under different contact angles of axis is proposed. The relationship among contact angle, load and contact deformation, contact stiffness and contact area is established. The finite element method is used to simulate the elastic-plastic contact process of the cylinder. The influence of the load and radius of the cylinder model on the contact deformation and the contact stiffness is compared and analyzed under different contact angles. The error of the analysis results of the finite element and the mechanical model is within 9%. On this basis, the influence of contact deformation, contact area and contact angle on the contact stiffness of the outer cylinder in elastic and plastic stage is explored. The results show that in the stage of elastic and plastic deformation, the amount of contact deformation and contact area increase with the increase of load. The contact stiffness decreases with the increase of contact angle and increases with the increase of cylinder radius. The amount of contact deformation decreases with the increase of cylinder radius, and tends to constant gradually. In the elastic stage, the contact stiffness increases with the increase of load. The contact area decreases with the increase of contact angle and increases with the increase of cylinder radius. In the plastic stage, the contact stiffness is constant with the increase of load, and the contact area is independent of contact angle and cylinder radius.

The evaluation of the weak link of machine tool structural stiffness is the key link to improve the machining performance of the machine tool. It is proposed that the serial structure of the machine tool be equivalent to a cantilever beam structure and the static rigidity of the machine tool be studied by using the method of dynamic test. A theoretical method for evaluating the position of the weak link of cantilever beam stiffness and the magnitude of stiffness by using the curve angle index is proposed. This paper mainly studies the evaluation effect of indicators. Taking the MATLAB finite element numerical model of cantilever beam structure as a numerical example, the dynamic test data of each node of the numerical model are obtained by using the state space method. After Fourier transform, the angle index is studied by taking the amplitude of 0 Hz. The weakening of the elastic modulus of the element is used to simulate the weak link of stiffness, and the evaluation effect of the corner index is studied under the three conditions of weakening the stiffness of a single element, weakening the stiffness of two elements, weakening the stiffness of three elements and involving noise. The results of simulation and experiment show that the curve angle can be used to better evaluate the weak link of the cantilever beam, which has a certain practical value in engineering.

This paper separates the regular and periodic morphology features from the random tough components in the typical machining surface, extracts the microscopic morphology features on the machined surface, building several joint surface models with regular surface features. This project is based on the combination of cylindrical waveform topography surface and start with the Hertz contact theory, using the analytical solution method to reconstruct the constitution relation of the cylindrical waveform surface contact.

ACC (air cooled condenser) is widely used in coal-fired power plants. It has the advantages of water saving and energy saving, and the system is simple. The fan bridge is an important part of the ACC. At present, the vibration problem of the fan bridge is very much, and the experimental data of the bridge vibration is single, and the fundamental vibration source problem is not revealed. Therefore, it is important to study the vibration causes of the wind turbine bridge. This paper analyzes the possible causes of vibration of the fan bridge. Through the combination of field test and theoretical analysis, the main causes of bridge vibration are analyzed. Research shows that air disturbance is the main cause of bridge vibration. The research results provide basis for bridge design.