WO2019210536A1 - 空气阻力测试天平 - Google Patents

空气阻力测试天平 Download PDF

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Publication number
WO2019210536A1
WO2019210536A1 PCT/CN2018/087701 CN2018087701W WO2019210536A1 WO 2019210536 A1 WO2019210536 A1 WO 2019210536A1 CN 2018087701 W CN2018087701 W CN 2018087701W WO 2019210536 A1 WO2019210536 A1 WO 2019210536A1
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Prior art keywords
hole
strain gauge
upper plate
force
double
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PCT/CN2018/087701
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English (en)
French (fr)
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李晓东
刘引
郑铭阳
陈超
高军辉
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北京航空航天大学
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Application filed by 北京航空航天大学 filed Critical 北京航空航天大学
Priority to ES18917518T priority Critical patent/ES2962477T3/es
Priority to EP18917518.5A priority patent/EP3671140B1/en
Publication of WO2019210536A1 publication Critical patent/WO2019210536A1/zh
Priority to US16/837,606 priority patent/US11300478B2/en

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M9/00—Aerodynamic testing; Arrangements in or on wind tunnels
    • G01M9/06—Measuring arrangements specially adapted for aerodynamic testing
    • G01M9/062—Wind tunnel balances; Holding devices combined with measuring arrangements
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01G—WEIGHING
    • G01G3/00—Weighing apparatus characterised by the use of elastically-deformable members, e.g. spring balances
    • G01G3/12—Weighing apparatus characterised by the use of elastically-deformable members, e.g. spring balances wherein the weighing element is in the form of a solid body stressed by pressure or tension during weighing
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L1/00—Measuring force or stress, in general
    • G01L1/20—Measuring force or stress, in general by measuring variations in ohmic resistance of solid materials or of electrically-conductive fluids; by making use of electrokinetic cells, i.e. liquid-containing cells wherein an electrical potential is produced or varied upon the application of stress
    • G01L1/22—Measuring force or stress, in general by measuring variations in ohmic resistance of solid materials or of electrically-conductive fluids; by making use of electrokinetic cells, i.e. liquid-containing cells wherein an electrical potential is produced or varied upon the application of stress using resistance strain gauges
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N19/00—Investigating materials by mechanical methods
    • G01N19/02—Measuring coefficient of friction between materials

Definitions

  • the present disclosure relates to a measuring device, and more particularly to an air resistance test balance.
  • the test piece In the device for measuring the friction of the flat plate, the test piece is generally placed in a wind tunnel with airflow flowing flush with the wind tunnel, and the strain of the test piece is measured by the strain gauge to measure the frictional force on the surface of the test piece.
  • a typical resistance balance is the single-point strain resistance balance shown in Figure 1.
  • the balance measures the differential pressure and the differential pressure moment while measuring the friction of the surface of the test piece.
  • the differential pressure is not uniform in the z direction, so its force arm varies with the entire z direction. At the same time, there is also a moment generated by the force in the z direction. So many forces increase the difficulty of the force measurement, especially the torque of the differential pressure is not clear and the strain generated by the z-direction moment.
  • the following formula is a single-point balance force expression:
  • the present disclosure designs a two-hole beam type load cell, which can utilize the structural features of the double-hole beam to eliminate the z-direction moment and the uncertainty band due to the pressure difference force arm. The resulting measurement uncertainty, so that the sensor only measures the force along the flow direction, thereby increasing the accuracy of the balance.
  • the air resistance test balance of the present disclosure is achieved by the following technical solutions.
  • the present disclosure provides an air resistance test balance comprising: 2N dual-hole beam sensors, and an upper plate; N is a positive integer;
  • 2N of the double-hole beam sensors are disposed under the upper plate and fixedly connected to the upper plate;
  • Each of the double-hole beam sensors includes a beam portion, an upper hole and a lower hole, the upper hole and the lower hole being disposed along a longitudinal direction of the beam portion, the upper hole being disposed at an upper portion of the beam portion, The lower hole is disposed at a lower portion of the beam portion.
  • the dual-hole beam sensor further includes a first strain gauge, a second strain gauge, a third strain gauge, and a fourth strain gauge; the first strain gauge and the third strain gauge Arranged outside the lower portion of the beam portion, the first strain gauge and the third strain gauge are symmetrically arranged with respect to the lower hole; the second strain gauge and the fourth strain gauge are disposed at the beam portion The upper outer side, the second strain gauge and the fourth strain gauge are symmetrically arranged with respect to the upper hole.
  • the beam portion has a rectangular parallelepiped shape.
  • the upper hole and the lower hole are both circular holes.
  • the upper end of the beam portion is fixedly coupled to the upper plate.
  • 2N of the double-hole beam sensors are distributed in a rectangular shape below the upper plate.
  • the upper plate is a rectangular flat plate
  • 2N of the double-hole beam sensors are respectively disposed at positions close to the four corners of the rectangular flat plate.
  • a lower plate is further included for securing a lower portion of the beam of 2N of the dual-hole beam sensors.
  • the upper and lower holes of each of the double-hole beam sensors communicate in a longitudinal direction of the beam portion.
  • the present disclosure provides a method of measuring friction of an upper surface of the upper plate using the air resistance test balance described above, including the following steps,
  • the original force of the upper plate is: tangential friction force F ⁇ , pressure difference force F(Z) ⁇ p of the arm and force F p in the z direction;
  • step 2) Simplify the original force of the upper plate in step 1), and translate the total force of the entire flow upward to the upper plate to the bottom of the upper plate, which is simplified as follows: the entire flow is upwardly received by the upper plate.
  • E is the Young's modulus of the double-hole beam
  • W is the bending section coefficient of the double-hole beam
  • ⁇ G is the strain generated by the gravity G at the strain gauge
  • L 1 is the bottom of the upper plate to the double-hole beam The distance from the center of the hole
  • L 2 is the distance from the bottom of the upper plate to the center of the lower hole of the double-hole beam
  • the reading strain of each double-hole beam sensor is: Based on the reading strain ⁇ d , the frictional force F received by the upper surface of the upper plate is obtained.
  • FIG. 1 is a schematic diagram of the force analysis of a single-point balance in the prior art.
  • FIG. 2 is a simplified schematic view of the force of an air resistance test balance of at least one embodiment of the present disclosure.
  • FIG 3 is a schematic structural view of a double-hole beam sensor of an air resistance balance according to at least one embodiment of the present disclosure.
  • FIG. 4 is a schematic overall structural view of an air resistance balance of at least one embodiment of the present disclosure.
  • the air resistance test balance includes: 4 double-hole beam sensors (the number of sensors is preferably 2, 4 or 6), and the upper plate; 4 double-hole beam sensors are arranged on the upper plate. Below and fixedly connected to the upper plate; each double-hole beam sensor includes a beam portion, an upper hole and a lower hole, the upper hole and the lower hole are arranged along the longitudinal direction of the beam portion, the upper hole is disposed at the upper portion of the beam portion, and the lower hole is disposed In the lower part of the beam.
  • the double-hole beam sensor includes a first strain gauge, a second strain gauge, a third strain gauge and a fourth strain gauge; the first strain gauge and the third strain gauge are disposed outside the lower portion of the beam portion, the first strain gauge and the third strain gauge
  • the sheet is symmetrically arranged with respect to the lower hole; the second strain gauge and the fourth strain gauge are disposed outside the upper portion of the beam portion, and the second strain gauge and the fourth strain gauge are symmetrically arranged with respect to the upper hole.
  • the beam is in the shape of a rectangular parallelepiped. Both the upper and lower holes are circular holes. The upper end of the beam is fixedly connected to the upper plate.
  • the four double-hole beam sensors are rectangularly distributed below the upper plate.
  • the upper plate is a rectangular plate, and the four double-hole beam sensors are respectively disposed at positions close to the four corners of the rectangular plate.
  • the air resistance test balance also includes a lower plate for securing the lower portion of the beam of the four dual-hole beam sensors.
  • the upper and lower holes of each of the double-hole beam sensors communicate in the longitudinal direction of the beam.
  • the method for measuring the frictional force of the upper surface of the upper plate using the air resistance test balance of the present embodiment includes the following steps,
  • the original force analysis is performed on the upper plate.
  • the original force of the upper plate is: tangential friction force F ⁇ , pressure difference force F(Z) ⁇ p and force F p in the z direction;
  • step 2) Simplify the original force of the upper plate in step 1), and translate the total force of the entire flow upward to the upper plate to the bottom of the upper plate, which is simplified as: the total force received by the entire flow upward plate The magnitude of the force F that is translated after being translated to the bottom of the upper plate, the force moment M caused by the translation of the force, and the gravity G in the z direction;
  • E is the Young's modulus of the double-hole beam
  • W is the bending section coefficient of the double-hole beam
  • ⁇ G is the strain generated by the gravity G at the strain gauge
  • L 1 is the bottom of the upper plate to the double-hole beam The distance from the center of the hole
  • L 2 is the distance from the bottom of the upper plate to the center of the lower hole of the double-hole beam
  • the reading strain of each double-hole beam sensor is: Based on the reading strain ⁇ d , the frictional force F received by the upper surface of the upper plate is obtained.
  • the original force of the test piece ie, the upper plate
  • the tangential friction force F ⁇ the differential pressure force F(Z) ⁇ p of the force arm
  • the force F p in the z direction The forces obtained by simplifying these forces are: the force F in the horizontal direction, the force G in the z direction, and the moment M. Then for a single dual-hole beam sensor, the reading strain is:
  • F is the magnitude of the force applied to the bottom of the test piece by the total force applied to the test piece
  • M is the force moment caused by the translation of the force.
  • E and W are the Young's modulus and resistance of the double-hole beam, respectively.
  • the bending section coefficient, ⁇ G is the strain generated by gravity G at the strain gauge, and L 1 and L 2 are the distances from the bottom of the test piece to the smallest section of the double-hole elastic beam (ie, the centers of the upper and lower holes). Further, the reading strain is:
  • the air resistance test balance can be integrally disposed in the recess of the wind tunnel to measure the air resistance (ie, the friction of the upper surface of the upper plate) received by the upper plate.
  • Each double-hole beam sensor can obtain the frictional force F of the upper surface of the upper plate.
  • the friction of the upper surface of the upper plate obtained by the above four double-hole beam sensors can be obtained.
  • the size of F is averaged as a measurement result.
  • the air resistance test balance of the present disclosure solves the problem that the resistance balance interferes with the strain generated by the z-direction force during the test and the pressure difference torque of the end wall is unknown, thereby directly measuring the force along the flow direction and improving the measurement accuracy.

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Fluid Mechanics (AREA)
  • Engineering & Computer Science (AREA)
  • Automation & Control Theory (AREA)
  • Health & Medical Sciences (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Chemical & Material Sciences (AREA)
  • Analytical Chemistry (AREA)
  • Biochemistry (AREA)
  • General Health & Medical Sciences (AREA)
  • Immunology (AREA)
  • Pathology (AREA)
  • Force Measurement Appropriate To Specific Purposes (AREA)
  • Aerodynamic Tests, Hydrodynamic Tests, Wind Tunnels, And Water Tanks (AREA)
  • Testing Or Measuring Of Semiconductors Or The Like (AREA)
  • Investigating Or Analyzing Materials By The Use Of Electric Means (AREA)

Abstract

一种空气阻力天平，包括：2N个双孔梁传感器，以及上板；2N个双孔梁传感器配置在上板的下方，并与上板固定连接；每个双孔梁传感器包括梁部、上孔和下孔，上孔和下孔沿梁部的纵向配置，上孔配置在梁部的上部，下孔配置在梁部的下部。还公开了一种使用空气阻力测试天平对上板的上表面的摩擦力进行测量的方法。

Description

空气阻力测试天平
相关申请的交叉引用
本申请要求于2018年5月2日提交的第201810408055.4号中国专利申请的优先权，其全部内容通过引用并入本申请中。
技术领域
本公开涉及一种测量装置，尤其涉及一种空气阻力测试天平。
背景技术
在测量平板摩擦力的装置中，一般将试件放置于与风洞管道平齐的有气流流动的风洞中，利用应变片测得试件的应变从而测得试件表面的摩擦力。一般的阻力天平是如图1所示的这种单支点的应变阻力天平。但是，这种天平在测得试件的表面的摩擦力的同时还会测得压差力以及压差力的力矩。而压差力在z方向上是不均匀的，所以其力臂是随着整个z方向变化的。同时，还存在着沿z方向的力产生的力矩。这么多的力使力的测量增加了难度，特别是压差力的力矩不明确和存在z向的力矩产生的应变。下式为单支点天平受力表达式:
Figure PCTCN2018087701-appb-000001
发明内容
为了解决至少一个上述技术问题，测量沿流向的阻力，本公开设计了双孔梁式的测力传感器，可以利用双孔梁的结构特点消除z向的力矩和由于压差力力臂不确定带来的测量不确定性，从而使传感器只测量到沿流向的力，从而增加天平的精确性。本公开的空气阻力测试天平通过以下技术方案实现。
一方面，本公开提供一种空气阻力测试天平，包括：2N个双孔梁 传感器，以及上板；N为正整数；
2N个所述双孔梁传感器配置在上板的下方，并与上板固定连接；
每个所述双孔梁传感器包括梁部、上孔和下孔，所述上孔和所述下孔沿所述梁部的纵向配置，所述上孔配置在所述梁部的上部，所述下孔配置在所述梁部的下部。
根据本公开的至少一个实施方式，所述双孔梁传感器还包括第一应变片、第二应变片、第三应变片和第四应变片；所述第一应变片和所述第三应变片配置在所述梁部的下部外侧，所述第一应变片和所述第三应变片关于所述下孔对称配置；所述第二应变片和所述第四应变片配置在所述梁部的上部外侧，所述第二应变片和所述第四应变片关于所述上孔对称配置。
根据本公开的至少一个实施方式，所述梁部为长方体形状。
根据本公开的至少一个实施方式，所述上孔和所述下孔均为圆形孔。
根据本公开的至少一个实施方式，所述梁部的上端与所述上板固定连接。
根据本公开的至少一个实施方式，2N个所述双孔梁传感器呈矩形分布在所述上板的下方。
根据本公开的至少一个实施方式，所述上板为矩形平板，2N个所述双孔梁传感器分别配置在靠近所述矩形平板的四角的位置。
根据本公开的至少一个实施方式，还包括下板，所述下板用于将2N个所述双孔梁传感器的梁部的下部固定。
根据本公开的至少一个实施方式，每个所述双孔梁传感器的上孔和下孔沿所述梁部的纵向连通。
另一方面，本公开提供一种使用上述的空气阻力测试天平对所述上板的上表面的摩擦力进行测量的方法，包括以下步骤，
1)对所述上板进行原始受力分析，上板原始受力为：切向摩擦力F τ，力臂未知的压差力F(Z) Δp和z方向的力F p；
2)对步骤1)中的上板的原始受力进行简化，将整个流向上所述上板受到的总的力大小平移到上板的底部，简化为：整个流向上所述上板 受到的总的力大小平移到上板底部后受到的力的大小F，力的平移引起的力偶矩M，以及z方向的重力G；
3)对每个所述双孔梁传感器，其读数应变为：ε d＝ε 1-ε 2-ε 3+ε 4，其中ε 1～ε 4分别为第一应变片、第二应变片、第三应变片和第四应变片的应变大小；第一应变片、第二应变片、第三应变片和第四应变片的应变大小分别为：
Figure PCTCN2018087701-appb-000002
Figure PCTCN2018087701-appb-000003
Figure PCTCN2018087701-appb-000004
Figure PCTCN2018087701-appb-000005
其中，E为双孔梁的杨氏模量，W为双孔梁的抗弯截面系数，ε G为重力G在应变片处产生的应变，L 1为上板的底部到双孔梁的上孔的中心的距离，L 2为上板的底部到双孔梁的下孔的中心的距离；
4)每个双孔梁传感器的读数应变为：
Figure PCTCN2018087701-appb-000006
根据读数应变ε d，得到上板的上表面受到的摩擦力F。
上述技术方案中的“第一”、“第二”、“第三”、“第四”仅是为了标识，并不限定相关部件的结构。
附图说明
附图示出了本公开的示例性实施方式，并与其说明一起用于解释本公开的原理，其中包括了这些附图以提供对本公开的进一步理解，并且附图包括在本说明书中并构成本说明书的一部分。
图1是现有技术中的单支点天平的受力分析示意图。
图2是本公开至少一个实施方式的空气阻力测试天平的受力化简示意图。
图3是本公开至少一个实施方式的空气阻力天平的双孔梁传感器的结构示意图。
图4是本公开至少一个实施方式的空气阻力天平的整体结构示意图。
具体实施方式
下面结合附图和实施例对本公开作进一步的详细说明。可以理解的是，此处所描述的具体实施例仅用于解释相关内容，而非对本公开的限定。另外还需要说明的是，为了便于描述，附图中仅示出了与本公开相关的部分。
需要说明的是，在不冲突的情况下，本公开中的实施例及实施例中的特征可以相互组合。下面将参考附图并结合实施例来详细说明本公开。
如图2-4所示，空气阻力测试天平，包括：4个双孔梁传感器(传感器的数目优选2个、4个或6个)，以及上板；4个双孔梁传感器配置在上板的下方，并与上板固定连接；每个双孔梁传感器包括梁部、上孔和下孔，上孔和下孔沿梁部的纵向配置，上孔配置在梁部的上部，下孔配置在梁部的下部。双孔梁传感器包括第一应变片、第二应变片、第三应变片和第四应变片；第一应变片和第三应变片配置在梁部的下部外侧，第一应变片和第三应变片关于下孔对称配置；第二应变片和第四应变片配置在梁部的上部外侧，第二应变片和第四应变片关于上孔对称配置。梁部为长方体形状。上孔和下孔均为圆形孔。梁部的上端与上板固定连接。4个双孔梁传感器呈矩形分布在上板的下方。上板为矩形平板，4个双孔梁传感器分别配置在靠近矩形平板的四角的位置。空气阻力测试天平还包括下板，下板用于将4个双孔梁传感器的梁部的下部固定。每个双孔梁传感器的上孔和下孔沿梁部的纵向连通。
本实施方式的使用空气阻力测试天平对上板的上表面的摩擦力进行测量的方法，包括以下步骤，
1)对上板进行原始受力分析，上板原始受力为：切向摩擦力F τ，力臂未知的压差力F(Z) Δp和z方向的力F p；
2)对步骤1)中的上板的原始受力进行简化，将整个流向上上板受到的总的力大小平移到上板的底部，简化为：整个流向上上板受到的总的力大小平移到上板底部后受到的力的大小F，力的平移引起的力偶矩M， 以及z方向的重力G；
3)对每个双孔梁传感器，其读数应变为：ε d＝ε 1-ε 2-ε 3+ε 4，其中ε 1～ε 4分别为第一应变片、第二应变片、第三应变片和第四应变片的应变大小；第一应变片、第二应变片、第三应变片和第四应变片的应变大小分别为：
Figure PCTCN2018087701-appb-000007
Figure PCTCN2018087701-appb-000008
Figure PCTCN2018087701-appb-000009
Figure PCTCN2018087701-appb-000010
其中，E为双孔梁的杨氏模量，W为双孔梁的抗弯截面系数，ε G为重力G在应变片处产生的应变，L 1为上板的底部到双孔梁的上孔的中心的距离，L 2为上板的底部到双孔梁的下孔的中心的距离；
4)每个双孔梁传感器的读数应变为：
Figure PCTCN2018087701-appb-000011
根据读数应变ε d，得到上板的上表面受到的摩擦力F。
更详细的，下面描述本公开的空气阻力测试天平的工作原理。
如图2所示，试件(即上板)原始受力为切向摩擦力F τ，力臂未知的压差力F(Z) Δp和z方向的力F p。将这些力化简后得到的力为：水平方向的力F，z方向的力G和力矩M。那么对一个单一的双孔梁传感器，其读数应变为：
Figure PCTCN2018087701-appb-000012
其中，U 0为传感器测得的电压，U AC传感器供电电压，K为应变片灵敏系数，ε 1～ε 4分别为应变片R1～R4受到的应变大小，ε d称为读数应变，即应变仪上的显示的数字。对于每一个应变片所受到的力与力矩产生的应变有：
Figure PCTCN2018087701-appb-000013
Figure PCTCN2018087701-appb-000014
Figure PCTCN2018087701-appb-000015
Figure PCTCN2018087701-appb-000016
其中F为整个流向上试件受到的总的力大小平移到试件底部受到的力的大小，M为力的平移引起的力偶矩，E与W分别为双孔梁的杨氏模量和抗弯截面系数，ε G为重力G在应变片处产生的应变，L 1与L 2分别为试件底部到双孔弹性梁最小截面处(即上孔和下孔的中心)的距离。进而，读数应变为：
Figure PCTCN2018087701-appb-000017
这样得到的应变只是由沿流向方向上的力产生，刚好消除了重力G和力偶矩M，只剩下需要测得的沿流向的力F。从而可以不必考虑z向的力G和压差力F(Z) Δp的力臂未知问题。
空气阻力测试天平可以整体配置在风洞的凹室内，来测量上板受到的空气阻力(即上板的上表面的摩擦力)。
每个双孔梁传感器均能获得上板的上表面的摩擦力F的大小，可选的，为了测量的准确，可以例如对上述4个双孔梁传感器获得的上板的上表面的摩擦力F的大小取平均值来作为测量结果。
本公开的空气阻力测试天平解决了阻力天平在测试时对于z向力产生的应变的干扰问题和端壁的压差力力矩未知的问题，从而直接测量得到沿流向的力，提高测量的精度。
本领域的技术人员应当理解，上述实施方式仅仅是为了清楚地说明本公开，而并非是对本公开的范围进行限定。对于所属领域的技术人员而言，在上述公开的基础上还可以做出其它变化或变型，并且这些变化或变型仍处于本公开的范围内。

Claims (10)

  1. 空气阻力测试天平，其特征在于，包括：2N个双孔梁传感器，以及上板；N为正整数；
    2N个所述双孔梁传感器配置在上板的下方，并与上板固定连接；
    每个所述双孔梁传感器包括梁部、上孔和下孔，所述上孔和所述下孔沿所述梁部的纵向配置，所述上孔配置在所述梁部的上部，所述下孔配置在所述梁部的下部。
  2. 根据权利要求1所述的空气阻力测试天平，其特征在于，
    所述双孔梁传感器还包括第一应变片、第二应变片、第三应变片和第四应变片；所述第一应变片和所述第三应变片配置在所述梁部的下部外侧，所述第一应变片和所述第三应变片关于所述下孔对称配置；所述第二应变片和所述第四应变片配置在所述梁部的上部外侧，所述第二应变片和所述第四应变片关于所述上孔对称配置。
  3. 根据权利要求1或2所述的空气阻力测试天平，其特征在于，
    所述梁部为长方体形状。
  4. 根据权利要求1或2所述的空气阻力测试天平，其特征在于，
    所述上孔和所述下孔均为圆形孔。
  5. 根据权利要求1或2所述的空气阻力测试天平，其特征在于，
    所述梁部的上端与所述上板固定连接。
  6. 根据权利要求1或2所述的空气阻力测试天平，其特征在于，
    2N个所述双孔梁传感器呈矩形分布在所述上板的下方。
  7. 根据权利要求6所述的空气阻力测试天平，其特征在于，
    所述上板为矩形平板，2N个所述双孔梁传感器分别配置在靠近所述矩形平板的四角的位置。
  8. 根据权利要求7所述的空气阻力测试天平，其特征在于，
    还包括下板，所述下板用于将2N个所述双孔梁传感器的梁部的下部固定。
  9. 根据权利要求1或2所述的空气阻力测试天平，其特征在于，
    每个所述双孔梁传感器的上孔和下孔沿所述梁部的纵向连通。
  10. 使用权利要求1-9任一项所述的空气阻力测试天平对所述上板 的上表面的摩擦力进行测量的方法，其特征在于，包括以下步骤，
    1)对所述上板进行原始受力分析，上板原始受力为：切向摩擦力F τ，力臂未知的压差力F(Z) Δp和z方向的力F p；
    2)对步骤1)中的上板的原始受力进行简化，将整个流向上所述上板受到的总的力大小平移到上板的底部，简化为：整个流向上所述上板受到的总的力大小平移到上板底部后受到的力的大小F，力的平移引起的力偶矩M，以及z方向的重力G；
    3)对每个所述双孔梁传感器，其读数应变为：ε d＝ε 1-ε 2-ε 3+ε 4，其中ε 1～ε 4分别为第一应变片、第二应变片、第三应变片和第四应变片的应变大小；第一应变片、第二应变片、第三应变片和第四应变片的应变大小分别为：
    Figure PCTCN2018087701-appb-100001
    Figure PCTCN2018087701-appb-100002
    Figure PCTCN2018087701-appb-100003
    Figure PCTCN2018087701-appb-100004
    其中，E为双孔梁的杨氏模量，W为双孔梁的抗弯截面系数，ε G为重力G在应变片处产生的应变，L 1为上板的底部到双孔梁的上孔的中心的距离，L 2为上板的底部到双孔梁的下孔的中心的距离；
    4)每个双孔梁传感器的读数应变为：
    Figure PCTCN2018087701-appb-100005
    根据读数应变ε d，得到上板的上表面受到的摩擦力F。
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