大型立式玻璃磨边机关键力学问题研究
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摘要
目前我国建筑单位面积能耗是发达国家的2至3倍，建筑能耗占能源消费总量的27.45%。玻璃门窗产生的热损失占建筑总能耗的50%，被称为“热洞”。中空玻璃具有隔热、隔音、防结露等优点，是一种高性价比的建筑节能材料，具有广阔的市场前景。
玻璃磨边是中空玻璃生产过程中的一道重要工序，可以消除原片玻璃切割后玻璃边缘存在的微观裂纹、应力集中等缺陷，提高钢化工序的成品率，避免对操作人员及设备造成伤害。立式玻璃磨边机具有占地面积小、调整简单、自动识别玻璃长宽尺寸等优点，适合多品种、多规格尺寸玻璃的批量加工。
目前国内立式玻璃磨边机市场被韩国明日之星、瑞士百超等国外公司所垄断。自主研发的立式玻璃磨边机存在砂轮堵转、砂轮架振动较大及启动慢等问题，主要原因是对磨削力、砂轮架动力学分析、传动系统快速响应特性等关键力学问题的研究不足。因此，上述关键力学问题的研究和突破，对大型立式玻璃磨边机的国产化、替代进口及设备的合理使用，具有重要的理论意义和实际应用价值。
磨削力是磨削过程的重要参数。本文针对立式磨边机砂轮悬臂安装、空间狭小、工作环境恶劣等特点，创造性地设计了一种以阶梯轴套为弹性元件的应变式磨削测力装置，并对磨削力进行正交实验研究，建立了磨削力预测模型，其预测精度与实际测量值的平均误差小于5%。实验数据的极差分析和方差分析表明：砂轮线速度vc、进给速度vf和倒角大小c等磨削工艺参数对磨削力影响的主次关系为：c最大、vf次之、vc最小；切向磨削力和径向磨削力均随c和vf的增加而增加，切向磨削力随vc的增加而减小，vc对径向磨削力没有显著影响。动态磨削力信号的平稳性、周期性及频谱分析表明：玻璃磨边磨削力信号是一种具有宽平稳性的周期振动信号，其特征频率为砂轮的旋转频率。研究结果为玻璃磨边磨削控制方案设计和磨削工艺参数优化奠定了理论基础，解决了砂轮堵转问题。
砂轮与砂轮架的振动直接影响磨边质量。论文针对砂轮架的结构特点，建立了1DOF和2DOF两种动力学模型，对周期激振力作用下砂轮架和砂轮的振动特性和规律进行理论分析。1DOF模型分析结果表明：砂轮架的振动响应过程包括瞬态响应和稳态响应两部分，增大系统的轴向刚度，可提高系统的固有频率，从而缩短瞬态响应过程、减小稳态振动的振幅；增加阻尼比ξ，可减小稳态振动振幅。2DOF模型分析结果表明：砂轮架与砂轮的振动与系统的质量比μ、固有频率比α和阻尼比ξ等参数有关，导出了合理μ、α、ξ值的算式，使砂轮与砂轮架在共振时具有相同且较小的动力放大因子，成功地解决了立式玻璃磨边机的动力学设计问题。
固有频率和主振型是系统的固有属性，由系统的结构本身所决定，与外载荷无关。本文采用基于ANSYS的参数化设计语言APDL，建立了考虑运动结合面动态特性的砂轮架参数化有限元分析模型，分析了砂轮架的前四阶固有频率和振型，与实验模态分析结果相比，该模型的平均计算误差小于23%。通过APDL程序批量计算，分析了丝杠直径、滑块安装板厚度、丝杠轴承及丝杠螺母结合面刚度、砂轮架位置等参数对系统固有频率的影响规律，为结构动态特性改进及设备的合理使用提供了科学依据。改进设计后，砂轮架的各阶固有频率提高10%以上，改善了其动态特性，提高了抗振能力。
为满足砂轮架的快速响应特性要求，本文以砂轮架的启动加速度最大为目标，建立了基于惯量匹配、速度匹配、转矩匹配等约束条件的砂轮架升降传动系统传动比优化设计数学模型，采用内点惩罚函数法求传动比的最优解，并将优化结果用于第二代立式磨边机，测试数据表明启动加速度提高了22.95%，额定进给速度提高了77.78%。
根据上述研究成果开发的第2代立式磨边机，已有2家国内用户正式投产使用，一年多的生产实践证明设备使用情况良好。
At present, the building energy consumption of unit area in China is two or threetimes as much as one of developed country, energy consumption of building is about27.45percent of the national one. Glass window and door is called heat cavitybecause the heat loss via it is high to50percent of total building energy consumption.Insulating glass is a building energy saving material with high performance to priceratio because of its heat and noise insulation effect, it has wide market foreground.
Grinding glass edge is an important process of insulating glass manufacture, itcan eliminate disfigurements like micro-crack and stress centralization of glass edgeproduced by cutting process, avoid damage to operator or machine of next processesand improve finished product rate of glass tempering procedure. Vertical glass edgegrinding machine has many excellent performances such as small floor area, easyadjustment and automatic identifying the length and width of glass, which is suitablefor batch machining of multi-variety and multi-specification glass.
The market of vertical glass edge grinding machine in China has been occupiedby foreign corporations such as Rising Star Glass Machinery Corporation of Koreaand Bystronic Group of Switzerland. The vertical glass edge grinding machinedeveloped by China has some problems such as locked rotation of grinding wheel,significant vibration and lower starting acceleration of grinding wheel carriage etc.,due to the lack of research on key mechanics problems like grinding force, dynamicanalysis of grinding wheel carriage and its rapid response characteristic of drivingsystem. Hence, the study and breakthrough on above key problems of mechanics hasimportant theoretical and practical values for the domestic manufacture, importsubstitution and appropriate use of large vertical glass edge grinding machine.
Grinding force is an important parameter during grinding process. According tothe structural characteristics of vertical glass edge grinding machine like grindingwheel cantilever installation, narrow space and wretched environment etc., the paperinnovatively designed a strain type grinding dynamometer which adopted ladder shaftsleeve as elastic component, finished orthogonal test of grinding force and establishedgrinding force forecast model. The average error is less than5percent between valuescalculated by grinding force forecast model and actual measuring values. The extremedifference and variance analysis of orthogonal test data indicates that grindingparameters have important influence on grinding force, the primary factor is chamfersize c, the secondary one is feed rate vfand the tertiary one is grinding wheel velocityvc, tangential and radial grinding forces increase with the accretion of c and vf,tangential grinding force decreases with the increase of vcwhich has little effect onradial grinding force. According to the analysis results about stationarity, periodicity and spectrum of dynamic grinding force signals, the grinding force signals of edgingglass are periodic vibration signals with stationarity, its characteristic frequency isequal to the rotating frequency of grinding wheel. The research results establish thetheoretical base for the design of grinding process control strategy and theoptimization of grinding parameters about vertical glass edge grinding machine, theproblem about locked rotation of grinding wheel is solved.
The grinding quality of glass edge was influenced directly by the vibration ofgrinding wheel and grinding wheel carriage. Two dynamic models called1DOF and2DOF system were founded according to the structure of grinding wheel carriage, thevibration characteristics and rules of grinding wheel and grinding wheel carriageeffected by periodic force were analyzed. The analyzing result of1DOF model showsthat the vibration response of grinding wheel carriage includes transient response andsteady response. The system natural frequency will be improved, transient responseprocess will be shortened and steady vibration amplitude will be reduced byenhancing the axial rigidity of system, steady vibration amplitude decreases with theincrease of damping ratio ξ. The analyzing result of2DOF model indicates thatvibrations of grinding wheel carriage and grinding wheel are related with mass ratio μ,natural frequency ratio α and damping ratio ξ of system, the expressions of reasonableμ, α and ξ were educed in order to get small and equal dynamic amplification factor ofgrinding wheel and grinding wheel carriage at resonance, which successfully resolvesthe problem on dynamic design of vertical glass edge grinding machine.
Natural frequency and modal shape are inherent attribute of system, they aredetermined by system structure instead of outside force. The finite element model(FEM) of grinding wheel carriage was established based on ANSYS parametricdesign language (APDL) which considering dynamic characteristics of moving joints,frontal four modal shapes and natural frequencies were analyzed, the average errorcalculated by FEM is less than23percent compared with the result of experimentalmodal analysis. The influences on natural frequency of system by the diameter of ballscrew, the fixing board thickness of slide block, the contact rigidity of ball screw andbearings and the working position of grinding wheel carriage were investigated. Theresearch results offer a scientific basis for the improvement of dynamic characteristicand reasonable use of vertical glass edge grinding machine. After improvement,natural frequencies of grinding wheel carriage are increased more than10percent, soits dynamic characteristic and anti-vibration ability are improved.
In order to improve the rapid response ability of grinding wheel carriage, theoptimization design model on the transmission ratio of lifting drive system based onmaximum starting acceleration of grinding wheel carriage was established, whichconsiders restriction conditions such as inertia match, speed match and torque match.The optimal transmission ratio was calculated by in-point method of SUMT (Sequential Unconstrained Minimization Technique) and was applied to the design ofsecond generation glass edge grinding machine. The maximum starting accelerationof grinding wheel carriage was improved22.95percent and its feed rate wasimproved77.78percent based on actual test data after optimization.
The second generation glass edge grinding machine based on above researchresult was used by two corporations in China, its actual application for more than oneyear shows the machine is in good condition.
玻璃磨边是中空玻璃生产过程中的一道重要工序，可以消除原片玻璃切割后玻璃边缘存在的微观裂纹、应力集中等缺陷，提高钢化工序的成品率，避免对操作人员及设备造成伤害。立式玻璃磨边机具有占地面积小、调整简单、自动识别玻璃长宽尺寸等优点，适合多品种、多规格尺寸玻璃的批量加工。
目前国内立式玻璃磨边机市场被韩国明日之星、瑞士百超等国外公司所垄断。自主研发的立式玻璃磨边机存在砂轮堵转、砂轮架振动较大及启动慢等问题，主要原因是对磨削力、砂轮架动力学分析、传动系统快速响应特性等关键力学问题的研究不足。因此，上述关键力学问题的研究和突破，对大型立式玻璃磨边机的国产化、替代进口及设备的合理使用，具有重要的理论意义和实际应用价值。
磨削力是磨削过程的重要参数。本文针对立式磨边机砂轮悬臂安装、空间狭小、工作环境恶劣等特点，创造性地设计了一种以阶梯轴套为弹性元件的应变式磨削测力装置，并对磨削力进行正交实验研究，建立了磨削力预测模型，其预测精度与实际测量值的平均误差小于5%。实验数据的极差分析和方差分析表明：砂轮线速度vc、进给速度vf和倒角大小c等磨削工艺参数对磨削力影响的主次关系为：c最大、vf次之、vc最小；切向磨削力和径向磨削力均随c和vf的增加而增加，切向磨削力随vc的增加而减小，vc对径向磨削力没有显著影响。动态磨削力信号的平稳性、周期性及频谱分析表明：玻璃磨边磨削力信号是一种具有宽平稳性的周期振动信号，其特征频率为砂轮的旋转频率。研究结果为玻璃磨边磨削控制方案设计和磨削工艺参数优化奠定了理论基础，解决了砂轮堵转问题。
砂轮与砂轮架的振动直接影响磨边质量。论文针对砂轮架的结构特点，建立了1DOF和2DOF两种动力学模型，对周期激振力作用下砂轮架和砂轮的振动特性和规律进行理论分析。1DOF模型分析结果表明：砂轮架的振动响应过程包括瞬态响应和稳态响应两部分，增大系统的轴向刚度，可提高系统的固有频率，从而缩短瞬态响应过程、减小稳态振动的振幅；增加阻尼比ξ，可减小稳态振动振幅。2DOF模型分析结果表明：砂轮架与砂轮的振动与系统的质量比μ、固有频率比α和阻尼比ξ等参数有关，导出了合理μ、α、ξ值的算式，使砂轮与砂轮架在共振时具有相同且较小的动力放大因子，成功地解决了立式玻璃磨边机的动力学设计问题。
固有频率和主振型是系统的固有属性，由系统的结构本身所决定，与外载荷无关。本文采用基于ANSYS的参数化设计语言APDL，建立了考虑运动结合面动态特性的砂轮架参数化有限元分析模型，分析了砂轮架的前四阶固有频率和振型，与实验模态分析结果相比，该模型的平均计算误差小于23%。通过APDL程序批量计算，分析了丝杠直径、滑块安装板厚度、丝杠轴承及丝杠螺母结合面刚度、砂轮架位置等参数对系统固有频率的影响规律，为结构动态特性改进及设备的合理使用提供了科学依据。改进设计后，砂轮架的各阶固有频率提高10%以上，改善了其动态特性，提高了抗振能力。
为满足砂轮架的快速响应特性要求，本文以砂轮架的启动加速度最大为目标，建立了基于惯量匹配、速度匹配、转矩匹配等约束条件的砂轮架升降传动系统传动比优化设计数学模型，采用内点惩罚函数法求传动比的最优解，并将优化结果用于第二代立式磨边机，测试数据表明启动加速度提高了22.95%，额定进给速度提高了77.78%。
根据上述研究成果开发的第2代立式磨边机，已有2家国内用户正式投产使用，一年多的生产实践证明设备使用情况良好。
At present, the building energy consumption of unit area in China is two or threetimes as much as one of developed country, energy consumption of building is about27.45percent of the national one. Glass window and door is called heat cavitybecause the heat loss via it is high to50percent of total building energy consumption.Insulating glass is a building energy saving material with high performance to priceratio because of its heat and noise insulation effect, it has wide market foreground.
Grinding glass edge is an important process of insulating glass manufacture, itcan eliminate disfigurements like micro-crack and stress centralization of glass edgeproduced by cutting process, avoid damage to operator or machine of next processesand improve finished product rate of glass tempering procedure. Vertical glass edgegrinding machine has many excellent performances such as small floor area, easyadjustment and automatic identifying the length and width of glass, which is suitablefor batch machining of multi-variety and multi-specification glass.
The market of vertical glass edge grinding machine in China has been occupiedby foreign corporations such as Rising Star Glass Machinery Corporation of Koreaand Bystronic Group of Switzerland. The vertical glass edge grinding machinedeveloped by China has some problems such as locked rotation of grinding wheel,significant vibration and lower starting acceleration of grinding wheel carriage etc.,due to the lack of research on key mechanics problems like grinding force, dynamicanalysis of grinding wheel carriage and its rapid response characteristic of drivingsystem. Hence, the study and breakthrough on above key problems of mechanics hasimportant theoretical and practical values for the domestic manufacture, importsubstitution and appropriate use of large vertical glass edge grinding machine.
Grinding force is an important parameter during grinding process. According tothe structural characteristics of vertical glass edge grinding machine like grindingwheel cantilever installation, narrow space and wretched environment etc., the paperinnovatively designed a strain type grinding dynamometer which adopted ladder shaftsleeve as elastic component, finished orthogonal test of grinding force and establishedgrinding force forecast model. The average error is less than5percent between valuescalculated by grinding force forecast model and actual measuring values. The extremedifference and variance analysis of orthogonal test data indicates that grindingparameters have important influence on grinding force, the primary factor is chamfersize c, the secondary one is feed rate vfand the tertiary one is grinding wheel velocityvc, tangential and radial grinding forces increase with the accretion of c and vf,tangential grinding force decreases with the increase of vcwhich has little effect onradial grinding force. According to the analysis results about stationarity, periodicity and spectrum of dynamic grinding force signals, the grinding force signals of edgingglass are periodic vibration signals with stationarity, its characteristic frequency isequal to the rotating frequency of grinding wheel. The research results establish thetheoretical base for the design of grinding process control strategy and theoptimization of grinding parameters about vertical glass edge grinding machine, theproblem about locked rotation of grinding wheel is solved.
The grinding quality of glass edge was influenced directly by the vibration ofgrinding wheel and grinding wheel carriage. Two dynamic models called1DOF and2DOF system were founded according to the structure of grinding wheel carriage, thevibration characteristics and rules of grinding wheel and grinding wheel carriageeffected by periodic force were analyzed. The analyzing result of1DOF model showsthat the vibration response of grinding wheel carriage includes transient response andsteady response. The system natural frequency will be improved, transient responseprocess will be shortened and steady vibration amplitude will be reduced byenhancing the axial rigidity of system, steady vibration amplitude decreases with theincrease of damping ratio ξ. The analyzing result of2DOF model indicates thatvibrations of grinding wheel carriage and grinding wheel are related with mass ratio μ,natural frequency ratio α and damping ratio ξ of system, the expressions of reasonableμ, α and ξ were educed in order to get small and equal dynamic amplification factor ofgrinding wheel and grinding wheel carriage at resonance, which successfully resolvesthe problem on dynamic design of vertical glass edge grinding machine.
Natural frequency and modal shape are inherent attribute of system, they aredetermined by system structure instead of outside force. The finite element model(FEM) of grinding wheel carriage was established based on ANSYS parametricdesign language (APDL) which considering dynamic characteristics of moving joints,frontal four modal shapes and natural frequencies were analyzed, the average errorcalculated by FEM is less than23percent compared with the result of experimentalmodal analysis. The influences on natural frequency of system by the diameter of ballscrew, the fixing board thickness of slide block, the contact rigidity of ball screw andbearings and the working position of grinding wheel carriage were investigated. Theresearch results offer a scientific basis for the improvement of dynamic characteristicand reasonable use of vertical glass edge grinding machine. After improvement,natural frequencies of grinding wheel carriage are increased more than10percent, soits dynamic characteristic and anti-vibration ability are improved.
In order to improve the rapid response ability of grinding wheel carriage, theoptimization design model on the transmission ratio of lifting drive system based onmaximum starting acceleration of grinding wheel carriage was established, whichconsiders restriction conditions such as inertia match, speed match and torque match.The optimal transmission ratio was calculated by in-point method of SUMT (Sequential Unconstrained Minimization Technique) and was applied to the design ofsecond generation glass edge grinding machine. The maximum starting accelerationof grinding wheel carriage was improved22.95percent and its feed rate wasimproved77.78percent based on actual test data after optimization.
The second generation glass edge grinding machine based on above researchresult was used by two corporations in China, its actual application for more than oneyear shows the machine is in good condition.
引文
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