基于磁力弹簧的非公路车辆驾驶员座椅悬架系统研究
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摘要
研究表明，对于长期作业和行驶在恶劣环境中的农用车辆、林用车辆以及工程车辆等非公路车辆，采用座椅悬架提高其乘坐舒适性是最为简单直接和经济的方法。因此，深入研究驾驶员座椅悬架系统，采用切实可行的技术措施，隔离由于地面激励而引起的通过车辆底盘和座椅传递到人体的振动，是提高非公路车辆乘坐舒适性的一个重要而实际的课题。
基于非公路车辆对驾驶员座椅悬架的要求，结合当前国内外在驾驶员座椅悬架系统方面的研究现状，以及磁力弹簧刚度可调可控的特点，本课题将一种混合式单向磁力弹簧引入到座椅悬架中，研制了垂向力一位移特性呈非线性且垂向等效刚度可以调节的磁力驾驶员座椅悬架。主要完成的工作和取得的结论归纳如下：
1、剪式座椅悬架静动态特性的研究。选取当前应用较为广泛的弹簧水平上置式剪式驾驶员座椅悬架作为磁力座椅悬架的结构基础，运用理论分析、动力学仿真和实验研究相结合的方法对其进行了全面系统的研究，为磁力座椅悬架的研究提供了理论指导和实验参照。研究结果表明：微幅振动条件下，所研究的剪式座椅悬架可近似简化为线性振动系统，其垂向等效刚度在工作行程内基本保持不变；座椅悬架中的弹簧布置方式、悬架几何参数以及弹簧刚度对垂向等效刚度均具有一定的影响；系统的振动固有频率、阻尼比、位移传递率以及响应加速度均方根值均与等效簧载质量(即驾驶员体重)有关，而且，等效簧载质量对位移传递率的影响程度与减振器的阻尼系数大小有关；由于座椅悬架中各运动构件间存在较大的摩擦，以及剪杆及其连接杆自身的重力和转动惯量的影响，实验过程中座椅悬架在低频小振幅激振时出现“锁止”现象，其位移传递率的峰值频率随激振幅值的增加而减小，在位移激振幅值较小时，实验测得的位移传递率的峰值频率大于理论研究和仿真研究的结果。
2、带附加弹性元件的剪式座椅悬架刚度调节特性的理论研究。首先理论分析了附加弹性元件在剪式座椅悬架中的布置方式，在布置方式确定的情况下，构建了带附加弹性元件的剪式座椅悬架的理论模型，分析了弹性元件的刚度对座椅悬架垂向力—位移特性、垂向等效刚度以及振动固有频率的影响，考察了通过对附加弹性元件刚度的调节实现座椅悬架垂向等效刚度调节的可行性，为垂向等效刚度可调的磁力座椅悬架的研制提供了理论基础。研究结果表明：带附加弹性元件的座椅悬架，其工作行程内的垂向力—位移特性呈明显的非线性特性，且非线性特性随附加弹性元件刚度的增加而显著增强；垂向等效刚度与振动固有频率在悬架处于不同行程高度时具有不同的值，且在悬架伸张行程内的值总是大于其在压缩行程内的值；附加弹性元件的刚度对悬架的垂向力一位移特性，垂向等效刚度和振动固有频率均具有显著的影响。
3、磁力弹簧的构建及其磁场理论分析。对刚度可调的附加弹性元件—混合式单向磁力弹簧的主要设计参数进行了系统的分析和计算，内容包括磁力弹簧所需磁场力和工作气隙大小的计算，电磁铁与永磁铁的材料和工作特性参数的选择，电磁铁和永磁铁几何参数的确定。在此基础上，运用静电学与电动力学理论，推导了气隙磁通密度和轴向磁场力的表达式，并分析了各种因素对它们的影响，为磁力弹簧的实验研究提供了理论指导。研究结果表明：所构建的磁力弹簧的气隙磁通密度除与电磁线圈中的电流大小、永磁铁的直径与长度以及工作气隙大小有关外，还与电磁线圈的匝数、线圈的高度和厚度、铁心的长度以及退磁因子等诸多因素有关；磁力弹簧的轴向磁场力主要由气隙中平面z_m上的轴向和径向磁通密度大小以及同极相对的磁铁半径决定，平面z_m在气隙中的位置则由两侧的磁铁在气隙中产生的磁通密度大小决定。
4、磁力弹簧的实验研究。实验研究了不同磁极形状的电磁铁在不同电磁线圈端电压下的空间场强分布，以及不同尺寸柱状永磁铁的空间场强分布；构建了磁力弹簧磁力特性测试实验台，实验研究了电磁线圈端电压、永磁铁尺寸以及不同永磁铁尺寸的组合对磁力弹簧磁力特性的影响。研究结果表明：在各主要几何参数及电磁线圈端电压相同的情况下，无极帽平头磁极电磁铁的平均气隙磁通密度大于其它两种磁极形状的电磁铁；永磁铁的表面及气隙磁通密度在一定程度上取决于其长径比；排斥型磁力弹簧，当同极相对的两个磁极上的磁通密度相差较大时，磁极间的排斥力在气隙小至一定程度时将随气隙的进一步减小而减小，使磁力弹簧呈现负刚度特性，而当同极相对的两个磁极上的磁通密度值相近时，磁极间的排斥力随气隙的减小将呈非线性关系增大；随着电磁线圈端电压的增大，磁力弹簧的轴向磁场力呈线性关系增加，磁力特性曲线沿力轴向上移动，并且其非线性度随电磁线圈端电压的增大而增大。
5、磁力座椅悬架的研制及其实验研究。研制了基于磁力弹簧的磁力座椅悬架系统，理论分析了其垂向等效刚度的构成；构建了磁力座椅悬架系统研究实验台，实验研究了磁力座椅悬架的动态特性，主要包括其位移传递率、位移传递率的峰值频率以及悬架上板的加速度响应，考察了它们随悬架的等效簧载质量、电磁线圈端电压、激振振幅和激振频率的变化情况，并与原剪式座椅悬架进行了比较分析。研究结果显示：磁力座椅悬架的位移传递率在振动放大区，随电磁线圈端电压的增大而减小，随等效簧载质量的增大而增大；在隔振区，位移传递率几乎与电磁线圈端电压的变化无关，而随等效簧载质量的增大而减小；位移传递率的峰值频率和响应加速度均方根值均随电磁线圈端电压的增大而增大，随等效簧载质量的增大而减小；与有减振器的磁力座椅悬架相比，无减振器的磁力座椅悬架的位移传递率的峰值频率和响应加速度均方根值均较小，且它们受等效簧载质量的影响程度均较小。此外，无减振器的磁力座椅悬架的振动放大频段较窄，加速度的响应幅值比激振幅值减小约2／3。
通过本课题的研究，有望为基于磁力弹簧的垂向力—位移特性呈非线性且垂向等效刚度可调的半主动驾驶员座椅悬架的研究提供理论基础和技术支持。
Researches show that it is the simplest, directest and most economic method utilizingseat suspension to improve the ride comfort for the off-road vehicles such as agriculturaland forestry machinery, construction and quarrying vehicles and machinery etc., whichcommonly work and run in worse environment. Therefore carrying out an in-depth studyon the driver's seat suspension system and taking feasible technical measurements toisolate the vibration transmitting from the vehicle bottom to human body through thevehicle chassis and the seat is an important and practical subject for improving the ridecomfort of off-road vehicles.
Based on the requirements of the off-road vehicles for the driver's seat suspension, thenowaday study actualities of driver's seat suspension system home and abroad and theadjustability and controllability of the magnetic spring stiffness, a kind of mingledsingle-direction magnetic spring composed of electromagnet and permanent magnet wasadded to a scissors linkage seat suspension to establish the driver's seat suspension whosevertical equivalent stiffness is non-linear and can be controlled. The finished work andachieved results are generalized as follows:
1. Researches of the static and dynamic characteristics of the scissors linkage seatsuspension. One kind of scissors linkage seat suspension was chosen as the structural baseof the magnetic force seat suspension and the complete and systematical study about itsstatic and dynamic characteristics and their effect factors was made through theoreticalanalysis, dynamical simulation and experiment. Study results show that the seat suspensionsystem can be approximately treated as a linear system and its vertical equivalent stiffnessis almost unchanged in the working stroke; the spring layout mode, suspension geometryparameters and the spring stiffness all affect the seat suspension vertical equivalentstiffness in some degree; the natural frequency, damping ratio, dynamic amplificationfactor and the acceleration root of mean squares of the seat suspension are all related to theequivalent sprung mass. Moreover, the effect degree of the mass on the dynamicamplification factor is related to the damping coefficient of the damper; because of thefriction between motion parts and the gravity and rotary inertia of the scissors linkages the seat suspension appears "locked" when the excitation frequency is low and the magnitudeis small. The peak value frequency of the dynamic amplification factor in experiment isbigger than the theory and simulation results and it obviously decreases with the excitationmagnitude increasing.
2. Researches on the stiffness adjustability of the scissors linkage seat suspension withadditional elastic part. First the layout mode of the additional elastic part in the scissorslinkage seat suspension was theoretically analyzed and then the theoretical model of theseat suspension with additional elastic part was established. Based on the theoretical modelthe effect of the additional elastic part on the characteristic relationship, the seat verticalequivalent stiffness and the suspension vibration natural frequency were analyzed and thefeasibility of changing vertical equivalent stiffness by adjusting the stiffness of theadditional elastic part was discussed, which will build theoretical base for the constructionof the magnetic force seat suspension whose vertical equivalent stiffness is adjustable.Research results show that the relationship between the vertical load and displacement ofthe seat suspension with the additional elastic part behaves nonlinearity and thenonlinearity becomes stronger with the stiffness of additional elastic part increasing; theseat suspension vertical equivalent stiffness and the vibration natural frequency havedifferent values in different suspension position and their values in the suspensionextending stroke are much larger than which in compressing stroke; the stiffness of theadditional elastic part has obvious effect on the characteristic relationship, the verticalequivalent stiffness and the suspension vibration natural frequency.
3. Construction of the magnetic spring and theoretical analysis of its magnetic field.Systematical analysis and calculation were made on the main design parameters of theadditional elastic part with adjustable stiffness—the mingled single-direction magneticspring, and the contents included calculation of the magnetic field force and the working airgap required by the magnetic spring, choice of the material and the working parameters ofthe electromagnet and the permanent magnet and determination of the geometry parametersof the magnets. In addition, the formulation of the air gap magnetic flux density and theaxial magnetic field force were deduced according to the theory of static electrics andelectrodynamics and their effecting factors were analyzed, which are theoretical guide forthe experimental study of the magnetic spring. Research results show that the air gapmagnetic flux density of the magnetic spring is related not only to the electromagnetismwinding current, the diameter and length of the permanent magnetic and the working air gap but also to many other factors such as the circles, length and thickness of theelectromagnetism winding, the length of the iron core and the demagnetizing factor etc.;the axial magnetic field force of the magnetic spring is mainly decided by the axial andradial magnetic flux density on the plane z_m in the air gap and the diameter of the facedmagnet, and the position of the plane z_m is decided by the magnetic flux density in the airgap produced by the magnets.
4. Experimental study on the magnetic spring. The space distribution of the magneticflux density of the electromagnet with different magnetic pole shape under differentelectromagnetism winding voltage and that of the permanent magnet with differentdimension were experimentally studied; the experimental system for magnetic forcecharacteristics test of magnet spring was Constructed and the effecting factors of themagnetic force characteristics such as electromagnetism winding voltage, permanentmagnet dimension and the combination of different permanent magnet 1 and 2 wereexperimentally studied. Research results show that the average air gap magnetic fluxdensity of the electromagnet with flat magnetic pole without cap is larger than that of theother two magnetic poles; the surface and air gap magnetic flux density of permanentmagnet is decided by its ratio of length to diameter; For the repulsive type magnetic spring,when the surface magnetic flux density values of the two faced magnetic poles have bigdisparity and the air gap is small to some degree the repulsive force will decrease with theair gap decreasing and the magnetic spring stiffness behaves negative stiffness; and whenthe surface magnetic flux density values of the two faced magnetic poles are nearly samethe repulsive force will increase with the air gap decreasing; with the electromagnetismwinding voltage increasing the axial magnetic force increases linearly and the magneticforce characteristic curves move up along the force axis; moreover the curvature of thecharacteristic curves also increase with the electromagnetism winding voltage increasing.
5. Development and experimental study of the magnetic force seat suspension. Themagnetic force seat suspension system was developed and its vertical equivalent stiffnessconstitution was theoretically analyzed; the experimental system for the magnetic force seatstudy was established and the dynamic characteristics of the magnetic force seat suspensionwere experimentally studied. Research results show that the dynamic amplification factorof the magnetic force seat suspension decreases with the electromagnetism winding voltageincreasing and increases with the equivalent sprung mass increasing in thevibration-amplifying zone and in the vibration-isolating zone it decreases with the equivalent sprung mass increasing and nearly have no relation with the change of thevoltage; the peak value frequency of the dynamic amplification factor and the respondingacceleration r.m.s, both increase with the electromagnetism winding voltage increasing anddecrease with the equivalent sprung mass increasing; compared with the magnetic forceseat suspension with damper the peak value frequency of the dynamic amplification factorand the responding acceleration r.m.s, of the magnetic force seat suspension withoutdamper are both lower and the degree of the equivalent sprung mass effecting on them issmaller.
It is expected to build theoretical base and technological support for the in-depth studyof the semi-active seat suspension that is based on the magnetic spring and whoserelationship between vertical load and displacement behaves nonlinearity and the verticalequivalent stiffness can be adjustable.
基于非公路车辆对驾驶员座椅悬架的要求，结合当前国内外在驾驶员座椅悬架系统方面的研究现状，以及磁力弹簧刚度可调可控的特点，本课题将一种混合式单向磁力弹簧引入到座椅悬架中，研制了垂向力一位移特性呈非线性且垂向等效刚度可以调节的磁力驾驶员座椅悬架。主要完成的工作和取得的结论归纳如下：
1、剪式座椅悬架静动态特性的研究。选取当前应用较为广泛的弹簧水平上置式剪式驾驶员座椅悬架作为磁力座椅悬架的结构基础，运用理论分析、动力学仿真和实验研究相结合的方法对其进行了全面系统的研究，为磁力座椅悬架的研究提供了理论指导和实验参照。研究结果表明：微幅振动条件下，所研究的剪式座椅悬架可近似简化为线性振动系统，其垂向等效刚度在工作行程内基本保持不变；座椅悬架中的弹簧布置方式、悬架几何参数以及弹簧刚度对垂向等效刚度均具有一定的影响；系统的振动固有频率、阻尼比、位移传递率以及响应加速度均方根值均与等效簧载质量(即驾驶员体重)有关，而且，等效簧载质量对位移传递率的影响程度与减振器的阻尼系数大小有关；由于座椅悬架中各运动构件间存在较大的摩擦，以及剪杆及其连接杆自身的重力和转动惯量的影响，实验过程中座椅悬架在低频小振幅激振时出现“锁止”现象，其位移传递率的峰值频率随激振幅值的增加而减小，在位移激振幅值较小时，实验测得的位移传递率的峰值频率大于理论研究和仿真研究的结果。
2、带附加弹性元件的剪式座椅悬架刚度调节特性的理论研究。首先理论分析了附加弹性元件在剪式座椅悬架中的布置方式，在布置方式确定的情况下，构建了带附加弹性元件的剪式座椅悬架的理论模型，分析了弹性元件的刚度对座椅悬架垂向力—位移特性、垂向等效刚度以及振动固有频率的影响，考察了通过对附加弹性元件刚度的调节实现座椅悬架垂向等效刚度调节的可行性，为垂向等效刚度可调的磁力座椅悬架的研制提供了理论基础。研究结果表明：带附加弹性元件的座椅悬架，其工作行程内的垂向力—位移特性呈明显的非线性特性，且非线性特性随附加弹性元件刚度的增加而显著增强；垂向等效刚度与振动固有频率在悬架处于不同行程高度时具有不同的值，且在悬架伸张行程内的值总是大于其在压缩行程内的值；附加弹性元件的刚度对悬架的垂向力一位移特性，垂向等效刚度和振动固有频率均具有显著的影响。
3、磁力弹簧的构建及其磁场理论分析。对刚度可调的附加弹性元件—混合式单向磁力弹簧的主要设计参数进行了系统的分析和计算，内容包括磁力弹簧所需磁场力和工作气隙大小的计算，电磁铁与永磁铁的材料和工作特性参数的选择，电磁铁和永磁铁几何参数的确定。在此基础上，运用静电学与电动力学理论，推导了气隙磁通密度和轴向磁场力的表达式，并分析了各种因素对它们的影响，为磁力弹簧的实验研究提供了理论指导。研究结果表明：所构建的磁力弹簧的气隙磁通密度除与电磁线圈中的电流大小、永磁铁的直径与长度以及工作气隙大小有关外，还与电磁线圈的匝数、线圈的高度和厚度、铁心的长度以及退磁因子等诸多因素有关；磁力弹簧的轴向磁场力主要由气隙中平面z_m上的轴向和径向磁通密度大小以及同极相对的磁铁半径决定，平面z_m在气隙中的位置则由两侧的磁铁在气隙中产生的磁通密度大小决定。
4、磁力弹簧的实验研究。实验研究了不同磁极形状的电磁铁在不同电磁线圈端电压下的空间场强分布，以及不同尺寸柱状永磁铁的空间场强分布；构建了磁力弹簧磁力特性测试实验台，实验研究了电磁线圈端电压、永磁铁尺寸以及不同永磁铁尺寸的组合对磁力弹簧磁力特性的影响。研究结果表明：在各主要几何参数及电磁线圈端电压相同的情况下，无极帽平头磁极电磁铁的平均气隙磁通密度大于其它两种磁极形状的电磁铁；永磁铁的表面及气隙磁通密度在一定程度上取决于其长径比；排斥型磁力弹簧，当同极相对的两个磁极上的磁通密度相差较大时，磁极间的排斥力在气隙小至一定程度时将随气隙的进一步减小而减小，使磁力弹簧呈现负刚度特性，而当同极相对的两个磁极上的磁通密度值相近时，磁极间的排斥力随气隙的减小将呈非线性关系增大；随着电磁线圈端电压的增大，磁力弹簧的轴向磁场力呈线性关系增加，磁力特性曲线沿力轴向上移动，并且其非线性度随电磁线圈端电压的增大而增大。
5、磁力座椅悬架的研制及其实验研究。研制了基于磁力弹簧的磁力座椅悬架系统，理论分析了其垂向等效刚度的构成；构建了磁力座椅悬架系统研究实验台，实验研究了磁力座椅悬架的动态特性，主要包括其位移传递率、位移传递率的峰值频率以及悬架上板的加速度响应，考察了它们随悬架的等效簧载质量、电磁线圈端电压、激振振幅和激振频率的变化情况，并与原剪式座椅悬架进行了比较分析。研究结果显示：磁力座椅悬架的位移传递率在振动放大区，随电磁线圈端电压的增大而减小，随等效簧载质量的增大而增大；在隔振区，位移传递率几乎与电磁线圈端电压的变化无关，而随等效簧载质量的增大而减小；位移传递率的峰值频率和响应加速度均方根值均随电磁线圈端电压的增大而增大，随等效簧载质量的增大而减小；与有减振器的磁力座椅悬架相比，无减振器的磁力座椅悬架的位移传递率的峰值频率和响应加速度均方根值均较小，且它们受等效簧载质量的影响程度均较小。此外，无减振器的磁力座椅悬架的振动放大频段较窄，加速度的响应幅值比激振幅值减小约2／3。
通过本课题的研究，有望为基于磁力弹簧的垂向力—位移特性呈非线性且垂向等效刚度可调的半主动驾驶员座椅悬架的研究提供理论基础和技术支持。
Researches show that it is the simplest, directest and most economic method utilizingseat suspension to improve the ride comfort for the off-road vehicles such as agriculturaland forestry machinery, construction and quarrying vehicles and machinery etc., whichcommonly work and run in worse environment. Therefore carrying out an in-depth studyon the driver's seat suspension system and taking feasible technical measurements toisolate the vibration transmitting from the vehicle bottom to human body through thevehicle chassis and the seat is an important and practical subject for improving the ridecomfort of off-road vehicles.
Based on the requirements of the off-road vehicles for the driver's seat suspension, thenowaday study actualities of driver's seat suspension system home and abroad and theadjustability and controllability of the magnetic spring stiffness, a kind of mingledsingle-direction magnetic spring composed of electromagnet and permanent magnet wasadded to a scissors linkage seat suspension to establish the driver's seat suspension whosevertical equivalent stiffness is non-linear and can be controlled. The finished work andachieved results are generalized as follows:
1. Researches of the static and dynamic characteristics of the scissors linkage seatsuspension. One kind of scissors linkage seat suspension was chosen as the structural baseof the magnetic force seat suspension and the complete and systematical study about itsstatic and dynamic characteristics and their effect factors was made through theoreticalanalysis, dynamical simulation and experiment. Study results show that the seat suspensionsystem can be approximately treated as a linear system and its vertical equivalent stiffnessis almost unchanged in the working stroke; the spring layout mode, suspension geometryparameters and the spring stiffness all affect the seat suspension vertical equivalentstiffness in some degree; the natural frequency, damping ratio, dynamic amplificationfactor and the acceleration root of mean squares of the seat suspension are all related to theequivalent sprung mass. Moreover, the effect degree of the mass on the dynamicamplification factor is related to the damping coefficient of the damper; because of thefriction between motion parts and the gravity and rotary inertia of the scissors linkages the seat suspension appears "locked" when the excitation frequency is low and the magnitudeis small. The peak value frequency of the dynamic amplification factor in experiment isbigger than the theory and simulation results and it obviously decreases with the excitationmagnitude increasing.
2. Researches on the stiffness adjustability of the scissors linkage seat suspension withadditional elastic part. First the layout mode of the additional elastic part in the scissorslinkage seat suspension was theoretically analyzed and then the theoretical model of theseat suspension with additional elastic part was established. Based on the theoretical modelthe effect of the additional elastic part on the characteristic relationship, the seat verticalequivalent stiffness and the suspension vibration natural frequency were analyzed and thefeasibility of changing vertical equivalent stiffness by adjusting the stiffness of theadditional elastic part was discussed, which will build theoretical base for the constructionof the magnetic force seat suspension whose vertical equivalent stiffness is adjustable.Research results show that the relationship between the vertical load and displacement ofthe seat suspension with the additional elastic part behaves nonlinearity and thenonlinearity becomes stronger with the stiffness of additional elastic part increasing; theseat suspension vertical equivalent stiffness and the vibration natural frequency havedifferent values in different suspension position and their values in the suspensionextending stroke are much larger than which in compressing stroke; the stiffness of theadditional elastic part has obvious effect on the characteristic relationship, the verticalequivalent stiffness and the suspension vibration natural frequency.
3. Construction of the magnetic spring and theoretical analysis of its magnetic field.Systematical analysis and calculation were made on the main design parameters of theadditional elastic part with adjustable stiffness—the mingled single-direction magneticspring, and the contents included calculation of the magnetic field force and the working airgap required by the magnetic spring, choice of the material and the working parameters ofthe electromagnet and the permanent magnet and determination of the geometry parametersof the magnets. In addition, the formulation of the air gap magnetic flux density and theaxial magnetic field force were deduced according to the theory of static electrics andelectrodynamics and their effecting factors were analyzed, which are theoretical guide forthe experimental study of the magnetic spring. Research results show that the air gapmagnetic flux density of the magnetic spring is related not only to the electromagnetismwinding current, the diameter and length of the permanent magnetic and the working air gap but also to many other factors such as the circles, length and thickness of theelectromagnetism winding, the length of the iron core and the demagnetizing factor etc.;the axial magnetic field force of the magnetic spring is mainly decided by the axial andradial magnetic flux density on the plane z_m in the air gap and the diameter of the facedmagnet, and the position of the plane z_m is decided by the magnetic flux density in the airgap produced by the magnets.
4. Experimental study on the magnetic spring. The space distribution of the magneticflux density of the electromagnet with different magnetic pole shape under differentelectromagnetism winding voltage and that of the permanent magnet with differentdimension were experimentally studied; the experimental system for magnetic forcecharacteristics test of magnet spring was Constructed and the effecting factors of themagnetic force characteristics such as electromagnetism winding voltage, permanentmagnet dimension and the combination of different permanent magnet 1 and 2 wereexperimentally studied. Research results show that the average air gap magnetic fluxdensity of the electromagnet with flat magnetic pole without cap is larger than that of theother two magnetic poles; the surface and air gap magnetic flux density of permanentmagnet is decided by its ratio of length to diameter; For the repulsive type magnetic spring,when the surface magnetic flux density values of the two faced magnetic poles have bigdisparity and the air gap is small to some degree the repulsive force will decrease with theair gap decreasing and the magnetic spring stiffness behaves negative stiffness; and whenthe surface magnetic flux density values of the two faced magnetic poles are nearly samethe repulsive force will increase with the air gap decreasing; with the electromagnetismwinding voltage increasing the axial magnetic force increases linearly and the magneticforce characteristic curves move up along the force axis; moreover the curvature of thecharacteristic curves also increase with the electromagnetism winding voltage increasing.
5. Development and experimental study of the magnetic force seat suspension. Themagnetic force seat suspension system was developed and its vertical equivalent stiffnessconstitution was theoretically analyzed; the experimental system for the magnetic force seatstudy was established and the dynamic characteristics of the magnetic force seat suspensionwere experimentally studied. Research results show that the dynamic amplification factorof the magnetic force seat suspension decreases with the electromagnetism winding voltageincreasing and increases with the equivalent sprung mass increasing in thevibration-amplifying zone and in the vibration-isolating zone it decreases with the equivalent sprung mass increasing and nearly have no relation with the change of thevoltage; the peak value frequency of the dynamic amplification factor and the respondingacceleration r.m.s, both increase with the electromagnetism winding voltage increasing anddecrease with the equivalent sprung mass increasing; compared with the magnetic forceseat suspension with damper the peak value frequency of the dynamic amplification factorand the responding acceleration r.m.s, of the magnetic force seat suspension withoutdamper are both lower and the degree of the equivalent sprung mass effecting on them issmaller.
It is expected to build theoretical base and technological support for the in-depth studyof the semi-active seat suspension that is based on the magnetic spring and whoserelationship between vertical load and displacement behaves nonlinearity and the verticalequivalent stiffness can be adjustable.
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