CN109977566B - Method for constructing mathematical model of convective heat exchange coefficient of friction plate of wet clutch - Google Patents
Method for constructing mathematical model of convective heat exchange coefficient of friction plate of wet clutch Download PDFInfo
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Abstract
According to the method for constructing the mathematical model of the convective heat exchange coefficient of the friction plate of the wet clutch, which is related by the invention, a sliding friction acting expression is firstly established for the clutch in the clutch combining process, then the clutch combining process is divided into a plurality of infinitesimal equal time periods, the clutch infinitesimal sliding friction acting quantity in each infinitesimal equal time period is obtained according to the clutch sliding friction acting model, and the friction plate temperature change quantity and the cooling oil temperature change quantity in each infinitesimal equal time period are respectively measured; and obtaining the internal energy variable quantity of the friction plate, obtaining the internal energy variable quantity of the cooling oil according to the clutch infinitesimal slip friction work quantity and the internal energy variable quantity of the friction plate, obtaining the infinitesimal heat exchange coefficient according to the internal energy variable quantity of the cooling oil, obtaining a heat exchange coefficient curve in the clutch combining process, and finally obtaining a heat exchange coefficient mathematical model.
Description
Technical Field
The invention belongs to the field of automobiles, and particularly relates to a method for constructing a mathematical model of a convection heat exchange coefficient of a friction plate of a wet clutch.
Background
In recent years, with the development of transmission technology, wet-type dual clutch automatic transmissions have been widely used in automobiles. Because of the continuous start, stop and gear shifting requirements during the running process of the automobile, the clutch needs to be frequently engaged and disengaged during the working process. During the clutch engagement process, the friction plate continuously generates heat in the continuous sliding friction process from relative sliding to complete synchronization, so that the temperature of the friction plate is increased, the friction plate is easy to ablate and damage, and the clutch is caused to fail early. In order to improve the thermal load of the clutch and reduce the thermal failure fault, the engineering adopts a lubricating oil cooling mode to improve the thermal state of the surface of the friction plate, and in order to ensure the thermal reliability of the system operation, the thermal state judgment and evaluation of the design result are generally required.
At present, three approaches are generally adopted for obtaining the heat balance temperature of the friction steel sheet: (1) friction steel sheet surface heat test. The device is influenced by factors such as high-speed running of a clutch, complex shape of a groove structure on the surface of a friction steel sheet, oil wetting on the surface of the friction steel sheet, narrow working surface of the clutch and the like, has high requirements on test components and equipment such as a temperature sensor and temperature data acquisition required by thermal test, is difficult to install, and generally needs higher cost and time in the test process. Currently, no transmission production enterprises in China have the capability and conditions for carrying out the work, and most of the enterprises need to entrust foreign professional companies to carry out the work. (2) finite element software based simulation analysis. And carrying out thermal simulation analysis by means of finite element software, and obtaining the temperature distribution condition of the friction steel sheet by solving the temperature field. Although the temperature distribution obtained by the method has better visibility, the method cannot directly extract temperature data and transmit the obtained temperature data to a cooling system control module, so that engineering application targets of a real-time regulation cooling system are realized, and meanwhile, a thermal simulation process is complex and has higher requirements on thermal simulation professional skills of operators. (3) numerical simulation analysis based on mathematical model. The method comprises the steps of establishing a mathematical model of heat exchange between a friction steel sheet and cooling oil, solving a clutch friction steel sheet surface temperature prediction model, and rapidly obtaining a friction sheet local temperature value under any working condition; the temperature prediction mathematical model can be conveniently embedded into a clutch temperature control module, and can compare the predicted temperature value of the friction steel sheet surface with the set threshold value result of the system in real time, so that the cooling oil flow state is quickly regulated and controlled, the purpose of overheat protection of the clutch is achieved, and meanwhile, the quick judgment and evaluation of the friction steel sheet surface temperature in various vehicle types and various working conditions can be conveniently realized. However, the acquisition of the heat exchange coefficient of the friction steel sheet and the cooling oil is a main difficulty of numerical thermal simulation analysis.
Accurate acquisition of the heat exchange coefficient is a key link of accuracy of the temperature prediction mathematical model. Because the clutch friction plate has a complex structure, more oil grooves and irregular shape, the calculation cannot be directly carried out by using a classical empirical model of heat transfer chemistry. The friction plate and cooling oil heat exchange process involves factors such as heating state, structure and heat transfer area, cooling flow state and cooling oil quality of the friction plate at each stage in the clutch combination process, and is a complex dynamic process related to multiple factors, and no classical mathematical expression can be used as a reference at the present stage, so that the friction plate and cooling oil heat exchange process becomes the biggest difficulty in solving a temperature prediction model.
Disclosure of Invention
The present invention has been made to solve the above problems, and an object of the present invention is to provide a method for obtaining a heat exchange coefficient in a mathematical model of heat exchange between a friction steel sheet and cooling oil by using a sliding friction work expression in combination with an energy conservation law.
The invention provides a method for constructing a mathematical model of a convective heat exchange coefficient of a friction plate of a wet clutch, which has the characteristics that:
step S1, establishing a sliding friction acting expression (1) for the clutch in the clutch combining process,
wherein W is total sliding friction work; t (T) cl The maximum torque is transmitted for the clutch,
μ is the coefficient of friction, n is the engine speed; r is R 0 、R 1 Is the inner radius and the outer radius of the clutch; p is the engagement oil pressure; t is t 1 The clutch combination starting time is the clutch combination starting time; t is t 2 The clutch driving disc and the clutch driven disc are combined and the slip moment is stopped; omega 1 Is the angular velocity of the active disc; omega 2 Is the driven end disk speed;
s2, dividing the clutch combining process into a plurality of infinitesimal equal time periods, obtaining clutch infinitesimal slip friction work doing quantity in each infinitesimal equal time period according to a clutch slip friction work doing model, and respectively measuring the temperature change quantity of a friction plate and the temperature change quantity of cooling oil in each infinitesimal equal time period;
step S3, obtaining the internal energy variable quantity of the friction plate according to the internal energy calculation formula (2) according to the temperature variable quantity of the friction plate,
△Q＝c*m*△t (2)
wherein DeltaQ is the variable quantity of the internal energy of the friction plate, c is the specific heat capacity of the friction plate, m is the mass of the friction plate, deltat is the time period of infinitesimal and the like;
s4, obtaining a relation (4) between the internal energy variable quantity of the cooling oil and the internal energy variable quantity of the friction plate through an energy conservation formula (3) according to the clutch infinitesimal slip friction work quantity and the internal energy variable quantity of the friction plate,
△W＝△Q+△U (3)
|△Q|＝|△U| (4)
wherein DeltaW is clutch infinitesimal slip friction work amount, deltaQ is internal energy variable amount of the friction plate, deltaU is internal energy variable amount of cooling oil;
s5, obtaining a micro-element heat exchange coefficient through a cooling oil temperature absorption relation formula (5) according to the energy change quantity in the cooling oil,
△U＝h(△t)*△T oil (5)
wherein DeltaU is the energy change quantity of cooling oil, h (Deltat) is a micro-element heat exchange coefficient, deltaT oil The temperature change of the cooling oil;
s6, obtaining a heat exchange coefficient curve in the clutch combining process according to the infinitesimal heat exchange coefficient;
and S7, performing fitting analysis on the heat exchange coefficient curve to obtain a heat exchange coefficient mathematical model.
The method for constructing the mathematical model of the convective heat exchange coefficient of the friction plate of the wet clutch provided by the invention can also have the following characteristics: wherein the time period of the infinitesimal equal time period is 0.1-0.2 seconds.
The method for constructing the mathematical model of the convective heat exchange coefficient of the friction plate of the wet clutch provided by the invention can also have the following characteristics: in step S2, the friction plate temperature variation and the cooling oil temperature variation may be obtained by any method of thermal experiment or thermal simulation.
The method for constructing the mathematical model of the convective heat exchange coefficient of the friction plate of the wet clutch provided by the invention can also have the following characteristics: in step S6, the infinitesimal heat exchange coefficients are correlated by engineering analysis software to obtain a heat exchange coefficient curve.
The method for constructing the mathematical model of the convective heat exchange coefficient of the friction plate of the wet clutch provided by the invention can also have the following characteristics: in step S7, a heat exchange coefficient curve is fitted according to a least square method to obtain a mathematical model of the heat exchange coefficient.
Effects and effects of the invention
According to the method for constructing the mathematical model of the convective heat exchange coefficient of the friction plate of the wet clutch, which is related by the invention, a sliding friction acting expression is firstly established for the clutch in the clutch combining process, then the clutch combining process is divided into a plurality of infinitesimal equal time periods, the clutch infinitesimal sliding friction acting quantity in each infinitesimal equal time period is obtained according to the clutch sliding friction acting model, and the friction plate temperature change quantity and the cooling oil temperature change quantity in each infinitesimal equal time period are respectively measured; and obtaining the internal energy variable quantity of the friction plate, obtaining the internal energy variable quantity of the cooling oil according to the clutch infinitesimal slip friction work quantity and the internal energy variable quantity of the friction plate, obtaining the infinitesimal heat exchange coefficient according to the internal energy variable quantity of the cooling oil, obtaining a heat exchange coefficient curve in the clutch combining process, and finally obtaining a heat exchange coefficient mathematical model.
Therefore, the method for constructing the mathematical model of the convection heat exchange coefficient of the wet clutch friction plate is provided by combining thermal simulation (or thermal test) and thermal numerical analysis to construct the mathematical model of the convection heat exchange coefficient of the clutch friction plate and cooling oil by utilizing the sliding friction working expression and combining the energy conservation law to obtain the heat exchange coefficient of the friction steel plate and the mathematical model of the cooling oil. The method successfully solves the problem of accurate acquisition of the complex surface fluid-solid heat exchange coefficient, greatly improves the accuracy of acquiring the complex-shape surface heat exchange coefficient by adopting a simplified heat exchange model in the past, provides a new theoretical method for constructing the complex surface fluid-solid heat exchange coefficient model, and provides convenience for temperature prediction and evaluation in the development process of the wet clutch product for the vehicle.
Drawings
FIG. 1 is a flow chart of a method for constructing a mathematical model of convective heat transfer coefficients of a wet clutch friction plate in an embodiment of the invention;
FIG. 2 is a graph of variation in vehicle transmission torque, engine speed, and clutch speed obtained during actual wet clutch engagement in an embodiment of the present invention;
FIG. 3 is a graph of clutch plate temperature, cooling oil, and clutch friction work over clutch engagement in an embodiment of the invention; and
FIG. 4 is a graph of clutch-to-time heat exchange coefficient in an embodiment of the invention.
Detailed Description
In order to make the technical means, creation characteristics, achievement purposes and effects of the invention easy to understand, the following embodiment describes a method for constructing a mathematical model of a convective heat exchange coefficient of a friction plate of a wet clutch according to the invention with reference to the accompanying drawings.
As shown in fig. 1, a method S100 for constructing a mathematical model of a convective heat exchange coefficient of a friction plate of a wet clutch, wherein the wet clutch is a clutch for cooling and protecting the friction plate of the clutch by using cooling oil in a clutch combining process, and is characterized by comprising the following steps:
step S1: a sliding friction acting expression (1) is established for the clutch in the clutch combining process,
wherein W is the totalSliding friction work; t (T) cl The maximum torque is transmitted for the clutch,
μ is the coefficient of friction, n is the engine speed; r is R 0 、R 1 Is the inner radius and the outer radius of the clutch; p is the engagement oil pressure; t is t 1 The clutch combination starting time is the clutch combination starting time; t is t 2 The clutch driving disc and the clutch driven disc are combined and the slip moment is stopped; omega 1 Is the angular velocity of the active disc; omega 2 Is the driven end disk speed;
in this example, the target car preparation mass is 1975kg, starting with gear 1 on a slope with a grade of 25%; the gear 1 transmission ratio is 15.35, the maximum output torque of the engine matched with the gear 1 transmission ratio is 250 N.m, and the maximum torque rotating speed range is 2400 rpm-4800 rpm.
When the automobile starts at the 1 st gear, the clutch starts to transmit torque, the engine speed is instantaneously increased to 2500rpm from 800rpm, and then the engine is kept to work at about 2500 rpm; the rotation speed of the driven end of the clutch gradually increases from zero to 2500rpm, the rotation speed difference between the clutch and the driven end is linearly reduced in the process, the rotation speed difference is zero when synchronization is achieved, and the clutch engagement time in the process is 2.9s; the cooling oil supply flow rate was 10L/min.
Actual measurements of this example resulted in a plot of the change in transfer torque, engine speed, and clutch speed during wet clutch engagement as shown in fig. 2.
The clutch establishment slip work expression established in two stages based on the relevant data obtained from experience and actual measurement well known in the art for this example is:
step S2: dividing a clutch combining process into a plurality of infinitesimal equal time periods, obtaining clutch infinitesimal slip friction work doing quantity in each infinitesimal equal time period according to a clutch slip friction work doing model, and respectively measuring friction plate temperature change quantity and cooling oil temperature change quantity in each infinitesimal equal time period;
the time length of the infinitesimal period is 0.1-0.2 seconds, and the temperature change of the friction plate and the temperature change of the cooling oil can be obtained by any method of thermal experiments or thermal simulation.
In the present embodiment, the duration of the infinitesimal period is 0.1 seconds.
The clutch disk and cooling oil temperature values measured by thermal experiments are shown in table 1:
thermal test data for 1-gear starting condition of automobile ramp
| Time/ |
0 | 0.1 | 0.2 | 0.3 | 0.4 | … | 2.7 | 2.8 | 2.9 |
| Oil temperature/. Degree.C | 90 | 90.90 | 91.09 | 92 | 92.54 | … | 125.09 | 125.63 | 125.81 |
| Steel sheet temperature/°c | 90 | 90.22 | 90.41 | 92.64 | 98.81 | … | 286.7 | 278.4 | 272.0 |
The thermal experiment method is to install a temperature sensor on a friction steel sheet of the clutch, and acquire the temperature value of the friction plate in the clutch combining process through a wireless test system.
Based on the obtained correlation data, the clutch plate temperature, cooling oil temperature, and clutch slip work change curves throughout the clutch engagement process are plotted as shown in FIG. 3.
Step S3: obtaining the internal energy variable quantity of the friction plate according to the internal energy calculation formula (2) according to the temperature variable quantity of the friction plate,
△Q＝c*m*△t (2)
wherein DeltaQ is the variable quantity of the internal energy of the friction plate, c is the specific heat capacity of the friction plate, m is the mass of the friction plate, deltat is the time period of infinitesimal and the like;
in this embodiment, the amount of energy change in the clutch plate is derived from the change in the clutch plate temperature throughout the clutch engagement process. Steel sheet specific heat capacity c=460J/(kg·deg.c), friction plate mass m=0.4 kg.
Step S4: obtaining a relation (4) between the internal energy variable quantity of the cooling oil and the internal energy variable quantity of the friction plate through an energy conservation formula (3) according to the clutch infinitesimal slip friction work quantity and the internal energy variable quantity of the friction plate,
△W＝△Q+△U (3)
|△Q|＝|△U| (4)
wherein DeltaW is clutch infinitesimal slip friction work amount, deltaQ is internal energy variable amount of the friction plate, deltaU is internal energy variable amount of cooling oil;
in this embodiment, for the steel sheet temperature and cooling oil temperature curve obtained by the thermal test, the clutch friction plate heat variation Δq in each time period is obtained by means of a method using a infinitesimal function numerical analysis, and the cooling oil energy Δu in the same infinitesimal time period is obtained by using the relationship of the cooling oil energy variation in the same infinitesimal time period and the cooling oil energy variation in the friction plate.
Step S5: obtaining a micro-element heat exchange coefficient through the cooling oil temperature absorption relation (5) according to the energy change quantity of the cooling oil,
△U＝h(△t)*△T oil (5)
wherein DeltaU is the energy change quantity in the cooling oil, h (Deltat) is the infinitesimal heat exchange coefficient,
△T oil the temperature change of the cooling oil;
step S6: obtaining a heat exchange coefficient curve in the clutch combining process according to the micro-element heat exchange coefficient; and correlating the micro-element heat exchange coefficients through engineering analysis software to obtain a heat exchange coefficient curve.
In this embodiment, by means of MATLAB analysis software, the discrete heat exchange coefficient points are represented in a numerical form and connected, discrete points are removed through data processing, and mathematical fitting of the heat exchange coefficients is performed according to a least square method, wherein the mathematical fitting is to use a continuous function or discrete equation to infinitely approximate a curve formed by discrete data, and the discrete data are summarized into an empirical formula. The fitting can be performed by adopting a mathematical fitting function of the heat exchange coefficient, preferably a quadratic function according to the actual fitting condition of a plurality of times.
The heat exchange coefficient curve of the automobile shown in fig. 4, which varies with the target clutch engagement time when starting with 1 st gear on a slope having a gradient of 25%, is obtained.
Step S7: and carrying out fitting analysis on the heat exchange coefficient curve to obtain a heat exchange coefficient mathematical model. And fitting the heat exchange coefficient curve by a least square method to obtain a heat exchange coefficient mathematical model.
In this embodiment, a numerical analysis method is applied, specifically, a function approximation analysis is performed on a heat exchange coefficient curve formed by the infinitesimal point heat exchange coefficients, and finally, a mathematical model of the heat exchange coefficient in the clutch sliding and friction process under the first-gear starting working condition of the ramp is obtained through a least square fitting analysis of curve fitting:
effects and effects of the examples
According to the method for constructing the mathematical model of the convective heat exchange coefficient of the friction plate of the wet clutch, which is related to the embodiment, a sliding friction acting expression is firstly established for the clutch in the clutch combining process, then the clutch combining process is divided into a plurality of infinitesimal equal time periods, the clutch infinitesimal sliding friction acting quantity in each infinitesimal equal time period is obtained according to the clutch sliding friction acting model, and the friction plate temperature change quantity and the cooling oil temperature change quantity in each infinitesimal equal time period are respectively measured; and obtaining the internal energy variable quantity of the friction plate, obtaining the internal energy variable quantity of the cooling oil according to the clutch infinitesimal slip friction work quantity and the internal energy variable quantity of the friction plate, obtaining the infinitesimal heat exchange coefficient according to the internal energy variable quantity of the cooling oil, obtaining a heat exchange coefficient curve in the clutch combining process, and finally obtaining a heat exchange coefficient mathematical model.
Therefore, the method for constructing the mathematical model of the convection heat exchange coefficient of the wet clutch friction plate of the embodiment is to obtain the heat exchange coefficient of the friction steel sheet and the mathematical model of the cooling oil heat exchange by utilizing the sliding friction working expression and combining the energy conservation law, and the method for constructing the mathematical model of the convection heat exchange coefficient of the clutch friction plate and the mathematical model of the cooling oil heat exchange coefficient by combining thermal simulation (or thermal test) and thermal numerical analysis is provided. The method successfully solves the problem of accurate acquisition of the complex surface fluid-solid heat exchange coefficient, greatly improves the accuracy of acquiring the complex-shape surface heat exchange coefficient by adopting a simplified heat exchange model in the past, provides a new theoretical method for constructing the complex surface fluid-solid heat exchange coefficient model, and provides convenience for temperature prediction and evaluation in the development process of the wet clutch product for the vehicle.
The above embodiments are preferred examples of the present invention, and are not intended to limit the scope of the present invention.
Claims (5)
1. The method for constructing the mathematical model of the convective heat exchange coefficient of the friction plate of the wet clutch is characterized by comprising the following steps of:
step S1, establishing a sliding friction acting expression (1) for the clutch in the clutch combining process,
wherein W is total sliding friction work; t (T) cl The maximum torque is transmitted for the clutch,
μ is the coefficient of friction, n is the engine speed; r is R o 、R i Is the inner radius and the outer radius of the clutch; p is the engagement oil pressure; t is t 1 The clutch combination starting time is the clutch combination starting time; t is t 2 The clutch driving disc and the clutch driven disc are combined and the slip moment is stopped; omega 1 Is the angular velocity of the active disc; omega 2 Is the driven end disk speed;
s2, dividing the clutch combining process into a plurality of infinitesimal equal time periods, obtaining clutch infinitesimal slip friction work doing quantity in each infinitesimal equal time period according to the clutch slip friction work doing model, and respectively measuring the friction plate temperature change quantity and the cooling oil temperature change quantity in each infinitesimal equal time period;
step S3, obtaining the internal energy variable quantity of the friction plate according to the internal energy calculation formula (2) according to the temperature variable quantity of the friction plate,
△Q＝c*m*△t (2)
wherein DeltaQ is the energy variation of the friction plate, c is the specific heat capacity of the friction plate, m is the mass of the friction plate, deltat is the time period of the infinitesimal and the like;
step S4, according to the clutch infinitesimal slip friction work amount and the friction plate internal energy variable amount, the internal energy expression (3) is passed, and according to the energy conservation law, a relation formula (4) of the cooling oil internal energy variable amount and the friction plate internal energy variable amount is obtained,
△W＝△Q+△U (3)
|△Q|＝|△U| (4)
wherein DeltaW is clutch infinitesimal slip friction work amount, deltaQ is internal energy variable amount of the friction plate, deltaU is internal energy variable amount of cooling oil;
s5, obtaining a infinitesimal heat exchange coefficient through the cooling oil temperature absorption relation (5) according to the internal energy variable quantity of the cooling oil,
△U＝h(△t)*△T oil (5)
wherein DeltaU is the energy change quantity of cooling oil, h (Deltat) is the micro-element heat exchange coefficient, deltaT oil A temperature change amount of the cooling oil;
s6, obtaining a heat exchange coefficient curve in the clutch combining process according to the infinitesimal heat exchange coefficient;
and S7, performing fitting analysis on the heat exchange coefficient curve to obtain a heat exchange coefficient mathematical model.
2. The method for constructing the mathematical model of the convective heat exchange coefficient of the friction plate of the wet clutch according to claim 1, wherein the method comprises the following steps of:
wherein the time length of the infinitesimal equal time period is 0.1-0.2 seconds.
3. The method for constructing the mathematical model of the convective heat exchange coefficient of the friction plate of the wet clutch according to claim 1, wherein the method comprises the following steps of:
in step S2, the friction plate temperature variation and the cooling oil temperature variation may be obtained by any method of thermal experiment or thermal simulation.
4. The method for constructing the mathematical model of the convective heat exchange coefficient of the friction plate of the wet clutch according to claim 1, wherein the method comprises the following steps of:
in step S6, the infinitesimal heat exchange coefficient is correlated by engineering analysis software to obtain the heat exchange coefficient curve.
5. The method for constructing the mathematical model of the convective heat exchange coefficient of the friction plate of the wet clutch according to claim 1, wherein the method comprises the following steps of:
in step S7, the heat exchange coefficient curve is fitted according to a least square method to obtain the mathematical model of the heat exchange coefficient.
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| CN110426201A (en) * | 2019-07-26 | 2019-11-08 | 上海交通大学 | Slip clutch transient temperature measuring method and device based on six parameter models |
| CN110705138B (en) * | 2019-08-23 | 2022-06-28 | 中国第一汽车股份有限公司 | Speed changer thermal model modeling method |
| CN110702404A (en) * | 2019-08-29 | 2020-01-17 | 中国第一汽车股份有限公司 | Method, device and equipment for measuring temperature of clutch and storage medium |
| CN113312816B (en) * | 2021-05-26 | 2023-03-17 | 青岛理工大学 | Method for analyzing reliability of brake pad |
| CN113868775B (en) * | 2021-10-30 | 2023-01-06 | 蜂巢传动科技河北有限公司 | Method for constructing temperature simulation model of automatic transmission clutch |
| CN115859844B (en) * | 2022-07-29 | 2023-10-13 | 江苏新能源汽车研究院有限公司 | Lubrication and cooling simulation method for wet clutch |
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