When doing the vibration isolation design, the required rubber stiffness value is calculated, but the manufacturer only provides the Shore hardness value. How do you correspond to the two?

　　Rubber hardness and stiffness

　　There is no corresponding relationship between rubber hardness and rigidity. The hardness is the characteristic of the rubber compound after mixing, mixing and vulcanization. The rigidity is the characteristic of the rubber product, but the structure size is fixed, and the rigidity increases with the increase of the hardness.

The manufacturer should provide force-deformation information. If not, it can be estimated by combining hardness + geometry (if regular).

　　In addition to estimation, estimation has to be measured, such as the amount of compression under static load, to determine whether it can work

Stiffness can only calculate static stiffness. Manufacturers need to do stress and strain tests. Static stiffness can be calculated through abaqus. The error is generally less than 10%.

　　The hardness of the rubber compound increases as the sulfur content increases. For natural rubber compounds, if the amount of sulfur is increased by 1 to 3 parts, the hardness will increase by 5 degrees; for the natural/butadiene/butadiene rubber compound, the amount of sulfur will be increased by 1.5 to 4 parts, and the hardness will be increased by 5 degrees. At first, as the amount of sulfur increases, the degree of cross-linking also increases, and its hardness increases. After sulfur is added to a certain amount, over-sulfur occurs. For any rubber, not only cross-linking occurs during vulcanization, but also due to heat and other factors. The effect produces the scission of the production chain and the molecular chain. This phenomenon runs through the entire vulcanization process. In the over-sulfur stage, if the cross-linking is still dominant, the rubber will become hard and the tensile strength will continue to rise. On the contrary, the rubber will become soft and return to the original.

　　Force/displacement = static stiffness of rubber.

　　Hardness, tensile strength, etc. are all related to static stiffness.

The greater the hardness, the greater the static stiffness. As for the tensile strength data, there is but no analysis. You can count the data and analyze the data yourself, and then you can draw a conclusion.

　　Static stiffness is the stiffness index of rubber. It is generally controlled by hardness. It is proportional to hardness and constant extension.

How much should the static stiffness of 4kg/mm ​​correspond to the Shore hardness of rubber?

　　The static stiffness is new to the overall elasticity of the finished product. Each compression of 1 mm requires 4 kilograms of force, which is related to the cross section and height of the product. The Shore hardness is a measured value that describes the hardness of the rubber material itself. If the product structure is determined, the rubber hardness can be adjusted to meet 4Kg/mm. On the contrary, if the hardness of the material is determined, the product structure size can be adjusted to achieve the specified value of static stiffness. Obviously, leave this test and debugging to It is more convenient for the rubber manufacturer to do it, and the design user only needs the static stiffness result for acceptance. In general design, the elastic modulus at 60 degrees Shore A is used for design calculation, and small deviations are adjusted by production. You can ask the rubber manufacturer for a sample of 10 mm in diameter and 10 mm in height to determine the elastic modulus of the hardness rubber.

How to distinguish stiffness, strength, and hardness

　　Hardness is a material characteristic, and stiffness is a component characteristic. Hardness is the processing/process performance. It reflects the ability of the material to resist local deformation. Think about your HB or 2B pencil. That refers to its hardness. Stiffness refers to the ability of a component to resist deformation (overall deformation). Imagine a bamboo and a telephone pole. The stiffness is not only related to the size of the section, but also related to the length of the member and its boundary conditions.

It is interesting to ask about the relationship between hardness and elastic modulus and stiffness. First of all, the elastic modulus specifically refers to the stiffness of the material level, which reflects the proportional relationship between stress and strain. There is actually a certain relationship between hardness and elastic modulus. The so-called rebound method measures the strength of concrete. If I remember correctly, it uses the regression relationship between hardness, elastic modulus and strength. But note that this is a statistical regression relationship. I don't know whether there is a deterministic relationship between the three in physics. I would like to ask the Fang family here to explain. ——It feels to be explained from the perspective of physical mechanics

Hardness, hardness, is used to measure the ability of a material to resist plastic deformation. The rough method of hardness measurement is to press a hard indenter of a known shape into the material and then unload it. The maximum force divided by the area of ​​the indentation is the hardness. According to different indenter shapes and test conditions, the hardness can be divided into several types.

Stiffness, used to measure the ability of a material or structure to resist deformation under load, is generally expressed by a matrix, that is, the stiffness matrix. For materials, the stiffness matrix is ​​the partial derivative of the stress tensor to the variable tensor, sometimes called the Jacobian matrix. In elastic deformation, the matrix can be directly calculated from modulus and Poisson's ratio; in elastic-plastic deformation, it is slightly more complicated, and plastic strain and strain hardening need to be considered. The stiffness matrix of the structure is meaningful only after the structure is discrete. Borrowing the terminology of the finite element method, it is the global stiffness matrix, which links the load and displacement: F=[K]U.

The stress-strain relationship of a material (which can also be considered as the stiffness matrix of the material) is the basic parameter of the mechanical properties of the material, but the hardness is not. In other words, once the stress-strain relationship of the material is known, its hardness can be calculated, of course, generally through the finite element method. Since hardness is a very commonly used parameter, many studies have proposed some empirical formulas (either based on experiments or based on numerical calculations) to correlate hardness with other parameters. For example, Tabor: H=CY, H is the hardness, Y is the yield strength, and C is a constant; another example is Johnson: H/Y=2/3*[2+1og(1/3*E*tan(r)/Y )]. In addition, there are other forms, but they all have a certain scope of application.