Calculation method of surface temperature of large electric brake resistor based on constant temperature drop

Abstract

The present invention discloses a method for calculating the surface temperature of a large electric brake resistor based on a constant temperature drop. The method includes the following steps: establishing a thermal equilibrium state control equation for the large electric brake resistor; organizing the thermal equilibrium state control equation based on a constant temperature drop to obtain a formula for the resistor temperature rise after the resistor is energized; collecting relevant data; determining the convection heat transfer coefficient α; and substituting the collected data and the convection heat transfer coefficient α into the resistor temperature rise formula after the resistor is energized to calculate the resistor temperature rise Δt after the resistor is energized. b ; Compare the initial air temperature t0 with the resistor temperature rise △t after the resistor is energized b Add them together to obtain the resistor surface temperature t after the resistor is energized. b The present invention combines formula calculation with experimental data summary, and can accurately and quickly calculate the surface temperature of the resistor after the resistor is energized.

Description

Technical Field

[0001] The invention relates to the technical field of design and manufacturing of temperature rise control, and in particular to a method for calculating the surface temperature of a large electric brake resistor based on a constant temperature drop. Background Art

[0002] Large electric brakes utilize electrical principles to achieve braking, ensuring that equipment can be quickly and safely decelerated or stopped when needed. They are widely used in industries such as water conservancy, hydropower, and municipal transportation. Because electric brakes utilize a periodic high current input during operation, their main components will still experience a significant temperature rise even under forced mechanical ventilation. This process is a short-term transient temperature rise, and the temperature rise is affected by external factors such as the current and ventilation system. Furthermore, because the geometric parameters of the assembly space influence the heat dissipation process, the temperature rise and heat dissipation are a complex, nonlinear coupled process. Determining the surface temperature of the resistor is crucial for selecting the operating characteristics of the components and selecting the materials for the electric brake.

[0003] There is currently no formula for calculating the surface temperature of an electric brake resistor in the existing technology. Generally, a method combining physical models and numerical modeling is used to empirically estimate the resistor surface temperature. However, this method has the following problems:

[0004] First, the cost of using physical models and numerical modeling is very high;

[0005] Second, the error of empirical estimates is large. Summary of the Invention

[0006] In view of the shortcomings of the prior art, the present invention proposes a method for calculating the surface temperature of a large electric brake resistor based on a constant temperature drop, which can accurately and quickly calculate the surface temperature of the electric brake resistor.

[0007] To achieve the above object, the present invention provides a method for calculating the surface temperature of a large electric brake resistor based on a constant temperature drop, which is particularly characterized by comprising the following steps:

[0008] S1) Establishing a thermal equilibrium state control equation for a large electric brake resistor, wherein the thermal equilibrium state control equation includes

[0009] Heat production equation: dQ1=0.86I 2 Rdτ

[0010] Heat dissipation equation: dQ2=αF(t b -t)dτ

[0011] Heat gain equation of resistance: dQ3=Gcd(t b -t0) Air heat equation: dQ4=Vmγ k ck d(t-t0) According to heat balance: ndQ2=dQ4

[0012] Where,

[0013] Q1 is the heat generated by the resistor,

[0014] I is the braking current of the input resistor,

[0015] R is the resistance of the resistor,

[0016] τ is the heating time of the resistor,

[0017] Q2 is the heat dissipation of the resistor,

[0018] α is the convection heat transfer coefficient of the resistor surface,

[0019] F is the heat transfer area of ​​the resistor surface,

[0020] t b is the resistor surface temperature,

[0021] t is the air temperature,

[0022] Q3 is the heat gain of the resistor,

[0023] G is the weight of the resistor,

[0024] c is the specific heat of the resistor,

[0025] d is the differential symbol,

[0026] t0 is the initial air temperature,

[0027] Q4 is the heat gain of the air,

[0028] V is the spatial volume of the large electric brake,

[0029] m is the air influence coefficient,

[0030] γ k is the specific gravity of air,

[0031] c k is the specific heat of air,

[0032] n is the coefficient caused by radiation and heat absorption of the surrounding wall;

[0033] S2) Based on the constant rate of temperature reduction, the formula in step S1) is sorted out to obtain the temperature rise formula of the resistor after the resistor is energized:

[0034] Δt b =Δt 1b +Δt 2b

[0035]

[0036] Where,

[0037] △t b The temperature rise of the resistor after the resistor is energized.

[0038] Δt 1b =t b -t,

[0039] Δt 2b =t-t0,

[0040] t b is the resistor surface temperature,

[0041] t is the air temperature,

[0042] t0 is the initial air temperature,

[0043] N=0.86·I 2 R,

[0044]

[0045] C=Gc,

[0046] e represents a natural constant,

[0047] I is the braking current of the input resistor,

[0048] R is the resistance of the resistor,

[0049] α is the convection heat transfer coefficient of the resistor surface,

[0050] F is the heat transfer area of ​​the resistor surface,

[0051] γ k is the specific gravity of air,

[0052] c k is the specific heat of air,

[0053] L is the ventilation volume,

[0054] G is the weight of the resistor,

[0055] c is the specific heat of the resistor;

[0056] S3) collecting relevant data, including ventilation volume L, initial air temperature t0, specific heat c of the resistor, heat transfer area F of the resistor surface, resistor density, and braking current I of the input resistor;

[0057] S4) determining the convective heat transfer coefficient α;

[0058] S5) Substituting the data in step S3) and the convection heat transfer coefficient α in step S4) into the resistor temperature rise formula after the resistor is energized in step S2) to calculate the resistor temperature rise Δt after the resistor is energized. b ;

[0059] S6) Compare the initial air temperature t0 with the resistor temperature rise △t after the resistor is energized. b Add them together to obtain the resistor surface temperature t after the resistor is energized. b .

[0060] Furthermore, in step S2), the heat equation dQ3=Gcd(t b -t0) to obtain the surface temperature rise of the resistor

[0061] From the air heat equation in step S1) dQ4 = Vmγ k c k d(t-t0) and heat dissipation equation dQ2=αF(t b -t)dτ to obtain the air temperature rise

[0062] Assume that the temperature rise of the resistor after the resistor is energized is Δt b =t b -t0=(t b -t)+(t-t0)=Δt 1b +Δt 2b , then the surface temperature of the resistor is

[0063] The ventilation volume Substitute the air temperature rise Then Δt 2b Substitute the surface temperature rise of the resistor Thus we get Divide both sides by dΔt 1b , dτ, and take the reciprocal and integral of both sides to get Then the temperature rise formula of the resistor after the resistor is powered on is obtained.

[0064] Furthermore, in S4), through actual process testing and analysis, the convective heat transfer coefficient α of the resistor under different wind speed conditions is fitted, and the corresponding relationship between the convective heat transfer coefficient α of the resistor and the wind speed is fitted into a table that can be directly referenced; according to the ventilation volume L and the spatial volume V of the large electric brake, the wind speed on the resistor surface is calculated, and the convective heat transfer coefficient α corresponding to the wind speed is found through the table in step S4).

[0065] Furthermore, in S5), the air temperature rise Δt is first calculated using the ventilation volume L. 2b, to ensure that the air temperature rise Δt 2b ≤60℃, then calculate the resistor temperature rise △t after the resistor is energized b .

[0066] The advantages of the present invention are:

[0067] 1. Based on the thermal equilibrium state control equation (including heat generation equation, heat dissipation equation, resistance heat gain equation, and air heat gain equation), the present invention analyzes the resistor temperature rise formula after the resistor is energized based on constant temperature drop, and then calculates the initial air temperature t0 and the resistor temperature rise △t after the resistor is energized. b Add them together to obtain the resistor surface temperature t after the resistor is energized. b ;

[0068] 2. The temperature rise of the resistor after the resistor is energized is △t b The resistor surface convection heat transfer coefficient α in the calculation formula, the present invention fits the heat transfer coefficient of the resistor under different wind speed conditions, and through a large number of actual tests and summaries, fits different wind speeds and corresponding heat transfer coefficients into a table that can be directly referenced; in calculating the resistor temperature rise △t after the resistor is energized b When the wind speed on the resistor surface is 0.01, you only need to find the corresponding heat transfer coefficient in the table;

[0069] The present invention is based on a method for calculating the surface temperature of a large-scale electrical brake resistor with constant temperature drop. Based on the constant temperature drop principle, the temperature rise formula of the resistor after the resistor is energized is analyzed from a series of thermal equilibrium state control equations, and the surface temperature of the resistor after the resistor is energized is further calculated. This improves the accuracy and speed of calculating the surface temperature of the large-scale electrical brake resistor. At the same time, it can be extended to the temperature rise control calculation of systems and components of large power system devices when large currents pass through them. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 Flowchart of the present invention. DETAILED DESCRIPTION

[0071] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0072] like Figure 1 As shown, the method for calculating the surface temperature of a large electric brake resistor based on a constant temperature drop of the present invention comprises the following steps:

[0073] S1) Establishing a thermal equilibrium state control equation for a large electric brake resistor, wherein the thermal equilibrium state control equation includes

[0074] Heat production equation: dQ1=0.86I 2 Rdτ

[0075] Heat dissipation equation: dQ2=αF(t b -t)dτ

[0076] Heat gain equation of resistance: dQ3=Gcd(t b -t0)

[0077] Air heat gain equation: dQ4=Vmγ k c k d(t-t0)

[0078] According to heat balance: ndQ2=dQ4

[0079] Where,

[0080] Q1 is the heat generated by the resistor,

[0081] I is the braking current of the input resistor,

[0082] R is the resistance of the resistor,

[0083] τ is the heating time of the resistor,

[0084] Q2 is the heat dissipation of the resistor,

[0085] α is the convection heat transfer coefficient of the resistor surface,

[0086] F is the heat transfer area of ​​the resistor surface,

[0087] t b is the resistor surface temperature,

[0088] t is the air temperature,

[0089] Q3 is the heat gain of the resistor,

[0090] G is the weight of the resistor,

[0091] c is the specific heat of the resistor,

[0092] d is the differential symbol,

[0093] t0 is the initial air temperature,

[0094] Q4 is the heat gain of the air,

[0095] V is the spatial volume of the large electric brake,

[0096] m is the air influence coefficient,

[0097] γ k is the specific gravity of air,

[0098] c k is the specific heat of air,

[0099] n is the coefficient caused by radiation and heat absorption of the surrounding walls.

[0100] S2) Based on the constant temperature drop, the air heat equation dQ4=Vmγ in step S1) is used. k c k d(t-t0) and heat dissipation equation dQ2=αF(t b -t)dτ to obtain the air temperature rise

[0101] From the resistance in step S1) we get the heat equation dQ3 = Gcd(t b -t0) to obtain the surface temperature rise of the resistor

[0102] Assume that the temperature rise of the resistor after the resistor is energized is Δt b =t b -t0=(t b -t)+(t-t0)=Δt 1b +Δt 2b , then the surface temperature of the resistor is

[0103] The ventilation volume Substitute the air temperature rise Then Δt 2b Substitute the surface temperature rise of the resistor Thus we get Divide both sides by dΔt 1b , dτ, and take the reciprocal and integral of both sides to get Then, the temperature rise formula of the resistor after the resistor is energized is obtained:

[0104] Δt b =Δt 1b +Δt 2b

[0105]

[0106] Where,

[0107] △t b The temperature rise of the resistor after the resistor is energized.

[0108] Δt 1b =t b -t,

[0109] Δt 2b =t-t0,

[0110] t b is the resistor surface temperature,

[0111] t is the air temperature,

[0112] t0 is the initial air temperature,

[0113] N=0.86·I 2 R,

[0114]

[0115] C=Gc,

[0116] e represents a natural constant,

[0117] I is the braking current of the input resistor,

[0118] R is the resistance of the resistor,

[0119] α is the convection heat transfer coefficient of the resistor surface,

[0120] F is the heat transfer area of ​​the resistor surface,

[0121] γ k is the specific gravity of air,

[0122] c k is the specific heat of air,

[0123] L is the ventilation volume,

[0124] G is the weight of the resistor,

[0125] c is the specific heat of the resistor.

[0126] S3) collecting relevant data, including ventilation volume L, initial air temperature t0, specific heat c of the resistor, heat transfer area F of the resistor surface, resistor density, and braking current I of the input resistor.

[0127] In this embodiment, the ventilation volume L is selected to be 30000m 3 / h, room volume 638m 3 , room cross-sectional area 35.6m 2 The calculated wind speed on the resistor surface is v = 1 m / s. The braking current I of the input resistor is 12550A, the braking time is 2s, the braking resistor resistance R is 0.635Ω (single phase), and the resistor material is iron-nickel-aluminum alloy.

[0128] S4) Determine the convective heat transfer coefficient α.

[0129] Specifically, through actual process testing and analysis, the convection heat transfer coefficient α of the resistor under different wind speed conditions was fitted, and the corresponding relationship between the convection heat transfer coefficient α of the resistor and wind speed was fitted into a table that can be directly referenced. The wind speed on the resistor surface was calculated based on the ventilation volume L and the spatial volume V of the large electric brake. The convection heat transfer coefficient α corresponding to this wind speed was found using the table in step S4). The convection heat transfer coefficient of the resistor surface in this embodiment is shown in Table 1.

[0130] Table 1 Resistor surface convection heat transfer coefficient

[0131]

[0132] In this embodiment, the wind speed on the resistor surface is v = 1m / s, so the convection heat transfer coefficient α is 12cal / m 2 ·℃.

[0133] S5) Substituting the data in step S3) and the convection heat transfer coefficient α in step S4) into the resistor temperature rise formula after the resistor is energized in step S2) to calculate the resistor temperature rise Δt after the resistor is energized. b .

[0134] Preferably, first use the ventilation volume L to calculate the air temperature rise Δt 2b , to ensure that the air temperature rise Δt 2b ≤60℃, then calculate the resistor temperature rise △t after the resistor is energized b .

[0135] In this embodiment, C=G·c=183.816,N=0.86×12550 2 ×0.635×3=25.8×10 4 , τ b =2Substitute Get Δt 2b =54.33≤60℃.

[0136] Finally, the temperature rise of the resistor after the resistor is energized is calculated as Δt b =779.031℃.

[0137] S6) Compare the initial air temperature t0 with the resistor temperature rise △t after the resistor is energized. b Add them together to obtain the resistor surface temperature t after the resistor is energized. b .

[0138] In this embodiment, the surface temperature of the resistor after the resistor is energized is t b =t0+Δt b =809.031℃.

[0139] The present invention is based on a method for calculating the surface temperature of a large-scale electrical brake resistor with constant temperature drop. Based on the constant temperature drop principle, the temperature rise formula of the resistor after the resistor is energized is analyzed from a series of thermal equilibrium state control equations, and the surface temperature of the resistor after the resistor is energized is further calculated. This improves the accuracy and speed of calculating the surface temperature of the large-scale electrical brake resistor. At the same time, it can be extended to the temperature rise control calculation of systems and components of large power system devices when large currents pass through them.

[0140] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be considered as equivalent replacement methods and are included in the scope of protection of the present invention.

Claims

1. A method for calculating the surface temperature of a large electric brake resistor based on a constant temperature drop, characterized in that: The steps include: S1) Establishing a thermal equilibrium state control equation for a large electric brake resistor, wherein the thermal equilibrium state control equation includes Heat production equation: dQ1=0.86I 2 Rdτ Heat dissipation equation: dQ2=αF(t b -t)dτ Heat gain equation of resistance: dQ3=Gcd(t b -t0) Air heat gain equation: dQ4=Vmγ k c k d(t-t0) According to heat balance: ndQ2=dQ4 Where, Q1 is the heat generated by the resistor, I is the braking current of the input resistor, R is the resistance of the resistor, τ is the heating time of the resistor, Q2 is the heat dissipation of the resistor, α is the convection heat transfer coefficient of the resistor surface, F is the heat transfer area of ​​the resistor surface, t b is the resistor surface temperature, t is the air temperature, Q3 is the heat gain of the resistor, G is the weight of the resistor, c is the specific heat of the resistor, d is the differential symbol, t0 is the initial air temperature, Q4 is the heat gain of the air, V is the spatial volume of the large electric brake, m is the air influence coefficient, γ k is the specific gravity of air, c k is the specific heat of air, n is the coefficient caused by radiation and heat absorption of the surrounding wall; S2) Based on the constant rate of temperature reduction, the formula in step S1) is sorted out to obtain the temperature rise formula of the resistor after the resistor is energized: Δt b =Δt 1b +Δt 2b Where, △t b The temperature rise of the resistor after the resistor is energized. Δt 1b =t b -t, Δt 2b =t-t0, t b is the resistor surface temperature, t is the air temperature, t0 is the initial air temperature, N=0.86·I 2 R, C=Gc, e represents a natural constant, I is the braking current of the input resistor, R is the resistance of the resistor, α is the convection heat transfer coefficient of the resistor surface, F is the heat transfer area of ​​the resistor surface, γ k is the specific gravity of air, c k is the specific heat of air, L is the ventilation volume, G is the weight of the resistor, c is the specific heat of the resistor; S3) collecting relevant data, including ventilation volume L, initial air temperature t0, specific heat c of the resistor, heat transfer area F of the resistor surface, resistor density, and braking current I of the input resistor; S4) determining the convective heat transfer coefficient α; S5) Substituting the data in step S3) and the convection heat transfer coefficient α in step S4) into the resistor temperature rise formula after the resistor is energized in step S2) to calculate the resistor temperature rise Δt after the resistor is energized. b ; S6) Compare the initial air temperature t0 with the resistor temperature rise △t after the resistor is energized. b Add them together to obtain the resistor surface temperature t after the resistor is energized. b .

2. The method for calculating the surface temperature of a large electric brake resistor based on a constant temperature drop according to claim 1, characterized in that: In S2), From the resistance in step S1) we get the heat equation dQ3 = Gcd(t b -t0) to obtain the surface temperature rise of the resistor From the air heat equation in step S1) dQ4 = Vmγ k c k d(t-t0) and heat dissipation equation dQ2=αF(t b -t)dτ to obtain the air temperature rise Assume that the temperature rise of the resistor after the resistor is energized is Δt b =t b -t0=(t b -t)+(t-t0)=Δt 1b +Δt 2b , then the surface temperature of the resistor is The ventilation volume Substitute the air temperature rise Then Δt 2b Substitute the surface temperature rise of the resistor Thus we get Divide both sides by dΔt 1b , dτ, and take the reciprocal and integral of both sides to get Then the temperature rise formula of the resistor after the resistor is powered on is obtained.

3. The method for calculating the surface temperature of a large electric brake resistor based on a constant temperature drop according to claim 2, characterized in that: In S4), through actual process testing and analysis, the convection heat transfer coefficient α of the resistor under different wind speed conditions is fitted, and the corresponding relationship between the convection heat transfer coefficient α of the resistor and the wind speed is fitted into a table that can be directly referenced; According to the ventilation volume L and the spatial volume V of the large electric brake, the wind speed on the resistor surface is calculated, and the convective heat transfer coefficient α corresponding to the wind speed is found through the table in step S4).

4. The method for calculating the surface temperature of a large electric brake resistor based on a constant temperature drop according to claim 3, characterized in that: In S5), first use the ventilation volume L to calculate the air temperature rise Δt 2b , to ensure that the air temperature rise Δt 2b ≤60℃, then calculate the resistor temperature rise △t after the resistor is energized b .

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