The contact stiffness of the machined surface has an important effect on the performance of the complex mechanical product. A modified fractal model based on oblique asperity contact is proposed in this research. First, the contact radius and the critical contact area are analyzed based on oblique contact condition. The normal contact stiffness and elastic–plastic force are calculated. The ratio of the actual contact area and a new parameter related to the current contact angle are introduced. Second, numerical simulations indicate the difference. The results show that the stiffness of the oblique contact is smaller, and with the increment of the fractal dimension, the extent of the stiffness reduction is larger. In contrast, the uniform distribution has the lower proportion of the elastic force in the total normal contact force. Finally, experiments including specimen surface observation and load-deformation measurement are utilized to obtain contact stiffness of the machined surface. To some extent, the modified fractal stiffness model is more reasonable and accurate from the result.

An accurate equivalent method of metal joint interface is of great significance to optimize the dynamic performance of the whole machine. Therefore, it is necessary to establish an accurate equivalent method of joint interface. The virtual material method is a precise equivalent method of joint interface. The traditional virtual material method is based on the M–B fractal contact theory. By modeling the contact mechanics of the joint interface, the physical properties of the virtual material are obtained separately, such as elastic modulus, Poisson’s ratio and density. In this paper, Persson contact theory is used to establish the interface contact mechanics model to find the physical properties of virtual materials. The virtual material methods constructed by two theories are respectively applied to the modal simulation to obtain the natural frequencies of the joint interface. By comparing the natural frequencies obtained by modal experiment and modal simulation, it is found that the natural frequencies obtained by the virtual material method based on Persson contact theory are closer to the results obtained by the modal experiment, and the error is within 5%. The error of the natural frequencies obtained by the virtual material method based on the M–B fractal contact theory is within 10%. Therefore, the Persson contact theory can establish a more accurate equivalent method of metal’s joint interface.

Modal performance of a bolted structure is important when considering a precise mechanical product. Joint interface is a critical aspect of a bolted structure, which is difficult to analyze because of its rough profiles. Equivalent material (EM) is used to simplify the joint interface, which reduces the computational cost and modeling difficulty. Using a modified fractal model based on an oblique asperity contact, we calculated the elastic modulus, the shear modulus, the Poisson’s ratio, and the density of EM. The finite element method was applied to discriminate between the resonant frequencies of bolted structures with EM and without EM. The simulation results are compared with the classical frequency response experiment. The errors between experiments and the bolted structures with EM are less than 10%, which are much less than those without EM. It can be concluded that bolted structures with EM are more reliable and reasonable. Furthermore, the effect of EM is more obvious when the joint interface has a small size, roughness, and tightening torque.

In order to effectively improve the dynamic characteristics of the fixed metal joint interface, it is important to establish a correct equivalent model of the metal joint interface. In this paper, three equivalent methods for simulating the metal joint interface are analyzed, including the virtual material method, spring damping method, finite element method, and verification by modal experiment. First, according to the contact mechanics model of the constructed metal joint interface, the physical properties of the three-dimensional models of the fixed joint interface are assigned in the ANSYS software. Then, three methods are used for the modal analysis and compared with a modal experiment. The results show that the modal shapes of the three theoretical methods are consistent with those of the experimental modes. The first five natural frequencies obtained by the virtual material method are closest to the experimental natural frequencies, and the errors are within 10%. The errors of the other two methods are between 9% and 39%. Therefore, the virtual material method is a better equivalent method of the metal joint interface.

The contact mechanism for joint surfaces is important for predicting the loading process and dynamic properties of precision machinery products. A multiasperity model considering the lateral interaction and coalescence of contact regions with oblique asperity contact, the interacting and coalescing Hertzian asperities (ICHA) model, is introduced in this work. Contact angle $\alpha$ and radius of curvature $R(r)$ are vital parameters that are directly calculated based on grid points measured from the milling and grinding surfaces. Numerical simulations of $\alpha$ and $R(r)$ were analysed. The results show that the proposed model is more effective at improving the contact area versus force relationship than various asperity models for low and middle contact forces. $\alpha$ and $R(r)$ follow a Gaussian distribution. Because of the existence of coalescence, they decrease with increasing contact force. Furthermore, the $\alpha$ and $R(r)$ in the startup phase are crucial data that can be used to judge the effects of oblique asperity contact. They are greatly influenced by fractal dimension $D$ and fractal roughness G. From the comparisons with the surfaces generated by Weierstrass-Mandelbrot function, it is suggested that to obtain an accurate contact prediction in the loading process, oblique contact is as important as lateral interaction and coalescence.

To address the difficulty in obtaining a large number of labeled jamming signals in complex electromagnetic environments, this paper proposes a small-sample communication jamming signal recognition method based on WDCGAN-SA (Wasserstein Deep Convolution Generative Adversarial Network–Self Attention) and C-ResNet (Convolution Block Attention Module–Residual Network). Firstly, leveraging the DCGAN architecture, we integrate the Wasserstein distance measurement and gradient penalty mechanism to design the jamming signal generation model WDCGAN for data augmentation. Secondly, we introduce a self-attention mechanism to make the generation model focus on global correlation features in time–frequency maps while optimizing training strategies to enhance the quality of generated samples. Finally, real samples are mixed with generated samples and fed into the classification network, incorporating cross-channel and spatial information in the classification network to improve jamming signal recognition rates. The simulation results demonstrate that under small-sample conditions with a Jamming-to-Noise Ratio (JNR) ranging from −10 dB to 10 dB, the proposed algorithm significantly outperforms GAN, WGAN and DCGAN comparative algorithms in recognizing six types of communication jamming signals.