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A splash lubrication simulation model of a planetary gear train was established based on the moving particle semi-implicit （MPS） method, and it was verified by experiments to explore the splash lubrication behavior of the planetary transmission. Through the simulation, the oil distribution characteristics, the number of lubricating oil particles in the engagement zones, and the churning loss of the rotating components were studied. The results show that in the rotation of the planetary gear train, the interior space of the gearbox can be divided into three regions: the oil-pool region, the oil-dragging region, and the oil-poor region. The number of oil particles in different engagement zones and the churning torque of each component show periodic variations during the planet gear passes through the three regions. The numbers of oil particles in the inner and outer engagement zones reach the peak when the planet gear runs into the oil-pool region, and both drop rapidly to a minimum value after entering the oil-poor region. The churning torque of the planet gear rises sharply to the peak after entering the oil-pool region and keeps the peak value until the planet gear enters the oil-dragging region, then the churning torque turns to fall until stabilizing at a very low level when the planet gear enters the oil-poor region. Different from the planet gear, the churning torque of the planetary frame drops sharply when one of the planet gears enters the oil-pool region and rises rapidly when that planet gear enters the oil-dragging region and the next one has not entered the oil-pool region. The churning torque of the sun gear is small and insensitive to the planet gear positions. Among the total churning power of the planetary gear train, the sum of the three planet gears accounts for about 60%, followed by the planetary frame, and the sun gear accounts for the least.

In this study, a three-dimensional model of the planetary gear train with straight cylindrical gears is established, and a virtual prototype model is constructed by using dynamics simulation software. Through the dynamics analysis, the accuracy and feasibility of the virtual prototype simulation model are verified. The study shows that the supporting stiffness of each component in the transmission system has a significant effect on the uniform load characteristics, and the change of the supporting stiffness of the planetary gear has the most sensitive effect on the uniform load characteristics. The uniform load characteristics of the transmission system is not sensitive to the change of the flexible supporting stiffness of the sun gear, but it is more sensitive to the change of the flexible supporting stiffness of the planetary gear, and the uniform load coefficient has obvious changes. The effect of gear tooth meshing stiffness changes on the uniform load characteristics of the transmission system is independent, simultaneously reducing the internal and external meshing stiffness has a more obvious uniform load effect than reducing the meshing stiffness alone.

The distribution of the load on the tooth surface greatly affects the performance of the power split of the planetary transmission system. This study mainly studies the load sharing characteristics of the planetary gear transmission system and summarizes the current research status of this problem. The basic problems related to load sharing are expounded. Then, the analysis methods and calculation models of load sharing characteristics in planetary transmission are compared and analyzed. The methods and mechanisms of load-sharing which are commonly used at present are reviewed. It can be found that error is the root cause of uneven load distribution, and the most effective way to improve the uniform load is to reduce the sensitivity of the system to error. At present, dynamic analysis and the influence of nonlinear factors are the focus of research on uniform load problems. Floating parts and flexible parts are still commonly used uniform load methods.

In order to analyze the lubrication characteristics of the planetary gear transmission of shield main drive reducers, a simulation model of splash lubrication of the single-stage planetary gear train is established using the moving particle semi-implicit (MPS) method. By comparing the distribution of lubricating oil particles, velocity field, pressure field, the number of lubricating oil particles in the meshing area of gear teeth and the churning resistance moment produced by each rotating part during the planetary gear train movement under different working conditions, the influence of input speed, initial oil level height and oil temperature on the system lubrication effect and churning loss power are studied. The results show that the oil particle velocity and pressure increase with the increase of the input speed and oil level, and the low speed and oil level height will lead to the uneven distribution of oil particles in the reducer. The number of particles in the meshing zone between planetary gears, sun gears and inner gear rings decreases with the increase of input speed and oil temperature, and decreases with the decrease of oil level height. The meshing area of sun gears is the risk area of poor lubrication. The power loss of the system is most significantly affected by the input speed, and increases exponentially with the increase of the speed, while the influence of oil level height and oil temperature is relatively small. In each working condition, the churning loss power generated by the three planetary gears takes the largest proportion in the total churning loss power.

Aiming at the difficulty of analyzing the meshing contact characteristics of gear transmission system under the big data formed by multiple working conditions and uncertain parameters, a meshing contact characteristics analysis method of gear transmission system based on data mining technology is proposed. Based on the principle of multi-dimensional Gaussian distribution and the finite element model of gear transmission system, the meshing contact characteristic data set of the system is constructed. The correlation between system parameters and meshing contact characteristics is analyzed using the maximum information coefficient, which provides a candidate feature subset for the prediction model. Then, the prediction model of meshing contact characteristics of the system is established using support vector machine and random forest algorithm, which realizes the efficient prediction of meshing contact characteristics of the system. The results show that the prediction error of the prediction model based on support vector machine is the smallest, and the average absolute percentage error is 3.87%, which is far less than the theoretical calculation error. Under the optimal feature subset, the prediction error index of contact characteristics of the prediction model based on support vector machine decreases significantly, and its average absolute percentage error reaches 3.03%, which is 21.71% lower than the prediction error of contact characteristics before optimization. These have verified the accuracy and effectiveness of the proposed method.

The mesh stiffness calculation and load distribution among teeth of helical gear are the basis of its dynamics analysis and strength calculation. Aiming at the accuracy of approximate replacement method of mesh stiffness of helical gear, the quasi-static elastic model of helical gear was established based on the change rule of contact length, quasi-parabolic model of single tooth mesh stiffness per unit of contact length and ISO6336-1 standard, and a comparative study was conducted with the approximate replacement method based on quasi-static rigid model and ISO6336-1 standard. The results showed that the results calculated by quasi-static elastic model were in good agreement with the ISO standard results when the ratio of the minimum stiffness to the maximum stiffness of single tooth αk is 0.55, and the errors of the quasi-static rigid model and ISO standard were large. Based on the quasi-static elastic model, the effects of geometric parameters and broken teeth failure on meshing stiffness and load distribution coefficient of helical gear were analyzed and discussed, which provided a basis for the study of fault dynamics.

The calculation method of equivalent load for crane reducer under variable load condition is analyzed. Application factor formulas for the calculation of gear fatigue strength and bearing fatigue life are deduced,and the index value of the fatigue strength calculation of gear is recalculated based on the life coefficient. In addition,the differences of load spectral coefficients in gear and bearing fatigue calculations are pointed out. The calculation method has a guiding significance for the design and calculation of crane reducer.

Taking one new type crane reducer with two supporting points as the research object,the three-dimensional model of reducer is established by using SolidWorks,and the virtual prototype is established by importing the 3D model into the mechanical dynamics simulation software ADAMS. In order to ensure the accuracy of the simulation model,the virtual prototype model is analyzed by the contact force constraint,the angular velocity characteristic curve and the gear meshing force variation curve of each drive shaft are obtained. The simulation of the actual value and the theoretical calculation results are compared and found that the transmission shaft angular velocity and the actual the transmission error value in 0. 17%,engaging in 4% errors are very small,so the simulation model is correct. The research results provide data support for calculate gear strength and fatigue life more accurately.

Based on the strength and modal analysis,the lightweight design of gearbox housing is carried out by using the topological optimization method. Under the condition of meet the reliability of the gearbox,the housing weight is reduced about 15% after structural optimization. The rationality of housing improvement is verified through the contrast analysis on the reducer housing performance before and after optimization.

Considering the factors such as complex alternating load,meshing stiffness,meshing clearance,manufacturing and installation errors,the nonlinear multi-degree-of-freedom dynamics model of the clearance between the gear pair of the bridge crane reducer under complex excitation is established. By using the Runge-Kutta method of MATLAB/Simulink,the simulation solution of the nonlinear dynamic model of gear clearance is carried out. The effects of parameters such as load,tooth backlash,excitation frequency and damping ratio on the dynamic performance of the system are analyzed.

Reducer is the key component of hoisting equipment,and the case is the carrier of the gear system and plays the role of support and fixation. The three-dimensional finite element model of the gearbox is established by Solid Works software and imported it into ANSYS Workbench. The statics analysis is accomplished for each actual loading condition,the changing curve of the maximum stress and the deformation is obtained,the analysis results can provide the data support for the subsequent structure improvement and light-weight design. The natural frequency and vibration type is obtained by completing the modal analysis of the case,and whether the resonance phenomenon happens can be determined by comparing the natural frequency of the reducer with the meshing frequency and the rotational frequency.

Based on the relationship between shear stress and Hardness,using the linear regression method,the calculation formula of effective case depth of carburized gear was derived,and it was verified by example. The results show that the accuracy of the derived simple computational formula can meet the requirements for gear design. Using this formula,the effective case depth of gear was obtained,and the model for the distribution of effective case depth of gear was established.

Based on a typical component in the large crane reducer as the object,a three-dimensional tolerance model is established.Through sensitivity numeric analysis,the critical and non-critical dimensions influencing the assembly requirements can be found out,the reasonable distribution of each component tolerances can be achieved,which lays a basis for the optimization of components accuracy design.

The frequency response analysis of gearbox housing of large- sized bridge crane is carried out under the excitation frequency,and the displacement response curves of every bearing bore on the housing and the greatest response position of the housing are obtained. The results show that when the meshing frequencies under the rated speed,the natural frequency of the housing can be avoided and it should not cause the resonance.