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Robust Reliability Optimization Design of Cycloidal Pinwheel Planetary Reducer Li Yonghua (School of Mechanical Engineering, Dalian Jiaotong University, Dalian 116028, Liaoning Province) Considering the requirements of robustness, the sensitivity of reliability to uncertainty parameters is minimized to achieve design quality robustness. Claim. In this way, the robust reliability optimization design model of cycloidal pinion planetary reducer is established and optimized by example.
414: A In practical applications, the reliability of the cycloidal pinion planetary reducer will be affected by some uncertain factors from the outside or itself. It is often difficult to eliminate these factors, and sometimes it can be costly to eliminate them. However, it is easy to reduce the impact of these factors, which means that product reliability is not very sensitive to these factors. According to this guiding ideology, it is very meaningful to study an engineering robust reliability optimization design method that can improve the reliability and robustness of the reducer.
Reliability design and robust design are two advanced design ideas, albeit intrinsically consistent. However, the starting point and design requirements of their specific design are still different. The starting point of reliability design is that it can meet certain reliability requirements through a set of reasonable design methods and means under the premise of knowing the distribution characteristics or fluctuation range of uncertain parameters. The reliability optimization design method includes reliability as one of the optimization objectives to be achieved and reliability as the constraint function of the design variables. 111. The starting point of robust design is to make the product resistant to certain products by selecting reasonable design variable values. The degree of uncertainty of the disturbance, so that the tolerance of various quality or performance indicators is as small as possible, so that the product has more stable quality and performance | 21. This article combines these two design ideas, in the predecessors Based on the discussion of robust reliability optimization design method. On the basis of general reliability optimization design, considering the requirements of robustness, the reliability optimization design is added to the reliability optimization design with reliability as the constraint function to add the minimum objective function with minimum sensitivity. According to this method, the mathematical model of the robust reliability optimization of the corresponding cycloidal pinion planetary reducer is established, and the model is optimized by example.
1 Robust reliability optimization design model based on sensitivity analysis The following mathematical model of reliability optimization design: for the unified optimization model, including the optimization problem with reliability as the objective function, and considering the reliability requirements in the constraint conditions Optimization problem.
Assuming that there are uncertainties in the design variables and design parameters, the values ​​will change. And represent it as a vector of N=n+q dimension, ie z=T=T. Usually, for design parameters, it can only be designed according to one of their estimates, and in the course of use due to various human factors or The influence of external environment and other factors, according to the definition of sensitivity |31, the sensitivity of the objective function and the constraint function to the uncertain parameters are If3/zl, g/%l and I, respectively.
By adding the sensitivity-based objective function term, the optimization model (1) is transformed into a new multi-objective optimization problem that increases an objective function term, that is, a robust reliability optimization model. The specific optimization model is expressed as follows: where model (I) is an optimization model considering both the objective function and the sensitivity of the constraint function to the uncertainty parameter; the type () is to add the degree of the constraint function to the function, only the constraint is considered. An optimization model for the sensitivity of the uncertainty to the uncertainty. The net type is suitable for reliability optimization with reliability as a constraint function; the model (I) is an optimization model that only adds the sensitivity of the objective function to the objective function, taking into account the sensitivity of the objective function to the uncertainty of the uncertainty parameter. The model is suitable for optimization problems where reliability is the objective function. The selection of the constant term dr is such that the two items in the new objective function have the same value at some points or are selected according to the importance of the two items in the objective function. The methods for solving this model are various and can be directly applied to various algorithms for multi-objective optimization problems.
2 Robust reliability optimization of cycloidal pinwheel planetary reducer The cycloidal pinion planetary reducer mechanism is mainly composed of a cycloidal pin wheel and an output mechanism disk, as shown in the drawing. Five independent parameters are selected as design variables, namely the cycloidal radius Rz, the cycloidal tooth width coefficient, the short-width coefficient K, the needle diameter coefficient K2 and the pin radius ¢. All other parameters are used as design constants. SP: pin tooth engagement loss coefficient, Xb = Kz. / z, is the mechanism loss coefficient, <= 8A / XnDw).
The optimization design of the cycloidal pinion planetary reducer can be the overall structural size of the reducer, or it can be a performance indicator such as load carrying capacity and transmission efficiency. Reducing the volume of the reducer has important practical significance in engineering. Therefore, the minimum volume of the reducer is used as the objective function of the design of the cycloidal pinion planetary reducer under the condition that the given requirements are met. According to the structure of the cycloidal pinion planetary reducer, the main parameters determining the structure of the cycloidal pinion planetary reducer are the volume V1 of the cycloidal wheel and the volume V21791 of the output shaft disk. Therefore, the volume of the reducer can be approximated: The objective function of the reliability optimization of the cycloidal pinion planetary reducer can be expressed as: To ensure that the reliability of the mechanical parts is not very sensitive to the uncertainty of the uncertainties, it is necessary to adjust the reliability constraints to the uncertainty. The sensitivity of the factor is minimal as an additional objective function, and considering that the input power p and the input shaft speed n in the design parameters are affected by the external factor 1 and change A, the additional objective function i is Souse.Allrightsresd.http:/ Therefore, the objective function of the robust reliability optimization of the cycloidal pinion planetary reducer is: the optimization model contains 5 variables, 14 constraints, and 2 objective functions. The method of solving the model adopts the unified target method. 11. The whole robust reliability optimization process is solved by the MATLAB optimization toolbox to solve 1W|. 3 example analysis design a cycloidal pinwheel planetary reducer|891, input power Nh=4, input The shaft speed = 29 works 8 hours per day, and the working reliability is R0=0 98. The calculated results are shown in the attached table.
Scheduled cycloidal pinion planetary reducer optimization result comparison design variable optimization method pin wheel radius wheel width coefficient short coefficient pin diameter coefficient pin radius reducer volume general reliability optimization robust reliability design can be seen from the results in the attached table The volume of the cycloidal pin planetary reducer obtained by the method is slightly larger than that of the general reliability optimized design, but the stability of the reducer is increased and the design parameters are made. It is insensitive to the sensitivity of the disturbance of the reliability constraint and is minimized, thereby improving the quality robustness of the reducer. The advantage of this method is that the reliability of the uncertainty parameter is considered to meet the requirements of product robustness based on the reliability optimization. However, this method increases the robustness of the structure at the cost of increasing the volume of the structure.
4 Conclusion According to the method of this paper, the robust reliability optimization design of the cycloidal pinwheel planetary reducer is carried out, and the corresponding robust reliability optimization model is established. It can be seen from the example optimization results that the sensitivity of the reliability constraint to the uncertainty parameter is minimized as the robust reliability optimization result of the additional objective function, which is slightly higher than the conventional optimization result. The main reason for this situation is The sensitivity of the constraint condition to the uncertainty parameter is taken into account when establishing the optimization model. However, the design of the cycloidal pinion planetary reducer in this way not only considers the reliability requirements, but also considers the robustness requirements of product quality.