Method of estimating thermal stress of heat-resistant member

Abstract: A method of estimating thermal stress of a heat-resistant member, part of the whole of which is to be heated to a high temperature, comprises heating a model (2) formed by a high-­ thermal expansion material and having a shape similar to that of the heat-resistant member, and measuring thermal strain of the model (2) at each of predetermined positions by strain gauges (4) adhered thereto.

Description: BACKGROUND OF THE INVENTION The present invention relates to a method of estimating the thermal stress of a heat-resistant member, part or the whole of which is to be heated to such a high temperature as 500°C or higher. Heat-insulating members repeatedly placed under heated and cooled conditions, for instance, exhaust gas equipments such as exhaust manifolds used in internal engines of automobiles, etc., are required to be designed such that they undergo a minimum thermal strain, to prevent their breakage such as cracking during operations. For instance, in the case of exhaust manifolds of automobiles, they are subjected to increasingly higher temperatures and thermal loads, because engines having increasing higher performance have been developed. Therefore, the exhaust manifolds should be designed such that thermal cracks are prevented from generating in them due to thermal strains. Conventionally, the measurement of a thermal strain distribution of a manifold, etc. is conducted by using high-temperature strain gauges as disclosed in Japanese Patent Publication No. 51-42947 when the temperature of measurement is 200°C or higher. However, the high-temperature strain gauges have high stiffness and suffer from a thermal strain because they are attached to the measurement sites of a manifold by welding. Accordingly, in portions having small radii of curvature, reliable data cannot be obtained due to peeling off from the measurement sites. Further, even with the above strain gauges, the linearity of measurement data will be lost at a temperature higher than 500°C. Therefore, the strain distribution on the overall manifold surface at a high temperature was conventionally presumed from data at 500°C or lower. In addition, in the above method, test samples are produced by casting and subjected to a bench test, and the modification of cast product designs is conducted based on the data obtained with respect to cast samples. Accordingly, such method requires a long period of time for determining the best design of a heat-resistant member such as an exhaust manifold, resulting in high development costs. VDI Zeitschrift, Vol. 118, No. 17, September 1976, pages 829 to 834 refers to the stress distribution in component parts which are difficult to compute and the determination of the effects of a strain gauge on the expansion of a component part. DE-B-23 05 308 relates to a method of making visible deformations of cavities in a model of elastically deformable material. Accordingly, an object of the present invention is to provide a method of estimating a thermal stress of a heat-resistant member which is to be heated to a temperature of 500°C or higher with high reliability and efficiency, without resorting to test samples made of the same metal materials as the heat-resistant member. This object is met by the features of claim 1 and 3. Thus, the method of estimating a thermal stress of a heat-resistant member according to the present invention comprises heating a model formed by a high-thermal expansion material and having a shape similar to that of the heat-resistant member; and measuring a thermal strain of the model at each of predetermined positions by strain gauges adhered thereto. Particularly, by measuring a stress while heating the model both in a restraint state and in a free state, or by measuring a stress while cooling the model from a high temperature to a low temperature both in a restraint state and in a free state, it is possible to obtain an extremely reliable thermal stress distribution. Further, more exact results are obtained where a stress is measured both in a restraint state and in a free state, in a heated state and in a cooled state, respectively. Further, much more exact results are obtained by measuring the temperature of the model by a temperature sensor, correcting the strain values measured by the strain gauges by the temperature measured by the temperature sensor, and calculating a true stress at each measurement temperature. BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 is a front view showing a model used in the method of the present invention; and Fig. 2 is a schematic view showing a thermal image-analyzing apparatus for measuring a temperature distribution of the model. DETAILED DESCRIPTION OF THE INVENTION In the present invention, a model having a shape similar to that of a heat-resistant member to be measured is formed by a material having a thermal expansion coefficient several tens times as large as that of the heat-resistant member. Such model material is preferably a hard foam material such as a polyurethane foam having a thermal expansion coefficient 20-25 times as large as that of spheroidal graphite cast iron. When a polyurethane foam model is used, the same thermal expansion as that of spheroidal graphite cast iron is obtained when heated to a temperature on the level of 1/20 - 1/25 that of the spheroidal graphite cast iron. Specifically, if a manifold made of spheroidal graphite cast iron is heated at 800°C during operation, the same thermal expansion as that of the spheroidal graphite cast iron can be obtained in a polyurethane foam model when heated only at 32-40°C. This temperature range is derived from the equation : 800 x 1/(20-25) = 32-40. In addition, the polyurethane foam is easily worked to a desired shape. The polyurethane foam is produced by a continuous foaming process, and has high uniformness in density (0.03-0.10 g/cm³). Further, it is expanded relatively slowly when heated. In one embodiment of the present invention, the thermal stress of a heat-resistant member is estimated by heating a model formed by a high-thermal expansion material and having a shape similar to that of the heat-resistant member; and measuring a thermal strain of the model at each of predetermined positions by strain gauges adhered thereto. In another embodiment of the present invention, the thermal stress of a heat-resistant member is estimated by heating a model formed by a high-thermal expansion material and having a shape similar to that of the heat-resistant member in a restraint state and a free state, respectively; measuring the strain of the model at each of predetermined positions in a heated state, by strain gauges adhered to the predetermined positions of the model; and calculating a stress at each predetermined position from the difference in a strain value between the restraint state and the free state, thereby estimating the stress of the heat-resistant member in a heated state. In a further embodiment of the present invention, the thermal stress of a heat-resistant member is estimated by cooling a model formed by a high-thermal expansion material and having a shape similar to that of the heat-resistant member in a restraint state and a free state, respectively, from a high temperature to a low temperature; measuring the strain of the model at each of predetermined positions in a cooled state, by strain gauges adhered to the predetermined positions of the model; and calculating a stress at each predetermined position from the difference in a strain value between the restraint state and the free state, thereby estimating the stress of the heat-resistant member in a cooled state. In a still further embodiment of the present invention, the thermal stress of a heat-resistant member is estimated by heating a model formed by a high-thermal expansion material and having a shape similar to that of the heat-resistant member in a restraint state and a free state, respectively, from a low temperature to a high temperature; measuring the strain of the model at each of predetermined positions in a heated state; cooling the model with or without restraint; measuring the strain of the model at each of predetermined positions in a cooled state; and calculating stresses at each predetermined position both in a heated state and in a cooled state, from the differences in a strain value between the restraint state and the free state, thereby estimating the stresses of the heat-resistant member both in a heated state and in a cooled state. In a still further embodiment of the present invention, the strain value of the model measured by the strain gauge is corrected by a temperature measured at each predetermined position, thereby calculating the true stress value of the model at a predetermined temperature. The measurement method according to each embodiment of the present invention will be described in detail referring to Fig. 1. A manifold model 2 made of a polyurethane foam is placed on a table (not shown) and adhered with a plurality of strain gauges 4, 4, ···. An exhaust gas outlet 3 of the manifold model 2 is connected to an exhaust gas pipe (not shown). It is placed in a restraint state by fixing its flange portions onto the table by bolts, and then heated by blowing a hot air into the model 2 through ports 8, 8, ··· by a drier (not shown) such that the surface temperature of the model 2 reaches about 50°C. At this high temperature and in a restraint state, strain values ε₁ are measured at various measurement sites a, b, c, ···. Next, in a free state where the flange portions 6, 6, ··· are not fixed, the polyurethane model 2 is similarly heated to measure strain values ε₂ at various measurement sites a, b, c, ···. As a result, the strain free from the influence of the restraint state at each site in a heated state is calculated by (ε₁ - ε₂). Stress σ is expressed as: σ = (ε₁ - ε₂) E, wherein E is a Young's modulus of the actual heat-resistant member (for instance, Young's modulus of spheroidal graphite cast iron at 800°C). Thus, the stress σ can be calculated from the above formula: (ε₁ - ε₂). Designing and design modification of the manifold can be conducted based on the stress distribution thus obtained. Specifically, if a stress is concentrated in a particular spot or portion, it is necessary to strengthen that spot or portion, or to change the shape of its adjacent portion. Since the stress distribution thus obtained is free from the influence of the restraint state, design modification of the manifold can be conducted with an extreme accuracy. In some cases, since it is likely that a stress distribution obtained in a heated state and that obtained in a cooled state are not equal, it is desirable to measure a thermal strain distribution not only in a heated state but also in a cooled state for a more accurate measurement. For this purpose, the thermal strain distribution of the model is measured not only after heating the model from a low temperature to a high temperature but also after cooling the model from a high temperature to a low temperature. Specifically, the model is first heated in a free state and then placed in a restraint state by fixing its flange portions by bolts. Next, the model 2 is cooled by blowing a cold air and then measured with respect to a strain ε'₁ at each predetermined position at a low temperature in a restraint state. Further, after heating the model in a free state, it is cooled without restraint and measured with respect to a strain ε′₂. (ε′₁ - ε′₂) is regarded as a strain free from the influence of the restraint state in a cooled state. Finally, the stress σ′ = (ε′₁ - ε′₂) E is calculated. The Young's modulus E is generally changeable with temperature and the thermal expansion coefficient of each material varies depending on the temperature. Accordingly, to estimate the stress distribution more accurately, temperature sensors (not shown) are attached to the model 2 at positions near the strain gauges 4, 4, ···, and the strain and stress values are corrected by the temperature measured by the temperature sensors. Specifically, the variation of Young's modulus with temperature inherently differs among various materials. Accordingly, the Young's modulus E′ of an actual metal material is measured at each temperature corresponding to the measurement temperature of the model 2 in advance, and the Young's modulus E′ is used to calculate the stress σ = εE′ . The temperature distribution of the model 2 is detected desirably by a thermal image-analyzing apparatus simultaneously with measuring the strain distribution. The thermal image-analyzing apparatus comprises, as shown in Fig. 2, an infrared camera 30 for detecting the thermal distribution of the model 2, a display 32 for showing the thermal distribution as thermal image in color, a personal computer 36 connected to the display 32 via a frame recorder 34 and having a display 32′ for showing the thermal image, and a color printer 38 for providing a printed output of the thermal image. The personal computer 36 conducts data analysis, too. By achieving an on-line connection between the frame recorder 34 and the personal computer 36, information on the thermal image can be obtained on real time. Alternatively, an off-line connection can also be used such that the thermal image information is stored in a floppy disk 40 in the frame recorder 34 and the information is read through a disk drive of the personal computer 36. By observing the temperature distribution in this manner, efficient modification of a model design can be conducted. The present invention will be described in further detail by the following Examples. Example 1 As shown in Fig. 1, a model 2 of an exhaust manifold was produced from a polyurethane foam ("KM-60" manufactured by Kinuura Kogyo K.K.), and a plurality of (seven) resistance wire strain gauges 4, 4, ··· were attached by an adhesive to a side surface of the model 2 at predetermined positions shown by "a" - "g." Using bolts made of the same polyurethane foam as the model 2, flanges of the model 2 were fixed onto a table at positions of bolt apertures 10, 10, ···. Next, a hot air was introduced by a drier into the model 2 through four ports 8, 8, ··· from below. The surface temperature of the model 2 reached about 50°C after 10 seconds, and heating was stopped to measure a strain ε₁ at each gauge position. The bolts were then detached from the model 2, leaving the model 2 on a table without restraint, and it was similarly heated to measure a strain ε₂ at each gauge position. Next, the model 2 was heated to about 50°C without restraint and fixed by bolts onto a table. In this restraint state, a cold air was introduced into the model 2 by a drier to cool the model 2. When the surface temperature of the model 2 reached about 20°C, cooling was stopped to measure a strain ε′₁ at each gauge position. Similarly, after heating to about 50°C without restraint, the model 2 was cooled in a free state (without restraint) to measure a strain ε′₂. Measurement Conditions: ε₁ : restraint, heated ε₂ : free, heated ε′₁ : restraint, cooled ε′₂ : free, cooled (ε₁ - ε₂) and (ε′₁ - ε′₂) at each gauge position are shown in table 1. Young's modulus E used was 17000 kgf/mm², as a Young's modulus of spheroidal graphite cast iron at 800°C, and a stress σ or σ′ at each predetermined position was calculated from the formulae: σ = (ε₁ - ε₂) E, or σ′= (ε′₁ - ε′₂) E. The results are shown in Table 1. Incidentally, it is known that when strain gauges are adhered to a model, most of the expansion of the model is absorbed by the expansion of an adhesive used, and that a thermal expansion measured by the strain gauge is 1/14.8 of that of the model itself. Accordingly, the values of (ε₁ - ε₂) and (ε′₁ - ε′₂) are those obtained by multiplying the measured strain values by 14.8. In Table 1, a stress with a minus (-) symbol means "compression stress," and a stress with a plus symbol (+) means "tensile stress." It is clear from Table 1 that there are relatively large strains at positions b, c, d and e, where there is a recess for providing a space for a tool for threading a flange bolt 10. Thus, the model 2 was somewhat elongated vertically without changing a cross-section area of each tubular portion extending from a flange 10, thereby reducing a space for a tool. After this modification of the model design, the strain values ε₁ measured when heated in a restraint state, the strain values ε₂ measured when heated in a free state, the strain values ε′₁ measured when cooled in a restraint state, and the strain values ε′₂ measured when cooled in a free state were obtained in the same manner as above. The values of (ε₁ - ε₂) and (ε′₁ - ε′₂), and the calculated values of stresses σ, σ′ are also shown in Table 1. As is clear from the comparison of each stress value, the overall stress was reduced by the modification of the model design. At the same time of the above stress measurement the temperature distribution of the model 2 was measured when heated and shown on a display as a thermal image by using an infrared camera ("TVS3000" manufactured by Nippon Avionics K.K.). The thermal image was also provided as a printer output in color. As a result, it was found that heat spots were decreased after the modification of a model design, resulting in a more uniform thermal distribution. Particularly, it was confirmed that heat spots in the recess for a tool were removed. As described above, since the thermal stress estimating method of the present invention uses a model formed by a heat-insulating, high-thermal expansion material to generate a low temperature distribution on its surface, strain gauges for detecting a thermal strain may be those commercially available. Accordingly, linearity of strain data can be ensured in a wide temperature range, with good reliability even in portions having small radii of curvature. As a result, the thermal stress distribution measurement is relatively easy on members having such shapes that thermal stress distribution measurements would be difficult if their polyurethane models are not used. In addition, since a strain is measured on the model both in a restraint state and in a free state and their difference is evaluated, the influence of the restraint condition can be excluded. Therefore, the modification of a model design per se can be evaluated easily, and the thermal stress distribution of the heat-resistant member can be obtained with high reliability.

Claims: A method of estimating a thermal stress of a heat-resistant member, part or the whole of which is to be heated to a high temperature, comprising: (a) heating a model formed of a high-thermal expansion material and having a shape similar to that of said heat-resistant member, said high-thermal expansion material having a thermal expansion coefficient greater than that of the material of the heat-resistant member (b) measuring the strain of said model at each of predetermined positions in a heated state in a restraint state and a free state, respectively, by strain gauges adhered to the predetermined positions of said model; and (c) calculating a stress at each predetermined position from the difference in a strain value between said restraint state and said free state. The method of claim 1, further comprising: (a) cooling said heated model with or without restraint; (b) measuring the strain of said model at each of predetermined positions in a cooled state in a restraint state and/or a free state, respectively; and (c) calculating a stress at each predetermined position both in the heated state and the cooled state from the difference in a strain value between said restraint state and said free state. A method of estimating a thermal stress of a heat-resistant member, part or the whole of which is to be heated to a high temperature, comprising: (a) cooling a model formed of a high-thermal expansion material and having a shape similar to that of said heat-resistant member from a high temperature to a low temperature, said high-thermal expansion material having a thermal expansion coefficient greater than that of the material of the heat-resistant member; (b) measuring the strain of said model at each of predetermined positions in a cooled state in a restraint state and a free state, respectively, by strain gauges adhered to the predetermined positions of said model; and (c) calculating a stress at each predetermined position from the difference in a strain value between said restraint state and said free state. The method of any one of claim 1 to 3, wherein the temperature of said model is measured by a temperature sensor at each of predetermined positions, and the strain value of said model measured by said strain gauge is corrected by the temperature at each predetermined position. The method of any one of claims 1 to 4, wherein said high-thermal expansion material is a foam material. The method according to claim 5, wherein said foam material is a polyurethane foam.

Inventors: HISASHI YASUDA, KENJI ITOH, MASATOSHI NAKAMIZO, MITSURU YANO, TAKASHI HATTORI, HISASHI, YASUDA, KENJI, ITOH, MASATOSHI, NAKAMIZO, MITSURU, YANO, TAKASHI, HATTORI
Applicants: HITACHI METALS LTD, HITACHI METALS, LTD.
Application year: 1990
Main classification: G01N3
IPC codes: G01N3, G01L1, G01N25, G09B25