CN107239644A - 柴油机板簧扭振减振器刚度和应力计算模型 - Google Patents

柴油机板簧扭振减振器刚度和应力计算模型 Download PDF

Info

Publication number
CN107239644A
CN107239644A CN201710649695.XA CN201710649695A CN107239644A CN 107239644 A CN107239644 A CN 107239644A CN 201710649695 A CN201710649695 A CN 201710649695A CN 107239644 A CN107239644 A CN 107239644A
Authority
CN
China
Prior art keywords
mrow
msub
msubsup
msup
mtd
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN201710649695.XA
Other languages
English (en)
Other versions
CN107239644B (zh
Inventor
田中旭
李广洲
宋秋红
张俊
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Shanghai Maritime University
Shanghai Ocean University
Original Assignee
Shanghai Maritime University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Shanghai Maritime University filed Critical Shanghai Maritime University
Priority to CN201710649695.XA priority Critical patent/CN107239644B/zh
Publication of CN107239644A publication Critical patent/CN107239644A/zh
Application granted granted Critical
Publication of CN107239644B publication Critical patent/CN107239644B/zh
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/10Geometric CAD
    • G06F30/17Mechanical parametric or variational design
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/06Power analysis or power optimisation

Landscapes

  • Physics & Mathematics (AREA)
  • Geometry (AREA)
  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Optimization (AREA)
  • Mathematical Analysis (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • General Engineering & Computer Science (AREA)
  • Computational Mathematics (AREA)
  • Other Investigation Or Analysis Of Materials By Electrical Means (AREA)
  • Nitrogen And Oxygen Or Sulfur-Condensed Heterocyclic Ring Systems (AREA)
  • Springs (AREA)

Abstract

一种柴油机技术领域的板簧扭振减振器计算模型,包括板簧扭振减振器的刚度计算模型和板簧应力计算模型,刚度计算模型通过分别计算簧片弯矩、两簧片之间相互作用力、末端挠度,总力矩和转角得出,板簧应力计算模型通过分别计算两簧片之间的相互作用力、簧片弯矩和抗弯截面模量得出。本发明设计合理,计算精度高,适用于板簧扭振减振器的选型和优化设计。

Description

柴油机板簧扭振减振器刚度和应力计算模型
技术领域
本发明涉及的是一种柴油机技术领域的板簧扭振减振器计算模型,包括刚度和应力计算模型。
背景技术
扭转减振器是船舶、汽车发动机上的重要元件,主要由惯性块、弹性元件和阻尼元件等组成。在发动机曲轴自由端上安装扭振减振器,减振器会吸收发动机曲轴系的扭转振动,对于发动机曲轴系的工作可靠性,以及振动和噪声控制具有重要意义。具体来说,扭振减振器具有调整发动机曲轴系扭转振动自然频率,吸收振动能量,降低发动机扭矩峰值,减轻扭转振动的作用。对于扭转减振器,刚度参数是减振器自然频率计算的基础,从而决定了减振器的设计,以及对发动机与减振器的合理匹配;应力参数是评价减振器强度和可靠性的基础,对减振器的设计和使用具有重要作用。
板簧扭振减振器主要应用于大功率柴油机,如船舶和发电机组用柴油机等,其刚度和应力计算较复杂,其计算模型还未见相关文献中出现,人们往往通过有限元分析等手段进行计算,计算效率偏低,过程繁琐,不利于设计中应用。
发明内容
本发明针对上述现有技术的不足,提供了一种新型刚度和应力计算模型,具有非常高的计算效率和精度。
本发明是通过以下技术方案来实现的,本发明包括板簧扭振减振器的刚度计算模型和板簧应力计算模型,其中刚度计算模型由以下公式构成:
簧片1的弯矩为
簧片2的弯矩为
根据梁弯曲理论计算,得到两簧片的挠度函数:
其中采用Maple软件计算得出挠度表达式中的各个函数如下:
根据两簧片在A点的变形协调条件,得出的两簧片之间的相互作用力为:
以下计算减振器的刚度。由挠度公式可以计算出簧片1的末端挠度为:
总力矩为:
Mz=nFR (5)
转角:
减振器扭转刚度:
因末端挠度vL中也含力F,刚度公式中的F可以消掉;
板簧应力计算模型由以下公式构成:
簧片1的应力为
簧片2的应力为
其中,W(x)为x处簧片的抗弯截面模量,其具体计算公式为:
FC前文已经给出;
其中,以上公式各变量名分别为:n为周向板簧的组数(每组两片),R为板簧弯曲部分最小半径,L为板簧有效弯曲长度,b为板簧宽度,E为材料的弹性模量,a1为簧片有效长度宽边高度,a2为簧片有效长度窄边高度,S为铜垫片所在弯曲部分的长度,h(x):h(x)=a1+kx为任意x处高度(其中),FC为铜垫片末端两簧片相互作用力,γ为最大扭转角度。
与现有技术相比,本发明具有如下有益效果为:本发明设计合理,计算精度高,计算周期短。
附图说明
图1为本发明的簧片应力计算流程图;
图2为簧片应力计算流程图;
图3为减振器簧片弯矩分布图;
图4为减振器簧片挠度曲线;
图5为减振器簧片弯曲应力分布图;
图6为簧片应力最大处分布图。
具体实施方式
下面结合附图对本发明的实施例作详细说明,本实施例以本发明技术方案为前提,给出了详细的实施方式和具体的操作过程,但本发明的保护范围不限于下述的实施例。
实施例
在本发明中,发明内容中的公式可以在EXCEL软件编制,并进行参数输入和计算。本发明给出的一个实施例子,按照表1设置各参数,计算后的刚度为7420.9kN.m/rad;计算得出的的两簧片的弯矩分布图见图3,挠度曲线见图4,弯曲应力分布曲线见图5。从挠度图像可以看出,两簧片只在A点接触,假设的计算方法正确。从计算结果中可以看出,簧片固定端(图6中B处)和垫片末端(图6中A处)是应力最大处,此两处应力值列于下表2。
表1减振器参数表
序号 变量 数值 单位
1 n 24
2 R 0.21 m
3 L 0.114 m
4 b 0.09975 m
5 E 210000 MPa
6 a1 0.013 m
7 a2 0.0056019 m
8 S 0.073 m
9 γ 3.55 mrad
表2簧片交变应力值

Claims (1)

1.一种柴油机板簧扭振减振器刚度和应力计算模型,其特征在于,包括板簧扭振减振器的刚度计算模型和板簧应力计算模型,其中刚度计算模型由以下公式构成:
簧片1的弯矩为
<mrow> <msub> <mi>M</mi> <mn>1</mn> </msub> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>F</mi> <mrow> <mo>(</mo> <mi>L</mi> <mo>-</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>F</mi> <mi>C</mi> </msub> <mrow> <mo>(</mo> <mi>S</mi> <mo>-</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>x</mi> <mo>&amp;Element;</mo> <mo>&amp;lsqb;</mo> <mn>0</mn> <mo>,</mo> <mi>S</mi> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>F</mi> <mrow> <mo>(</mo> <mi>L</mi> <mo>-</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>x</mi> <mo>&amp;Element;</mo> <mo>&amp;lsqb;</mo> <mi>S</mi> <mo>,</mo> <mi>L</mi> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
簧片2的弯矩为
<mrow> <msub> <mi>M</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>F</mi> <mi>C</mi> </msub> <mrow> <mo>(</mo> <mrow> <mi>S</mi> <mo>-</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>x</mi> <mo>&amp;Element;</mo> <mo>&amp;lsqb;</mo> <mn>0</mn> <mo>,</mo> <mi>S</mi> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>x</mi> <mo>&amp;Element;</mo> <mo>&amp;lsqb;</mo> <mi>S</mi> <mo>,</mo> <mi>L</mi> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
根据梁弯曲理论计算,得到两簧片的挠度函数:
<mrow> <msub> <mi>v</mi> <mn>1</mn> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>v</mi> <mn>11</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>x</mi> <mo>&amp;Element;</mo> <mrow> <mo>&amp;lsqb;</mo> <mrow> <mn>0</mn> <mo>,</mo> <mi>S</mi> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>v</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>x</mi> <mo>&amp;Element;</mo> <mrow> <mo>&amp;lsqb;</mo> <mrow> <mi>S</mi> <mo>,</mo> <mi>L</mi> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>v</mi> <mn>2</mn> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>v</mi> <mn>21</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>x</mi> <mo>&amp;Element;</mo> <mrow> <mo>&amp;lsqb;</mo> <mrow> <mn>0</mn> <mo>,</mo> <mi>S</mi> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>v</mi> <mn>22</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>x</mi> <mo>&amp;Element;</mo> <mrow> <mo>&amp;lsqb;</mo> <mrow> <mi>S</mi> <mo>,</mo> <mi>L</mi> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
其中采用Maple软件计算得出挠度表达式中的各个函数如下:
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>v</mi> <mn>11</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>6</mn> <mo>(</mo> <mo>-</mo> <mn>2</mn> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mi>F</mi> <mi>k</mi> <mi>x</mi> <mo>+</mo> <mn>2</mn> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <msub> <mi>F</mi> <mi>C</mi> </msub> <mi>k</mi> <mi>x</mi> <mo>-</mo> <msub> <mi>Fa</mi> <mn>1</mn> </msub> <msup> <mi>k</mi> <mn>2</mn> </msup> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>F</mi> <mi>C</mi> </msub> <msub> <mi>a</mi> <mn>1</mn> </msub> <msup> <mi>k</mi> <mn>2</mn> </msup> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>FLk</mi> <mn>3</mn> </msup> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>-</mo> <msub> <mi>F</mi> <mi>C</mi> </msub> <msup> <mi>Sk</mi> <mn>3</mn> </msup> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>+</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <mi>ln</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>k</mi> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <msubsup> <mi>Fa</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mi>k</mi> <mi>x</mi> <mo>-</mo> <mn>2</mn> <mi>ln</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>k</mi> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <msub> <mi>F</mi> <mi>C</mi> </msub> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mi>k</mi> <mi>x</mi> <mo>-</mo> <mn>2</mn> <mi>ln</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>k</mi> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <msub> <mi>F</mi> <mi>C</mi> </msub> <msubsup> <mi>a</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mo>+</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <mi>ln</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>k</mi> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <msubsup> <mi>Fa</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mo>-</mo> <mn>2</mn> <mi>ln</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msubsup> <mi>Fa</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mi>k</mi> <mi>x</mi> <mo>+</mo> <mn>2</mn> <mi>ln</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>F</mi> <mi>C</mi> </msub> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mi>k</mi> <mi>x</mi> <mo>-</mo> <mn>2</mn> <mi>ln</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msubsup> <mi>Fa</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mo>+</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <mi>ln</mi> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> <msub> <mi>F</mi> <mi>C</mi> </msub> <msubsup> <mi>a</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mo>)</mo> <mo>/</mo> <mo>(</mo> <mrow> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <msup> <mi>Ebk</mi> <mn>3</mn> </msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>k</mi> <mi>x</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>v</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>6</mn> <mo>(</mo> <mn>2</mn> <msup> <mi>Sk</mi> <mn>2</mn> </msup> <mi>F</mi> <mi> </mi> <mi>ln</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>k</mi> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mi>x</mi> <mo>-</mo> <mn>2</mn> <mi>ln</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msubsup> <mi>Fa</mi> <mn>1</mn> <mn>2</mn> </msubsup> <msup> <mi>Sk</mi> <mn>2</mn> </msup> <mi>x</mi> <mo>+</mo> <mn>2</mn> <mi>ln</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>F</mi> <mi>C</mi> </msub> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <msup> <mi>Sk</mi> <mn>2</mn> </msup> <mi>x</mi> <mo>-</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <msup> <mi>Sk</mi> <mn>2</mn> </msup> <mi>ln</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>S</mi> <mi>k</mi> </mrow> <mo>)</mo> </mrow> <msub> <mi>F</mi> <mi>C</mi> </msub> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mi>x</mi> <mo>+</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> <msub> <mi>FLa</mi> <mn>1</mn> </msub> <msup> <mi>k</mi> <mn>3</mn> </msup> <mo>+</mo> <msup> <mi>Sx</mi> <mn>2</mn> </msup> <msup> <mi>FLk</mi> <mn>4</mn> </msup> <mo>-</mo> <msup> <mi>Sk</mi> <mn>3</mn> </msup> <msup> <mi>x</mi> <mn>2</mn> </msup> <msub> <mi>Fa</mi> <mn>1</mn> </msub> <mo>+</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <mi>F</mi> <mi> </mi> <mi>ln</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>k</mi> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <msubsup> <mi>a</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mi>S</mi> <mi>k</mi> <mo>+</mo> <mn>2</mn> <mi>k</mi> <mi>F</mi> <mi> </mi> <mi>ln</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>k</mi> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <msubsup> <mi>a</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mi>x</mi> <mo>-</mo> <mn>2</mn> <msubsup> <mi>FxSa</mi> <mn>1</mn> <mn>2</mn> </msubsup> <msup> <mi>k</mi> <mn>2</mn> </msup> <mo>+</mo> <mn>2</mn> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <msub> <mi>F</mi> <mi>C</mi> </msub> <msup> <mi>Sk</mi> <mn>2</mn> </msup> <mi>x</mi> <mo>-</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <mi>ln</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>S</mi> <mi>k</mi> </mrow> <mo>)</mo> </mrow> <msub> <mi>F</mi> <mi>C</mi> </msub> <msubsup> <mi>a</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mi>S</mi> <mi>k</mi> <mo>-</mo> <mn>2</mn> <mi>ln</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msubsup> <mi>Fa</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mi>k</mi> <mi>x</mi> <mo>-</mo> <mn>2</mn> <mi>ln</mi> <mi> </mi> <msubsup> <mi>Fa</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mi>S</mi> <mi>k</mi> <mo>+</mo> <mn>2</mn> <mi>ln</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>F</mi> <mi>C</mi> </msub> <msubsup> <mi>a</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mi>k</mi> <mi>x</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mn>2</mn> <mi>ln</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>F</mi> <mi>C</mi> </msub> <msubsup> <mi>a</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mi>S</mi> <mi>k</mi> <mo>-</mo> <mn>2</mn> <mi>k</mi> <mi> </mi> <mi>ln</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>S</mi> <mi>k</mi> </mrow> <mo>)</mo> </mrow> <msub> <mi>F</mi> <mi>C</mi> </msub> <msubsup> <mi>a</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mi>x</mi> <mo>-</mo> <msup> <mi>k</mi> <mn>2</mn> </msup> <msup> <mi>Fx</mi> <mn>2</mn> </msup> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>-</mo> <msup> <mi>S</mi> <mn>2</mn> </msup> <msup> <mi>x</mi> <mn>2</mn> </msup> <msub> <mi>F</mi> <mi>C</mi> </msub> <msup> <mi>k</mi> <mn>4</mn> </msup> <mo>+</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>F</mi> <mi>C</mi> </msub> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <msup> <mi>S</mi> <mn>2</mn> </msup> <msup> <mi>k</mi> <mn>2</mn> </msup> <mo>-</mo> <mn>2</mn> <msubsup> <mi>Fa</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mi>x</mi> <mi>k</mi> <mo>+</mo> <mn>2</mn> <msubsup> <mi>a</mi> <mn>1</mn> <mn>3</mn> </msubsup> <msub> <mi>F</mi> <mi>C</mi> </msub> <mi>S</mi> <mi>k</mi> <mo>-</mo> <mn>2</mn> <mi>ln</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msubsup> <mi>Fa</mi> <mn>1</mn> <mn>4</mn> </msubsup> <mo>+</mo> <mn>2</mn> <mi>ln</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>F</mi> <mi>C</mi> </msub> <msubsup> <mi>a</mi> <mn>1</mn> <mn>4</mn> </msubsup> <mo>+</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <mi>ln</mi> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>k</mi> <mi>x</mi> </mrow> <mo>)</mo> <msubsup> <mi>Fa</mi> <mn>1</mn> <mn>4</mn> </msubsup> <mo>-</mo> <mn>2</mn> <mi>ln</mi> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>S</mi> <mi>k</mi> </mrow> <mo>)</mo> <msub> <mi>F</mi> <mi>C</mi> </msub> <msubsup> <mi>a</mi> <mn>1</mn> <mn>4</mn> </msubsup> <mo>)</mo> <mo>/</mo> <mo>(</mo> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>k</mi> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <msup> <mi>k</mi> <mn>3</mn> </msup> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>S</mi> <mi>k</mi> </mrow> <mo>)</mo> </mrow> <mi>b</mi> <mi>E</mi> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>v</mi> <mn>21</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>6</mn> <msub> <mi>F</mi> <mi>C</mi> </msub> <mo>(</mo> <mo>-</mo> <mn>2</mn> <msubsup> <mi>kxa</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>-</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msup> <mi>k</mi> <mn>2</mn> </msup> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>Sk</mi> <mn>3</mn> </msup> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>+</mo> <mn>2</mn> <mi>ln</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>k</mi> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <msubsup> <mi>a</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mo>+</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <mi>ln</mi> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>k</mi> <mi>x</mi> </mrow> <mo>)</mo> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mi>k</mi> <mi>x</mi> <mo>-</mo> <mn>2</mn> <mi>ln</mi> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> <msubsup> <mi>a</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mo>-</mo> <mn>2</mn> <mi>ln</mi> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mi>k</mi> <mi>x</mi> <mo>)</mo> <mo>/</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <msup> <mi>Ebk</mi> <mn>3</mn> </msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>k</mi> <mi>x</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> 1
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>v</mi> <mn>22</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mn>6</mn> <msub> <mi>F</mi> <mi>C</mi> </msub> <mo>(</mo> <mo>-</mo> <mn>2</mn> <mi>ln</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>S</mi> <mi>k</mi> </mrow> <mo>)</mo> </mrow> <msubsup> <mi>a</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mo>-</mo> <mn>2</mn> <mi>ln</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>S</mi> <mi>k</mi> </mrow> <mo>)</mo> </mrow> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mi>k</mi> <mi>S</mi> <mo>+</mo> <mn>2</mn> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mi>S</mi> <mi>k</mi> <mo>+</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <msup> <mi>S</mi> <mn>2</mn> </msup> <msup> <mi>k</mi> <mn>2</mn> </msup> <mo>+</mo> <mn>2</mn> <mi>ln</mi> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> <msubsup> <mi>a</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mo>+</mo> <mn>2</mn> <mi>ln</mi> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mi>S</mi> <mi>k</mi> <mo>-</mo> <msup> <mi>k</mi> <mn>3</mn> </msup> <msup> <mi>xS</mi> <mn>2</mn> </msup> <mo>)</mo> <mo>/</mo> <mo>(</mo> <mrow> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <msup> <mi>k</mi> <mn>3</mn> </msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>S</mi> <mi>k</mi> </mrow> <mo>)</mo> </mrow> <mi>b</mi> <mi>E</mi> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>
根据两簧片在A点的变形协调条件,得出的两簧片之间的相互作用力为:
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>F</mi> <mi>C</mi> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mi>F</mi> <mo>(</mo> <mo>-</mo> <mn>2</mn> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mi>S</mi> <mi>k</mi> <mo>-</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msup> <mi>S</mi> <mn>2</mn> </msup> <msup> <mi>k</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>Lk</mi> <mn>3</mn> </msup> <msup> <mi>S</mi> <mn>2</mn> </msup> <mo>+</mo> <mn>2</mn> <mi>ln</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>S</mi> <mi>k</mi> </mrow> <mo>)</mo> </mrow> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mi>k</mi> <mi>S</mi> <mo>+</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <mi>ln</mi> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>S</mi> <mi>k</mi> </mrow> <mo>)</mo> <msubsup> <mi>a</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mo>-</mo> <mn>2</mn> <mi>ln</mi> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mi>S</mi> <mi>k</mi> <mo>-</mo> <mn>2</mn> <mi>ln</mi> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> <msubsup> <mi>a</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mo>)</mo> <mo>/</mo> <mo>(</mo> <mo>-</mo> <mn>2</mn> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mi>S</mi> <mi>k</mi> <mo>-</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <msup> <mi>S</mi> <mn>2</mn> </msup> <msup> <mi>k</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>S</mi> <mn>3</mn> </msup> <msup> <mi>k</mi> <mn>3</mn> </msup> <mo>+</mo> <mn>2</mn> <mi>ln</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>S</mi> <mi>k</mi> </mrow> <mo>)</mo> </mrow> <msubsup> <mi>a</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mo>+</mo> <mn>2</mn> <mi>ln</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>S</mi> <mi>k</mi> </mrow> <mo>)</mo> </mrow> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mi>k</mi> <mi>S</mi> <mo>-</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <mi>ln</mi> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> <msubsup> <mi>a</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mo>-</mo> <mn>2</mn> <mi>ln</mi> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mi>S</mi> <mi>k</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>
以下计算减振器的刚度。由挠度公式可以计算出簧片1的末端挠度为:
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>v</mi> <mi>L</mi> </msub> <mo>=</mo> <mn>6</mn> <mo>(</mo> <msup> <mi>L</mi> <mn>2</mn> </msup> <msup> <mi>SFk</mi> <mn>3</mn> </msup> <mo>+</mo> <msup> <mi>L</mi> <mn>2</mn> </msup> <msub> <mi>Fa</mi> <mn>1</mn> </msub> <msup> <mi>k</mi> <mn>2</mn> </msup> <mo>-</mo> <msup> <mi>LS</mi> <mn>2</mn> </msup> <msub> <mi>F</mi> <mi>C</mi> </msub> <msup> <mi>k</mi> <mn>3</mn> </msup> <mo>-</mo> <mn>2</mn> <msub> <mi>LSFa</mi> <mn>1</mn> </msub> <msup> <mi>k</mi> <mn>2</mn> </msup> <mo>-</mo> <mn>2</mn> <msubsup> <mi>LFa</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mi>k</mi> <mo>+</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msup> <mi>S</mi> <mn>2</mn> </msup> <msub> <mi>F</mi> <mi>C</mi> </msub> <msup> <mi>k</mi> <mn>2</mn> </msup> <mo>+</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <mi>k</mi> <mi>S</mi> <mi>F</mi> <mi> </mi> <mi>ln</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>k</mi> <mi>L</mi> </mrow> <mo>)</mo> </mrow> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>-</mo> <mn>2</mn> <mi>k</mi> <mi>S</mi> <mi> </mi> <mi>ln</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>S</mi> <mi>k</mi> </mrow> <mo>)</mo> </mrow> <msub> <mi>F</mi> <mi>C</mi> </msub> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <mn>2</mn> <msubsup> <mi>ka</mi> <mn>1</mn> <mn>2</mn> </msubsup> <msub> <mi>F</mi> <mi>C</mi> </msub> <mi>S</mi> <mo>-</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <mi>k</mi> <mi> </mi> <mi>ln</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msubsup> <mi>Fa</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mi>S</mi> <mo>+</mo> <mn>2</mn> <mi>k</mi> <mi> </mi> <mi>ln</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>F</mi> <mi>C</mi> </msub> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mi>S</mi> <mo>+</mo> <mn>2</mn> <mi>ln</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>F</mi> <mi>C</mi> </msub> <msubsup> <mi>a</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mo>+</mo> <mn>2</mn> <mi>F</mi> <mi> </mi> <mi>ln</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>k</mi> <mi>L</mi> </mrow> <mo>)</mo> </mrow> <msubsup> <mi>a</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mo>-</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <mi>ln</mi> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> <msubsup> <mi>Fa</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mo>-</mo> <mn>2</mn> <mi>ln</mi> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>S</mi> <mi>k</mi> </mrow> <mo>)</mo> <msub> <mi>F</mi> <mi>C</mi> </msub> <msubsup> <mi>a</mi> <mn>1</mn> <mn>3</mn> </msubsup> <mo>)</mo> <mo>/</mo> <mo>(</mo> <mrow> <mi>E</mi> <mi>b</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <mi>S</mi> <mi>k</mi> </mrow> <mo>)</mo> </mrow> <msubsup> <mi>a</mi> <mn>1</mn> <mn>2</mn> </msubsup> <msup> <mi>k</mi> <mn>3</mn> </msup> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>
总力矩为:
Mz=nFR (5)
转角:
<mrow> <mi>&amp;gamma;</mi> <mo>=</mo> <mfrac> <msub> <mi>v</mi> <mi>L</mi> </msub> <mi>R</mi> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
减振器扭转刚度:
<mrow> <mi>K</mi> <mo>=</mo> <mfrac> <msub> <mi>M</mi> <mi>z</mi> </msub> <mi>&amp;gamma;</mi> </mfrac> <mo>=</mo> <mfrac> <mrow> <msup> <mi>nR</mi> <mn>2</mn> </msup> <mi>F</mi> </mrow> <msub> <mi>v</mi> <mi>L</mi> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
因末端挠度vL中也含力F,刚度公式中的F可以消掉;
板簧应力计算模型由以下公式构成:
簧片1的应力为
<mrow> <msub> <mi>&amp;sigma;</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>M</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>W</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mfrac> <mrow> <mi>F</mi> <mrow> <mo>(</mo> <mrow> <mi>L</mi> <mo>-</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>F</mi> <mi>C</mi> </msub> <mrow> <mo>(</mo> <mrow> <mi>S</mi> <mo>-</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mi>W</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mtd> <mtd> <mrow> <mi>x</mi> <mo>&amp;Element;</mo> <mrow> <mo>&amp;lsqb;</mo> <mrow> <mn>0</mn> <mo>,</mo> <mi>S</mi> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mfrac> <mrow> <mi>F</mi> <mrow> <mo>(</mo> <mrow> <mi>L</mi> <mo>-</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mi>W</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mtd> <mtd> <mrow> <mi>x</mi> <mo>&amp;Element;</mo> <mrow> <mo>&amp;lsqb;</mo> <mrow> <mi>S</mi> <mo>,</mo> <mi>L</mi> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
簧片2的应力为
<mrow> <msub> <mi>&amp;sigma;</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>M</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>W</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mfrac> <mrow> <msub> <mi>F</mi> <mi>C</mi> </msub> <mrow> <mo>(</mo> <mrow> <mi>S</mi> <mo>-</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mi>W</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mtd> <mtd> <mrow> <mi>x</mi> <mo>&amp;Element;</mo> <mrow> <mo>&amp;lsqb;</mo> <mrow> <mn>0</mn> <mo>,</mo> <mi>S</mi> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>x</mi> <mo>&amp;Element;</mo> <mrow> <mo>&amp;lsqb;</mo> <mrow> <mi>S</mi> <mo>,</mo> <mi>L</mi> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
其中,W(x)为x处簧片的抗弯截面模量,其具体计算公式为:
<mrow> <mi>W</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> <mi>b</mi> <mi>h</mi> <msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow> 2
FC前文已经给出;
其中,以上公式各变量名分别为:n为周向板簧的组数(每组两片),R为板簧弯曲部分最小半径,L为板簧有效弯曲长度,b为板簧宽度,E为材料的弹性模量,a1为簧片有效长度宽边高度,a2为簧片有效长度窄边高度,S为铜垫片所在弯曲部分的长度,h(x):h(x)=a1+kx为任意x处高度(其中),FC为铜垫片末端两簧片相互作用力,γ为最大扭转角度。
CN201710649695.XA 2017-08-02 2017-08-02 柴油机板簧扭振减振器刚度和应力计算模型 Active CN107239644B (zh)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201710649695.XA CN107239644B (zh) 2017-08-02 2017-08-02 柴油机板簧扭振减振器刚度和应力计算模型

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201710649695.XA CN107239644B (zh) 2017-08-02 2017-08-02 柴油机板簧扭振减振器刚度和应力计算模型

Publications (2)

Publication Number Publication Date
CN107239644A true CN107239644A (zh) 2017-10-10
CN107239644B CN107239644B (zh) 2020-07-28

Family

ID=59989027

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201710649695.XA Active CN107239644B (zh) 2017-08-02 2017-08-02 柴油机板簧扭振减振器刚度和应力计算模型

Country Status (1)

Country Link
CN (1) CN107239644B (zh)

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109086473A (zh) * 2018-06-09 2018-12-25 上海海洋大学 一种柴油机卷簧扭振减振器刚度计算方法
CN114761703A (zh) * 2020-01-20 2022-07-15 舍弗勒技术股份两合公司 具有扭矩限制装置的扭振减震器
CN115859493A (zh) * 2022-10-31 2023-03-28 北京小米移动软件有限公司 板簧刚度值确定方法、装置、电子设备和机器人

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103742593A (zh) * 2014-01-24 2014-04-23 哈尔滨工程大学 轴系扭振异向振动控制方法
WO2016007689A1 (en) * 2014-07-09 2016-01-14 Qatar Foundation For Education, Science And Community Development Drill string axial vibration attenuator
CN105550453A (zh) * 2015-12-22 2016-05-04 成都市新筑路桥机械股份有限公司 一种有轨电车及其嵌入式轨道耦合动力学模型的建模方法
CN106777677A (zh) * 2016-12-14 2017-05-31 华南理工大学 一种适用于乘用车不同工况传动系扭振分析的建模方法

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103742593A (zh) * 2014-01-24 2014-04-23 哈尔滨工程大学 轴系扭振异向振动控制方法
WO2016007689A1 (en) * 2014-07-09 2016-01-14 Qatar Foundation For Education, Science And Community Development Drill string axial vibration attenuator
CN105550453A (zh) * 2015-12-22 2016-05-04 成都市新筑路桥机械股份有限公司 一种有轨电车及其嵌入式轨道耦合动力学模型的建模方法
CN106777677A (zh) * 2016-12-14 2017-05-31 华南理工大学 一种适用于乘用车不同工况传动系扭振分析的建模方法

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
EKREM BUYUKKAYA 等: "Thermal analysis of a ceramic coating diesel engine piston using 3-D finite element method", 《SURFACE AND COATINGS TECHNOLOGY》 *
M.A.BADIE 等: "Automotive composite driveshafts: investigation of the design variables effects", 《INTERNATIONAL JOURNAL OF ENGINEERING AND TECHNOLOGY》 *
汪萌生: "柴油机硅油减振器减振机理及匹配仿真技术研究", 《中国博士学位论文全文数据库 工程科技Ⅱ辑》 *
田中旭 等: "橡胶扭振减振器刚度模型研究", 《柴油机》 *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109086473A (zh) * 2018-06-09 2018-12-25 上海海洋大学 一种柴油机卷簧扭振减振器刚度计算方法
CN109086473B (zh) * 2018-06-09 2023-04-28 上海海洋大学 一种柴油机卷簧扭振减振器刚度计算方法
CN114761703A (zh) * 2020-01-20 2022-07-15 舍弗勒技术股份两合公司 具有扭矩限制装置的扭振减震器
CN115859493A (zh) * 2022-10-31 2023-03-28 北京小米移动软件有限公司 板簧刚度值确定方法、装置、电子设备和机器人

Also Published As

Publication number Publication date
CN107239644B (zh) 2020-07-28

Similar Documents

Publication Publication Date Title
Ding et al. Nonlinear isolation of transverse vibration of pre-pressure beams
Dai et al. Optimal design of tuned mass damper inerter with a Maxwell element for mitigating the vortex-induced vibration in bridges
Yao et al. Using grounded nonlinear energy sinks to suppress lateral vibration in rotor systems
CN107239644A (zh) 柴油机板簧扭振减振器刚度和应力计算模型
Yang et al. Vibration power flow and force transmission behaviour of a nonlinear isolator mounted on a nonlinear base
CN101315114B (zh) 一种汽车副车架上的减振吸能装置及其方法
US20060169557A1 (en) Constrained layer viscoelastic laminate tuned mass damper and method of use
Hua et al. Optimal design of a beam-based dynamic vibration absorber using fixed-points theory
CN112575672B (zh) 一种基于网络综合法设计抑制桥梁涡振动力吸振器的方法
Viet et al. On a combination of ground-hook controllers for semi-active tuned mass dampers
CN103699721A (zh) 一种橡胶减振垫最佳隔振效果多参数优选评价方法
Jin et al. Suppressing random response of a regular structure by an inerter-based dynamic vibration absorber
JP6498924B2 (ja) 二重動吸振器及び二重動吸振器の設計方法
JP5440415B2 (ja) 構造体設計支援装置
CN110287631B (zh) 一种l型管路卡箍系统建模的方法
Manolis et al. Vibrations of flexible pylons with time‐dependent mass attachments under ground induced motions
CN114662246B (zh) 一种基于内共振原理的齿轮系统扭转振动减振方法
Hassaan Optimal design of a vibration absorber-harvester dynamic system
JP6613956B2 (ja) 動吸振器の開発支援方法,開発支援装置及び開発支援プログラム
CN109829183B (zh) 一种安装支架模拟随机振动过程中的强度校核方法
Wang et al. Stability analysis and vibration reduction for a two-dimensional nonlinear system
CN112032243A (zh) 一种用于精密仪器低频减振的局域共振型隔振系统
CN103522862B (zh) 一种确定半主动悬架等效阻尼最大值的方法
JP2015094384A (ja) スライド型平行板ばね式動吸振器
Heidari et al. The effect of fractional viscoelastic supports on the response of a flexible rotor based on H∞ and H2 optimization methods

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant