Replacing the two ordinary glasses in the ordinary vacuum glass structure with fully tempered glass is the fully tempered vacuum glass. As a new generation of energy-saving glass, fully tempered vacuum glass is widely used in the field of construction, home appliances, agriculture, and photovoltaic buildings due to its advantages of avoiding condensation, energy-saving and heat insulation, sound insulation and noise reduction, high strength, and wind pressure resistance. chemical field. With the growing call for energy saving, the structure and performance of fully tempered vacuum glass have received more and more attention.

The support is an important component of the fully tempered vacuum glass, and its design is the key to the production of the fully tempered vacuum glass. In the research of fully tempered vacuum glass supports, relevant scholars have studied the mechanical theory involved in the design process of supports and analyzed the mechanical properties of supports in practical applications. The influence law of thermal conductivity of glass. However, there are few reports on the correlation between the parameters of the fully tempered vacuum glass support and the thermal conductivity. Study the relationship between the thermal conductivity of fully tempered vacuum glass and support parameters, determine which of the many support parameters is the primary influencing factor and which is the secondary influencing factor, and rationally design the support parameters in the preparation of high energy-saving fully tempered glass. The vacuum glass needs to be solved urgently.

The grey system theory provides a way to solve the above problems, and establishes a link between the support parameters and the macroscopic properties of fully tempered vacuum glass. The introduction of grey system theory in the study of the correlation between the support parameters and thermal conductivity of fully tempered vacuum glass can avoid the randomness of a large number of experimental data and the difficulty of controlling many support parameters. influencing factors. In this paper, the influence of various parameters of the support on the thermal conductivity of the fully tempered vacuum glass is analyzed first, and then the parameters of the support (material, shape, size, spacing, arrangement) are regarded as a gray system, and the gray system correlation calculation method is used to study the whole system. Correlation between the thermal conductivity of tempered vacuum glass and support parameters.

1. The influence of the support on the thermal conductivity

Since the fully tempered vacuum glass is in a vacuum state, the upper and lower sheets of glass are affected by atmospheric pressure, so the main function of the support is to resist the atmospheric pressure and avoid glass deformation. The thermal conductivity of the central area of the fully tempered vacuum glass is composed of radiation thermal conductivity, support thermal conductivity, and residual gas thermal conductivity. As shown in Figure 1, the choice of support parameters can have an important impact on the thermal conductivity of the glass.

^{F}^{igure 1 Schematic diagram of the structure of fully tempered vacuum glass}

**1.1 The material of the support**

The choice of support material should first meet the requirements of glass safety performance. In the past, organic non-metallic, glass, and metal materials have been selected for common vacuum glass supports. For tempered glass, studies have shown that the compressive strength of the selected supports needs to reach at least IGPa. The selection of glass materials is a hot spot in the current research on vacuum glass supports. It has good light transmittance and high aesthetics, but its strength and stiffness cannot meet the requirements, so it has not been put into use in large numbers. 304 stainless steel is a widely used support material at present, and its thermal conductivity is 13.2 W/(m·K) within 100℃. The thermal conductivity of the support C support is shown in formula (1)

*In the formula:*

**r is the radius of the contact area between the support and the glass, m; **

*h is the height of the support, m; *

*d is the spacing between the supports, m; *

*U glass is the thermal conductivity of the glass, about 1 W/(m·K); *

**U is the thermal conductivity of the support material, W/(m K).**

According to formula (1), it can be known that the thermal conductivity of the support material and the thermal conductivity of the support are close to a proportional relationship. It can be concluded that the reduction of the thermal conductivity of the support material will lead to the reduction of the thermal conductivity of the fully tempered vacuum glass.

**1.2 Shape and size of support**

At present, the common supports on the market have three shapes: sphere, cylinder, and ring. Among them, the sphere is easy to manufacture, but the point contact is prone to indentation; the cylinder is easy to deploy, but it is not conducive to the thermal insulation effect of the glass; in contrast, the ring has advantages in layout and thermal insulation, and is relatively inefficient. It is easy to cause indentation. The size of the support should not be too large or too small. If the support is too large, the heat transfer will be accelerated, which is not conducive to the effect of thermal insulation; if the support is too small, the contact stress with the glass will be increased, resulting in the generation of glass indentation. The thermal resistance of single annular support is shown in formula (2).

**In the formula: **

*R insider and R outsider are the contact areas between the annular support and the glass, respectively ***the inner and outer radii of the domain, m.**

Changes in the shape and size of the support will affect the contact area between the support and the glass. According to formula (2), the larger the difference between the inner and outer radii of the support, the smaller the contact area between the support and the glass, and the smaller the thermal conductivity of the support. . Theoretically, the contact area between the spherical support and the glass is the smallest under the same outer diameter, but under the action of atmospheric pressure, support stress and glass stress, the support, and the glass undergo plastic deformation, and the effective contact area of the spherical support and the glass is similar to that of a cylinder. The contact area between the shape and the glass. Therefore, under the same outer diameter, the thermal conductivity of the annular support is the smallest.

**1.3 Arrangement spacing of supports**

According to formula (1), it can be seen that the larger the spacing d, the smaller the thermal conductivity of the support. According to the international standard, the thermal conductivity of the fully tempered vacuum glass with the support arrangement spacing of 50mm, 60mm, 70mm, and 80mm was measured through experiments under the same other parameters (see Figure 2).

^{Figure 2 The relationship between the spacing of supports and the thermal conductivity of fully tempered vacuum glass}

It can be seen from Figure 2 that with the increase of the spacing between the supports, the thermal conductivity of the fully tempered vacuum glass decreases. The experimental results are consistent with the theoretical analysis results, which verifies the feasibility of the theoretical analysis.

**1.4 Arrangement of supports**

There are three common arrangements of supports: equilateral triangle, square, and hexagon. Table 1 shows the number of supports per unit area under different arrangements. It can be seen from Table 1 that under the same arrangement spacing, the number of supports per unit area arranged in a regular hexagon is the least, and the total thermal conductivity of the supports is the smallest.

**Table 1 The number of supports per unit area under different arrangements**

The placement spacing / mm | The number of supports per unit area | ||

Equilateral triangle | Square | Hexagon | |

50 | 449 | 400 | 394 |

60 | 330 | 289 | 286 |

70 | 247 | 225 | 215 |

80 | 188 | 169 | 167 |

2. Grey correlation analysis of support parameters and thermal conductivity

**2.1 Selection of support parameters**

To quantitatively analyze the importance of the influence of support parameters on the thermal conductivity of fully tempered vacuum glass, through market research and analysis, three supports with different parameters were selected and listed in Table 2. However, the parameters of the supports are not quantified data except for the arrangement spacing, and the gray correlation calculation cannot be performed. Therefore, it is necessary to quantify the qualitative factors first and use the mapping quantity to indirectly represent the system behavior: the thermal conductivity of the material is used to represent the influence of the support material on the thermal conductivity of the glass, and the volume of single support is used to represent the size of the support, the shape of the support is expressed by the contact area between single support and the glass, and the arrangement of the supports is expressed by the number of supports per unit area (㎡).

**Table 2 The support parameters**

Number | Material | Size/mm | Shape | Arrangement | The placement spacing/mm |

A1 | Impervious steel | Diameter 0.5 | Round ball | Regular triangle | 50 |

A2 | Aluminum oxide | Diameter 0.5 Height 0.5 | Round cylinder | Square | 60 |

A3 | Nickel-based alloys | Outer diameter 0.6 Inner diameter 0.3 Height 0.5 | Round ring | Hexagon | 70 |

**Table 3 The quantified support parameters**

Number | Thermal conductivity of materials W/ (m * K) | Volume/mm³ | Contact area/mm² | Quantity per square meter | Placement spacing/mm |

A1 | 13 | 0.065 | 0.393 | 449 | 50 |

A2 | 16 | 0.141 | 0.565 | 289 | 60 |

A3 | 12 | 0.106 | 0.424 | 215 | 70 |

**2.2 Calculation of thermal conductivity of fully tempered vacuum glass**

**2.2.1 The parameter selection**

The length and width of the fully tempered vacuum glass are 0.3 m and the thickness is 4 mm. One side is fully tempered Low-E glass with an emissivity of 0.10, and the other side is fully tempered float glass with an emissivity of 0.84. The edge is made of glass solder. For sealing, the degree of vacuum is less than 0.01 Pa.

**2.2.2 Thermal conductivity calculation**

According to the international standard, the thermal conductivity of the vacuum glass is characterized by the thermal conductivity of the central area of the vacuum glass, so the thermal conductivity of the sealing material is not considered. When the vacuum degree is less than 0.01 Pa, the thermal conductivity of residual gas can also be ignored, so the thermal conductivity of fully tempered vacuum glass can be determined by the formula (3).

In the formula: R inside is the heat transfer resistance of the inner surface of the glass; R outside is the outer surface heat transfer resistance of the glass; R1 is the thermal resistance of the inner glass plate; R2 is the thermal resistance of the outer glass plate; C radiation is the radiation thermal resistance.

In the formula: T1 T2 is the absolute temperature of the two inner surfaces facing the vacuum layer, K; is the Steffen-Boltzmann constant, whose value is 5.67*10^{-8} w/(M^{2 }· K^{4}); £ effectively is the inner Surface effective emissivity.

Among them, R inside + R outside is a fixed value of 0.1584, when the glass thickness is 4mm, R[=R2=0.004. Substitute the emissivity of the two pieces of glass into Equation (4) to obtain C radiation = 0.45. Substitute the support parameters into formula (1) to obtain the support thermal conductivity C support corresponding to Al, A2, and A3. Finally, substitute the data into formula (3) to obtain the thermal conductivity of three groups of fully tempered vacuum glass with different support parameters, which are 0.588 W/(mK), 0.537 W/(m*K), and 0.446 W/(m*K), respectively.

**2.3 Grey relational analysis**

(1) Assuming that the thermal conductivity column is within the parent sequence x, and the support parameters are listed as subsequence Xz (i is 1, i is 1 to 3, followed by the number of columns), each sequence is

The initial value of the column is obtained by dividing the value of each row by the value of the first row, and the calculation results are shown in Table 4.

**Table 4 Initial value of each sequence**

Initial value | k | ||

1 | 2 | 3 | |

X_{1}_{ }(k) | 1 | 1.231 | 0.923 |

X_{2 }(k) | 1 | 2.169 | 1.631 |

X_{3 }(k) | 1 | 1.438 | 1.079 |

X_{4} (k) | 1 | 0.657 | 0.479 |

X_{5 }(k) | 1 | 1.200 | 1.400 |

Y_{1}_{ }(k) | 1 | 0.913 | 0.759 |

(2) Calculate the difference between the mother sequence and the subsequence of the initial value, and the calculation result is as follows shown in Table 5.

**Table 5 Difference between parent sequence and subsequence difference **

Difference | k | ||

1 | 2 | 3 | |

I Y_{1}(k) -X_{1}(k) I | 0 | 0.3187 | 0.164 |

I Y_{1}(k) -X_{2}(k) I | 0 | 1.256 | 0.872 |

I Y_{1}(k) -X_{3}(k) I | 0 | 0.525 | 0.320 |

I Y_{1}(k) -X_{4}(k) I | 0 | 0.256 | 0.280 |

I Y_{1}(k) -X_{5}(k) I | 0 | 0.287 | 0.641 |

△i(k) = I Yi(k) -Xi(k) I (k is the number of columns) (5)

(3) Calculate the maximum difference and the minimum difference between the two poles.

M = max △i (k), m = min △i (k) (6)

It can be seen from Table 5: M= 1.256, m=0.

(4) Calculate the correlation coefficient.In the formula: Self is the resolution coefficient, generally taken as 0.5. The calculation results are shown in Table 6.

**Table 6 Correlation values of each sequence**

Correlation coefficient % | k | ||

1 | 2 | 3 | |

Γ_{1 }(K) | 1 | 0.664 | 0.793 |

Γ_{2}(K) | 1 | 0.333 | 0.419 |

Γ_{3}(K) | 1 | 0.545 | 0.662 |

Γ_{4}(K) | 1 | 0.710 | 0.692 |

Γ5(K) | 1 | 0.686 | 0.495 |

(5) Calculate the correlation degree (P=3), the value of which is shown in Table 7.

**Table 7 Correlation between support parameters and thermal conductivity**

Support parameter | Correlation coefficient |

Material | 0.819 |

Size | 0.584 |

Shape | 0.735 |

Arrangement | 0.872 |

Placement Spacing | 0.727 |

It can be seen from Table 7 that the contributions of different support parameters to the thermal conductivity are different. From the correlation degree value, it can be seen that the correlation degree between the support parameters of the fully tempered vacuum glass and its thermal conductivity is in descending order: the arrangement of the support, the thermal conductivity of the support material, the shape of the support, and the cloth of the support. Put the spacing, and the size of the support. It can be seen from the results that the thermal conductivity of the fully tempered vacuum glass has the greatest gray correlation with the arrangement of the supports. It is inferred that the arrangement of the supports has the greatest contribution to the thermal conductivity of the glass, followed by the material of the supports, that is, the supports The thermal conductivity of the material also has a great influence on the thermal conductivity of the glass. Therefore, the number of supports per unit area should be reduced in the design process of fully tempered vacuum glass supports, which will greatly reduce the thermal conductivity of fully tempered vacuum glass

3. Conclusions

(1)The thermal conductivity of the fully tempered vacuum glass has the greatest gray correlation with the arrangement of the supports. It is inferred that the arrangement of the supports has the greatest contribution to the thermal conductivity of the fully tempered vacuum glass. Therefore, in the design process of fully tempered vacuum glass, especially in the initial *tempered glass production and processing*, the number of supports per unit area should be minimized to help minimize the thermal conductivity of the glass.

(2) The thermal conductivity of the support material is also closely related to the thermal conductivity of the fully tempered vacuum glass, second only to the arrangement. The correlation degree between other support parameters and the thermal conductivity of fully tempered vacuum glass is sorted as follows: the shape of the support, the spacing of the support, and the size of the support.

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