变速箱减振与降噪的动力仿真与优化设计
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摘要
为了降低变速箱箱体的振动和噪音,在箱体薄壳的内表面粘贴阻尼层和约束层,形成约束阻尼结构。考虑到箱体结构的复杂性,为了降低计算量、提高效率,本文将箱体中最容易产生振动和噪音的拱板结构单独隔离出来,在拱板内表面粘贴阻尼层和约束层,对边界条件进行简化处理,基于ABAQUS软件平台对其进行动力仿真分析,并对约束阻尼结构各层厚度在许用范围内进行减振降噪效果最佳结构优化设计和造价最经济结构优化设计,分别得到结构质量约束下的振动加速度级最小化结构和振动加速度级约束下的造价最小化结构。主要工作可总结为如下内容:
(1)减振降噪效果最佳结构优化设计。以约束阻尼结构中基础层厚度、阻尼层厚度和约束层厚度为设计变量;约束条件为满足结构的总质量上限值要求;以结构上多个点的最大法向振动加速度最小为目标函数,建立减振降噪效果最佳结构优化模型。这是一个多目标优化模型,利用K-S函数将多个典型点的最大法向振动加速度处理为结构的振动综合指标,进而采用该振动综合指标的振动加速度级值作为结构减振降噪效果的评价参数,运用响应面方法将其显式化,建立以结构的振动加速度级值为目标的单目标优化模型。序列二次规划求解优化模型,程序运行稳定,得到了较理想的减振降噪结构。
(2)造价最经济结构优化设计。由于结构面积不变,粘贴阻尼层和约束层的加工费用是固定的,可以不考虑,因此只考虑结构的材料费用。以约束阻尼结构各层厚度为设计变量;约束条件为满足环境标准规定的振动噪音上限值要求;建立造价最经济结构优化模型。该优化模型是一个线性规划优化模型,采用设计变量的倒数作为新的设计变量,运用响应面方法将结构的振动加速度级约束条件显式化为倒变量的函数,将倒变量的造价目标函数进行泰勒二阶展开,得到标准的二次规划求解优化模型,优化程序收敛速度快,得到了满足结构性能约束下的最经济结构。
(3)响应面方法是对样本点及其响应值的近似拟合,在进行初次响应面拟合后对拟合得到的显式函数进行检验和拟合精度运算,提高拟合函数的精确性和拟合效率。
To reduce the vibration and noise of the gear-box structure, the damping layer and constraint layer are pasted on the surface of thin shell, forming the constraint damping structure. Due to the complication of the gear-box model,the arched plate structure which arises the most serious vibration and noise, is isolated from the gear-box to reduce the computing amount. The constraint layer and the damping layer are pasted on the inner surface of the arched plate. The boundary conditions are simplified. The dynamic simulation of the arched plate structure is made based on ABAQUS, and the optimal designs for the most effective structure of vibration and noise reduction and the most economical structure of cost are made in the allowable ranges of the thickness of each layer of the constraint damping. The optimization of the vibration acceleration level with the mass condition and the optimization of cost with the vibration acceleration level condition are obtained respectively. The main researches are summarized as follows:
(1) The optimal design for the most effective structure of vibration and noise reduction. The design variables are respectively the thickness of basic layer, the thickness of damping layer and the thickness of constraint layer in the constrained damping structure; the designing constraint is to meet the total mass requirement; the objective functions are minimizing the normal maximal vibration acceleration of a few nodes on the structure, establishing the optimal model of the most effective structure of reducing vibration and noise, which is a multiobjective optimization. The K-S function is adopted to process the normal maximal acceleration of all representative points as a synthesis parameter, with the vibration acceleration level of it as the evaluation parameter for effect of reducing vibration and noise. The response surface methodology is used to explicit the vibration acceleration level function. The new model with a signal objective of the vibration acceleration level of the structure is obtained, which is solved by the sequential quadratic programming stably and gives out the more ideal structure.
(2) The optimal design for the most economical structure of cost. As the structure of the same size, the cost of processing the damping layer and the constraint layer is fixed, which could be out of considering. The material cost of the structure is the only to be think about. Thickness of each layer of the constraint damping structure are taken as design variables; meeting upper limit of the vibration noise required by the environmental standards is the designing constraint; establish the most economical structure optimization model, which is a linear programming optimization. Reciprocals of the designing variables are used as the new designing variables. The constraint of vibration acceleration level is explicated as the function of the reciprocal variables with the response surface methodology. The objective function of the reciprocal variables can be lunched as the second-order Taylor function. The standard model of sequential quadratic programming is obtained and solved. The convergence speed of the optimal program is fast. The most economical structure satisfying the performance condition is also obtained.
(3) Response surface methodology(RSM) is the curve fitting of the relationship between the inputs(variables) and outputs(responses) of a physical system by explicit functions. For RSM function of the first fitting, tests and fitting precision are made to improve the fitting accuracy and the fitting efficiency.
(1)减振降噪效果最佳结构优化设计。以约束阻尼结构中基础层厚度、阻尼层厚度和约束层厚度为设计变量;约束条件为满足结构的总质量上限值要求;以结构上多个点的最大法向振动加速度最小为目标函数,建立减振降噪效果最佳结构优化模型。这是一个多目标优化模型,利用K-S函数将多个典型点的最大法向振动加速度处理为结构的振动综合指标,进而采用该振动综合指标的振动加速度级值作为结构减振降噪效果的评价参数,运用响应面方法将其显式化,建立以结构的振动加速度级值为目标的单目标优化模型。序列二次规划求解优化模型,程序运行稳定,得到了较理想的减振降噪结构。
(2)造价最经济结构优化设计。由于结构面积不变,粘贴阻尼层和约束层的加工费用是固定的,可以不考虑,因此只考虑结构的材料费用。以约束阻尼结构各层厚度为设计变量;约束条件为满足环境标准规定的振动噪音上限值要求;建立造价最经济结构优化模型。该优化模型是一个线性规划优化模型,采用设计变量的倒数作为新的设计变量,运用响应面方法将结构的振动加速度级约束条件显式化为倒变量的函数,将倒变量的造价目标函数进行泰勒二阶展开,得到标准的二次规划求解优化模型,优化程序收敛速度快,得到了满足结构性能约束下的最经济结构。
(3)响应面方法是对样本点及其响应值的近似拟合,在进行初次响应面拟合后对拟合得到的显式函数进行检验和拟合精度运算,提高拟合函数的精确性和拟合效率。
To reduce the vibration and noise of the gear-box structure, the damping layer and constraint layer are pasted on the surface of thin shell, forming the constraint damping structure. Due to the complication of the gear-box model,the arched plate structure which arises the most serious vibration and noise, is isolated from the gear-box to reduce the computing amount. The constraint layer and the damping layer are pasted on the inner surface of the arched plate. The boundary conditions are simplified. The dynamic simulation of the arched plate structure is made based on ABAQUS, and the optimal designs for the most effective structure of vibration and noise reduction and the most economical structure of cost are made in the allowable ranges of the thickness of each layer of the constraint damping. The optimization of the vibration acceleration level with the mass condition and the optimization of cost with the vibration acceleration level condition are obtained respectively. The main researches are summarized as follows:
(1) The optimal design for the most effective structure of vibration and noise reduction. The design variables are respectively the thickness of basic layer, the thickness of damping layer and the thickness of constraint layer in the constrained damping structure; the designing constraint is to meet the total mass requirement; the objective functions are minimizing the normal maximal vibration acceleration of a few nodes on the structure, establishing the optimal model of the most effective structure of reducing vibration and noise, which is a multiobjective optimization. The K-S function is adopted to process the normal maximal acceleration of all representative points as a synthesis parameter, with the vibration acceleration level of it as the evaluation parameter for effect of reducing vibration and noise. The response surface methodology is used to explicit the vibration acceleration level function. The new model with a signal objective of the vibration acceleration level of the structure is obtained, which is solved by the sequential quadratic programming stably and gives out the more ideal structure.
(2) The optimal design for the most economical structure of cost. As the structure of the same size, the cost of processing the damping layer and the constraint layer is fixed, which could be out of considering. The material cost of the structure is the only to be think about. Thickness of each layer of the constraint damping structure are taken as design variables; meeting upper limit of the vibration noise required by the environmental standards is the designing constraint; establish the most economical structure optimization model, which is a linear programming optimization. Reciprocals of the designing variables are used as the new designing variables. The constraint of vibration acceleration level is explicated as the function of the reciprocal variables with the response surface methodology. The objective function of the reciprocal variables can be lunched as the second-order Taylor function. The standard model of sequential quadratic programming is obtained and solved. The convergence speed of the optimal program is fast. The most economical structure satisfying the performance condition is also obtained.
(3) Response surface methodology(RSM) is the curve fitting of the relationship between the inputs(variables) and outputs(responses) of a physical system by explicit functions. For RSM function of the first fitting, tests and fitting precision are made to improve the fitting accuracy and the fitting efficiency.
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