卷筒纸印刷机含间隙折页机构动力学研究及稳健设计
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摘要
高速、高精度和高稳定性是现代印刷机械的重要特征和必然要求。卷筒纸印刷机是目前世界上印刷速度最高的大型设备,而折页机构是制约卷筒纸印刷机速度进一步提高的关键因素之一。本文结合印刷机械特点和发展趋势,以卷筒纸印刷机折页机构为研究对象,围绕提高折页机构的精度和稳定性,对折页机构进行含间隙机构动力学研究和稳健设计。
针对运动副间隙和轴承滚子变形引起的折页机构非线性动态响应问题,提出刚性杆与弹簧组合假设,建立了折页机构间隙动力学模型。根据折页机构运动副的实际情况,对运动副间隙引用刚性杆假设；对滚子变形,提出滚子径向刚度,将滚子假设为弹簧。刚性杆与弹簧组合假设使折页机构增加了四个广义自由度和八个局部自由度,形成多自由度的复杂机械系统。间隙动力学模型由三部分组成：运动学分析得出折页机构运动输出与输入、运动副间隙角、弹簧变形及转角的运动学关系；拉格朗日方程建立的求解各运动副间隙角的动力学方程组；达朗伯原理建立的各构件平衡方程,求解各运动副约束反力,进而求出弹簧的变形及转角。对含二阶偏微分方程组的含间隙折页机构动力学模型,采用龙格—库塔法进行求解。最后,通过折页机构动态测试,对含间隙折页机构动力学模型进行了验证。
得出了动态响应与折页机构转速和运动副间隙的定量关系,并提出折页机构动态响应分化点和动载系数。运用动态响应分化点,分析不同运动副间隙状态下折页机构稳定运转的最高速度；通过动载系数,分析在正常工作速度下折页机构允许的最大运动副间隙。折刀头的横向位移直接影响折页精度。运用有限元方法分析折刀杆变形,建立了折刀头横向位移模型,研究了折页精度与运转速度和运动副间隙的关系。
考虑设计变量和加工误差等因素对折页机构性能的影响,首次采用灵敏度分析法和方差分析法,研究折页机构的稳健性。利用间隙动力学模型,推导出折页机构灵敏度分析模型和方差分析模型。动态响应的灵敏度能直观地反映出设计变量对折页机构性能影响的强弱。动态响应的方差可以分析出加工误差等随机因素引起折页机构性能偏差的概率。
在稳健性分析的基础上,对折页机构进行了稳健设计研究。以折页机构折页偏差和灵敏度最小为目标,建立设计变量均值的稳健设计模型。以容差分析法为基础,结合加工成本与容差的关系,建立折页机构设计变量公差稳健设计模型。结合两种模型的优点,构建了折页机构稳健设计综合模型。稳健设计综合模型,能同时求解出设计变量的均值和公差,解决了设计变量均值与公差不相融的问题,避免了公差稳健设计模型的复杂计算。通过原设计方案与稳健设计方案设计结果对比动态响应测试实验,验证了稳健设计综合模型的有效性和可行性。
High speed, high precision and high stability are the important features and inevitable requirement of modern printing machinery. Web offset press is the highest speed large equipment, but the folding mechanism is one of the critical factors to restrict the printing speed of web offset press. In this paper, combined with the characteristics and development tendencies of modern printing machinery, and around with improving the accuracy and stability of folding mechanism, dynamics of mechanism with clearance and robust design to the folding mechanism are studied.
To the nonlinear dynamic response of folder system caused by the pair clearance and the bearing stiffness, the hypothesis of rigid role and spring combination is put forward, and the dynamics model of folder mechanism with clearance is established. According to the actual situation of folding mechanism's pair, rigid pole hypothesis is quoted to the pair clearance, and the roller is assumed as a spring to it's deformation, by defined the roller radial stiffness. The hypothesis makes folder system to be a multi-freedom complex mechanical system by adding four broad freedoms and eight local freedoms. The dynamics model consists of three parts:kinematics analysis which can draw the relationship of kinematics output to input, the clearance angle, the spring deformation and angle, dynamics equations which is established by Lagrangian equation to solve the clearance angles, and each component's balance equationg which is derived by D'alembert's principle to solve the clearance's constrain forces and the spring's deformation and angle. The dynamics model which contains second order partial differential equations, is solved by Longur-Coulthard method. The dynamic model is verified by the dynamic testing to the folding machainism.
The quantitative relation between dynamic responses to the working speed and the clearance is gotten, and folding mechanism's response differentiation point and dynamic load coefficient, are provided. The response differentiation point can be used to analysis the folding mechanism's highest speed in different clearance. Dynamic load coefficient can be used to analysis the maximum allowable clearance in working speed. The fold cutter's lateral deformation is the key factor to influence the folding precision. The cutter's lateral deformation model is established to research the relationship of the folding precision to the working speed and the clearance, by the finite element method and the analysis to the deformatin of folding stem.
Considering the design variables and processing error influence on the performance of folding mechanism, the sensitivity analysis method and variance analysis method are firstly used to research the robustness of folding mechanism. The sensitivity analysis model and variance analysis model are derived by folding mechanism's clearance dynamics model. The response sensitivity can intuitivey reflect the affect degree of each design variables to the folding mechanism's performance. The response variance can analysis the performance deviation probability of folding mechanism caused by the random factors such as processing error.
Based on the robustness analysis, the robust design mothed is studied. Used the minimization of folding deviation and sensitivity as the goals, the robust design model to the mean design variables is established. Based on the variance analysis, and combined with the relationship of processing cost and tolerance, the robust design model to the design variables'tolerance is derived. Combined with the advantages of two models, the folding mechanism robust design integrated model is constructed. The robust design integrated model can simultaneously solved the mean design variables and the design variables'tolerance, which can solved the no-consistency problem of the mean design variables and the design variables'tolerance, and avoid the complex calculation in the robust design model to the design variables'tolerance. A contrast test, which is to the results of the original scheme and robust design scheme, is done on the device. The test result confirms the validity and feasibility of robust desigh mothed.
针对运动副间隙和轴承滚子变形引起的折页机构非线性动态响应问题,提出刚性杆与弹簧组合假设,建立了折页机构间隙动力学模型。根据折页机构运动副的实际情况,对运动副间隙引用刚性杆假设；对滚子变形,提出滚子径向刚度,将滚子假设为弹簧。刚性杆与弹簧组合假设使折页机构增加了四个广义自由度和八个局部自由度,形成多自由度的复杂机械系统。间隙动力学模型由三部分组成：运动学分析得出折页机构运动输出与输入、运动副间隙角、弹簧变形及转角的运动学关系；拉格朗日方程建立的求解各运动副间隙角的动力学方程组；达朗伯原理建立的各构件平衡方程,求解各运动副约束反力,进而求出弹簧的变形及转角。对含二阶偏微分方程组的含间隙折页机构动力学模型,采用龙格—库塔法进行求解。最后,通过折页机构动态测试,对含间隙折页机构动力学模型进行了验证。
得出了动态响应与折页机构转速和运动副间隙的定量关系,并提出折页机构动态响应分化点和动载系数。运用动态响应分化点,分析不同运动副间隙状态下折页机构稳定运转的最高速度；通过动载系数,分析在正常工作速度下折页机构允许的最大运动副间隙。折刀头的横向位移直接影响折页精度。运用有限元方法分析折刀杆变形,建立了折刀头横向位移模型,研究了折页精度与运转速度和运动副间隙的关系。
考虑设计变量和加工误差等因素对折页机构性能的影响,首次采用灵敏度分析法和方差分析法,研究折页机构的稳健性。利用间隙动力学模型,推导出折页机构灵敏度分析模型和方差分析模型。动态响应的灵敏度能直观地反映出设计变量对折页机构性能影响的强弱。动态响应的方差可以分析出加工误差等随机因素引起折页机构性能偏差的概率。
在稳健性分析的基础上,对折页机构进行了稳健设计研究。以折页机构折页偏差和灵敏度最小为目标,建立设计变量均值的稳健设计模型。以容差分析法为基础,结合加工成本与容差的关系,建立折页机构设计变量公差稳健设计模型。结合两种模型的优点,构建了折页机构稳健设计综合模型。稳健设计综合模型,能同时求解出设计变量的均值和公差,解决了设计变量均值与公差不相融的问题,避免了公差稳健设计模型的复杂计算。通过原设计方案与稳健设计方案设计结果对比动态响应测试实验,验证了稳健设计综合模型的有效性和可行性。
High speed, high precision and high stability are the important features and inevitable requirement of modern printing machinery. Web offset press is the highest speed large equipment, but the folding mechanism is one of the critical factors to restrict the printing speed of web offset press. In this paper, combined with the characteristics and development tendencies of modern printing machinery, and around with improving the accuracy and stability of folding mechanism, dynamics of mechanism with clearance and robust design to the folding mechanism are studied.
To the nonlinear dynamic response of folder system caused by the pair clearance and the bearing stiffness, the hypothesis of rigid role and spring combination is put forward, and the dynamics model of folder mechanism with clearance is established. According to the actual situation of folding mechanism's pair, rigid pole hypothesis is quoted to the pair clearance, and the roller is assumed as a spring to it's deformation, by defined the roller radial stiffness. The hypothesis makes folder system to be a multi-freedom complex mechanical system by adding four broad freedoms and eight local freedoms. The dynamics model consists of three parts:kinematics analysis which can draw the relationship of kinematics output to input, the clearance angle, the spring deformation and angle, dynamics equations which is established by Lagrangian equation to solve the clearance angles, and each component's balance equationg which is derived by D'alembert's principle to solve the clearance's constrain forces and the spring's deformation and angle. The dynamics model which contains second order partial differential equations, is solved by Longur-Coulthard method. The dynamic model is verified by the dynamic testing to the folding machainism.
The quantitative relation between dynamic responses to the working speed and the clearance is gotten, and folding mechanism's response differentiation point and dynamic load coefficient, are provided. The response differentiation point can be used to analysis the folding mechanism's highest speed in different clearance. Dynamic load coefficient can be used to analysis the maximum allowable clearance in working speed. The fold cutter's lateral deformation is the key factor to influence the folding precision. The cutter's lateral deformation model is established to research the relationship of the folding precision to the working speed and the clearance, by the finite element method and the analysis to the deformatin of folding stem.
Considering the design variables and processing error influence on the performance of folding mechanism, the sensitivity analysis method and variance analysis method are firstly used to research the robustness of folding mechanism. The sensitivity analysis model and variance analysis model are derived by folding mechanism's clearance dynamics model. The response sensitivity can intuitivey reflect the affect degree of each design variables to the folding mechanism's performance. The response variance can analysis the performance deviation probability of folding mechanism caused by the random factors such as processing error.
Based on the robustness analysis, the robust design mothed is studied. Used the minimization of folding deviation and sensitivity as the goals, the robust design model to the mean design variables is established. Based on the variance analysis, and combined with the relationship of processing cost and tolerance, the robust design model to the design variables'tolerance is derived. Combined with the advantages of two models, the folding mechanism robust design integrated model is constructed. The robust design integrated model can simultaneously solved the mean design variables and the design variables'tolerance, which can solved the no-consistency problem of the mean design variables and the design variables'tolerance, and avoid the complex calculation in the robust design model to the design variables'tolerance. A contrast test, which is to the results of the original scheme and robust design scheme, is done on the device. The test result confirms the validity and feasibility of robust desigh mothed.
引文
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