Trajectory optimization of maypole braiding machine carrier

Unreasonable trajectory is the main factor that limits the stable motion of the carrier of maypole braiding machine. The kinematical model of the carrier is established. The acute change of the load causes severe vibration of the carrier in the straight line segment of the “∞”-shape trajectory. Combination curve of modified trapezoid is used for optimizing trajectory. The result shows that the maximum dimensionless jerk of the carrier is decreased obviously. The trajectory of tangent equal circles (simplified TEC) is obtained in the optimization objective of minimum load fluctuation and leads to the vibration and noise of braiding machine be reduced notability. The design theory of machine has been provided in this research, which can improve the overall performance of the braiding machine

Trajectory optimization of maypole braiding machine carrier

Unreasonable trajectory is the main factor that limits the stable motion of the carrier of maypole braiding machine. The kinematical model of the carrier is established. The acute change of the load causes severe vibration of the carrier in the straight line segment of the “∞”-shape trajectory. Combination curve of modified trapezoid is used for optimizing trajectory. The result shows that the maximum dimensionless jerk of the carrier is decreased obviously. The trajectory of tangent equal circles (simplified TEC) is obtained in the optimization objective of minimum load fluctuation and leads to the vibration and noise of braiding machine be reduced notability. The design theory of machine has been provided in this research, which can improve the overall performance of the braiding machine

Flow field calculation and dynamic characteristic analysis of spherical hybrid gas bearings based on passive grid

In order to research the spherical spiral groove hybrid gas bearings, the Realizable k − ε turbulence model of gas film was established based on FLUENT. The simulation calculation method of 6-degrees of freedom passive grid was used, which can simulate the lubrication characteristics of the gas film transient flow field accurately. And the gas film pressure distribution and dynamic characteristic coefficients are numerically calculated. The dynamic and static pressure coupling effects of the gas flow field were analyzed, and the axis motion trajectory was simulated. The effect of rotation speed, gas supply pressure and tangential angle on the dynamic characteristic coefficients during bearing operation was analyzed. And the stability of the gas bearing was studied. The conclusion from the analysis shows that different rotation speed and gas supply pressure will change the pressure distribution of the gas bearing during the operation. The dynamic characteristics of the gas film can be changed by reasonably optimizing the operation parameters, which can change the whirl characteristics of the gas film and improve the stability. Through calculation and analysis, the tangential angle is selected between 55° and 60°, to ensure that the gas film has a high stiffness, while it also can obtain the larger damping. The simulation results and the experimental results are compared and analyzed to verify the correctness and effectiveness of the simulation method. At the same time, the research of this paper provided a theoretical basis for optimizing the bearing structure and operating parameters, improving the dynamic characteristics of gas bearings and improving the operation stability

Study on dynamic characteristics of gas films of spherical spiral groove hybrid gas bearings

According to the gas film force variation law, when the bearing axis is slightly displaced from the static equilibrium position, displacement and velocity disturbance relation expressions for the gas film force increment are constructed. Moreover, combined with the bearing rotor system motion equation, calculation model equations for the gas film stiffness and damping coefficients are established. The axial and radial vibration and velocity of the gas bearings during operation are collected. The instantaneous stiffness and damping coefficients of the gas film are calculated by the rolling iteration algorithm using MATLAB. The dynamic changes in the gas film stiffness and damping under different motion states are analyzed, and the mechanism of the gas film vortex and oscillation is studied. The results demonstrate the following: (1) When the gas bearing is running in the linear steady state in cycle 1, the dynamic pressure effect is enhanced and the stability is improved by increasing the eccentricity; when the gas supply pressure is increased, the static pressure effect is enhanced and the gas film vortex is reduced, but the oscillation is strengthened. (2) With the increase in rotational speed, the gas film vortex force gradually exceeds the gas film damping force, and the stability gradually worsens, causing a fluctuation in the gas film stiffness and damping, following which singularity occurs and a half-speed vortex is formed. Meanwhile, the gas film oscillation is intensified, and the rotor enters the nonlinear stable cycle 2 state operation. (3) As the fluctuation of the film force increases, the instantaneous stiffness and damping oscillation of the film intensifies, most of the stiffness and damping coefficients exhibit distortion, and the rotor operation will enter a chaotic or unstable state. Therefore, the gas bearing stiffness and damping variation characteristics can be used to study and predict the gas bearing operating state. Finally, measures for reducing the vortex and oscillation of the gas film and improving the stability of the gas bearing operation are proposed

Dynamic Stability Prediction of Spherical Spiral Groove Hybrid Gas Bearings Rotor System

Taking the hemisphere spiral groove hybrid gas bearings (HSGHGB) as the research object, the nonlinear dynamic lubrication analysis mathematical model of spherical hybrid gas bearings is established with the axis instantaneous position and instantaneous displacement speed as the parameters. The perturbation pressure control equation is solved by means of the finite difference method in generalized coordinate system. The calculation program is prepared based on VCþþ6.0, and the transient perturbation pressure distribution of three-dimensional (3D) gas film, nonlinear gas film force, and dynamic stiffness and damping coefficients are numerically calculated. The influences of different speeds, eccentricity ratios, and gas supply pressures on the dynamic characteristic coefficients of gas film are studied. The results show that the influence of bearing's supply pressure, speed, and eccentricity on the dynamic characteristics of gas film is significant. The dynamic equations of rotor-bearing system containing the gas film dynamic stiffness and the damping coefficients are established, and the stability of the gas film is predicted based on the Routh-Hurwitz stability criterion. The research provides the theoretical foundation for actively controlling the bearing running stiffness and damping and stemming the instability of gas film

The meso-structures analysis of truss-like lightweight materials based on symmetric groups

Truss-like lightweight materials (TLLMs) with superior mechanical performance and excellent energy absorption capability are extensively used in aerospace and automobile industries. The performance of TLLM was closely related to its meso-structure, but the lack of innovation and variety in the geometric configuration of TLLM’s meso-structure limits the reinforcement effect and strength enhancement. Hence, it is important to thoroughly study the theoretical design method for TLLM’s meso-structure. Inspired by the symmetric feature of TLLM’s meso-structures, the symmetric groups were applied to describe, classify and design TLLM’s meso-structures. First of all, it was found that the representative volume unit (RVU) of TLLM corresponded to point groups that contained the symmetry of TLLM’s meso-structure. Space groups, which consist of point groups and space lattices, could be used to describe the geometric configuration of TLLM’s meso-structures. Then, TLLM’s meso-structures were classified according to different types of point groups. Finally, a description and design method for TLLM’s meso-structure based on the symmetric group theory was proposed. In addition, a novel TLLM’s meso-structure was deduced through the symmetric operations of space group, which could verify the feasibility of the method. Therefore, the present study provides a basis for the design of high-performance TLLMs

Study on the Load Sharing Capability of Closed-loop Gear Transmission in Braiding Machine

The static model is established based on the structural characteristics of closed loop gear transmission. The influence law of manufacturing and assembly error with load sharing coefficient was researched. The formula among transmission gear errors and load sharing coefficient is established. According to the formula of error coupling in the same angular frequency, transmission errors in closed loop gear transmission are coupled. The measure for reducing the transmission error is put forward. The study provides a theoretical basis for the design of high speed braiding machine

A New Approach to the Degradation Stage Prediction of Rolling Bearings Using Hierarchical Grey Entropy and a Grey Bootstrap Markov Chain

Degradation stage prediction, which is crucial to monitoring the health condition of rolling bearings, can improve safety and reduce maintenance costs. In this paper, a novel degradation stage prediction method based on hierarchical grey entropy (HGE) and a grey bootstrap Markov chain (GBMC) is presented. Firstly, HGE is proposed as a new entropy that measures complexity, considers the degradation information embedded in both lower- and higher-frequency components and extracts the degradation features of rolling bearings. Then, the HGE values containing degradation information are fed to the prediction model, based on the GBMC, to obtain degradation stage prediction results more accurately. Meanwhile, three parameter indicators, namely the dynamic estimated interval, the reliability of the prediction result and dynamic uncertainty, are employed to evaluate the prediction results from different perspectives. The estimated interval reflects the upper and lower boundaries of the prediction results, the reliability reflects the credibility of the prediction results and the uncertainty reflects the dynamic fluctuation range of the prediction results. Finally, three rolling bearing run-to-failure experiments were conducted consecutively to validate the effectiveness of the proposed method, whose results indicate that HGE is superior to other entropies and the GBMC surpasses other existing rolling bearing degradation prediction methods; the prediction reliabilities are 90.91%, 90% and 83.87%, respectively

Study on the Load Sharing Capability of Closed-loop Gear Transmission in Braiding Machine

The static model is established based on the structural characteristics of closed loop gear transmission. The influence law of manufacturing and assembly error with load sharing coefficient was researched. The formula among transmission gear errors and load sharing coefficient is established. According to the formula of error coupling in the same angular frequency, transmission errors in closed loop gear transmission are coupled. The measure for reducing the transmission error is put forward. The study provides a theoretical basis for the design of high speed braiding machine

Effect of Groove Width on Micromachine Groove Texture Tribology Characteristics of 0Cr17Ni7Al

Friction and wear are the main forms of material surface failure. Surface modification is very effective in friction reduction and wear resistance systems. Therefore, as a method of surface modification to improve the tribological properties of materials, surface texture has been widely loved by scholars. However, most scholars use laser and other processing methods to prepare the surface texture. Although these processing methods have a high preparation efficiency, they cannot obtain a surface texture with high dimensional accuracy due to their non-contact processing characteristics. Moreover, previous studies on different surface texture preparation methods are insufficient. Scholars have not fully studied the size parameters of surface modification. Micromachining is a contact machining method. It has high dimensional accuracy. Therefore, the surface groove texture of 0Cr17Ni7Al material commonly used in sliding bearings was prepared by micromachining in this paper. Under dry friction conditions, the effects of different groove widths on the tribological properties of surface texture were studied. The results show that the friction coefficient at the 0.6 mm-wide groove texture is the lowest, σ = 0.632. The minimum wear rate is ω = 3.351 × 10−4 mm3/(N·mm). The friction coefficient and wear rate of all groove textures are lower than those of untextured surfaces. It can be judged that the groove texture prepared by micromachining has good friction reduction and wear resistance under the same load, time, and linear speed. With the increase of the groove width, the friction coefficient and wear rate of groove texture decrease first and then increase