Method for calculating surface temperature of resistor of large-scale electric brake based on constant-speed temperature drop

Abstract

The invention discloses a method for calculating the surface temperature of a resistor of a large electric brake based on constant-speed temperature drop. The method comprises the following steps: establishing a heat balance state control equation of a large-scale electric brake resistor, and sorting the heat balance state control equation based on constant-speed cooling to obtain a resistor temperature rise formula after the electrification of the resistor is finished; collecting related data; determining a convective heat transfer coefficient alpha; substituting the collected data and the convective heat transfer coefficient alpha into a resistor temperature rise formula after the electrification of the resistor is finished, and solving the resistor temperature rise tb after the electrification of the resistor is finished; and adding the initial air temperature t0 and the resistor temperature rise tb after the electrifying of the resistor is finished to obtain the surface temperature tb of the resistor after the electrifying of the resistor is finished. According to the method, formula calculation and experimental data summarization are combined, and the surface temperature of the resistor after electrification of the resistor is finished can be accurately and quickly calculated.

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 are devices that use electrical principles to achieve braking, ensuring that the equipment can quickly and safely slow down or stop when needed. They are widely used in industries such as water conservancy, hydropower, and municipal transportation. Since electric brakes use periodic input of large currents during operation, their main components will still produce a large temperature rise under forced mechanical ventilation. The process is a short-term transient temperature rise process, and the temperature rise value is affected by external factors such as current and ventilation system. In addition, since the geometric parameters of the assembly space affect the heat dissipation process, temperature rise and heat dissipation are a complex nonlinear coupling process. Determining the surface temperature of the resistor is crucial for the selection of component working characteristics and material selection of the electric brake.

[0003] There is no calculation formula for the surface temperature of the electric brake resistor in the prior art. Generally, a method combining physical model and numerical modeling is used to empirically estimate the surface temperature of the resistor. 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 estimation 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 designs a method for calculating the surface temperature of a large electric brake resistor based on a constant temperature drop, which is particularly characterized in that it includes 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 generation 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] In the formula,

[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 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 rearranged to obtain the temperature rise formula of the resistor after the resistor is energized:

[0034] Δt b =Δt 1b +Δt 2b

[0035]

[0036] In the formula,

[0037] △t b It is the temperature rise of the resistor after the resistor is powered on.

[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 exchange 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) Substitute 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 △t 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] Further, 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 powered on is Δt b =t b -t0=(t b -t)+(t-t0)=Δt 1b +Δt 2b , then the surface temperature rise of the resistor is

[0063] The ventilation volume Substitute the air temperature rise Then Δt 2b Substitute the surface temperature rise of the resistor into Thus we get Divide both sides by dΔt 1b , dτ, and take the inverse and integration of both sides to obtain 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 out 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 temperature rise of the resistor after the resistor is powered on. 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, resistor heat gain equation, and air heat gain equation), the present invention analyzes the resistor temperature rise formula after the resistor is powered on based on constant temperature drop, and then calculates the initial air temperature t0 and the resistor temperature rise △t after the resistor is powered on. 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 powered on. b The heat transfer coefficient α of the resistor surface in the calculation formula is fitted by the present invention under different wind speed conditions, and through a large number of actual tests and summaries, different wind speeds and corresponding heat transfer coefficients are fitted into a table that can be directly referenced; when calculating the resistor temperature rise △t after the resistor is powered on, b When the wind speed on the resistor surface is , 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 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, thereby improving the calculation accuracy and rapidity of the surface temperature of the large electrical brake resistor. At the same time, it can be extended to the temperature rise control calculation of the system and components of a large power system device when a large current passes through it. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0071] The present invention is further described in detail below in conjunction with 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 generation 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 equation: dQ4=Vmγ k c k d(t-t0)

[0078] According to heat balance: ndQ2 = dQ4

[0079] In the formula,

[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 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 rate of cooling, 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), 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 powered on is Δt b =t b -t0=(t b -t)+(t-t0)=Δt 1b +Δt 2b , then the surface temperature rise of the resistor is

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

[0104] Δt b =Δt 1b +Δt 2b

[0105]

[0106] In the formula,

[0107] △t b It is the temperature rise of the resistor after the resistor is powered on.

[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) Collect 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 wind speed on the resistor surface is calculated to be v = 1m / 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 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 surface of the resistor is calculated, and the convection heat transfer coefficient α corresponding to the wind speed is found through 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) Substitute 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 △t after the resistor is energized b .

[0134] Preferably, 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 temperature rise of the resistor after the resistor is powered on. 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 resistor temperature rise after the resistor is powered on 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 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, thereby improving the calculation accuracy and rapidity of the surface temperature of the large electrical brake resistor. At the same time, it can be extended to the temperature rise control calculation of the system and components of a large power system device when a large current passes through it.

[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 equivalent replacement methods and are included in the protection scope 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 generation 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 equation: dQ4=Vmγ k c k d(t-t0) According to heat balance: ndQ2 = dQ4 In the formula, 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 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 rearranged to obtain the temperature rise formula of the resistor after the resistor is energized: Δt b =Δt 1b +Δt 2b In the formula, △t b The temperature rise of the resistor after the resistor is powered on. 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 exchange 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) Substitute 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 △t 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: S2), From the resistance in step S1), 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 powered on is Δt b =t b -t0=(t b -t)+(t-t0)=Δt 1b +Δt 2b , then the surface temperature rise of the resistor is The ventilation volume Substitute the air temperature rise Then Δt 2b Substitute the surface temperature rise of the resistor into Thus we get Divide both sides by dΔt 1b , dτ, and take the inverse and integration of both sides to obtain 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 convection 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 temperature rise of the resistor after the resistor is powered on. b .

Images