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yabo亚博
体积22.那20.21.
文章Number 3.7.
页数) 15.
迪伊 Https://doi.org/10.1051/meca/2021035
在线发布 0.1June 2021

© Y. Chao et al., Published by EDP Sciences 2021

Licence Creative CommonsT.His is an Open Access article distributed under the terms of the Creative Commons Attribution License (<一种Href="https://creativecommons.org/licenses/by/4.0" target="_blank">https://creativecommons.org/licenses/by/4.0.)那which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1Introduction

It is generally accepted that there are many effects of mattresses on sleep comfort and health, such as thermal comfort [<一种name="InR1">1那<一种name="InR2">2]以及支持睡眠质量,生理和心理健康的支持舒适性。床垫的主要功能是支持人体,允许肌肉和脊柱椎间盘通过在人床垫接口和脊柱对准中提供合理的压力分布来从持续载荷中恢复[<一种name="InR3">3.],这极大地受到床垫的坚定性的影响[<一种name="InR4">4.那<一种name="InR5">5.], individual anthropometric parameters [<一种name="InR6">6.那<一种name="InR7">7.]. Therefore, depending on spinal alignment and pressure distribution of human-mattress interface [<一种name="InR8">8.], the ideal mattress should be positively adapted to the changes in lying postures and human dimensions. This is an urgent need, but still a challenge. At present, the main firmness adjustment of mattresses is based on pressure distribution of human-mattress interface, however, it is sufficient to avoid the peak of concentrated pressure for healthy people during sleep [<一种name="InR9">9.].

T.HE.variable firmness adjustment has been a hot area of the mattress during the past two decades [<一种name="InR10">10.], in particular, the Alternating Pressure Mattress (APM) adjusts distribution of firmness by regulating inside air pressure, providing personalized support to various parts of human body. A great deal of effort has been devoted to both variable firmness air mattress and non-air mattress. Among representative results, the main principle of air mattress is to change the stiffness of the air chamber by periodically inflating and deflating, so that human body tissues are not compressed for long time [<一种name="InR11">11.]. Furthermore, several studies [<一种name="InR12">12.那<一种name="InR13">13.]表明,APM对静压溃疡预防和管理有一个优点,但有些研究人员认为交替的压力床垫比静态更糟糕[<一种name="InR14">14.]. Moreover, Tsuda [<一种name="InR15">15.]发现空气床垫对姿势的变化敏感,表明根据姿势进行自我调整的可能性。以上分析主要是关于气动床垫的被动调整,并且活跃的减压床垫更为显着。例如,有源减压空气床垫定量测量人床垫接口的体压分布,并通过飞行时间光学压力传感器成功调整床垫的坚固性,提供相对理想的体压分布[<一种name="InR16">16.], however, spinal alignment was still not taken into consideration. Verhaert [<一种name="InR17">17.那<一种name="InR18">18.], had studied spinal alignment in lying position further, including identifying spinal morphology by indentation on mattress surface and adjusting it by alternating stiffness of a specially designed mattress, which is an important step towards regulating spinal alignment. In addition to air mattresses, artificial composite characterized by nonlinear stiffness is used in mattress to provide ideal pressure distribution of human-mattress interface [<一种name="InR19">19.]. Previous studies, however, were mainly limited to prevention of pressure ulcers [<一种name="InR20">20.-<一种name="InR22">22.]. Mattresses with variable stiffness are usually made of cubic and rod-shaped air chambers. Due to their bulky size, it is almost impossible to accurately predict and adjust their stiffness to a certain level to maintain natural spinal alignment, which is another limitation of air mattresses. Although the hybrid spiral steel spring used in ergonomic mattresses overcome the limitations of air chambers to some extent by providing predictable and variable stiffness [<一种name="InR23">23.那<一种name="InR24">24.], they also fail to accommodate personalized lying postures and body dimensions. On the basis of previous studies, a novel spring characterized by variable and predictable stiffness needs to be explored. The research questions are: How to design an air spring for mattresses? What are the influence factors of stiffness? How to predict and adjust the stiffness by relevant parameters?

T.o answer these questions, the first aim of this study is to explore a novel air spring for ergonomic mattresses and analyze its mechanical properties and its influence factors. The second aim is to establish an analytical model for predicting and adjusting the vertical stiffness of air springs. Compared with previous studies, this research has made breakthroughs in the following aspects: (1) A variable stiffness air spring was proposed to replace the traditional air chamber. (2) The mechanical properties of the air spring and its influence factors were analyzed. (3) A universal analytical model was established to predict the vertical stiffness of any equilibrium position. The study may provide a potential solution for stiffness adaptive mattresses to maintain natural spinal alignment during sleep.

2。材料和方法

2.1材料和实验

T.HE.Composite is a combination of Thermoplastic Polyurethane (TPU) elastomeric film and chemical fabric film. Information on materials and specimens is shown in<一种Href="//www.ygodb.com/articles/meca/full_html/2021/01/mi210007/mi210007.html">T.一种B.le 1一种nd<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figure 1。空气弹簧由多个空气室由每个表面中心的出口彼此连接,并且腔室的底部被传递到空气泵。当空气弹簧不膨胀时,所有表面都是平坦的,并且当它膨胀时,所有表面都是弧形的。有关设备,仪器和主要工作条件的信息<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">表2.。金属压缩板直径为100mm,水平安装在机械夹具上。将空气弹簧放置在金属凳上,其中孔在中间冲压并水平放置在压缩板下方。装卸速度为25mm / min。实验连接的示意图显示在<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figure 2。

T.一种B.le 1

Information of material and specimen.

thumbnail 图。1

材料和空气弹簧。

表2.

Working information of equipment and instruments.

thumbnail 图2

实验连接图。

2。2Experimental procedure

一种s depicted in<一种Href="//www.ygodb.com/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figure 3,在单轴压缩下在九个初始压力条件下测试三种空气弹簧,其间隔为0.002MPa的间隔。

thumbnail 图3.

Experimental procedure.

2。3.Data processing and analytical model

为了分析空气弹簧的机械性能及其影响因素,各种工作条件的实验数据处理如下:

  • T.HE.E.ffect of initial internal pressure on vertical stiffness was compared.

  • T.HE.E.ffect of radius on vertical stiffness was compared.

  • 基于几何参数和初始内部压力的可变垂直刚度的通用分析模型,并根据空气弹簧的机械性能和影响因素验证。

3。结果与讨论

3.1压缩下的机械性能

3.1.1影响因素分析

所有实验条件的结果都显示出一致的趋势,因此将在0.010MPa的初始压力下工作的三腔空气弹簧作为示例,如图所示<一种Href="//www.ygodb.com/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figure 4。随着位移的增加,负载,内部压力和刚度增加非线性,这表明负载和初始压力之间存在正相关性。

Number of stack chambers indicates initial volumes of air spring is different, and its effect on mechanical properties is shown in<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figure 5。T.HE.initial volume, load and stiffness of the air spring are negatively correlated. When initial internal pressure and displacement are constant, the load and stiffness decrease with the increase of initial volume

thumbnail 图4.

压缩过程中的负载和内部压力。(a)负载曲线,(​​b)内部压力曲线。

thumbnail 图5.

Curves of force and displacement for different air spring.

3.1.2装卸过程的特征

以三腔空气弹簧为例。初始压力为0.026 MPa的装载和卸载曲线显示在<一种Href="//www.ygodb.com/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figure 6。的物理意义th之间的区域E.Curve and the horizontal axis is the energy needed for the air spring to work. Hysteresis in unloading curve may be due to heat exchange, indicating heat flow into the atmosphere, however, the temperature inside the air spring remains constant because of slow compression. During loading, mechanical energy is converted to internal energy of gas, and heat exchange takes place, that is, energy loss. Therefore, the energy during unloading is less than loading. In other words, the vertical stiffness of the air spring decreases slightly during unloading. In this experiment, the enclosed area between the two curves showed an energy loss of 0.1497 KJ.

可以确定的是,垂直刚度和高度,初始压力和空气弹簧初始容积之间存在定量关系。因此,为了描述各种空气弹簧的可变刚度,需要基于几何参数和初始压力的分析模型来预测任何位置的刚度。

thumbnail 图6.

Curves of loading and unloading.

3.。2一种nalytical model

3.2.1垂直刚度的一般表达

一种universal analytical model is established based on the Ideal Gas Law [<一种name="InR25">25.]表示等式<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(1),参考汽车悬架空气弹簧的建模方法[<一种name="InR26">26.那<一种name="InR27">27.]. When compressed slowly, the air temperature inside the spring can be considered constant. Therefore, the thermodynamic parameterλ等于一个。理想的气体定律表示为方程式<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(1)一种nd<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(2):<一种name="FD1">(1)(2)

wherev0.vp0.一种ndp分别是初始和任意位置的体积和内部压力。

任何均衡位置的负载都可以表示为<一种name="FD3">(3)

whereFp一种nd一种E.是load, internal pressure and effective area.

梳理E.quations<一种Href="//www.ygodb.com/articles/meca/full_html/2021/01/mi210007/mi210007.html">(2)一种nd<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(3),给出了负载方程:<一种name="FD4">(4)

区分方程式<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(4)产生通用垂直刚度的空气弹簧:<一种name="FD5">(5)

whereK.H是任意均衡位置的垂直刚度和高度。

体积和有效区域是内部压力和空气弹簧高度的功能。通过分析方程分析<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(5),通用垂直刚度包括两个项目,即分别变化和面积的变化引起的体积刚度和面积刚度。从等式<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(5)可以看出,有效面积,有效量及其变化率是影响垂直刚度的关键因素。

3.。2。2V.E.rtical initial stiffness

V.E.rtical initial stiffness of the air spring implies inherent rigidity, with no load balancing balancing due to the tension between atmospheric pressure, internal pressure and the air-spring chamber. When installed in a mattress system, the air spring slightly compressed due to the gravity of the cushion, there approximately is an equation asv0. = v那the load of air spring at the initial equilibrium position is expressed as equation<一种Href="//www.ygodb.com/articles/meca/full_html/2021/01/mi210007/mi210007.html">(6):<一种name="FD6">(6)

whereF0.一种E.0.是load and effective area of initial equilibrium position.

T.HE.radius of the uninflated air spring is expressed inR.0.那一种fter extended, the surface is curved, as shown in<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figure 7一种。T.HE.K.E.y parameters are initial radiusR.0.,装配高度H和房间的数量n。Each surface in its natural state is a spherical cap surface, as shown in<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figure 7B.。T.HE.volume loss due to welding is negligible. The differences between the air springs in the mattress and the automotive suspensions given in<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">表3indicate that vehicle suspension models are not applicable to a mattress.

T.HE.upper surface is approximately spherical cap, the area is expressed as<一种name="FD7">(7)

where一种一种0.R.一种H0.是initial area, radius and height of spherical cap.

一种ssuming that the material is close to incompressible and the surface of the air spring is unstretchable. When the air spring is not inflated, its surface area is the area of the plane:<一种name="FD8">(8)

梳理E.quations<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(7)一种nd<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(8)那the radius of spherical cap is expressed as<一种name="FD9">(9)

它可以在等式中找到<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(9)球形帽的半径是高度的隐式功能,满足方程,它表示独立变量与从属变量之间没有一对一的对应关系。因此,任意组装高度不确定球形帽的半径,腔室的体积应该是功能H0.。空气弹簧的体积近似等于所有空气室的容积之和。半腔室的体积表示为<一种name="FD10">(10)

梳理E.quations<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(8)一种nd<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(10),可以容易地获得空气弹簧的体积:<一种name="FD11">(11)

wherev0.n是空气弹簧的初始容积和总和。

一种t the initial equilibrium position, the equivalent diagram of the force is shown in<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figure 8, 在哪里T.is the tension of the expanded spherical cap. It should be emphasized that<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figure 8示出了二维理想力图,穿过垂直轴的横截面,并且所有横截面的所有张力相对于垂直轴向对称地分布。在理想状态下,三维图由无数相同的二维图组成。除此之外,张力只是该过程中的变量,并且不参与最终计算。因此,二维理想力图用作本文中的分析对象。空气弹簧通过张力,大气压和内部空气压力平衡。均衡方程表示为<一种name="FD12">(12)

whereθ是张力和水平线之间的角度。

通过分析几何,梳理方程<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(9)一种nd<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(12)那θ可以很容易地计算:<一种name="FD13">(13)

考虑两个极端情况:

  • When the air spring is not inflated, there are two equations:H0. = 0,θ = 一种COS(1 - 0)= 0。

  • 当空气弹簧充分膨胀时,θ可以计算H0.一种ndR.0.。通过分析几何,最大值2θ等于π一种nd the spherical cap is exactly hemisphere withR.一种 = H0.,将其替换为等式<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(9)产生球形帽的高度:

Neither of the two extremes is actually possible, consequently, the range ofθ一种ndH0.

Hereto, the parameters of the initial state,R.0.H0.nv0.一种nd一种E.0.那一种ll can be calculated. When air spring slightly deformed at initial state, there are following equations:v = v0.一种E. = 一种E.op = p0.,将其替换为等式<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(5)一种nd simplifying obtain vertical initial stiffness:<一种name="FD14">(14)

whereis rate of change of effective area.

梳理E.quations<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(11)那<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(12)一种nd<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(14)那the vertical initial stiffness is given by the equation<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(15):<一种name="FD15">(15)

whereK.org.p0.R.0.v0.是垂直初始刚度,初始内部压力,平面半径和空气弹簧的初始体积。

thumbnail 图7.

空气弹簧弯曲球形帽(A)空气弹簧结构图;(b)单曲面的力图。

表3

Compare with air spring in automotive suspension.

thumbnail 图8

T.HE.force diagram of the spherical cap.

3.。2。3.V.E.rtical stiffness of arbitrary equilibrium position

根据方程式<一种Href="//www.ygodb.com/articles/meca/full_html/2021/01/mi210007/mi210007.html">(5)那vertical stiffness of of arbitrary equilibrium position is determined by effective area一种E.那E.ffective volumeV.一种nd their rate of change with height.

(1)Effective area and its rate of change.

压缩板和空气弹簧上表面之间的接触表面形成圆形板,其半径随着轴向位移的增加而增加。为了便于计算和分析,变形空气弹簧大致被视为类似于圆柱体的组合和包裹在弯曲表面上的体积的几何形状,其中汽缸的直径是接触表面的直径。为了建立恒定方程式,以下假设是:

  • TPU薄膜织物复合材料几乎可压缩。

  • Under axial vertical deformation, the surface area of the air spring is invariable and the geometry shape is only changed.<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figure 9显示近似的形状和力。

    thumbnail 图9.

    Diagram of air spring structure and force.

B.一种sed on the analysis of<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figure 9,N室空气弹簧的球形帽的高度表示为<一种name="FD16">(16)

wherelB.n一种ndH是H一种lf height of the chamber, the sum of chambers and the height of air spring at arbitrary equilibrium positions.

根据几何公理,每个腔室边缘的弧长表示为<一种name="FD17">(17)

wheres一种r一种一种ndψ是弧length, radius of arc and angle between the tension at the edge of and plumb line.

On the basis of the above assumption, the following equation were derived:<一种name="FD18">(18)

whererB.R.0.是the radius of contact surface and circular plate of air spring without inflating respectively.

梳理<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figures 8一种nd<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">9.那the equilibrium equations are given:<一种name="FD19">(19)

whereF那T.并且P是气室的负载,张力和内部压力。

T.HE.Contact area of chamber is calculated by<一种name="FD20">(20)

T.Hrough analytic geometry, yield the following equation:<一种name="FD21">(21)

梳理E.quations<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(19)-<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(21)那the effective area can be easily calculated:<一种name="FD22">(22)

T.HE.H一种lf height of the chamber is obtained by geometric relations:<一种name="FD23">(23)

R.E.一种rrange the equation<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(23)那the mixed trigonometric formula is given:<一种name="FD24">(24)

解决方程式<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(24)产生角度ψ。区分方程式<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(22)一种nd combing equation<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(16)那the rate of change in effective area can be calculated:<一种name="FD25">(25)

whereψis determined by formula<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(24)。

(2)Effective volume and its rate of change

近似几何体的有效体积由两部分组成,圆柱面接触表面,定义为vC那一种nd the volume enclosed by the approximate cambered surface, defined asv。一种single air chamber is shown in<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figure 10。

根据近似弧形表面的浅表面积的轴影,获得了以下等式:<一种name="FD26">(26)

wherel一种是空气室的近似弧形表面的中心与接触表面边缘的铅线和腔室的边缘之间的距离和工作期间的近似弧形表面的面积。

梳理E.quations<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(16)一种nd<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(26),通过等式给出空气弹簧的有效体积<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(27):<一种name="FD27">(27)

区分方程式<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(27)那the rate of change of effective volume can be easily obtained:<一种name="FD28">(28)

HERETO,通过公式计算任何平衡位置的空气弹簧的垂直刚度<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">表4.。

thumbnail 图。10.

一种pproximate geometry of single air chamber depressed.

表4.

变量的计算公式。

3.3V.E.rification and modification of the model

3.3.1初始几何模型的性能

给出了实验中空气弹簧的几何参数<一种Href="//www.ygodb.com/articles/meca/full_html/2021/01/mi210007/mi210007.html">表5.。T.o obtain a better understanding of the influence of parameters on vertical initial stiffness, setn = 3,λ = 1 and other initial parameters for equation<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(15)分别显示在<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">表6.。V.E.rtical initial stiffness values at different values of initial pressure and radius are shown in<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figure 11A,B和不同半径的初始体积和装配高度的值<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figure 11c和d。

一种CCording to the analysis of<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figure 11A,当几何参数恒定时,初始垂直刚度和初始内部压力之间存在正线性相关性,这意味着减少初始内压可以减少空气弹簧的刚度。通过分析<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figure 11B,初始垂直刚度和板半径之间存在负的非线性相关性,这意味着半径的增加可以减小空气弹簧刚度,与方程一致<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(15)。<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figure 11Cindicates that initial volume increases with the increase of radius.<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figure 11d demonstrates that the assembly height of an air spring increases proportionally with the increase in radius.

WhenR.0.等于4. cm, the difference between the calculated values and measured values for the height, initial volume and assembly height of the spherical cap are shown in<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">表7.。它们之间的误差是由于球形帽的高度分配(1.886cm),其小于测量值(2cm),但误差是相对较小的并且可接受的。

In order to validate the accuracy of equation<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(11), 放R.0. = 4 cm,n = 3,H0. = 2 cm then calculated the initial volume and compared it with the measured value. The results are shown in<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">表8.,这表明分析模型非常精确。

表5.

Geometric parameters of air spring.

表6.

可变参数设置。

thumbnail 图。11

参数对刚度(a)初始刚度和初始压力,(b)初始刚度和半径,(c)初始体积和初始半径,(d)高度和初始半径的影响。

表7.

计算和测量空气弹簧几何参数值。

表8.

Difference between calculated and measured values of volume.

3.3。2P.E.rformance of model for any equilibrium position

表9.显示四个高度值的预测负载和中间变量,以及测量的负载,以及<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figure 12图示了负载预测和测量之间的差异。从中可以看出<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">表9.一种nd<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figure 12,计算和实验测量之间的误差随着垂直凹陷的增加而降低,并且所有计算值大于测量值,可能是由于近似的几何形状,这与小凹陷中的实际几何形状不同但是当压缩更大时,更接近真实几何。在此基础上,假设错误是高度的函数,并且提出了校正功能来修改模型。

表9.

Calculation results of arbitrary height of air spring.

thumbnail 图。12

预测和实验值。

3.3。3.P.E.rformance of modified model

如公式所示<一种Href="//www.ygodb.com/articles/meca/full_html/2021/01/mi210007/mi210007.html">(5)一种nd<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figure 12那the load required for compression is a function of the height and initial internal pressure, so the relative error of these two parameters should also be related to the height of air spring. According to experimental data, the error function of initial internal pressure and height can be established by polynomial fitting. The general approach is as follows:

  • 首先,负载和高度的多项式函数在九个初始内部压力下装配,然后多变量函数的系数由矩阵表示一种分别。

  • 其次,装配多项式系数和相应的九个初始内部压力之间的多项式函数,然后通过矩阵表示多项式函数的系数B.分别。

  • 第三,矩阵一种times matrixB.一种nd obtain vectorC。T.HE.E.lements of vectorC是Coefficients of the power terms of a polynomial from the highest to the lowest power respectively.

T.HE.E.rror function is described as equation<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(29),两次拟合后的修改功能作为等式呈现<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">(30):<一种name="FD29">(29)(30)

whereC(r)R.(h)FCor是modifying function, error function and load modified by correction function respectively.

Finally, the modification function is expressed as<一种name="FD31">(31)

T.一种B.le 10显示校正功能的拟合结果,以及<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">Figure 13gives the predicted and measured values for initial internal pressure of 0.020 MPa.

T.HE.model for calculation modified by twice fitting can predict load more accurately, and the predicted load and height change trend are in good agreement with the experimental results, which shows that the model is credible in general. There are still some errors in the revised model, and possible sources of error are:

  • 超越方程的角度只能找到近似的根,而不是精确的根。

  • 校正功能无法完全消除拟合两次后的误差,但只能减少错误。在第二拟合中,该示例中的最大装配电力为3.通过提高拟合能力,可以提高精度,但不是大大。

T.一种B.le 10

改性功能配件的结果。

thumbnail 图13.

Measured values and predicted values with modifying function.

3.4床垫中的应用前景

In previous studies, ergonomic mattresses were designed primarily on the basis of body pressure distribution (BPD) at human-mattress interface, which is an indirect indicator of comfort. In addition to BPD, many direct physiological indicators are related to sleep comfort and health, such as oxygen content in blood, heart rate, respiration and spinal alignment, which should be used to help improve mattress comfort. Spinal alignment is an important factor in sleep comfort and health, and abnormal spinal alignment can lead to muscle fatigue and even damage the musculoskeletal system. Conventional mattress support is constant in strength, but sleep behavior is a dynamic processes. Therefore, the mattress can not adjust the support performance according to the sleep posture, which means that the spine is not adequately supported for different sleep behaviors. Although some mattresses with conventional air bags can provide variable stiffness, which is enough to improve the BPD at the human-mattress interface, they fail to enhance spinal alignment during sleep due to the unpredictable deformation.

这种新型空气弹簧对符合人体工程学的床垫的应用将提供改善脊柱对准的可能性。结果<一种Href="//www.ygodb.com/articles/meca/full_html/2021/01/mi210007/mi210007.html">S.E.Ction 3.1indicate that this novel air spring with the same geometry size can obtain different stiffness by adjusting initial air pressure, thus satisfying different requirements of different human body parts and different user groups. The method of adjusting the stiffness of air spring is convenient, which provides the possibility for the design of the variable rigidity of mattress. The results of<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">第3.2节一种nd<一种Href="/articles/meca/full_html/2021/01/mi210007/mi210007.html">3.3表示可以设计具有不同垂直刚度的任何空气弹簧,并且任意平衡位置处的垂直刚度是可预测的。理论上,当安装在床垫中时,可以计算经受人体重力的这种新型空气弹簧的高度,因此脊柱下方的空气弹簧高度用于描述脊柱对准。当需要改善脊柱对准时,调节脊柱下方的相应空气弹簧的内部压力,并改变其垂直刚度,以获得正常脊柱对准所需的新高度。

4。结论

在这部作品中,空气spr的机械性能ing and its influence factors were studied, and a general analytical model of variable stiffness has been established according to the Ideal Gas Law and the approximate geometrical parameters of the air chamber. Finally, the analytical models of initial geometry, initial vertical stiffness and the stiffness of arbitrary equilibrium positions were verified and modified. Some valuable conclusions are as follows:

  • T.HE.vertical stiffness of air spring is negatively related to the volume and positively related to initial pressure. The vertical stiffness decreases nonlinearly with the increase of volume and increases linearly with increase of initial pressures.

  • 建立和修改了初始垂直刚度的计算模型,通过使用关键几何参数提供了设计空气弹簧的理论指导。

  • In this work, an analytical model of polynomial fitting error is adopted, with an average error of 6.96%.

  • R.E.搜索H一种s shown that the air springs have potential applications in providing personalized support and maintaining normal spinal alignment.

该研究有两个局限性。一方面,没有考虑材料的密度,尤其是在分析模型中,当它们由不同材料制成时可能影响空气弹簧的刚度。另一方面,仅研究了空气弹簧的垂直刚度,并且横向刚度可能影响其在工作过程中的性质。因此,材料密度对垂直和横向刚度的影响需要进一步研究。即使,实验结果和可变刚度空气弹簧的通用分析模型仍然对设计和工程应用具有重要的理论意义。总而言之,垂直刚度模型可以在任何高度准确地预测空气弹簧的机械性能,并为设计具有特殊刚度的空气弹簧提供理论指导

利益冲突

T.HE.一种uthors certify that there is no conflict of interest.

符号列表

P.0.:初始位置的空气弹簧内压(MPa)

p:Internal pressure of air spring of arbitrary position during the working process (MPa)

vo:初始位置的空气弹簧的体积(cm3.

v:体积of air spring of arbitrary position during the working process (cm3.

H:在工作过程中的任意位置的空气弹簧高度(cm)

一种E.:在工作过程中的任意位置的空气弹簧的等效支撑区域(cm2

一种E0.:T.HE.E.quivalent support area of the air spring of initial position (cm2

R.0.:T.HE.radius of plate of air spring not inflated (cm)

一种一种0.:T.HE.是一种of plate of air spring not inflated, which is a constant (cm2

R.一种:T.HE.radius of spherical cap of air spring (cm)

H0.:T.HE.HE.ight of spherical cap of air spring (cm)

H:空气弹簧的高度任意位置的during the working process (cm)

lB.:T.HE.HE.ight of single air chamber of arbitrary position during the working process (cm)

θ:T.HE.一种ngle between the tension of the air spring and the horizontal plane in the initial state (rad)

K.org.:V.E.rtical initial stiffness of air spring of initial position (KN · m-1

S.一种:球形帽表面穿过轴(cm)的电弧长度

r一种:T.HE.radius of approximate cambered surface of chambers during the working process (cm)

rB.:接触表面半径(cm)

一种B.:T.HE.是一种of contact surface of air spring during the working process (cm2

l:空气室的近似弧形表面的中心与接触表面边缘的垂直线(CM)的垂直线之间的距离

一种:T.HE.是一种of the approximate cambered surface of chamber during the working process (cm2

Ψ:张力室之间的角度和垂直line during the working process (rad)

致谢

由江苏省(KYCX20_0859)的研究生研究与实践创新计划和由全国一流学科(PNFD)提供的项目提供支持。

一种uthor contribution statement

T.HE.first author performed the experiment and wrote the article. The second author made an important suggestion on the analysis of experimental data and made important improvements to this study. The third author assisted with the experiments and made the instrument needed for the experiment.

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Cite this article as:Y. Chao, L.M. Shen, M.P. Liu, Mechanical characteristic and analytical model of novel air spring for ergonomic mattress, Mechanics & Industry22.那3.7.(2021)

所有表格

T.一种B.le 1

Information of material and specimen.

表2.

Working information of equipment and instruments.

表3

Compare with air spring in automotive suspension.

表4.

变量的计算公式。

表5.

Geometric parameters of air spring.

表6.

可变参数设置。

表7.

计算和测量空气弹簧几何参数值。

表8.

Difference between calculated and measured values of volume.

表9.

Calculation results of arbitrary height of air spring.

T.一种B.le 10

改性功能配件的结果。

所有数字

thumbnail 图。1

材料和空气弹簧。

In the text
thumbnail 图2

实验连接图。

In the text
thumbnail 图3.

Experimental procedure.

In the text
thumbnail 图4.

压缩过程中的负载和内部压力。(a)负载曲线,(​​b)内部压力曲线。

In the text
thumbnail 图5.

Curves of force and displacement for different air spring.

In the text
thumbnail 图6.

Curves of loading and unloading.

In the text
thumbnail 图7.

空气弹簧弯曲球形帽(A)空气弹簧结构图;(b)单曲面的力图。

In the text
thumbnail 图8

T.HE.force diagram of the spherical cap.

In the text
thumbnail 图9.

Diagram of air spring structure and force.

In the text
thumbnail 图。10.

一种pproximate geometry of single air chamber depressed.

In the text
thumbnail 图。11

参数对刚度(a)初始刚度和初始压力,(b)初始刚度和半径,(c)初始体积和初始半径,(d)高度和初始半径的影响。

In the text
thumbnail 图。12

预测和实验值。

In the text
thumbnail 图13.

Measured values and predicted values with modifying function.

In the text

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