Experimental method for simulating temperature field of elastic element with hole

1 Introduction

Elastic elements with holes are widely used in the fields of force measurement and weighing. In some special occasions, such as rocket launches, metallurgical production and other measurement and control equipment, when used as basic parts, they are often in non-uniform temperature fields and generate thermal stress, which leads to measurement errors. In order to eliminate this error, corresponding compensation measures must be taken. This requires the study of the temperature and stress distribution state of elastic elements with holes under the influence of local heat.

The rapid development of computer technology has greatly promoted the improvement of numerical methods such as finite element and boundary element, making it easy to perform numerical simulations such as temperature field and stress field analysis of elastic elements with holes, which can be theoretically attributed to plane problems. In comparison, the use of experimental methods to study temperature and stress problems seems a bit old-fashioned and time-consuming. But even so, the experimental method still has its unique advantages. First, it can provide a means of verification for numerical calculation results, because if the parameters are improperly selected or the mathematical model is biased in numerical calculations, large errors will still occur; second, calculations are often unable to be carried out due to the constraints of computer and software conditions, while experiments are easy to implement because the equipment and conditions are not demanding.

Determining the temperature field is a prerequisite for studying thermal stress. Due to space limitations, this article only discusses the experimental research method of the temperature field of elastic elements under the influence of local steady-state heat.

2 Introduction to the basic methods of experimental research

2.1 Theoretical basis of experimental research

According to the basic theory of photoelastic experiments, under plane strain state, the thermal stress between elastic elements and experimental models has the following relationship [1]:

The subscripts "H" and "M" represent the elastic element and the model respectively, where σH and σM represent the thermal stress of the elastic element and the model respectively; EH and EM are the elastic moduli of the two; αH and αM are the thermal expansion coefficients; υH and υM are the Poisson coefficients; △TH and △TM are the temperature differences. The ratio

of the shortest time to obtain a stable stress state on the elastic remote component and the model is [1]

In the formula, CH, CM are specific heat capacity; ρH, ρM are material density; lH, lM are the corresponding dimensions of the elastic element and the model.

The above formulas show that when the material performance parameters are known and the thermal equilibrium conditions are met, the model can be used to study the thermal stress state of the elastic element.

2.2 Material selection and model making

The model material is a resin material 3Д-6M with a thickness of 8mm. It is made by mechanical processing according to the geometric dimensions similar to the element [2]. It should be noted that a small processing allowance should be maintained to prevent excessive residual stress on the model. The finished model needs to be placed in a heat preservation furnace for 24 hours of annealing to effectively eliminate the residual stress. The heater is made of 3Д-6M material as the skeleton and is wound with fine copper wire. An adjustable voltage is applied to both ends of the fine copper wire to achieve the purpose of heating and changing the temperature.

2.3 Preparation and calibration of thermocouples

The thermocouple is made of a fine copper wire with a diameter of 0.33mm and a constantan wire with a diameter of 0.4mm welded in 40V voltage and 96% alcohol. Before use, the manufactured thermocouple needs to be calibrated. The calibration device is shown in Figure 2-1.

1 - Thermocouple measuring end; 2 - Heating container containing oil; 3 - Adjustable transformer; 4 - Voltmeter;
5 - Mercury thermometer; 6 - Transposition switch; 7 - Pointer multimeter; 8 - Container containing ice-water mixture

The hot end (measuring end) of the thermocouple is placed in a container 2 containing oil, and the cold end (compensation end) is placed in a container 8 containing an ice-water mixture. The oil temperature is controlled by adjusting the transformer 3 to change the temperature of the container 2, while the voltage value is read by the voltmeter 4, the oil temperature is read by the mercury thermometer 5, and the temperature of the thermocouple is read by the pointer multimeter 7. The indications of multiple thermocouples can be read by turning the switch.

The prepared thermocouple is calibrated three times in the range of 20℃～80℃, and the average value is taken to perform numerical fitting using the least squares method, and the regression equation

T＝2.4＋2.59 V is obtained

, where T is the temperature value and V is the voltage value. In the above temperature range, the calibration curve is an ideal straight line.

2.4 Determination of temperature field

The key parts of the elastic element with holes are selected for research in the experiment, and a series of thermocouples are arranged on the model to study the distribution of the temperature field. Its structure and thermocouple arrangement are shown in Figure 2-2. Figure 2-2a studies the relationship between the temperature distribution of the model along the height direction and the model length B; Figure 2-2b studies the relationship between the temperature distribution of the model along the length direction and the model height B; Figure 2-2c studies the relationship between the temperature distribution of the single-hole model along the circumferential direction and the aperture D; Figure 2-2d studies the relationship between the temperature distribution of the double-hole model along the height direction and the aperture D. [page]

The experimental device for determining the temperature field of the model is shown in Figure 2-3. The width of the model heating zone is 20mm, the temperature of the surface of the heating zone is 70℃, and the temperature is maintained for more than 20 minutes. At this time, the thermocouple readings do not change. It is considered that the temperature field of the model under study is a steady-state temperature field, and there is a local heat source on the boundary. The boundary condition of the model belongs to convective heat transfer. Only two-dimensional problems are considered here, and the heat transfer on both sides of the model is ignored, which will bring certain errors to the experiment. The comparison between this experimental method and the theoretical calculation results has been described [1], so it will not be explained here. The entire experiment was carried out in a room with a constant room temperature (20℃) and little air circulation.

The experimental result data was processed by least squares fitting and obtained as follows

In the formula, Tx is the temperature value at a distance x from the heating zone on the model;
T∞ is the temperature value at an infinite distance from the heating zone, where the ambient temperature is 20°C.

Some results processed and sorted based on experimental data are shown in Table 2-1, where B and D are model geometric parameters, k is the exponential term parameter of the regression equation, η and mη are the confidence and average fitting error of the regression equation, respectively.

3 Conclusion

The experimental simulation method discussed in this paper can be used as a general method for studying the two-dimensional temperature field simulation experiment of various complex-shaped elastic elements.

References
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Weimin1 Na Rongqi1 Ya·Kon·Nikin2
1．Beijing Institute of Technology，Beijing 100081；2．Department of Instrument Manufacturing，Kiev National University of Technology，Ukraine(end)