CN103940678B - Annulus radially bends measurement apparatus and the measuring method of elastic modelling quantity - Google Patents
Annulus radially bends measurement apparatus and the measuring method of elastic modelling quantity Download PDFInfo
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Abstract
The present invention provides the measurement apparatus and measuring method that a kind of annulus radially bends elastic modelling quantity, measurement apparatus includes the lower clamp clamping tested annulus arch bottom, clamp the upper clamp at tested annulus vault place, it is arranged on the vertical displacement meter below upper clamp, it is separately positioned on two horizontal displacement meters at haunch place, tested annulus both sides and is removably disposed in upper clamp top and multiple masses identical in quality, measuring method includes: is placed in ground grading by lower clamp and clamps the arch bottom of tested annulus, upper clamp is clamped vault place, it is respectively mounted vertical displacement meter and horizontal displacement meter, multistage loadings mass difference reading in upper clamp, with the coefficient of relationship of its top-loaded weight and finally calculating annulus according to computing formula radially bends elastic modelling quantity to utilize limited element analysis technique to calculate the vertical displacement of annulus。This measurement apparatus is structurally and operationally simple, measures accurately, measures efficiency height and is readily produced, stores and transports。
Description
Technical field
The invention belongs to the fields of measurement of elastic modelling quantity, relate to measurement apparatus and the measuring method of a kind of elastic modelling quantity。
Background technology
Elastic modelling quantity measuring method has static measurement, resonance method, impulse method etc.。Wherein, resonance method and impulse method certainty of measurement are higher, but measure more complicated, high to measuring instrument requirements；And static measurement is fairly simple。
Static measurement is exactly the stress and strain measuring object after object loads, and calculates elastic modelling quantity (E) according to specific formula, mainly has pulling method and straight beam bending method etc.。
The experiment of modal measurement elasticity modulus of materials is the stretching experiment of mild steel。Mild steel obeys Hooke's law proportional limit planted agent, by measuring the elongation after shaft-like mild steel tension, thus calculating elastic modelling quantity。Mild steel relation between deformation and load in proportional limit is:
In formula, Δ l is rod component axial elongation amount；P is tensile load suffered by rod member；A0Amass for rod member initial cross-section；L0For rod member initial length。But, although static measurement is fairly simple, but but currently suffer from the restriction of detected materials geometry, do not have the measurement apparatus that a kind of simple and reliable and easily operated annulus radially bends elastic modelling quantity can obtain annulus relatively easily so far and radially bend elastic modelling quantity。
Summary of the invention
The present invention is directed to the deficiencies in the prior art, it is therefore intended that provide a kind of easily operated and simple annulus of computational methods to radially bend measurement apparatus and the measuring method of elastic modelling quantity。
For reaching above-mentioned purpose, the solution of the present invention is:
A kind of annulus radially bends the measurement apparatus of elastic modelling quantity, including clamping the lower clamp of tested annulus arch bottom, clamping the upper clamp at tested annulus vault place, be arranged on the vertical displacement meter below upper clamp, be separately positioned on two horizontal displacement meters at haunch place, tested annulus both sides and be removably disposed in upper clamp top and multiple masses identical in quality。
Above-mentioned lower clamp includes base plate, lower circular arc block and four run through lower circular arc block and the bottom fishbolt being connected with base plate, and the arcwall face of lower circular arc block is inscribed within the inner headed face of tested annulus。Further, above-mentioned upper clamp includes being horizontally placed at the top board at vault place, upper circular arc block and four run through circular arc block and the upper pinch bolt being connected with top board, and the arcwall face of upper circular arc block is inscribed within the inner headed face of tested annulus。Further, the arcwall face of above-mentioned lower circular arc block is identical with the curvature of the arcwall face of upper circular arc block, and the radius of curvature of the arcwall face of the radius of curvature of the arcwall face of upper circular arc block and lower circular arc block is 0.6～0.8 times of inner headed face radius of tested annulus。
A kind of annulus radially bends the measuring method of elastic modelling quantity, employs above-mentioned measurement apparatus, comprises the steps:
(1), lower clamp it is placed in ground grading and clamps the arch bottom of tested annulus；
(2), upper clamp is fixed on the vault place of tested annulus and clamps vault place；
(3), vertical displacement meter is arranged on the lower section of upper clamp and two horizontal displacement meters are separately mounted to haunch place, tested annulus both sides；
(4), in upper clamp the mass of the quality such as multistage loadings and obtain respectively every grade load under vertical displacement meter and the reading value of horizontal displacement meter；
(5) limited element analysis technique, is utilized to calculate the vertical displacement of tested annulus under every grade of loading and the coefficient of relationship of its top-loaded weight；
(6) what, according to coefficient of relationship and computing formula calculate tested annulus under loading at different levels radially bends elastic modelling quantity, takes under loading at different levels the meansigma methods radially bending elastic modelling quantity of tested annulus as elastic modelling quantity measured value。
In above-mentioned steps (2), the point of contact of the top board of upper clamp and tested annulus periphery and the upper circular arc block of upper clamp are respectively positioned on the surface in the tested annulus center of circle with the point of contact of tested annulus inner headed face。
In above-mentioned steps (3), vertical displacement meter is arranged on the lower section of the upper circular arc block of upper clamp and its measuring point is positioned at the surface in the tested annulus center of circle, and the measuring point height of horizontal displacement meter is identical with the center of circle height of tested annulus。
In above-mentioned steps (4), the number of mass is be more than or equal to 6。
Owing to adopting such scheme, the invention has the beneficial effects as follows:
Radially bend in measurement apparatus and the measuring method of elastic modelling quantity at the annulus of the present invention, measurement apparatus is only made up of lower clamp, upper clamp, vertical displacement meter, horizontal displacement meter and multiple mass identical in quality, therefore this measurement apparatus simple in construction, it is easy to produce, store and transport；Additionally, measurement process only needs in upper clamp, place mass step by step and obtain corresponding reading value at vertical displacement meter and horizontal displacement meter, just can radially bending elastic modelling quantity according to what computing formula calculated annulus to be measured, therefore this measurement apparatus is simple to operate, measure and accurately, significantly simplified the method that the annulus modulus of elasticity in static bending is measured the efficiency that improve measurement。
Accompanying drawing explanation
Fig. 1 is the structural representation that the annulus of the embodiment of the present invention radially bends the measurement apparatus of elastic modelling quantity。
Fig. 2 is the structural representation of the lower clamp of the embodiment of the present invention。
Fig. 3 is the measuring method flow chart of the embodiment of the present invention。
Fig. 4 is the installation site figure of the lower clamp of the embodiment of the present invention。
Fig. 5 is the installation site figure of the upper clamp of the embodiment of the present invention。
Fig. 6 is the installation site figure of the displacement meter of the embodiment of the present invention。
Accompanying drawing labelling:
Ground grading 1, lower clamp 2, bottom fishbolt 3, tested annulus 4, upper clamp 5, horizontal displacement meter 6, upper pinch bolt 7, vertical displacement meter 8, upper circular arc block 9, lower circular arc block 10, top board 11, base plate 12, mass 13, arch bottom 14, vault place 15, haunch place 16。
Detailed description of the invention
Below in conjunction with accompanying drawing illustrated embodiment, the present invention is further illustrated。
Embodiment
Present embodiments provide a kind of annulus and radially bend the measurement apparatus of elastic modelling quantity。Operator only need to utilize this measurement apparatus to measure difference and load rank next one vertical displacement measuring point and two respective deformation quantities of horizontal displacement measuring point, just can use the computing formula that homogenizing annulus radially bends elastic modelling quantity that the elastic modelling quantity that radially bends of tested annulus is calculated。The present embodiment have employed practical operation experiment and measured for the deformation quantity of tested three measuring points of annulus。
Tested annulus 4 in the present embodiment adopts nylon material to make uniform thickness annulus, and its interior diameter is 54.3 centimetres, and overall diameter is 62 centimetres, and thickness is 3.85 centimetres, and width is 12 centimetres。It practice, tested annulus 4 can also adopt any isotropic homogeneous elasticity material, such as macromolecular material, various metal materials etc.。
As it is shown in figure 1, this measurement apparatus includes lower clamp 2, upper clamp 5,8, two horizontal displacement meters 6 of vertical displacement meter and multiple mass 13 identical in quality。
Lower clamp 2 is for clamping the arch bottom 14 of tested annulus 4, as shown in Figure 2。Lower clamp 2 includes base plate 12, lower circular arc block 10 and four bottom fishbolts 3。Base plate 12 is placed on smooth ground 1, the arcwall face of lower circular arc block 10 is inscribed within the inner headed face of the arch bottom 14 of tested annulus 4, four bottom fishbolts 3 run through lower circular arc block 10 and are connected with base plate 12, are clamped between base plate 12 and lower circular arc block 10 the arch bottom 14 of annulus 4。
Upper clamp 5 is arranged at the top of tested annulus 4, for clamping the vault place 15 of tested annulus 4。Upper clamp 5 includes top board 11, upper circular arc block 9 and four upper pinch bolts 7。Top board 11 is flatly placed in the vault place 15 of annulus 4。The arc surface of upper circular arc block 9 is inscribed within the inner headed face at the vault place 15 of annulus 4, and the arc surface of upper circular arc block 9 is identical with the curvature of the arc surface of lower circular arc block 10。As it is shown in figure 5, the radius of curvature R 1 of upper circular arc block 9 and the lower respective arcwall face of circular arc block can be 0.6～0.8 times of the inner headed face radius R2 of measured circle ring。Four upper pinch bolts 7 run through circular arc block 9 and are connected with top board 11, are clamped between top board 11 and upper circular arc block 9 by the vault 15 of tested annulus 4。Top board 11 and base plate 12 all adopt the iron plate that rigidity is bigger。
Vertical displacement meter 8 is arranged on the lower section of circular arc block 9, for measuring the vertical displacement of tested annulus 4 dome portions 15。Because upper clamp 5 clamps the vault place 15 of tested annulus 4, so upper clamp 5 and tested annulus 4 vault place 15 can keep synchronizing deformation, the reading value that vertical displacement meter 8 records is the shift value of upper clamp 5 is also the vertical displacement value at tested annulus 4 vault place 15。Two horizontal displacement meters 6 are separately positioned on the haunch place 16 of tested annulus 4 both sides, for measuring the horizontal displacement value at haunch place, tested annulus 4 both sides 16。
Mass 13 has at least six pieces, every piece identical in quality。These masses 13 can adopt counterweight。During measurement, one piece of mass 13 is placed in the top of top board 11, vertical displacement meter 8 and the reading value of horizontal displacement meter 6 is read respectively after the deformation of tested annulus 4 is stable, then proceed to be stacked on previous piece of mass 13 another block mass 13, treat that follow-up number of resuming studies is stablized in the deformation of tested annulus 4。So carry out multistage loadings。When multistage loadings mass 13, should ensure that the center of gravity of all masses 13 center of circle through tested annulus 4。During actual loaded, it is possible to judge whether to pass through the center of circle by being arranged on the reading of the horizontal displacement meter 6 at the haunch place 16 of tested annulus 4 both sides。When the displacement (i.e. the reading value of two horizontal displacement meters) measured by two horizontal displacement meters 6 close to time, can think that the center of gravity of loaded mass 13 is through the center of circle of tested annulus 4 approx。
The present embodiment additionally provides a kind of homogenizing annulus and radially bends the measuring method of elastic modelling quantity, the method uses measurement apparatus above-mentioned。As it is shown on figure 3, this measuring method comprises the steps:
The first step, as shown in Figure 4, is placed in ground grading 1 and clamps the arch bottom 14 of tested annulus 4 by lower clamp 2；
Second step as it is shown in figure 5, be fixed on the vault place 15 of tested annulus 4 and clamp this vault place 15 by upper clamp 5 so that the top board 11 of upper clamp 5 is placed in the horizontal direction；
3rd step, as shown in Figure 6, is arranged on vertical displacement meter 8 lower section of the upper circular arc block 9 of upper clamp 5 and two horizontal displacement meters 6 is separately mounted to haunch place, tested annulus 4 both sides 16；
4th step as it is shown in figure 1, on the top board 11 of upper clamp 5 multistage loadings mass 13 and read respectively every grade load under vertical displacement meter and the reading value of horizontal displacement meter；
5th step, utilizing limited element analysis technique to set up numerical model annulus, the physical dimension of this numerical model annulus is identical with the physical dimension of tested annulus, according to formulaCalculate the vertical displacement of tested annulus and the coefficient of relationship k of its top-loaded weight。
Wherein, k is relevant with the physical dimension of tested annulus, including the cross sectional moment of inertia I of the kernel of section distance R to the center of circle of model annulus and tested annulus。
E' is the elastic modelling quantity that radially bends of numerical model annulus, unit: Pa,。Calculating shows, coefficient of relationship k is unrelated with Poisson's ratio, therefore, when Numerical modelling, is known that by experience or inquiry about value of the material characteristic parameter of tested annulus can obtain E'。
F' is the vertical active force of numerical model annulus, unit: N。
S' is the vertical displacement of numerical model annulus, unit: m。When numerical computations, vertical displacement result directly can be extracted。
R is the kernel of section distance to the numerical model annulus center of circle of tested annulus, unit: m。Wherein, R=(D-h)/2, D is the external diameter of tested annulus, unit: m；H is the thickness of tested annulus, namely the depth of section of tested annulus, unit: m。
I is the cross sectional moment of inertia of tested annulus, unit: m4。Wherein, I=bh3/ 12, b is the width of tested annulus, unit: m。
Therefore, by setting up the physical dimension numerical model annulus identical with tested annulus as computation model, arrange approx numerical model annulus elastic modulus E ' and other material property parameters, assume under vertical force F' effect, calculate the vertical displacement S' obtaining numerical model annulus, E', F', S' and physical dimension parameter value are substituted into formulaTry to achieve coefficient of relationship k。
When surveying every grade and loading, the first reading according to two horizontal displacement meters is wanted to judge that whether the center of gravity of mass 13 is through the center of circle of tested annulus 4, when the displacement measured by two horizontal displacement meters close to time, then think the center of gravity of the loaded mass center of circle by tested annulus approx。
6th step, load according to every grade under the vertical displacement of tested annulus and the coefficient of relationship k of its top-loaded weight calculate annulus and radially bend elastic modelling quantity, modulus of elasticity in static bending computing formula is:
Wherein, E is the measured value radially bending elastic modelling quantity of tested annulus, unit: Pa。
N is the total progression of loading of the top-loaded weight of tested annulus, and the total progression of general loading is 6～10 grades。
FiThe top-loaded weight of tested annulus when loading for i-stage, when namely i-stage loads top all masses weight and, unit: N。Wherein F0=0, (Fi-Fi-1) for i-stage load load increment。
SiThe reading value of vertical displacement meter, unit: m, wherein S when i-stage loads0=0。(Si-Si-1) for i-stage load vertical displacement increment。
Having only to during numerical model test calculate and once can obtain coefficient of relationship k, and add in reality when repeated loading mainly considers practical operation and have test error, by repeated loading, final E averages and can reduce measurement error。
The above-mentioned description to embodiment is to be understood that for ease of those skilled in the art and use the present invention。These embodiments obviously easily can be made various amendment by person skilled in the art, and General Principle described herein is applied in other embodiments without through performing creative labour。Therefore, the invention is not restricted to above-described embodiment, those skilled in the art's announcement according to the present invention, the improvement made without departing from scope and amendment all should within protection scope of the present invention。
Claims (8)
1. an annulus radially bends the measurement apparatus of elastic modelling quantity, it is characterised in that: the lower clamp, the upper clamp clamping tested annulus vault place that include clamping tested annulus arch bottom, it is arranged on the vertical displacement meter below described upper clamp, is separately positioned on two horizontal displacement meters at haunch place, tested annulus both sides and is removably disposed in described upper clamp top and multiple masses identical in quality；The measuring point of described vertical displacement meter is positioned at the surface in the described tested annulus center of circle, and the measuring point height of described horizontal displacement meter is identical with the center of circle height of described tested annulus。
2. annulus according to claim 1 radially bends the measurement apparatus of elastic modelling quantity, it is characterized in that: described lower clamp includes base plate, lower circular arc block and four run through described lower circular arc block and the bottom fishbolt being connected with described base plate, and the arcwall face of described lower circular arc block is inscribed within the inner headed face of described tested annulus。
3. annulus according to claim 2 radially bends the measurement apparatus of elastic modelling quantity, it is characterized in that: described upper clamp includes being horizontally placed at the top board at described vault place, upper circular arc block and four run through described upper circular arc block and the upper pinch bolt being connected with described top board, and the arcwall face of described upper circular arc block is inscribed within the inner headed face of described tested annulus。
4. annulus according to claim 3 radially bends the measurement apparatus of elastic modelling quantity, it is characterized in that: the arcwall face of described lower circular arc block is identical with the curvature of the arcwall face of described upper circular arc block, and the radius of curvature of the arcwall face of the radius of curvature of the arcwall face of described upper circular arc block and described lower circular arc block is 0.6～0.8 times of inner headed face radius of described tested annulus。
5. annulus radially bends a measuring method for elastic modelling quantity, employ arbitrary in Claims 1-4 as described in measurement apparatus, it is characterised in that: comprise the steps:
(1), lower clamp it is placed in ground grading and clamps the arch bottom of tested annulus；
(2), upper clamp is fixed on the vault place of described tested annulus and clamps described vault place；
(3), vertical displacement meter is arranged on the lower section of described upper clamp and two horizontal displacement meters are separately mounted to haunch place, described tested annulus both sides；
(4), in described upper clamp the mass of the quality such as multistage loadings and obtain respectively every grade load under described vertical displacement meter and the reading value of described horizontal displacement meter；
(5) limited element analysis technique, is utilized to calculate the vertical displacement of described tested annulus under every grade of loading and the coefficient of relationship of its top-loaded weight；
Utilizing limited element analysis technique to set up numerical model annulus, the physical dimension of this numerical model annulus is identical with the physical dimension of tested annulus, according to formulaCalculate the vertical displacement of tested annulus and the coefficient of relationship k of its top-loaded weight；
Wherein, E' is the elastic modelling quantity that radially bends of numerical model annulus, unit: Pa；
F' is the vertical active force of numerical model annulus, unit: N；
S' is the vertical displacement of numerical model annulus, unit: m；
R is the kernel of section distance to the numerical model annulus center of circle of numerical model annulus, unit: m；
I is the cross sectional moment of inertia of tested annulus, unit: m4；
(6) what, according to described coefficient of relationship and computing formula calculate described tested annulus under loading at different levels radially bends elastic modelling quantity, takes the meansigma methods radially bending elastic modelling quantity of described tested annulus under loading at different levels as elastic modelling quantity measured value；
Under loading according to every grade, the vertical displacement of tested annulus and the coefficient of relationship k of its top-loaded weight calculate annulus and radially bend elastic modelling quantity, and modulus of elasticity in static bending computing formula is:
Wherein, E is the measured value radially bending elastic modelling quantity of tested annulus, unit: Pa；
N is the total progression of loading of the top-loaded weight of tested annulus；
FiThe top-loaded weight of tested annulus when loading for i-stage, when namely i-stage loads top all masses weight and, unit: N；Wherein F0=0, (Fi-Fi-1) for i-stage load load increment；
SiThe reading value of vertical displacement meter, unit: m, wherein S when i-stage loads0=0, (Si-Si-1) for i-stage load vertical displacement increment。
6. annulus according to claim 5 radially bends the measuring method of elastic modelling quantity, it is characterized in that: in step (2), the point of contact of the top board of described upper clamp and described tested annulus periphery and the upper circular arc block of described upper clamp are respectively positioned on the surface in the described tested annulus center of circle with the point of contact of described tested annulus inner headed face。
7. annulus according to claim 5 radially bends the measuring method of elastic modelling quantity, it is characterized in that: in step (3), described vertical displacement meter is arranged on the lower section of the upper circular arc block of described upper clamp and its measuring point is positioned at the surface in the described tested annulus center of circle, and the measuring point height of described horizontal displacement meter is identical with the center of circle height of described tested annulus。
8. annulus according to claim 5 radially bends the measuring method of elastic modelling quantity, it is characterised in that: in step (4), the number of described mass is more than or equal to 6。
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| JP2002062231A (en) * | 2000-08-22 | 2002-02-28 | Bando Chem Ind Ltd | Measuring device for belt flexural rigidity |
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