考虑空气阻力影响的送纸机构仿真及优化研究
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摘要
复印机、打印机、传真机等办公设备的普及使用,大大提高了人们的办公效率。但这些办公设备在使用中经常出现卡纸、异常振动、噪声过大等现象,一直都是困扰世界各国生产厂商的技术难题。近年来,国外知名的办公设备制造商,如佳能、理光等都已经在送纸机构设计方面开展了大量的研究工作。我国环保总局也在2005年出台的环境标志认证技术中明确规定,非击打式办公设备的噪声应控制在55分贝以下。普遍认为,造成卡纸、噪声过大这些问题的主要原因是由于送纸机构的设计不合理,不能根据送纸速度、送纸力的大小和作用点等因素合理布置拾取轮、进给轮、导板等机构的尺寸和位置。通过建立准确有效的送纸机构仿真模型可以科学的指导办公设备的设计,缩短产品开发周期,节约成本。
研究表明,纸张在传送过程中受到摩擦、温度、气流和冲击等多重影响,准确模拟这些影响因素往往会使得建模过程非常复杂。因此目前研究主要集中在纸张的静态力学性能、传送过程中的动态性能分析等方面,对考虑这些复杂影响因素的纸张真实运动状态的仿真研究尚不多见。又由于纸张本身具有重量轻、面积大的特点,在办公设备高速送纸的过程中,空气阻力成为纸张的运动形态和受力状况的关键影响因素之一。在以往的送纸机构仿真模型中,仿真环境均为真空,忽略了空气阻力的影响,显然这样的处理会影响仿真精度。
为了模拟纸张在送纸过程中的真实运动状态并对送纸机构进行优化设计,本文首先基于流体连续方程和Navier-Stokes方程建立了纸张与导板间空气流场的流体力学模型,推导了空气阻力分布微分方程。通过用户自定义子程序接口对送纸机构仿真软件RecurDyn进行二次开发,将该方程程序化,实现了考虑空气阻力影响的送纸过程数值仿真。
确定送纸机构模型中的关键参数并建立仿真模型,对考虑空气阻力的送纸过程进行了仿真计算。将仿真计算得出的纸张末端下落速度和纸张与导板的冲击力结果与实验结果进行对比,表明该模型可以有效地提高送纸过程的仿真精度,误差控制在5%以内。
基于所建立的送纸机构仿真模型,以纸张与导板的冲击力为目标函数,对导板的位置参数进行优化设计研究。提出的改进模型可以降低纸张与导板的冲击力,送纸机构布局更加紧凑合理,从而减小复印机的噪声水平。研究结果对解决送纸机构中出现的卡纸、振动、噪声等问题具有指导意义。
Copying machines, printers and fax machines have been widely used in daily life in order to increase the efficiency of office work. However, manufacturers are suffering paper jam, abnormal vibration and over-noise from theses office equipment. Recently, the well-known office equipment producers such as Canon and Ricoh have been evolved in a lot of research work in this field. Meanwhile, the environment label requirement issued by China Environment Protection Agency in 2005 also states that the noise of non-impact copying machines should be lower than 55dB. It is commonly believed that the reason of these problems is the irrational design of paper feeding mechanism which cannot offer a reasonable layout such as picking rollers, feeding rollers and guide. An accurate simulation model can provide scientific guidance for paper feeding mechanism to shorten the product develop cycle and save the cost.
The current research indicates that there are multiple effects acting on paper during the feeding process such as friction, temperature, air flow and impact. As a result, it is difficult to construct simulation models while considering the above factors. Therefore, most research is focusing on static property of paper and dynamic properties during paper feeding process. Research considering these effects to paper feeding process is quite limited. Also, because of the light-weight and big area of paper itself, under the condition of high speed movement, air resistance could be one of the key factors influencing paper shape and form. Obviously, the accuracy of previous simulation models are not enough due to neglect the air resistance effect, only dealing the simulation environment as vacuum.
In order to simulate a real paper movement status in office equipment and further propose an optimized design for paper feeding mechanism, firstly, based on the fluid continuous equation and Navier-Stokes equation, the air resistance distribution equation has been deduced. Applying this equation into RecurDyn user subroutine modulus, simulation process considering air resistance effect could be conducted through second-development to the software.
Simulation considering air resistance has been carried out after deciding the critical parameters in paper feeding mechanism. Comparing the simulation result with experiment result including the falling down velocity of paper end and impact force between guide plates, the calculation accuracy can be verified. The result demonstrated that the new simulation model can enhance the simulation accuracy greatly, whose error is controlled fewer than 5%.
Based on the simulation model considering air resistance, the position parameters of guide plates have been optimized with the impact force between paper and guide as objective function. The result after optimization shows that the impact force can be reduced to a great extend, which can suppress the noise in office equipment. The research can help solve the problems of paper jam, vibration and over-noise.
研究表明,纸张在传送过程中受到摩擦、温度、气流和冲击等多重影响,准确模拟这些影响因素往往会使得建模过程非常复杂。因此目前研究主要集中在纸张的静态力学性能、传送过程中的动态性能分析等方面,对考虑这些复杂影响因素的纸张真实运动状态的仿真研究尚不多见。又由于纸张本身具有重量轻、面积大的特点,在办公设备高速送纸的过程中,空气阻力成为纸张的运动形态和受力状况的关键影响因素之一。在以往的送纸机构仿真模型中,仿真环境均为真空,忽略了空气阻力的影响,显然这样的处理会影响仿真精度。
为了模拟纸张在送纸过程中的真实运动状态并对送纸机构进行优化设计,本文首先基于流体连续方程和Navier-Stokes方程建立了纸张与导板间空气流场的流体力学模型,推导了空气阻力分布微分方程。通过用户自定义子程序接口对送纸机构仿真软件RecurDyn进行二次开发,将该方程程序化,实现了考虑空气阻力影响的送纸过程数值仿真。
确定送纸机构模型中的关键参数并建立仿真模型,对考虑空气阻力的送纸过程进行了仿真计算。将仿真计算得出的纸张末端下落速度和纸张与导板的冲击力结果与实验结果进行对比,表明该模型可以有效地提高送纸过程的仿真精度,误差控制在5%以内。
基于所建立的送纸机构仿真模型,以纸张与导板的冲击力为目标函数,对导板的位置参数进行优化设计研究。提出的改进模型可以降低纸张与导板的冲击力,送纸机构布局更加紧凑合理,从而减小复印机的噪声水平。研究结果对解决送纸机构中出现的卡纸、振动、噪声等问题具有指导意义。
Copying machines, printers and fax machines have been widely used in daily life in order to increase the efficiency of office work. However, manufacturers are suffering paper jam, abnormal vibration and over-noise from theses office equipment. Recently, the well-known office equipment producers such as Canon and Ricoh have been evolved in a lot of research work in this field. Meanwhile, the environment label requirement issued by China Environment Protection Agency in 2005 also states that the noise of non-impact copying machines should be lower than 55dB. It is commonly believed that the reason of these problems is the irrational design of paper feeding mechanism which cannot offer a reasonable layout such as picking rollers, feeding rollers and guide. An accurate simulation model can provide scientific guidance for paper feeding mechanism to shorten the product develop cycle and save the cost.
The current research indicates that there are multiple effects acting on paper during the feeding process such as friction, temperature, air flow and impact. As a result, it is difficult to construct simulation models while considering the above factors. Therefore, most research is focusing on static property of paper and dynamic properties during paper feeding process. Research considering these effects to paper feeding process is quite limited. Also, because of the light-weight and big area of paper itself, under the condition of high speed movement, air resistance could be one of the key factors influencing paper shape and form. Obviously, the accuracy of previous simulation models are not enough due to neglect the air resistance effect, only dealing the simulation environment as vacuum.
In order to simulate a real paper movement status in office equipment and further propose an optimized design for paper feeding mechanism, firstly, based on the fluid continuous equation and Navier-Stokes equation, the air resistance distribution equation has been deduced. Applying this equation into RecurDyn user subroutine modulus, simulation process considering air resistance effect could be conducted through second-development to the software.
Simulation considering air resistance has been carried out after deciding the critical parameters in paper feeding mechanism. Comparing the simulation result with experiment result including the falling down velocity of paper end and impact force between guide plates, the calculation accuracy can be verified. The result demonstrated that the new simulation model can enhance the simulation accuracy greatly, whose error is controlled fewer than 5%.
Based on the simulation model considering air resistance, the position parameters of guide plates have been optimized with the impact force between paper and guide as objective function. The result after optimization shows that the impact force can be reduced to a great extend, which can suppress the noise in office equipment. The research can help solve the problems of paper jam, vibration and over-noise.
引文
[1] Manila M. Printers and Copiers: Copying with Paper Jams and Copier Problems[J]. Business World, 1999, 25(29):5-7.
[2] Hay D A.. Paper Document via the Electronic Control of Particles [J]. Journal of Electrostatics, 2000, 51:57-63.
[3] Cheryl D C. Getting out of Paper Jam [J]. American Printer, 2001, 204(7):13-17.
[4]孙大涌等.先进制造技术[M].北京:机械工业出版社, 2000.
[5]周济. CAD技术在中国制造业中的应用[J].机械与电子, 1998, 23(4):11-13.
[6]王锡山.中小型制造企业CAE应用[J].计算机辅助设计与制造, 2001, 18(3):5-6.
[7]刘勇谋.CAE软件发展的新动向[J].计算机辅助设计与制造,2001,(2):83～86.
[8] KunwooLee. Principles of CAD/CAM/CAE[M].Addison-Wesley Reading MA.1999.
[9] Soares M E S. Nonlinear Normal Modes of Planar Frames Discredited by the FEM [ J ]. Computers and Structures. 2000, 77(5): 485-493.
[10] Yoshida K, Kawauchi M. Analysis of Deformation and Behavior of Flexible Materials– 1st Report, Study of Spring-Mass Beam Model of the Sheet [C]. JSME, 1992, 58(552): 189-194.
[11] Heegaard J.H., Curnier A. An Augmented Lagrange Method for Discrete Large-Slip Contact Problems [J]. Journal of Numerical Method Engineering, 1993, 36(5), 569-593.
[12] Oliver J, Onate E. A Total Lagrange Formulation fro the Geometrically Nonlinea Analysis of Structure Using Finite Elements [J]. International Journal for Numerical Methods Engineering, 1986, 23(2): 253-274.
[13] Sheng G, Liu B. Generalized High-order Accurate Newmark Method for Head-desk Interface Dynamic in Magnetic Recording Theology [J]. Finite Element in Analysis and Design, 1998, 29(2): 78-103.
[14] Yoshida K, Kawauchi M. Analysis of Deformation and Behavior of Flexible Materials - 2nd Report, Static Analysis for Deformation of the Sheet in the Space Formed by Guide Plates [C]. JSME, 1994, 60(570): 212-216.
[15] Yoshida K., Kondo K. Simulation Technology for Flexible Media Handling Mechanism [J]. Journal of the Japan Society for Simulation Technology, 1998, 17(1): 35-43.
[16]蒋友谅.非线性有限元法[M].北京:北京工业学院出版社, 1988.
[17]王勖成,邵敏.有限单元法基本原理和数值方法(第二版)[M].北京:清华大学出版社, 1997.
[18] Oral. S, Barut, A . A Shear-flexible Facet Shell Element for Large Deflection and Instability Analysis [J]. Camp Meth in Apply Mechanical Engineering, 1991. 93(2): 415-431.
[19]陈雪峰,杨胜军,马军星. CAE技术在办公设备送纸机构中的应用[J].机械科学与技术, 2002, 21(6): 1020-1023.
[20]陈雪峰,李兵,何正嘉.办公纸张不同有限元计算模型的研究[J].小型微型计2004,25(1): 152-154.
[21]杨胜军,马军星,何正嘉.办公设备用纸力学特性的非线性有限元分析[J].西安交通大学学报, 2000, 34(9): 67-71.
[22]贾丽萍,张建武,崔东印.纸张大变形非线性有限元分析[J].上海交通大学学报, 2001, 35(7): 1085-1087.
[23] Yoshida K. Dynamic Analysis of Sheet Deformation Using Spring-Mass-Beam Model [C]. JSME, 1997, 63(615):231-236.
[24] Stefanou G D. Dynamic Response Analysis of Nonlinear structure Using Step-by step Integration techniques [J]. Computer and Structure, 1995, 57(6): 1063-1070.
[25] Yoshida K, Kawauchi M. Analysis of Deformation and Behavior of Flexible Materials– 3rd Report, Study of Discrete Beam Model of a Sheet for Tensional Deformation [C]. JSME, 1996, 62(598): 174-180.
[26] Bhattacharyya, S, Pal A. Unsteady MHD Squeezing Flow Between Two Parallel Rotating Discs [J]. Mechanics Research Communicates, 1997, 34(6): 615-623.
[27]朱应敏,贾建援,樊康旗. MEMS器件平板运动空气阻尼研究[J].电子科技大学学报, 2007, 36(5): 965-969.
[28] Yuancheng S., Minhang B. Modified Reynolds Equation for Squeeze-Film Air Damping of Slotted Plates in MEMS Devices [J]. Chinese Journal of Semiconductors. 2006, 27(3): 473-477.
[29] G. Roy, D. Vo-Ngoc. Behavior of Radial Incompressible Flow in Pneumatic Dimensional Control Systems [J]. Journal of Fluids Engineering, 2003, 125(9): 843-850.
[30] Ishizawa S., Watanabe T., Takahashi K. Unsteady Viscous Flow Between Parallel Disks with a Time-Varying Gap Width and Central Fluid Source[J]. Journal of Fluids Engineering, 1987, 109(4): 394-402.
[31] Emin. M. Flow due to parallel disks rotating about non-coincident axis with one of them oscillating in its plane [J]. International Journal of Non-Linear Mechanics, 1999, 34(7), 1019-1030.
[32] C.H. Ta., Y. Zhao. Parallel Computation of Unsteady Incompressible Viscous Flows Around Moving Rigid Bodies Using an Immersed Object Method with Overlapping Grids [J] Journal of Computational Physics, 2005, 207(6):151-172.
[33] Sadd M H, Stiffler A K. Squeeze Film Dampers: Amplitude Effect at Low Squeeze Numbers [J]. Jounal of Engineering for Industry 2005, 34(4): 33-47.
[34] Kumari. M, Takhar. H.S. Unsteady flow of a viscous fluid between two parallel disks with a time varying gap width and magnetic field [J]. International Journal of Engineering Science, 1995, 33(6): 781-791.
[35]张国强,吴家鸣.流体力学[M].北京:机械工业出版社, 2005.
[36] RecurDyn V7.0 User’s Help Library 2008.
[37]张志娟,关晓东. MSC Adams用户自定义子程序在卫星姿控系统仿真分析中的应用[J].计算机辅助工程, 2006, 15(9): 4-7.
[38]邱志勇,黄华,董明明.履带张紧装置柔体动力学模型及其仿真[J].计算机仿真, 2007, 24(1): 254-257.
[39]马军星. Daubechies小波有限元理论及工程应用研究. [博士学位论文],西安交通大学,2003.
[40]杨胜军,马军星,何正嘉.办公设备纸张自由振动阻尼特性研究[J].西安交通大学学报, 2000, 34(7): 48-51.
[41]马军星,杨胜军,薛继军.纸张动态分析中阻尼矩阵的实验确定方法[J].西安交通大学学报, 2002, 36(1): 51-57.
[42]谢友柏.论机械学[J].中国机械工程, 2001, 12(6):692～697.
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[2] Hay D A.. Paper Document via the Electronic Control of Particles [J]. Journal of Electrostatics, 2000, 51:57-63.
[3] Cheryl D C. Getting out of Paper Jam [J]. American Printer, 2001, 204(7):13-17.
[4]孙大涌等.先进制造技术[M].北京:机械工业出版社, 2000.
[5]周济. CAD技术在中国制造业中的应用[J].机械与电子, 1998, 23(4):11-13.
[6]王锡山.中小型制造企业CAE应用[J].计算机辅助设计与制造, 2001, 18(3):5-6.
[7]刘勇谋.CAE软件发展的新动向[J].计算机辅助设计与制造,2001,(2):83～86.
[8] KunwooLee. Principles of CAD/CAM/CAE[M].Addison-Wesley Reading MA.1999.
[9] Soares M E S. Nonlinear Normal Modes of Planar Frames Discredited by the FEM [ J ]. Computers and Structures. 2000, 77(5): 485-493.
[10] Yoshida K, Kawauchi M. Analysis of Deformation and Behavior of Flexible Materials– 1st Report, Study of Spring-Mass Beam Model of the Sheet [C]. JSME, 1992, 58(552): 189-194.
[11] Heegaard J.H., Curnier A. An Augmented Lagrange Method for Discrete Large-Slip Contact Problems [J]. Journal of Numerical Method Engineering, 1993, 36(5), 569-593.
[12] Oliver J, Onate E. A Total Lagrange Formulation fro the Geometrically Nonlinea Analysis of Structure Using Finite Elements [J]. International Journal for Numerical Methods Engineering, 1986, 23(2): 253-274.
[13] Sheng G, Liu B. Generalized High-order Accurate Newmark Method for Head-desk Interface Dynamic in Magnetic Recording Theology [J]. Finite Element in Analysis and Design, 1998, 29(2): 78-103.
[14] Yoshida K, Kawauchi M. Analysis of Deformation and Behavior of Flexible Materials - 2nd Report, Static Analysis for Deformation of the Sheet in the Space Formed by Guide Plates [C]. JSME, 1994, 60(570): 212-216.
[15] Yoshida K., Kondo K. Simulation Technology for Flexible Media Handling Mechanism [J]. Journal of the Japan Society for Simulation Technology, 1998, 17(1): 35-43.
[16]蒋友谅.非线性有限元法[M].北京:北京工业学院出版社, 1988.
[17]王勖成,邵敏.有限单元法基本原理和数值方法(第二版)[M].北京:清华大学出版社, 1997.
[18] Oral. S, Barut, A . A Shear-flexible Facet Shell Element for Large Deflection and Instability Analysis [J]. Camp Meth in Apply Mechanical Engineering, 1991. 93(2): 415-431.
[19]陈雪峰,杨胜军,马军星. CAE技术在办公设备送纸机构中的应用[J].机械科学与技术, 2002, 21(6): 1020-1023.
[20]陈雪峰,李兵,何正嘉.办公纸张不同有限元计算模型的研究[J].小型微型计2004,25(1): 152-154.
[21]杨胜军,马军星,何正嘉.办公设备用纸力学特性的非线性有限元分析[J].西安交通大学学报, 2000, 34(9): 67-71.
[22]贾丽萍,张建武,崔东印.纸张大变形非线性有限元分析[J].上海交通大学学报, 2001, 35(7): 1085-1087.
[23] Yoshida K. Dynamic Analysis of Sheet Deformation Using Spring-Mass-Beam Model [C]. JSME, 1997, 63(615):231-236.
[24] Stefanou G D. Dynamic Response Analysis of Nonlinear structure Using Step-by step Integration techniques [J]. Computer and Structure, 1995, 57(6): 1063-1070.
[25] Yoshida K, Kawauchi M. Analysis of Deformation and Behavior of Flexible Materials– 3rd Report, Study of Discrete Beam Model of a Sheet for Tensional Deformation [C]. JSME, 1996, 62(598): 174-180.
[26] Bhattacharyya, S, Pal A. Unsteady MHD Squeezing Flow Between Two Parallel Rotating Discs [J]. Mechanics Research Communicates, 1997, 34(6): 615-623.
[27]朱应敏,贾建援,樊康旗. MEMS器件平板运动空气阻尼研究[J].电子科技大学学报, 2007, 36(5): 965-969.
[28] Yuancheng S., Minhang B. Modified Reynolds Equation for Squeeze-Film Air Damping of Slotted Plates in MEMS Devices [J]. Chinese Journal of Semiconductors. 2006, 27(3): 473-477.
[29] G. Roy, D. Vo-Ngoc. Behavior of Radial Incompressible Flow in Pneumatic Dimensional Control Systems [J]. Journal of Fluids Engineering, 2003, 125(9): 843-850.
[30] Ishizawa S., Watanabe T., Takahashi K. Unsteady Viscous Flow Between Parallel Disks with a Time-Varying Gap Width and Central Fluid Source[J]. Journal of Fluids Engineering, 1987, 109(4): 394-402.
[31] Emin. M. Flow due to parallel disks rotating about non-coincident axis with one of them oscillating in its plane [J]. International Journal of Non-Linear Mechanics, 1999, 34(7), 1019-1030.
[32] C.H. Ta., Y. Zhao. Parallel Computation of Unsteady Incompressible Viscous Flows Around Moving Rigid Bodies Using an Immersed Object Method with Overlapping Grids [J] Journal of Computational Physics, 2005, 207(6):151-172.
[33] Sadd M H, Stiffler A K. Squeeze Film Dampers: Amplitude Effect at Low Squeeze Numbers [J]. Jounal of Engineering for Industry 2005, 34(4): 33-47.
[34] Kumari. M, Takhar. H.S. Unsteady flow of a viscous fluid between two parallel disks with a time varying gap width and magnetic field [J]. International Journal of Engineering Science, 1995, 33(6): 781-791.
[35]张国强,吴家鸣.流体力学[M].北京:机械工业出版社, 2005.
[36] RecurDyn V7.0 User’s Help Library 2008.
[37]张志娟,关晓东. MSC Adams用户自定义子程序在卫星姿控系统仿真分析中的应用[J].计算机辅助工程, 2006, 15(9): 4-7.
[38]邱志勇,黄华,董明明.履带张紧装置柔体动力学模型及其仿真[J].计算机仿真, 2007, 24(1): 254-257.
[39]马军星. Daubechies小波有限元理论及工程应用研究. [博士学位论文],西安交通大学,2003.
[40]杨胜军,马军星,何正嘉.办公设备纸张自由振动阻尼特性研究[J].西安交通大学学报, 2000, 34(7): 48-51.
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