CN201876396U - Measuring device of static normal direction contact stiffness of junction plane - Google Patents

Measuring device of static normal direction contact stiffness of junction plane Download PDF

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CN201876396U
CN201876396U CN2010206399652U CN201020639965U CN201876396U CN 201876396 U CN201876396 U CN 201876396U CN 2010206399652 U CN2010206399652 U CN 2010206399652U CN 201020639965 U CN201020639965 U CN 201020639965U CN 201876396 U CN201876396 U CN 201876396U
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test piece
measuring device
pressure sensor
measuring
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张进华
洪军
李小虎
王崴
杨国庆
庄艳
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Xian Jiaotong University
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Abstract

本实用新型公开了一种适用于结合面静态法向接触刚度的测量装置,该测量装置包括:测量支架、加载装置、测量装置、调节装置及待测试件;所述加载装置固定放置在测试支架的底部,其正上方依次是测量装置、待测试件及调节装置,加载装置、测量装置、待测试件及调节装置均位于测量支架内。本实用新型的测量装置结构简单,当加载不同的正压力时,本实用新型的测量装置能够针对不同的接触表面形貌、不同的正压力、不同的试验件材料特性等参数对结合面静态法向接触刚度进行测量,并利用实验结果分析接触表面形貌、正压力及试验件材料对法向接触刚度的影响规律。

Figure 201020639965

The utility model discloses a measuring device suitable for the static normal contact stiffness of a joint surface. The measuring device comprises: a measuring bracket, a loading device, a measuring device, an adjusting device and a piece to be tested; the loading device is fixedly placed on the testing bracket The bottom of the bottom, directly above it is the measuring device, the piece to be tested and the adjusting device in sequence, and the loading device, the measuring device, the piece to be tested and the adjusting device are all located in the measuring bracket. The measuring device of the utility model has a simple structure. When loading different positive pressures, the measuring device of the utility model can compare the joint surface static method with respect to parameters such as different contact surface topography, different positive pressures, and different test piece material properties. The contact stiffness in the normal direction is measured, and the influence law of the contact surface morphology, normal pressure and test piece material on the normal contact stiffness is analyzed by using the experimental results.

Figure 201020639965

Description

一种结合面静态法向接触刚度测量装置A joint surface static normal contact stiffness measurement device

技术领域:Technical field:

本实用新型属于测量领域,涉及一种法向接触刚度测量装置,尤其是一种结合面静态法向接触刚度测量装置。The utility model belongs to the field of measurement, and relates to a normal contact stiffness measuring device, in particular to a joint surface static normal contact stiffness measuring device.

背景技术:Background technique:

在机床、大型飞机等复杂机械系统中存在大量的结合面,它们破坏了机械系统结构的连续性,极大程度地影响机械系统的整机性能。结合面的连接特性呈现出非连续性,将结合面特性参数模型引入系统整机建模过程可以有效地提高产品设计阶段的整机性能预测能力。因此,准确构建结合面特性参数模型将为复杂机械部件结合面优化设计提供理论基础。There are a large number of joint surfaces in complex mechanical systems such as machine tools and large aircrafts, which destroy the continuity of the mechanical system structure and greatly affect the overall performance of the mechanical system. The connection characteristics of the joint surface show discontinuity, and introducing the characteristic parameter model of the joint surface into the modeling process of the whole system can effectively improve the performance prediction ability of the whole machine in the product design stage. Therefore, the accurate construction of the joint surface characteristic parameter model will provide a theoretical basis for the optimal design of the joint surface of complex mechanical parts.

结合面接触刚度作为结合面重要特性参数之一,其准确程度将直接影响结合面参数特性模型。结合面的接触刚度与两接触表面的表面形貌及接触状态有关,因此研究结合面的形貌及接触状态对结合面接触刚度的影响规律将有助于准确确定结合面特性参数模型。The contact stiffness of the joint surface is one of the important characteristic parameters of the joint surface, and its accuracy will directly affect the parameter characteristic model of the joint surface. The contact stiffness of the joint surface is related to the surface morphology and contact state of the two contact surfaces. Therefore, the study of the influence of the joint surface morphology and contact state on the contact stiffness of the joint surface will help to accurately determine the characteristic parameter model of the joint surface.

实用新型内容:Utility model content:

本实用新型的目的是提供一种静态法向接触刚度测量装置,通过直接测量结合面间的负载和位移,然后得到刚度。The purpose of the utility model is to provide a static normal contact stiffness measuring device, which can obtain the stiffness by directly measuring the load and displacement between the joint surfaces.

本实用新型是通过以下技术方案实现的,一种适用于结合面静态法向接触刚度的测量装置,该测量装置包括:测量支架、加载装置、测量装置、调节装置及待测试件;所述加载装置固定放置在测试支架的底部,其正上方依次是测量装置、待测试件及调节装置,加载装置、测量装置、待测试件及调节装置均位于测量支架内。The utility model is realized through the following technical solutions, a measuring device suitable for the static normal contact stiffness of the joint surface, the measuring device comprises: a measuring bracket, a loading device, a measuring device, an adjusting device and a piece to be tested; the loading The device is fixedly placed on the bottom of the test bracket, and directly above it are the measuring device, the piece to be tested and the adjustment device in sequence. The loading device, the measuring device, the piece to be tested and the adjustment device are all located in the measurement bracket.

所述测量装置包括一个压力传感器、传感器顶帽、压力传感器固定环和一个轴向引伸计;压力传感器固定在千斤顶的正上方,压力传感器顶帽套在压力传感器的测量顶端,压力传感器固定环固定在下支撑板上,对压力传感器及顶帽起到固定及导向作用,轴向引伸计在测量过程中两个刀刃分别夹持在两个待测试件上。The measuring device comprises a pressure sensor, a sensor top cap, a pressure sensor fixing ring and an axial extensometer; the pressure sensor is fixed directly above the jack, the pressure sensor top cap is set on the measuring top of the pressure sensor, and the pressure sensor fixing ring is fixed On the lower support plate, the pressure sensor and the top cap are fixed and guided, and the two blades of the axial extensometer are respectively clamped on the two test pieces during the measurement process.

所述调节装置包括调整螺杆、螺杆导套、中空导向套、第一锁紧螺钉、第二锁紧螺钉、调心球、试件固定环、钢球固定环;其中,带手柄的调整螺杆位于测量支架的正上方,螺杆导套与上支撑板紧固配合,与调整螺杆螺纹联接,中空导向套固定在上支撑板上,试件固定环设置于中空导向套内,位于待测试件的正上方,第一锁紧螺钉和第二锁紧螺钉设置于中空导向套上的螺纹通孔内,可旋入旋出,调心球通过钢球固定环封在试件固定环内,可以在试件固定环内自由旋转。The adjusting device includes an adjusting screw, a screw guide sleeve, a hollow guide sleeve, a first locking screw, a second locking screw, an aligning ball, a test piece fixing ring, and a steel ball fixing ring; wherein, the adjusting screw with a handle is located at Directly above the measuring bracket, the screw guide sleeve is tightly matched with the upper support plate, and is threadedly connected with the adjustment screw. The hollow guide sleeve is fixed on the upper support plate. Above, the first locking screw and the second locking screw are set in the threaded through hole on the hollow guide sleeve, which can be screwed in and out. The self-aligning ball is sealed in the test piece fixing ring through the steel ball fixing ring, which can be Free rotation within the retaining ring.

所述待测试件包括上试件和下试件,下试件位于压力传感器顶帽的正上方,上试件位于下试件的正上方,上试件的顶端有球窝,球窝的正上方是调心球,通过球头-球窝配合防止加载时结合面局部接触,保证整个结合面完全接触,在结合面附近轴向引伸计通过夹持刀刃固定在上试件及下试件上。The test piece includes an upper test piece and a lower test piece, the lower test piece is located directly above the top cap of the pressure sensor, the upper test piece is located directly above the lower test piece, the top of the upper test piece has a ball socket, and the ball socket is directly above the top cap of the pressure sensor. The upper part is a self-aligning ball, which prevents partial contact of the joint surface during loading through the ball-socket fit, ensuring complete contact of the entire joint surface, and the axial extensometer near the joint surface is fixed on the upper and lower specimens by clamping blades .

所述测量支架包括上支撑板、第一立柱和为第二立柱及下支撑板,三者装配为一体,在测量过程中始终保持固定不动。The measurement bracket includes an upper support plate, a first column, a second column and a lower support plate, the three are assembled as one, and remain fixed during the measurement process.

所述加载装置包括一个千斤顶,千斤顶固定在下支撑板内。The loading device includes a jack fixed in the lower support plate.

本实用新型的原理是通过直接测量结合面间的负载和变形,然后得到刚度,原理比较简单所以测量装置结构简单。当加载不同的正压力时,本实用新型的测量装置能够针对不同的接触表面形貌、不同的正压力、不同的试验件材料特性等参数对结合面静态法向接触刚度进行测量,并利用实验结果分析接触表面形貌、正压力及试验件材料对法向接触刚度的影响规律。The principle of the utility model is to obtain the stiffness by directly measuring the load and deformation between the bonding surfaces, and the principle is relatively simple so the structure of the measuring device is simple. When loading different normal pressures, the measuring device of the present invention can measure the static normal contact stiffness of the bonding surface according to parameters such as different contact surface topography, different normal pressures, and different test piece material properties, and use the experimental Results The influence of contact surface morphology, normal pressure and test piece material on normal contact stiffness was analyzed.

附图说明:Description of drawings:

图1为本实用新型的测量装置结构示意图;Fig. 1 is the structural representation of measuring device of the present utility model;

其中:1为调整螺杆;2为上支撑板;3-1为第一锁紧螺钉;3-2为第二锁紧螺钉;4为试件固定环;5为上试件;6为压力传感器固定环;7-1为第一立柱;7-2为第二立柱;8为下支撑板;9为千斤顶;10为压力传感器;11为压力传感器顶帽;12为下试件;13为轴向引伸计;14为钢球固定环;15为调心球;16为中空导向套;17为螺杆导套。Among them: 1 is the adjusting screw; 2 is the upper support plate; 3-1 is the first locking screw; 3-2 is the second locking screw; 4 is the test piece fixing ring; 5 is the upper test piece; 6 is the pressure sensor Fixed ring; 7-1 is the first column; 7-2 is the second column; 8 is the lower support plate; 9 is the jack; 10 is the pressure sensor; 11 is the top cap of the pressure sensor; 12 is the lower test piece; 13 is the shaft 14 is a steel ball fixing ring; 15 is a self-aligning ball; 16 is a hollow guide sleeve; 17 is a screw guide sleeve.

具体实施方式:Detailed ways:

下面结合附图对本实用新型做进一步详细描述:Below in conjunction with accompanying drawing, the utility model is described in further detail:

如图1所示,本实用新型是一种适用于结合面静态法向接触刚度的测量装置,该测量装置包括:测量支架、加载装置、测量装置、调节装置及待测试件。As shown in Figure 1, the utility model is a measuring device suitable for the static normal contact stiffness of the joint surface, which includes: a measuring bracket, a loading device, a measuring device, an adjusting device and a piece to be tested.

测量支架包括上支撑板2、第一立柱7-1和为第二立柱7-2及下支撑板8,三者装配为一体,在测量过程中始终保持固定不动。The measurement support includes an upper support plate 2, a first column 7-1, a second column 7-2 and a lower support plate 8, the three are assembled as one, and remain fixed during the measurement process.

加载装置包括一个千斤顶9,千斤顶9固定在下支撑板8内。The loading device includes a jack 9 fixed in the lower support plate 8 .

测量装置包括压力传感器10、压力传感器顶帽11、压力传感器固定环6和轴向引伸计13。其中:压力传感器10固定在千斤顶9的正上方,压力传感器顶帽11套在压力传感器10的测量顶端,压力传感器固定环6固定在下支撑板8上,对压力传感器10及顶帽11起到固定及导向作用,轴向引伸计13在测量过程中两个刀刃分别夹持在两个待测试件上。The measuring device includes a pressure sensor 10 , a pressure sensor top cap 11 , a pressure sensor fixing ring 6 and an axial extensometer 13 . Wherein: the pressure sensor 10 is fixed directly above the jack 9, the pressure sensor top cap 11 is set on the measuring top of the pressure sensor 10, the pressure sensor fixing ring 6 is fixed on the lower support plate 8, and the pressure sensor 10 and the top cap 11 are fixed. and guiding function, the two blades of the axial extensometer 13 are respectively clamped on the two test pieces during the measurement process.

调节装置包括调整螺杆1、螺杆导套17、中空导向套16、第一锁紧螺钉3-1和第二锁紧螺钉3-2、调心球15、试件固定环4、钢球固定环14。其中,带手柄的调整螺杆1位于测量支架的正上方,螺杆导套17与上支撑板2紧固配合,与调整螺杆1螺纹联接,中空导向套16固定在上支撑板2上,试件固定环4设置于中空导向套16内,位于待测试件的正上方,第一锁紧螺钉3-1和第二锁紧螺钉3-2设置于中空导向套16上的螺纹通孔内,可旋入旋出,调心球15通过钢球固定环14封在试件固定环4内,可以在试件固定环内4自由旋转。The adjustment device includes adjusting screw 1, screw guide sleeve 17, hollow guide sleeve 16, first locking screw 3-1 and second locking screw 3-2, self-aligning ball 15, specimen fixing ring 4, steel ball fixing ring 14. Among them, the adjusting screw 1 with a handle is located directly above the measuring bracket, the screw guide sleeve 17 is tightly matched with the upper supporting plate 2, and is threadedly connected with the adjusting screw 1, the hollow guiding sleeve 16 is fixed on the upper supporting plate 2, and the test piece is fixed. The ring 4 is arranged in the hollow guide sleeve 16 and is located directly above the test piece. The first locking screw 3-1 and the second locking screw 3-2 are arranged in the threaded through hole on the hollow guide sleeve 16, which can be rotated. In and out, the self-aligning ball 15 is sealed in the test piece fixing ring 4 by the steel ball fixing ring 14, and can freely rotate in the test piece fixing ring 4.

待测试件包括上试件5和下试件12,下试件12位于压力传感器顶帽11的正上方,上试件5位于下试件12的正上方,上试件5的顶端有球窝,球窝的正上方是调心球15,通过球头-球窝配合,可以防止加载时结合面局部接触,保证整个结合面完全接触,在结合面附近轴向引伸计13通过夹持刀刃固定在上试件5及下试件12上。The test piece to be tested includes an upper test piece 5 and a lower test piece 12, the lower test piece 12 is located directly above the top cap 11 of the pressure sensor, the upper test piece 5 is located directly above the lower test piece 12, and the top of the upper test piece 5 has a ball socket , directly above the ball socket is the self-aligning ball 15, through the ball-socket cooperation, it can prevent partial contact of the joint surface during loading, and ensure the complete contact of the entire joint surface, and the axial extensometer 13 is fixed by clamping the blade near the joint surface On the upper test piece 5 and the lower test piece 12.

采用本实用新型进行结合面静态法向接触刚度的测量时,具体实施过程包括下列步骤:When the utility model is used to measure the static normal contact stiffness of the joint surface, the specific implementation process includes the following steps:

1)调节调整螺杆1,使试件固定环4可以在中空导向套16内上下滑动,调节第一锁紧螺钉3-1和第二锁紧螺钉3-2,使试件固定环4固定在一个合适的位置方便放入试件;1) Adjust the adjustment screw 1, so that the test piece fixing ring 4 can slide up and down in the hollow guide sleeve 16, adjust the first locking screw 3-1 and the second locking screw 3-2, so that the test piece fixing ring 4 is fixed on the A suitable location for placing the test piece;

2)将具有特定表面粗糙度的下试件12放在压力传感器顶帽11的正上方,上试件5放在下试件12的正上方,通过调节调整螺杆1及第一锁紧螺钉3-1和第二锁紧螺钉3-2使调心球15嵌入球窝,固定试件;2) Place the lower test piece 12 with a specific surface roughness directly above the top cap 11 of the pressure sensor, place the upper test piece 5 directly above the lower test piece 12, and adjust the adjusting screw 1 and the first locking screw 3- 1 and the second locking screw 3-2 to embed the self-aligning ball 15 into the ball socket to fix the test piece;

3)千斤顶9均匀加力,直至到达预定的最大压力,结合面间的压力及试件的变形分别通过压力传感器10及轴向引伸计13测得,均匀采集力和变形的数据3) The jack 9 applies force evenly until the predetermined maximum pressure is reached. The pressure between the joint surfaces and the deformation of the test piece are respectively measured by the pressure sensor 10 and the axial extensometer 13, and the data of force and deformation are uniformly collected

4)一组实验做完以后,重复上述步骤,更换下一组试件,如此,可得到多组不同类型的结合面的测量数据4) After a group of experiments is completed, repeat the above steps and replace the next group of test pieces. In this way, multiple sets of measurement data of different types of bonding surfaces can be obtained

5)在每组试件中,得到多组压力与位移的数据后,进行数据后处理,得到每组试件结合面的压力-位移曲线,从而求得结合面间的静态法向接触刚度。5) In each group of test pieces, after obtaining multiple sets of pressure and displacement data, the data is post-processed to obtain the pressure-displacement curve of the joint surface of each set of test specimens, so as to obtain the static normal contact stiffness between the joint surfaces.

本实用新型的测量原理为,当在结合面两端施加法向正压力时,轴向引伸计测量的变形包括两个部分:一是结合面的法向变形,二是轴向引伸计两个夹持刀刃之间的材料的弹性变形。材料的弹性变形可由胡克定律

Figure BDA0000035984230000051
直接计算得到,其中,F为结合面间的法向正压力,A为结合面的名义接触面积,L为试件结合面端距离轴向引伸计夹持刀刃的距离。因此,结合面在法向正压力F的作用下所产生的法向变形:δ=W-ΔL1-ΔL2,其中,W是轴向引伸计测得的变形,ΔL1、ΔL2是理论计算得到的材料的弹性变形。这样,在多次加载下通过压力传感器测量正压力、轴向引伸计测量变形就可以得到结合面的力-位移曲线,从而求得结合面的静态法向接触刚度。The measurement principle of the utility model is that when a normal positive pressure is applied at both ends of the joint surface, the deformation measured by the axial extensometer includes two parts: one is the normal deformation of the joint surface, and the other is the two parts of the axial extensometer. Elastic deformation of the material held between the blades. The elastic deformation of materials can be determined by Hooke's law
Figure BDA0000035984230000051
It is directly calculated, where F is the normal positive pressure between the joint surfaces, A is the nominal contact area of the joint surface, and L is the distance between the joint surface end of the specimen and the clamping blade of the axial extensometer. Therefore, the normal deformation of the bonding surface under the action of the normal positive pressure F: δ=W-ΔL 1 -ΔL 2 , where W is the deformation measured by the axial extensometer, and ΔL 1 and ΔL 2 are the theoretical The calculated elastic deformation of the material. In this way, the force-displacement curve of the joint surface can be obtained by measuring the normal pressure with the pressure sensor and the deformation with the axial extensometer under multiple loadings, so as to obtain the static normal contact stiffness of the joint surface.

以上内容是结合具体的优选实施方式对本实用新型所作的进一步详细说明,不能认定本实用新型的具体实施方式仅限于此,对于本实用新型所属技术领域的普通技术人员来说,在不脱离本实用新型构思的前提下,还可以做出若干简单的推演或替换,都应当视为属于本实用新型由所提交的权利要求书确定专利保护范围。The above content is a further detailed description of the utility model in conjunction with specific preferred embodiments. It cannot be determined that the specific embodiment of the utility model is limited to this. Under the premise of the new concept, some simple deduction or replacement can also be made, which should be regarded as belonging to the utility model and the patent protection scope is determined by the submitted claims.

Claims (6)

1.一种适用于结合面静态法向接触刚度的测量装置,其特征在于:该测量装置包括:测量支架、加载装置、测量装置、调节装置及待测试件;所述加载装置固定放置在测试支架的底部,其正上方依次是测量装置、待测试件及调节装置,加载装置、测量装置、待测试件及调节装置均位于测量支架内。1. A measuring device applicable to the static normal contact stiffness of joint surfaces, characterized in that: the measuring device comprises: a measuring bracket, a loading device, a measuring device, an adjusting device and a test piece; the loading device is fixedly placed on the test The bottom of the bracket and directly above it are the measuring device, the piece to be tested and the adjusting device in sequence, and the loading device, the measuring device, the piece to be tested and the adjusting device are all located in the measuring bracket. 2.如权利要求1所述一种适用于结合面静态法向接触刚度的测量装置,其特征在于:所述测量装置包括一个压力传感器、传感器顶帽、压力传感器固定环和一个轴向引伸计;压力传感器固定在千斤顶的正上方,压力传感器顶帽套在压力传感器的测量顶端,压力传感器固定环固定在下支撑板上,对压力传感器及顶帽起到固定及导向作用,轴向引伸计在测量过程中两个刀刃分别夹持在两个待测试件上。2. A kind of measuring device applicable to the static normal contact stiffness of joint surface as claimed in claim 1, characterized in that: said measuring device comprises a pressure sensor, a sensor top cap, a pressure sensor retaining ring and an axial extensometer ;The pressure sensor is fixed directly above the jack, the top cap of the pressure sensor is set on the top of the pressure sensor, the fixing ring of the pressure sensor is fixed on the lower support plate, which plays a role of fixing and guiding the pressure sensor and the top cap, and the axial extensometer is in the During the measurement, the two blades are respectively clamped on the two test pieces. 3.如权利要求1所述一种适用于结合面静态法向接触刚度的测量装置,其特征在于:所述调节装置包括调整螺杆、螺杆导套、中空导向套、第一锁紧螺钉、第二锁紧螺钉、调心球、试件固定环、钢球固定环;其中,带手柄的调整螺杆位于测量支架的正上方,螺杆导套与上支撑板紧固配合,与调整螺杆螺纹联接,中空导向套固定在上支撑板上,试件固定环设置于中空导向套内,位于待测试件的正上方,第一锁紧螺钉和第二锁紧螺钉设置于中空导向套上的螺纹通孔内,可旋入旋出,调心球通过钢球固定环封在试件固定环内,在试件固定环内自由旋转。3. A measuring device suitable for static normal contact stiffness of joint surfaces as claimed in claim 1, characterized in that: said adjusting device comprises an adjusting screw, a screw guide sleeve, a hollow guide sleeve, a first locking screw, a second Two locking screws, self-aligning balls, test piece fixing ring, and steel ball fixing ring; among them, the adjusting screw with handle is located directly above the measuring bracket, the screw guide sleeve is tightly matched with the upper support plate, and is threadedly connected with the adjusting screw, The hollow guide sleeve is fixed on the upper support plate, the specimen fixing ring is set in the hollow guide sleeve, and is located directly above the test piece, and the first locking screw and the second locking screw are arranged in the threaded through hole on the hollow guide sleeve Inside, it can be screwed in and out. The self-aligning ball is sealed in the test piece fixing ring through the steel ball fixing ring, and can rotate freely in the test piece fixing ring. 4.如权利要求1所述一种适用于结合面静态法向接触刚度的测量装置,其特征在于:所述待测试件包括上试件和下试件,下试件位于压力传感器顶帽的正上方,上试件位于下试件的正上方,上试件的顶端有球窝,球窝的正上方是调心球,通过球头-球窝配合防止加载时结合面局部接触,保证整个结合面完全接触,在结合面附近轴向引伸计通过夹持刀刃固定在上试件及下试件上。4. A kind of measuring device applicable to the static normal contact stiffness of the bonding surface as claimed in claim 1, wherein the test piece includes an upper test piece and a lower test piece, and the lower test piece is located at the top of the pressure sensor cap. Directly above, the upper test piece is located directly above the lower test piece, the top of the upper test piece has a ball socket, directly above the ball socket is a self-aligning ball, through the ball-socket cooperation to prevent partial contact of the joint surface during loading, to ensure that the entire The joint surface is in full contact, and the axial extensometer near the joint surface is fixed on the upper and lower specimens by clamping the blade. 5.如权利要求1所述一种适用于结合面静态法向接触刚度的测量装置,其特征在于:所述测量支架包括上支撑板、第一立柱和为第二立柱及下支撑板,三者装配为一体,在测量过程中始终保持固定不动。5. A kind of measuring device applicable to the static normal contact stiffness of joint surface as claimed in claim 1, characterized in that: said measuring bracket comprises an upper support plate, a first column and a second column and a lower support plate, three The latter is assembled as a whole and remains fixed throughout the measurement process. 6.如权利要求1所述一种适用于结合面静态法向接触刚度的测量装置,其特征在于:所述加载装置包括一个千斤顶,千斤顶固定在下支撑板内。6 . A measuring device suitable for static normal contact stiffness of joint surfaces as claimed in claim 1 , wherein the loading device comprises a jack, and the jack is fixed in the lower support plate. 7 .
CN2010206399652U 2010-12-03 2010-12-03 Measuring device of static normal direction contact stiffness of junction plane Expired - Lifetime CN201876396U (en)

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