An analysis method and system for thermo-mechanical coupling effect based on elastic connection

Abstract

The present invention provides a method and system for analyzing thermo-mechanical coupling effects based on elastic connection, belonging to the field of stress analysis in the branch of elasticity. The method includes: constructing the boundary conditions of the heat balance equation for a model with an elastomeric constraint at one end of the object according to the measured environmental temperature; obtaining the dynamic temperature field equation for other regions of the model through the boundary conditions of the heat balance equation for a model with an elastomeric constraint at one end of the object; solving the stress fields at various locations in the model with an elastomeric constraint at one end of the object according to each temperature field; and obtaining the kinematic equations of the mechanical structures of each part of the object according to the stress fields at various locations in the model with an elastomeric constraint at one end of the object, and in combination with the thermal stress model and the elastomeric model, thereby analyzing the thermo-mechanical coupling effects. The present invention establishes a dynamic method considering thermal effects, which can be used to predict the thermal disturbance response of the measurement system of large space vehicles.

Description

Technical Field

[0001] The present invention belongs to the field of stress analysis in the branch of elasticity in solid mechanics, and more specifically, relates to a method and system for analyzing thermo-mechanical coupling effects based on elastic connection. Background Art

[0002] Temperature changes can cause deformation. A thermal environment with alternating high and low temperatures will cause thermal deformation and thermal stress in mechanical components, thereby introducing mechanical vibration.

[0003] As Figure 1 shown, if the temperature changes at each point in the object are uniform and both ends are free, its deformation is not restricted, that is, it can expand or contract freely, and only thermal deformation exists inside the object, and no thermal stress is generated on both end faces. As Figure 2 shown, if the expansion of the object is restricted, that is, the end faces are restricted. At this time, the deformation of the object due to heat expansion or cooling contraction is restricted, the object does not undergo thermal deformation, and thermal stress exists on both end faces of the object. The above are two extreme cases. In actual situations, the end faces of the object are connected to the outside. There is no corresponding technology publicly available on how to calculate the influence of the object's temperature effect on the outside, especially the thermo-mechanical coupling effect. For the above reasons, when designing and using mechanical structures, it is necessary to consider the temperature differences caused by factors such as thermal control and heat conduction, and take corresponding measures to control the temperature and reduce the deformation and vibration of the corresponding structures. Summary of the Invention

[0004] Aiming at the defects of the prior art, the present invention provides a method and system for analyzing thermo-mechanical coupling effects based on elastic connection, aiming to establish a model including measured temperature, calculate the stress distribution, and then analyze the thermo-mechanical coupling and establish a dynamic equation considering thermal effects.

[0005] To achieve the above object, the present invention provides a method for analyzing thermo-mechanical coupling effects based on elastic connection, including the following steps:

[0006] Step 1: Determine the temperature distribution of the object according to the measured environmental temperature, and combine the specific heat capacity, material density, and temperature change time of the object material to construct the boundary conditions of the heat balance equation of the elastic body constraint model at one end of the object;

[0007] Step 2: Based on the boundary conditions of the heat balance equation of the elastic body constraint model at one end of the object, and considering that the heat exchange between the elastic body and the surrounding medium satisfies Newton's cooling law, no heat exchange occurs on the surface of the elastic body, and the heat balance equation on the surface of the elastic body, calculate and obtain the dynamic temperature field equation of other regions of the model; where, other regions are the regions where the temperature is not measured in the elastic body constraint model at one end of the object;

[0008] Step 3: According to each temperature field and combined with the stress-strain constitutive relationship in the thermal effect, solve the stress field at each point in the elastic body constraint model at one end of the object;

[0009] Step 4: According to the stress field at each point in the elastic body constraint model at one end of the object, and combined with the thermal stress model and the elastic body model, obtain the kinematic equations of each part of the mechanical structure of the object, and then analyze the thermal-mechanical coupling effect.

[0010] Further preferably, the boundary conditions of the heat balance equation are:

[0011]

[0012] where C is the thermal conductivity; ρ is the material density; t is the time; and T is the measured temperature.

[0013] Further preferably, the dynamic temperature field equation is:

[0014]

[0015] where λ is the thermal conductivity; β is the heat exchange coefficient; T(x, y, z, t) is the temperature inside the object; T a is the temperature of the surrounding environmental medium; formula (1) indicates that the heat exchange between the elastic body and its surrounding medium satisfies Newton's cooling law;

[0016] T(x, y, z, t)| s = T s (t) (2)

[0017] where T s (t) is the surface temperature of the object; formula (2) indicates that there is no heat exchange on the surface of the elastic body;

[0018]

[0019] where w is the heat work exchanged with the outside, that is, the normal heat flux at any point on the surface of the object is equal to the exchange of work between this point and the outside; formula (3) indicates the heat balance on the surface of the elastic body.

[0020] Further preferably, the dynamic equation of the mechanical structure is:

[0021] (-ω 2 M + K)x = 0

[0022] where ω is the vibration frequency; M is the mass matrix of the mechanical structure; K is the stiffness matrix of the mechanical structure; and x is the displacement of the non-fixed free end of the mechanical structure.

[0023] On the other hand, the present invention provides a thermal-mechanical coupling effect analysis system based on elastic connection, including:

[0024] A construction module for the boundary conditions of the heat balance equation, which is used to determine the temperature distribution of an object according to the measured environmental temperature, and construct the boundary conditions of the heat balance equation with an elastomeric constraint model at one end of the object by combining the specific heat capacity, material density, and temperature change time of the object material;

[0025] A construction module for the dynamic temperature field equation, which is used to obtain the dynamic temperature field equation of other regions of the model through the boundary conditions of the heat balance equation with an elastomeric constraint model at one end of the object, based on the heat exchange between the elastomer and the surrounding medium satisfying Newton's cooling law, no heat exchange on the surface of the elastomer, and the heat balance equation on the surface of the elastomer;

[0026] A stress field solving module, which is used to solve the stress field at each location in the model with an elastomeric constraint model at one end of the object according to each temperature field and combining the stress-strain constitutive relationship in the thermal effect;

[0027] A thermal-mechanical coupling effect analysis module, which is used to obtain the kinematic equations of the mechanical structures of each part of the object according to the stress fields at each location in the model with an elastomeric constraint model at one end of the object and combining the thermal stress model and the elastomer model, and then analyze the thermal-mechanical coupling effect.

[0028] Further preferably, the boundary conditions of the heat balance equation are:

[0029]

[0030] Where C is the thermal conductivity; ρ is the material density; t is the time; T is the measured temperature.

[0031] Further preferably, the dynamic temperature field equation is:

[0032]

[0033] Where λ is the thermal conductivity; β is the heat exchange coefficient; T(x, y, z, t) is the temperature inside the object; T a is the temperature of the surrounding environmental medium; n is the temperature gradient direction vector; formula (1) represents that the heat exchange between the elastomer and its surrounding medium satisfies Newton's cooling law;

[0034] T(x, y, z, t)| s =T s (t) (2)

[0035] Where T s (t) is the surface temperature of the object; formula (2) represents that there is no heat exchange on the surface of the elastomer;

[0036]

[0037] Among them, w is the heat and work exchanged with the outside world; Equation (3) characterizes the heat balance on the surface of the elastic body.

[0038] Further preferably, the dynamic method of the mechanical structure is:

[0039] (-ω 2 M + K)x = 0

[0040] Among them, ω is the vibration frequency; M is the mass matrix of the mechanical structure; K is the stiffness matrix of the mechanical structure; x is the displacement of the non-fixed free end of the mechanical structure.

[0041] Generally speaking, compared with the prior art, the above technical solutions conceived by the present invention have the following beneficial effects:

[0042] The present invention provides an analysis method and system for thermal-mechanical coupling effect based on elastic connection. By establishing a model including measured temperature (determining the temperature distribution of an object according to the measured ambient temperature, combining the specific heat capacity, material density and temperature change time of the object material, and constructing the boundary conditions of the heat balance equation for an elastic body constraint model at one end of the object; through the boundary conditions of the heat balance equation for an elastic body constraint model at one end of the object, based on the heat exchange between the elastic body and the surrounding medium satisfying Newton's cooling law, no heat exchange on the surface of the elastic body, and the heat balance equation on the surface of the elastic body, obtaining the dynamic temperature field equation in other regions of the model;), calculating the stress distribution, and then analyzing the thermal-mechanical coupling, a dynamic equation considering thermal effects systematically is established. This method can reasonably predict the thermal disturbance response of large space vehicle measurement systems such as spaceborne electrostatic accelerometers. Description of the Drawings

[0043] Figure 1 is a schematic diagram of the model of free expansion or contraction of an object provided by an embodiment of the present invention;

[0044] Figure 2 is a schematic diagram of the model of an object when its expansion or cooling is restricted provided by an embodiment of the present invention;

[0045] Figure 3 is a flowchart of the analysis method for thermal-mechanical coupling effect based on elastic connection provided by an embodiment of the present invention;

[0046] Figure 4 is a schematic diagram of an elastic body constraint model at one end of an object provided by an embodiment of the present invention; Detailed Embodiments

[0047] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0048] As Figure 3 shown, the present invention provides an analysis method for thermo-mechanical coupling effect based on elastic connection, which specifically includes the following steps:

[0049] Step 1: According to the measured environmental temperature T, obtain the boundary conditions of the heat balance equation for the elastic body constraint model at one end of the object:

[0050]

[0051] where C is the thermal conductivity; ρ is the material density; t is the time;

[0052] Step 2: Through the boundary conditions of the heat balance equation for the elastic body constraint model at one end of the object, obtain the dynamic temperature field in other regions of the model; more specifically:

[0053] The heat exchange between the elastic body and its surrounding medium satisfies Newton's cooling law;

[0054]

[0055] where λ is the thermal conductivity; β is the heat exchange coefficient; T(x, y, z, t) is the temperature inside the object; T a is the temperature of the surrounding environmental medium; n is the temperature gradient direction vector;

[0056] There is no heat exchange on the surface of the elastic body, that is, the surface temperature of the object is the surface temperature of the contact body and is a function of time t;

[0057] T(x, y, z, t)| s = T s (t)

[0058] where T s (t) is the surface temperature of the object;

[0059] The heat balance on the surface of the elastic body, that is, the heat flux density at any point is equal to the product of the thermal conductivity and the temperature gradient at that point;

[0060]

[0061] where w is the heat work exchanged with the outside world, that is, the normal heat flux at any point on the surface of the object is equal to the exchange of work at this point with the outside world;

[0062] Step 3: Solve the stress field at each part in the elastic body constraint model at one end of the object according to each temperature field;

[0063] Step 4: According to the stress field at each part in the elastic body constraint model at one end of the object, and combining the thermal stress model and the elastic body model, obtain the kinematic equations of each part of the mechanical structure, and then analyze the thermo-mechanical coupling effect.

[0064] like Figure 4 As shown, the constraint at one end of the object is regarded as an elastic body, and the dynamic and thermodynamic equations are coupled;

[0065] by Figure 4 Based on the assumption that one end of the object shown is an elastic body constraint model, the stress distribution of thermal stress in each part of the mechanical structure is determined. Combined with the analysis of the elastic body model, the kinematic equations of each part of the mechanical structure can be obtained;

[0066] (-ω 2 M+K)x=0

[0067] Among them, ω is the vibration frequency; M is the mass matrix of the mechanical structure; K is the stiffness matrix of the mechanical structure; x is the displacement of the non-fixed free end of the mechanical structure. Substitute the stress-strain constitutive relationship including the thermal effect into:

[0068] σ=E(ε-ε T )

[0069] Among them, σ is the normal stress; ε is the original strain of the material; ε T is the normal strain of the material at temperature T;

[0070] In the above equations, since the deformation displacement of the object includes the thermal deformation of the object, and the resultant force includes temperature stress, that is, the thermodynamic conduction equation includes related kinematic variables such as the thermal deformation and vibration of the object, and the dynamic equation includes thermodynamic parameters such as the temperature at various locations of the object, it is necessary to solve the equations simultaneously, which constitutes a complete system equation of thermal-mechanical coupling effect.

[0071] In another aspect, the present invention provides a thermal-mechanical coupling effect analysis system based on elastic connection, comprising:

[0072] The module for constructing the boundary conditions of the thermal balance equation is used to determine the temperature distribution of the object according to the measured temperature of the environment, and to construct the boundary conditions of the thermal balance equation of the model with an elastic body constraint at one end of the object by combining the specific heat capacity, material density and temperature change time of the object material;

[0073] The building module of the dynamic temperature field equation is used to obtain the dynamic temperature field equation of other areas of the model through the boundary condition of the thermal balance equation of the elastic body constraint model at one end of the object, based on the heat exchange between the elastic body and the surrounding medium satisfying Newton's cooling law, no heat exchange on the surface of the elastic body, and the heat balance equation on the surface of the elastic body;

[0074] The stress field solving module is used to solve the stress fields at various locations in the model where one end of the object is constrained by an elastic body according to various temperature fields and the stress-strain constitutive relationship in the thermal effect;

[0075] The thermal-mechanical coupling effect analysis module is used to obtain the kinematic equations of the mechanical structures of each part of an object based on the stress fields at various positions in the elastic body constraint model at one end of the object, and by combining the thermal stress model and the elastic body model, and then analyze the thermal-mechanical coupling effect.

[0076] Further preferably, the boundary conditions of the heat balance equation are:

[0077]

[0078] Where C is the thermal conductivity; ρ is the material density; t is the time; T is the measured temperature.

[0079] Further preferably, the dynamic temperature field equation is:

[0080]

[0081] Where λ is the thermal conductivity; β is the heat exchange coefficient; T(x, y, z, t) is the temperature inside the object; T a is the temperature of the surrounding environmental medium; n is the temperature gradient direction vector; formula (1) indicates that the heat exchange between the elastic body and its surrounding medium satisfies Newton's cooling law;

[0082] T(x, y, z, t)| s = T s (t) (2)

[0083] Where T s (t) is the surface temperature of the object; formula (2) indicates that there is no heat exchange on the surface of the elastic body;

[0084]

[0085] Where w is the heat work exchanged with the outside; formula (3) indicates the heat balance on the surface of the elastic body.

[0086] Further preferably, the dynamic method of the mechanical structure is:

[0087] (-ω 2 M + K)x = 0

[0088] Where ω is the vibration frequency; M is the mass matrix of the mechanical structure; K is the stiffness matrix of the mechanical structure; x is the displacement of the non-fixed free end of the mechanical structure.

[0089] In summary, compared with the prior art, the present invention has the following advantages:

[0090] The present invention provides an analysis method and system for thermo-mechanical coupling effect based on elastic connection. By establishing a model including measured temperature, calculating the stress distribution, and further analyzing the thermo-mechanical coupling, a dynamic equation that systematically considers the thermal effect is established. This method can reasonably predict the thermal disturbance response of measurement systems of large space vehicles such as spaceborne electrostatic accelerometers.

[0091] Those skilled in the art can easily understand that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for analyzing the thermo-mechanical coupling effect based on elastic connection, characterized in that It includes the following steps: Step 1: Determine the temperature distribution of the object according to the measured environmental temperature. Combine the specific heat capacity, material density, and temperature change time of the object material to construct the boundary conditions of the heat balance equation with an elastomeric constraint model at one end of the object; Step 2: Through the boundary conditions of the heat balance equation with an elastomeric constraint model at one end of the object, based on the heat exchange between the elastomer and the surrounding medium satisfying Newton's cooling law, no heat exchange on the elastomer surface, and the heat balance equation on the elastomer surface, obtain the dynamic temperature field equation for other regions of the model; Step 3: According to each temperature field, combine the stress-strain constitutive relationship in the thermal effect to solve the stress field at each location in the elastomeric constraint model at one end of the object; Step 4: According to the stress field at each location in the elastomeric constraint model at one end of the object, and combine the thermal stress model and the elastomer model to obtain the kinematic equation of each part of the mechanical structure of the object, and then analyze the thermo-mechanical coupling effect; The dynamic temperature field equation is: （1） Among them, is the thermal conductivity; is the heat transfer coefficient; is the internal temperature of the object; is the temperature of the surrounding environmental medium; n is the temperature gradient direction vector; Formula (1) indicates that the heat exchange between the elastic body and its surrounding medium satisfies Newton's cooling law; （2） Among them, is the surface temperature of the object; Formula (2) represents that there is no heat exchange on the surface of the elastomer; （3） Among them, is the heat work exchanged between the object and the outside world; formula (3) characterizes the heat balance on the surface of the elastomer.

2. The thermo-mechanical coupling effect analysis method according to claim 1, wherein The boundary conditions of the heat balance equation are: Among them, C is the specific heat capacity of the material; is the material density; t is the temperature change time; T is the measured temperature.

3. The thermo-mechanical coupling effect analysis method according to claim 1, wherein The dynamic method of the mechanical structure is: Among them, is the vibration frequency; is the mechanical structure mass matrix; is the mechanical structure stiffness matrix; is the displacement of the non-fixed free end of the mechanical structure.

4. A thermal-mechanical coupling effect analysis system based on elastic connection, characterized in that It includes: A construction module for the boundary conditions of the heat balance equation, which is used to determine the temperature distribution of the object according to the measured environmental temperature, and combine the specific heat capacity, material density, and temperature change time of the object material to construct the boundary conditions of the heat balance equation with an elastomeric constraint model at one end of the object; A construction module for the dynamic temperature field equation, which is used to obtain the dynamic temperature field equation for other regions of the model through the boundary conditions of the heat balance equation with an elastomeric constraint model at one end of the object, based on the heat exchange between the elastomer and the surrounding medium satisfying Newton's cooling law, no heat exchange on the elastomer surface, and the heat balance equation on the elastomer surface; A stress field solving module, which is used to solve the stress field at each location in the elastomeric constraint model at one end of the object according to each temperature field, and combine the stress-strain constitutive relationship in the thermal effect; A thermo-mechanical coupling effect analysis module, which is used to obtain the kinematic equation of each part of the mechanical structure of the object according to the stress field at each location in the elastomeric constraint model at one end of the object, and combine the thermal stress model and the elastomer model, and then analyze the thermo-mechanical coupling effect; The dynamic temperature field equation is: （1） wherein, is the thermal conductivity; is the heat exchange coefficient; is the internal temperature of the object; is the temperature of the surrounding environmental medium; n is the temperature gradient direction vector; Equation (1) represents that the heat exchange between the elastic body and its surrounding medium satisfies Newton's cooling law; （2） Among them, is the surface temperature of the object; Formula (2) represents that there is no heat exchange on the surface of the elastomer; （3） wherein, is the heat work exchanged between the object and the outside world; Formula (3) characterizes the heat balance on the surface of the elastomer.

5. The thermo-mechanical coupling effect analysis system according to claim 4, wherein The boundary conditions of the heat balance equation are: Among them, C is the specific heat capacity of the material; is the material density; t is the temperature change time; T is the measured temperature.

6. The thermo-mechanical coupling effect analysis system according to claim 4, characterized in that The dynamic method of the mechanical structure is: Among them, is the vibration frequency; is the mechanical structure mass matrix; is the mechanical structure stiffness matrix; is the displacement of the non-fixed free end of the mechanical structure.

Images