CN112084603A - Method for acquiring quenching and heating technological parameters of heavy-load universal shaft fork head - Google Patents

Method for acquiring quenching and heating technological parameters of heavy-load universal shaft fork head Download PDF

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CN112084603A
CN112084603A CN202010979455.8A CN202010979455A CN112084603A CN 112084603 A CN112084603 A CN 112084603A CN 202010979455 A CN202010979455 A CN 202010979455A CN 112084603 A CN112084603 A CN 112084603A
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quenching
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杨晓红
朱健平
马淑瑾
许训
李俊杰
葛婧
何宜柱
胡磊
方凯
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Taier Heavy Industry Co Ltd
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Abstract

The invention discloses a method for acquiring quenching and heating technological parameters of a heavy-duty universal shaft fork head, which comprises the following steps of: step one, establishing a model by using a finite element method, and acquiring the depth of an austenitizing layer of a fork headhAnd depth of through-hardening layerc(ii) a Step two, using a Bowder method to ensure the depth of an austenitizing layerhNot lower than the minimumhminOn the basis of the depth of an austenitizing layer of the fork headhDepth of through-hardening layercThe difference between the two is an optimization target, and optimal quenching heating process parameters of the heavy-duty universal shaft fork head, namely heating temperature T and heating time T, are obtained. The method combines the finite element method with the optimization method to ensure that the heat treatment efficiency is improved and the heat treatment cost is reduced on the basis of guaranteeing the heat treatment quality of the fork. The method of the invention not only avoids energy waste and low production efficiency caused by overlong heating time, but also can not cause the problem of unqualified heat treatment quality caused by insufficient heating time.

Description

Method for acquiring quenching and heating technological parameters of heavy-load universal shaft fork head
Technical Field
The invention relates to a method for acquiring quenching and heating process parameters of a heavy-duty universal shaft fork head, which improves the heat treatment efficiency and reduces the heat treatment cost on the basis of ensuring the heat treatment quality of the heavy-duty universal shaft fork head. The invention belongs to the technical field of metal heat treatment.
Background
The heavy-duty cross-axle type universal coupling is an important mechanical transmission part and has wide application in the fields of heavy machinery, aerospace, metallurgy and the like. The fork head is used as a key component of a heavy-duty cross-axle type universal coupling, the fork head is used for transmitting the torque of a driving shaft and a driven shaft, the working condition is severe, the breakage failure and the abrasion failure are easy to occur, and once the fork head fails, the coupling cannot work, and the time and the labor are wasted when the fork head is replaced again. Therefore, after the heavy-duty universal shaft fork head is cast and formed, quenching and tempering heat treatment, namely quenching and high-temperature tempering, is needed to obtain comprehensive mechanical properties with good strength and toughness, so that the service life of the heavy-duty universal shaft fork head is prolonged, and the normal work of the coupler is ensured.
In the traditional quenching and heating process of the fork head, in order to ensure the depth of quenching, long-time austenitizing and heating are often carried outSometimes even the entire prong is heated above the austenitizing temperature, causing it to fully transform to austenite. However, in the subsequent quenching cooling process, only limited depth of quenching layer, namely depth of austenitizing layer of the fork head, can be obtained generally due to the limitation of cooling capacity of the cooling mediumhAnd depth of through-hardening layercThe difference is large. Therefore, the traditional quenching process of the fork head causes a great deal of energy waste and time waste during austenitizing heating. Therefore, it is necessary to provide a method for acquiring quenching and heating process parameters of the heavy-duty universal shaft fork, so that the quenching and heating efficiency is improved and the heat treatment cost is reduced under the requirement of ensuring the service performance of the heavy-duty universal shaft fork.
Disclosure of Invention
The invention aims to provide a method for acquiring quenching and heating process parameters of a heavy-duty universal shaft fork head, so as to improve the heat treatment efficiency and reduce the heat treatment cost on the basis of ensuring the heat treatment quality of the fork head.
The method combines a finite element method with an optimization method, and establishes temperature field distribution in the heating and cooling stages during quenching heat treatment of the fork heads with different sizes by the finite element method to obtain the depth of an austenitizing layer of the fork head with a given size D at different heating temperatures T and heating times ThAnd depth of through-hardening layer in subsequent quenchingc(ii) a On the basis, an optimization algorithm is used to obtain the optimal depth of an austenitizing layerhDepth of through-hardening layercAnd combining, wherein the heating temperature T and the heating time T at the moment are optimal quenching heating process parameters. The method of the invention not only avoids energy waste and low production efficiency caused by overlong heating time, but also can not cause the problem of unqualified heat treatment quality caused by insufficient heating time.
The invention discloses a method for acquiring quenching and heating technological parameters of a heavy-duty universal shaft fork head, which comprises the following steps of:
step one, establishing a model by using a finite element method, and acquiring the depth of an austenitizing layer of a fork headhAnd depth of through-hardening layerc
Step two, using a Bowder method to ensure the depth of an austenitizing layerhNot lower than the minimumhminOn the basis of the depth of an austenitizing layer of the fork headhDepth of through-hardening layercThe difference between the two is an optimization target, and optimal quenching heating process parameters of the heavy-duty universal shaft fork head, namely heating temperature T and heating time T, are obtained.
Wherein, the first step comprises the following specific steps:
step 1.1, modeling: establishing a heavy-load universal shaft fork head geometric model according to the size D of the fork head by using a finite element method, and dividing a grid by using tetrahedral units, wherein the size of the grid is 20 mm;
step 1.2, obtaining the depth of an austenitizing layer of a fork headh: adding boundary conditions of radiation heat exchange and convection heat exchange in the finite element model established in the step 1, wherein the environment temperature is the furnace temperature, and calculating and solving quenching heating temperature field distribution of the fork at the heating temperature T and the heating time T; extracting the depth of the region where the temperature of the base and the middle part of the fork head is greater than the austenite transformation starting temperature Ac1, and taking the minimum value as the depth of an austenitizing layerh
Step 1.3, acquiring the depth of a through hardening layer of the fork headc: adding a convection heat transfer boundary condition into the finite element model established in the step 1, wherein the environment temperature is the temperature of the quenching medium, and calculating and solving the quenching cooling temperature field distribution of the fork at the heating temperature T and the heating time T; the cooling speed of the pedestal and the middle part of the fork head is greater than the depth of a quenching critical cooling speed vc area, and the minimum value is taken as the depth of a through quenching layerc
Wherein, the second step comprises the following specific steps:
step 2.1, selecting an optimization function as follows:
Figure BDA0002686998730000031
in the formula, rkIs a penalty factor, and r1=1,rk+1=0.5rk(k=1,2,3...);
Step 2.2, selecting a group of initial heavy-load universal shaft fork head quenching and heating process parameters
Figure BDA0002686998730000032
And convergence accuracy, taking the initial set of cardinal directions as a unit coordinate vector system, i.e. S1 (1)=[1,0]T,S2 (1)=[0,1]T
Step 2.3, 1,2,3 for k, from X0 (k)Starting from, following S in sequence1 (k)And S2 (k)Performing one-dimensional golden section search to obtain 2 minimum value points X1 (k)And X2 (k)Constructing a new search direction S3 (k)=X2 (k)-X0 (k)And searching along the direction by using golden section method to obtain minimum value point X0 (k+1)
Step 2.4, substituting the X value obtained in the step 2.3 into the following formula for judgment
Figure BDA0002686998730000033
If it is not
Figure BDA0002686998730000034
Then X0 (k+1)The optimal quenching and heating technological parameters of the fork head of the heavy-duty universal shaft are obtained if
Figure BDA0002686998730000035
Then k is equal to k +1, go back to step 2.3 to search again to obtain the X value, go to step 2.4 to make a decision until it is satisfied
Figure BDA0002686998730000036
The golden section method in step 2.3 of step two comprises the following specific steps:
step one, determining an initial search space [ Ta,Tb]Let Tα=Ta+0.382(Tb-Ta)、Tβ=Ta+0.618(Tb-Ta) (ii) a The quenching is calculated by using the step 1.1 and the step 1.2 respectivelyThe heating temperature is TαHeating time t0 (k)Depth of austenitizing layer h and depth of through-hardening layer c, then the depth of austenitizing layer at this point is calculated by step 2.1
Figure BDA0002686998730000041
In the same way, can obtain
Figure BDA0002686998730000042
Step two, comparison
Figure BDA0002686998730000043
And
Figure BDA0002686998730000044
the size of (2): if it is
Figure BDA0002686998730000045
Then Tb=Tβ,Tβ=Tα
Figure BDA0002686998730000046
Tα=Ta+0.382(Tb-Ta) (ii) a Firstly, step 1.1 and step 1.2 are used to respectively calculate the quenching heating temperature as TαThe heating time is
Figure BDA0002686998730000047
Depth of austenitizing layer h and depth of through-hardening layer c, then the depth of austenitizing layer at this point is calculated by step 2.1
Figure BDA0002686998730000048
Otherwise, then Ta=Tα,Tα=Tβ
Figure BDA0002686998730000049
Tβ=Ta+0.618(Tb-Ta) And calculating the quenching heating temperature as T by using the step 1 and the step 2 respectivelyβThe heating time is
Figure BDA00026869987300000410
Depth of austenitizing layer h and depth of through-hardening layer c at this time, which are calculated using step 2.1
Figure BDA00026869987300000411
Step three, if b-a <, then
Figure BDA00026869987300000412
If not, the step (II) is carried out again until b-a <, and the minimum value point is obtained;
and fourthly, repeating the first step, the second step and the third step to obtain the minimum value point of the t.
Compared with the prior art, the method for acquiring the quenching and heating technological parameters of the heavy-duty universal shaft fork head has the beneficial effects that: (1) the finite element method is combined with the optimization method, namely the finite element method is used for establishing temperature field distribution of heating and cooling stages during quenching heat treatment of the forked heads with different sizes, so that the depth ha of an austenitizing layer of the forked head with a given size D and the depth hc of a quenching layer during subsequent cooling and quenching are obtained when the forked head with the given size is at different heating temperatures T and heating times T; on the basis, an optimal combination of the depth ha of the austenitizing layer and the depth hc of the through-hardening layer is obtained by using an optimization algorithm, so that the problems of energy waste and low production efficiency caused by overlong heating time and unqualified heat treatment quality caused by insufficient heating time are solved; (2) on the premise of ensuring the quality of the quenched product, the production efficiency is improved, and the electric energy consumption is reduced; when the heavy-duty universal shaft fork head is obtained by the Bowden method through quenching and heating heat treatment, the combination of the heating temperature and the heating time which are as low as possible can be obtained on the premise of ensuring that the depth of an austenitizing layer is not lower than the minimum value, the heat treatment efficiency is improved, and the heat treatment cost is reduced; in addition, the invention can avoid repeated field tests, and is beneficial to saving time, labor and material resources; (3) the defect that the temperature distribution is time-consuming and labor-consuming in quenching and heating heat treatment of the heavy-duty universal shaft fork head measured through a temperature measuring device in the prior art is overcome, the defect that workpieces can be damaged by measuring the internal temperature of the heavy-duty universal shaft fork head through punching is overcome, the time for acquiring quenching and heating process parameters of the heavy-duty universal shaft fork head is shortened, and the production cost is reduced.
Drawings
FIG. 1 is a schematic view of a heavy duty cardan shaft yoke.
FIG. 2 is a schematic view of the depth h of the austenitizing layer of the pick.
FIG. 3 is a schematic view of obtaining the depth of quench penetration c of the prong.
FIG. 4 is a schematic flow chart of the method of the present invention.
Detailed Description
The technical solution of the present invention will be further specifically described with reference to specific examples.
Example 1
Heavy-duty cardan shaft jaw: 1100mm, and obtaining the material ZG34Cr2Ni2Mo with optimized heating temperature T and heating time T of quenching heating heat treatment by the following steps:
step one, establishing a model by using a finite element method, and acquiring the depth h of an austenitizing layer and the depth c of a through quenching layer of a fork:
step 1.1, modeling: establishing a heavy-load universal shaft fork head geometric model according to the size D of the fork head by using a finite element method, and dividing a grid by using tetrahedral units, wherein the size of the grid is 20 mm;
step 1.2, obtaining the depth h of an austenitizing layer of the fork: adding boundary conditions of radiation heat exchange and convection heat exchange in the finite element model established in the step 1, wherein the environment temperature is the furnace temperature, and calculating and solving quenching heating temperature field distribution of the fork at the heating temperature T and the heating time T; and extracting the depth of the region where the temperature of the base and the middle part of the fork head is greater than the austenite transformation starting temperature Ac1, and taking the minimum value as the depth h of the austenitizing layer. In this example Ac1817 deg.C, taking its minimum value as the depth of austenitizing layerh
Step 1.3, obtaining the depth c of a through-hardening layer of the fork head: adding a convection heat transfer boundary condition into the finite element model established in the step 1, wherein the environment temperature is the temperature of the quenching medium, and calculating and solving the quenching cooling temperature field distribution of the fork at the heating temperature T and the heating time T; extraction forkThe cooling speed of the head base and the middle part is greater than the depth of a critical quenching cooling speed vc area, and the minimum value is taken as the depth c of a through quenching layer. In this example vc1 ℃/s, and the minimum value is taken as the depth of the through-hardening layerc
Step two, using a Bowder method to ensure the depth of an austenitizing layerhNot lower than the minimumhminOn the basis, the optimal quenching and heating process parameters of the heavy-duty universal shaft fork head, namely heating temperature T and heating time T, are obtained by taking the difference between the depth h of an austenitizing layer of the fork head and the depth c of a through quenching layer as an optimization target:
step 2.1, selecting an optimization function as follows:
Figure BDA0002686998730000061
in the formula, rkIs a penalty factor, and r1=1,rk+1=0.5rk(k ═ 1,2, 3.); in the present example, the number of the first and second,hmin=50mm;hminis a parameter defined according to the performance that the prong will eventually achieve, for a part of a particular size, material,hminis a known parameter;
step 2.2, selecting a group of initial heavy-load universal shaft and quenching and heating process parameters
Figure BDA0002686998730000062
And convergence accuracy, T in this example0 (1)=830℃、t0 (1)20h and 0.001, and taking the initial basic direction set as a unit coordinate vector system, namely S1 (1)=[1,0]T,S2 (1)=[0,1]T(ii) a Wherein the initial parameter T0 (1)、t0 (1)The values of (a) are from empirical formulas;
step 2.3, 1,2,3 for k, from X0 (k)Starting from, following S in sequence1 (k)And S2 (k)Performing one-dimensional golden section search to obtain 2 minimum value points X1 (k)And X2 (k)Constructing a new search direction S3 (k)=X2 (k)-X0 (k)And searching along the direction by using golden section method to obtain minimum value point X0 (k+1)(ii) a The golden section method comprises the following specific steps:
step one, determining an initial search space [ Ta,Tb]Let Ta=830℃,Tb930 deg.C, let Tα=Ta+0.382(Tb-Ta)=868.2℃,Tβ=Ta+0.618(Tb-Ta) 891.8 deg.C; firstly, step 1.1 and step 1.2 are used to respectively calculate the quenching heating temperature as TαAt 868.2 deg.C for a heating time t0 (1)The depth of the austenitizing layer h and the depth of the through-hardening layer c at 20h are then calculated by step 2.1
Figure BDA0002686998730000071
Similarly, the step 1.1 and the step 1.2 are used to calculate the quenching heating temperature T respectivelyβAt 891.8 deg.C for a heating time t0 (1)The depth of the austenitizing layer h and the depth of the through-hardening layer c at 20h are then calculated by step 2.1
Figure BDA0002686998730000072
Wherein, Ta、TbThe values of (a) are from empirical formulas;
step two, comparison
Figure BDA0002686998730000073
And
Figure BDA0002686998730000074
the size of (2): if it is
Figure BDA0002686998730000075
Then Tb=Tβ,Tβ=Tα
Figure BDA0002686998730000076
Tα=Ta+0.382(Tb-Ta) (ii) a Using the steps firstStep 1.1 and step 1.2 calculate the quenching heating temperature as TαThe heating time is
Figure BDA0002686998730000077
Depth of austenitizing layer h and depth of through-hardening layer c, then the depth of austenitizing layer at this point is calculated by step 2.1
Figure BDA0002686998730000078
Otherwise, then Ta=Tα,Tα=Tβ
Figure BDA0002686998730000079
Tβ=Ta+0.618(Tb-Ta) And calculating the quenching heating temperature as T by using the step 1 and the step 2 respectivelyβThe heating time is
Figure BDA00026869987300000710
Depth of austenitizing layer h and depth of through-hardening layer c at this time, which are calculated using step 2.1
Figure BDA00026869987300000711
Step three, if b-a <, then
Figure BDA00026869987300000712
If not, the step (c) is carried out again until b-a <, and the minimum value point is obtained.
And fourthly, repeating the first step, the second step and the third step to obtain the minimum value point of the t.
Step 2.4, substituting the X value obtained in the step 2.3 into the following formula for judgment
Figure BDA00026869987300000713
If it is not
Figure BDA00026869987300000714
Then X0 (k+1)The optimal quenching and heating technological parameters of the fork head of the heavy-duty universal shaft are obtained if
Figure BDA00026869987300000715
Then k is equal to k +1, go back to step 2.3 to search again to obtain the X value, go to step 2.4 to make a decision until it is satisfied
Figure BDA00026869987300000716
After optimization, the heating temperature of the optimized quenching heating process is 850 ℃ and the heating time is 9 h.
To fully illustrate the beneficial effects of the inventive examples, a number of comparative runs were conducted, with the quench heating process parameters for each run set shown in Table 1 below.
TABLE 1 quenching and heating Process parameter test data
Figure BDA0002686998730000081
In the tests 1 to 3, the diameter of the fork head is the same, the same heating temperature is adopted, but the heating time is different. Although the heating time of the test 2 is shorter, the end face teeth exceed the upper limit of hardness of 315HB, the quality is not satisfactory, and the quality of the test 1 and the quality of the test 3 both meet the requirements, therefore, the quenching heating process parameters of the test 1 and the test 3 can be adopted, but the heating time of the test 3 is shorter, the electricity consumption of each section is also lower, and therefore, the parameters of the test 3 are preferentially adopted. Therefore, when the diameter D of the fork head is 1100mm, the heating temperature T is 850 ℃ and the heating time T is 9h are the optimal quenching and heating process parameters of the heavy-duty universal shaft fork head, on the premise of ensuring the performance of the fork head, the difference between the depth h of an austenitizing layer and the depth c of a quenching layer of the fork head can be effectively reduced, the cost is saved, and the efficiency is improved.
In the description herein, references to the description of "one embodiment," "an example," "a specific example" or the like are intended to mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
The method of the invention combines the finite element method and the optimization method to obtain the optimal combination of the depth ha of the austenitizing layer and the depth hc of the through-hardening layer, thereby obtaining the optimal quenching temperature T and the optimal quenching time T. The method is not only suitable for the fork head, but also suitable for quenching other parts, thereby obtaining the optimal quenching temperature T and the optimal quenching time T.

Claims (5)

1. The method for acquiring the quenching and heating technological parameters of the heavy-duty universal shaft fork head is characterized by comprising the following steps of: it comprises the following steps:
step one, establishing a model by using a finite element method, and acquiring the depth h of an austenitizing layer and the depth c of a through-hardening layer of a fork head through the model;
and step two, obtaining the optimal quenching and heating process parameters, namely heating temperature T and heating time T, of the heavy-duty universal shaft fork head by using a Bowden method and taking the difference between the depth h of the austenitizing layer of the fork head and the depth c of the through-quenching layer as an optimization target.
2. The acquisition method according to claim 1, characterized in that:
the first step comprises the following specific steps:
step 1.1, modeling: establishing a heavy-load universal shaft fork head geometric model according to the size D of the fork head by using a finite element method, and dividing a grid by using tetrahedral units, wherein the size of the grid is 20 mm;
step 1.2, obtaining the depth h of an austenitizing layer of the fork: adding boundary conditions of radiation heat exchange and convection heat exchange in the finite element model established in the step 1, wherein the environment temperature is the furnace temperature, and calculating and solving quenching heating temperature field distribution of the fork at the heating temperature T and the heating time T; extracting the depth of a region where the temperature of the base and the middle part of the fork head is greater than the austenite transformation starting temperature Ac1, and taking the minimum value as the depth h of an austenitizing layer;
step 1.3, obtaining the depth c of a through-hardening layer of the fork head: adding a convection heat transfer boundary condition into the finite element model established in the step 1, wherein the environment temperature is the temperature of the quenching medium, and calculating and solving the quenching cooling temperature field distribution of the fork at the heating temperature T and the heating time T; and (3) the cooling speed of the pedestal and the middle part of the fork head is greater than the depth of a quenching critical cooling speed vc region, and the minimum value is taken as the depth c of a through-hardening layer.
3. The acquisition method according to claim 1 or 2, characterized in that:
the second step comprises the following specific steps:
step 2.1, selecting an optimization function as follows:
Figure FDA0002686998720000011
in the formula, rkIs a penalty factor, and r1=1,rk+1=0.5rk(k=1,2,3…);
Step 2.2, selecting a group of initial heavy-load universal shaft fork head quenching and heating process parameters
Figure FDA0002686998720000021
And convergence accuracy, taking the initial set of cardinal directions as a unit coordinate vector system, i.e. S1 (1)=[1,0]T,S2 (1)=[0,1]T
Step 2.3, for k ═ 1,2,3 …, from X0 (k)Starting from, following S in sequence1 (k)And S2 (k)Performing one-dimensional golden section search to obtain 2 minimum value points X1 (k)And X2 (k)Constructing a new search direction S3 (k)=X2 (k)-X0 (k)And searching along the direction by using golden section method to obtain minimum value point X0 (k+1)
Step 2.4, substituting the X value obtained in the step 2.3 into the following formula for judgment
Figure FDA0002686998720000022
If it is not
Figure FDA0002686998720000023
Then X0 (k+1)The optimal quenching and heating technological parameters of the fork head of the heavy-duty universal shaft are obtained if
Figure FDA0002686998720000024
Then k is equal to k +1, go back to step 2.3 to search again to obtain the X value, go to step 2.4 to make a decision until it is satisfied
Figure FDA0002686998720000025
4. The acquisition method according to claim 3, characterized in that:
the golden section method in step 2.3 of step two comprises the following specific steps:
step one, determining an initial search space [ Ta,Tb]Let Tα=Ta+0.382(Tb-Ta)、Tβ=Ta+0.618(Tb-Ta) (ii) a Firstly, step 1.1 and step 1.2 are used to respectively calculate the quenching heating temperature as TαHeating time t0 (k)Depth of austenitizing layer h and depth of through-hardening layer c, then the depth of austenitizing layer at this point is calculated by step 2.1
Figure FDA0002686998720000026
In the same way, can obtain
Figure FDA0002686998720000027
Step two, comparison
Figure FDA0002686998720000028
And
Figure FDA0002686998720000029
the size of (2):
if it is
Figure FDA00026869987200000210
Then Tb=Tβ,Tβ=Tα
Figure FDA00026869987200000211
Tα=Ta+0.382(Tb-Ta) (ii) a Firstly, step 1.1 and step 1.2 are used to respectively calculate the quenching heating temperature as TαThe heating time is
Figure FDA00026869987200000212
Depth of austenitizing layer h and depth of through-hardening layer c, then the depth of austenitizing layer at this point is calculated by step 2.1
Figure FDA00026869987200000213
Otherwise, then Ta=Tα,Tα=Tβ
Figure FDA00026869987200000214
Tβ=Ta+0.618(Tb-Ta) And calculating the quenching heating temperature as T by using the step 1 and the step 2 respectivelyβThe heating time is
Figure FDA00026869987200000215
Depth of austenitizing layer h and depth of through-hardening layer c at that time were calculated using step 3.1
Figure FDA0002686998720000031
Step three, if b-a <, then
Figure FDA0002686998720000032
If not, the step (c) is carried out again until b-a <, and the minimum value point is obtained.
And fourthly, repeating the first step, the second step and the third step to obtain the minimum value point of the t.
5. The acquisition method according to any one of claims 1 to 4, characterized in that: when the heavy-duty universal shaft fork head D is 1100mm and the material ZG34Cr2Ni2Mo is used, the optimized heating temperature T of quenching and heating heat treatment is 850 ℃, and the heating time T is 9 h.
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