Numerical simulation method for induction heating process of large-modulus rack
Technical Field
The invention belongs to the technical field of gear and rack heat treatment, and particularly relates to a numerical simulation method for an induction heating process of a large-modulus rack.
Background
The gear rack is one of the most common transmission mechanisms in various modern equipment, has the characteristics of high transmission efficiency, compact structure, long service life, reliable work and the like, and is widely applied to lifting systems of large-scale mechanical equipment such as mines, water conservancy and the like. For a long time, the three problems of short service life, low reliability and heavy structure become the development of the gear industry of China in the elbow, and the key for ensuring the performance is the heat treatment as one of the important processes for producing the gear rack. The national standardization regulatory commission of 6 months in 2020 promulgates the requirements for heat treatment of heavy-duty gears, wherein heavy-duty gears are defined as gears with high transmission power, high load bearing capacity, low speed and high impact load. For a heavy duty rack with a large modulus, good tooth surface wear resistance and hardness are necessary conditions for ensuring long-term operation in a severe environment, and sufficient depth of a hardened layer is ensured, because a large residual tensile stress exists in a hardening transition region, and if the hardened layer is too shallow, contact stress and residual tensile stress are superposed under a large load and an alternating load, which easily causes fatigue cracks in the hardening transition region, and further causes the hardened layer to be peeled off. Secondly, in order to improve the bending fatigue strength of the rack, the hardened layer of the rack is ensured to be continuously and uniformly distributed along the tooth profile.
At present, the induction quenching of the heavy-duty large-modulus rack mainly comprises two types of tooth-by-tooth quenching and tooth groove quenching. The tooth-by-tooth induction quenching process is simple, the wear resistance of a gear tooth contact surface can be effectively improved, but the method can only harden the tooth surface, a hardened layer does not exist in a tooth root area, the strength of the gear tooth is reduced due to the existence of a heat affected zone, and the tooth root of a rack is easy to break when the load is large. Although the tooth surface and the tooth root can be hardened by the quenching method along the tooth groove, a hardening layer is not arranged in the middle of the tooth top, and because the depth of the hardening layer required by the large-modulus heavy-duty rack is large, a great tensile stress can be formed in a transition region, and when the gear teeth bear alternating load, the rack is easy to generate internal cracks and even the gear teeth are broken integrally. Patent publication No. CN210117393U discloses a large module rack induction heating device, which proposes a heating method for moving rack-by-rack scanning, but does not consider that the magnetic field distribution inside the rack will change greatly due to the change of the geometric characteristics of the rack as the coil moves, and if the inductor and the rack keep the same moving speed all the time, the rack cannot obtain a temperature field uniformly distributed along the tooth profile after being heated. With the development of the computer industry, finite element analysis software is widely applied to engineering application, and the calculation result has good reliability under reasonable boundary conditions, so that the design cost can be greatly reduced, and the design time can be shortened. The induction heating process of the rack can also be solved by using finite element software, however, for the electromagnetic induction heating process containing the relative motion of the inductor and the rack, the numerical simulation not only comprises the coupling calculation of a magnetic field and a temperature field, but also considers the relative motion of the inductor and the rack, and no mathematical model and finite element software can accurately carry out the complete coupling of the electromagnetic-temperature-motion at present. Therefore, it is very urgent and necessary to find a numerical simulation method for the induction heating process of the large-modulus rack aiming at the large-modulus heavy-load rack and considering the magnetic field, the temperature field and the kinematic coupling calculation.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a numerical simulation method for the induction heating process of a large modulus rack. Establishing a material physical property parameter file library, establishing a rack three-dimensional model and a local coordinate system, activating a corresponding local coordinate system and establishing a geometric model of an inductor, determining load migration speed, determining load migration quantity and moving the inductor according to coil feeding speed and heating sub-cycle time, establishing an air model, dividing grids, respectively establishing an electromagnetic field and a temperature field solving environment, establishing a rack finite element simulation model, solving sub-cycle, judging whether the rack heating process is finished or not, if so, finishing the cycle, completing the whole simulation process, outputting a numerical simulation atlas of the large-modulus rack induction heating process, and otherwise, returning to reestablish the rack three-dimensional model and the local coordinate system. The invention solves the problem of electromagnetic-thermal-motion multi-field coupling in the rack scanning type induction heating process, and compared with static simulation, the result is more accurate and reliable, and the method has guiding significance for actual production.
The invention provides a numerical simulation method for an induction heating process of a large modulus rack, which comprises the following steps:
s1, establishing a material physical property parameter file library: collecting physical parameters of various materials for the rack, and establishing a material physical parameter file library;
s2, establishing a rack three-dimensional model and a local coordinate system: establishing a rack three-dimensional model, setting a plane where a tooth root is located to be coincident with an XOY plane under a global coordinate system, and establishing a local coordinate system by taking a load moving path as an x-axis and taking a load moving direction as an x-axis forward direction;
s3, activating a corresponding local coordinate system and establishing a geometric model of the sensor: the inductor is of a double-turn profiling coil structure, and according to the difference of the relative positions of the rack and the inductor, the specific establishment method of the geometric model of the inductor comprises the following steps:
if the heating part is a tooth root, a tooth top or an area from the tooth root to the tooth top, the right lower end point of the inductor is coincided with the origin of the local coordinate system; if the heating part is an area from the tooth top to the tooth root, the left lower end point of the inductor is superposed with the origin of the local coordinate system;
s4, determining load transfer speed: selecting a load migration speed according to whether the included angle between the positive direction of the x axis of the current activated coordinate system and the positive direction of the x axis of the global coordinate system is positive, negative or zero;
s5, determining load transfer volume and moving the inductor according to the coil feeding speed and the heating sub-cycle time;
s6, establishing an air model: in the process of electromagnetic induction heating of the rack, a magnetic field generated by the inductor is radiated into the surrounding air, and the distribution of the magnetic field generated by the inductor in the space is simulated by modeling the surrounding air of the rack;
s7, establishing a rack finite element simulation model: dividing a grid into a rack three-dimensional model, respectively establishing an electromagnetic field and a temperature field solving environment, and establishing a rack finite element simulation model;
s8, entering a rack finite element simulation model solving subcycle: reading the magnetic field physical environment to solve the magnetic field, reading the temperature field physical environment to solve the temperature field, judging whether the sub-cycle is finished, if so, executing the step S9; otherwise, returning to the step S7;
s9, judging whether the rack heating process is finished or not, if so, finishing the cycle, completing the whole simulation process, and outputting a numerical simulation map of the large-modulus rack induction heating process; otherwise, the procedure returns to step S2 to repeat the above steps.
Preferably, the step S4 specifically includes the following steps:
s41, judging whether the included angle between the positive direction of the x axis of the current activated coordinate system and the positive direction of the x axis of the global coordinate system is positive, negative or zero, and if the included angle is a region between a tooth root and a tooth top, executing a step S42; if the positive is negative, the heating surface of the inductor is the area between the tooth top and the tooth bottom, and step S43 is also executed; if the value is zero, the heating surface of the inductor is a tooth root or tooth top area, and the step S44 is executed;
s42, judging whether the load is located in the area above the pitch circle after moving, and if so, selecting the load transfer speed v-v2Otherwise, selecting the load transfer speed v ═ v1;
S43, judging whether the load is located in the area below the pitch circle after moving, and if so, selecting the load transfer speed v ═ v1Otherwise, selecting the load transfer speed v ═ v2;
S44, judging whether the vertical coordinate value of the original point of the currently activated local coordinate system is larger than zero, if so, taking the heating surface of the inductor as the tooth crest area, and selecting the load migration speed v as v3(ii) a Otherwise, the heating surface of the inductor is a tooth root area, and the load transfer speed v is selected to be v ═ v4。
Further, the step S8 specifically includes the following steps:
s81, reading a magnetic field physical environment, judging whether the heating is initial heating, if so, performing magnetic field solving by taking room temperature, namely 25 ℃ as a temperature load condition, otherwise, applying a temperature solving result in the last sub-step of the temperature solving cycle as the temperature load condition, and outputting the result by taking the heat generation rate as the result in the magnetic field solving;
s82, reading the physical environment of the temperature field, and applying and solving the load by using the output result of the magnetic field solution;
s83, judging whether the sub-loop is finished, if yes, finishing the sub-loop and executing the step S9; otherwise, the process returns to step S7 to perform the solution calculation again.
Further, the physical property parameters comprise rack material resistance, relative permeability, specific heat capacity, heat conduction coefficient, surface thermal convection coefficient, thermal radiation coefficient, induction coil material resistance, relative permeability, magnetizer material relative permeability and air relative permeability.
Further, the rack finite element simulation model solves the problem that the inductor in the sub-circulation carries out scanning type heating on the rack along the designated profiling path, and the distribution of the temperature field after the rack is heated is optimized by adjusting the relative movement speed of the inductor and the rack.
Further, according to the basic principle of electromagnetic induction heating, an electric field generated by alternating current in an inductor is called a source electric field, and when the rack is subjected to scanning type induction heating, the distribution change of the temperature field of the rack is influenced by the geometric characteristics of the rack and is unrelated to the source electric field; the inductor is used as a carrier of a source electric field, and the position change of the inductor does not influence the distribution form of the temperature field after the rack is heated.
Further, the method can be used for carrying out dynamic numerical simulation based on ANSYS software.
Compared with the prior art, the invention has the technical effects that:
1. the numerical simulation method for the induction heating process of the large-modulus rack, which is designed by the invention, considers the problem of inconsistent magnetic field distribution form caused by the change of the geometric characteristics of the rack when an inductor and the rack move relatively, further causes the uneven temperature field distribution of the rack in the tooth profile direction after induction heating, and adopts different-speed scanning to effectively improve the problem.
2. The numerical simulation method for the large-modulus rack induction heating process, which is designed by the invention, solves the problem of electromagnetic-thermal-motion multi-field coupling in the rack scanning type induction heating process, has more accurate and reliable results compared with static simulation, and has guiding significance for actual production.
Drawings
Other features, objects and advantages of the present application will become more apparent upon reading of the following detailed description of non-limiting embodiments thereof, made with reference to the accompanying drawings.
FIG. 1 is a flow chart of a numerical simulation method of a large modulus rack induction heating process of the present invention;
FIG. 2a is a graph of rack material resistivity as a function of temperature for an embodiment of the present invention;
FIG. 2b is a graph of relative permeability of rack material as a function of temperature for an embodiment of the present invention;
FIG. 2c is a graph of thermal conductivity versus temperature for a rack material according to an embodiment of the present invention;
FIG. 2d is a graph of specific heat capacity as a function of temperature for a rack material according to an embodiment of the present invention;
FIG. 3 is a schematic view of load shifting speed selection according to the present invention;
FIG. 4a is a schematic diagram of the geometric modeling of the inductor when the heating region is the tooth top region according to the present invention;
FIG. 4b is a schematic diagram of a geometric model of the inductor in the heating region between the tooth top and the tooth bottom according to the present invention;
FIG. 5 is a temperature cloud of the results of numerical simulations of embodiments of the present invention;
FIG. 6 is a schematic diagram of temperature extraction points according to an embodiment of the present invention;
FIG. 7 is a graph of node temperature variation according to an embodiment of the present invention.
Detailed Description
The present application will be described in further detail with reference to the following drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the relevant invention and not restrictive of the invention. It should be noted that, for convenience of description, only the portions related to the related invention are shown in the drawings.
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The present application will be described in detail below with reference to the embodiments with reference to the attached drawings.
Fig. 1 shows a numerical simulation method of a large module rack induction heating process of the present invention, which comprises the following steps:
s1, establishing a material physical property parameter file library: physical parameters of various materials for the rack are collected, a material physical parameter file library is established, and the physical parameters comprise rack material resistance, relative permeability, specific heat capacity, heat conduction coefficient, surface thermal convection coefficient, heat radiation coefficient, induction coil material resistance, relative permeability, magnetizer material relative permeability and air relative permeability.
S2, establishing a rack three-dimensional model and a local coordinate system: and establishing a rack three-dimensional model, setting a plane where tooth roots are located to be coincident with an XOY plane under a global coordinate system, and establishing a local coordinate system by taking a load moving path as an x-axis and a load moving direction as an x-axis forward direction.
S3, activating a corresponding local coordinate system and establishing a geometric model of the sensor: the inductor is of a double-turn profiling coil structure, and according to the difference of the relative positions of the rack and the inductor, the specific establishment method of the geometric model of the inductor comprises the following steps:
if the heating part is a tooth root, a tooth top or an area from the tooth root to the tooth top, the right lower end point of the inductor is coincided with the origin of the local coordinate system; if the heating part is the region from the tooth top to the tooth root, the left lower end point of the sensor coincides with the origin of the local coordinate system.
S4, determining load transfer speed: and selecting the load migration speed according to whether the included angle between the positive direction of the x axis of the current activated coordinate system and the positive direction of the x axis of the global coordinate system is positive, negative or zero.
S41, judging whether the included angle between the positive direction of the x axis of the current activated coordinate system and the positive direction of the x axis of the global coordinate system is positive, negative or zero, and if the included angle is a region between a tooth root and a tooth top, executing a step S42; if the positive is negative, the heating surface of the inductor is the area between the tooth top and the tooth bottom, and step S43 is also executed; if the value is zero, the heating surface of the inductor is a tooth root or tooth top area, and the step S44 is executed;
s42, judging whether the load is located in the area above the pitch circle after moving, and if so, selecting the load transfer speed v-v2Otherwise, selecting the load transfer speed v ═ v1;
S43, judging whether the load is in the area below the pitch circle after moving, if so, judging whether the load is in the area below the pitch circleThen choose the load migration velocity v ═ v1Otherwise, selecting the load transfer speed v ═ v2;
S44, judging whether the vertical coordinate value of the original point of the currently activated local coordinate system is larger than zero, if so, taking the heating surface of the inductor as the tooth crest area, and selecting the load migration speed v as v3(ii) a Otherwise, the heating surface of the inductor is a tooth root area, and the load transfer speed v is selected to be v ═ v4。
And S5, determining load transfer amount and moving the inductor according to the coil feeding speed and the heating sub-cycle time.
S6, establishing an air model: in the process of electromagnetic induction heating of the rack, a magnetic field generated by the inductor radiates into the ambient air, the distribution of the magnetic field generated by the inductor in the space is simulated by modeling the ambient air of the rack, and the volume of an air model is generally 3-5 times that of a rack-inductor system.
S7, establishing a rack finite element simulation model: and dividing a grid into the rack three-dimensional model, respectively establishing an electromagnetic field and a temperature field solving environment, and establishing a rack finite element simulation model.
S8, entering a rack finite element simulation model solving subcycle: reading the magnetic field physical environment to solve the magnetic field, reading the temperature field physical environment to solve the temperature field, judging whether the sub-cycle is finished, if so, executing the step S9; otherwise, the process returns to step S7.
And S81, reading the physical environment of the magnetic field, judging whether the heating is initial heating, if so, performing magnetic field solving by taking the room temperature, namely 25 ℃ as a temperature load condition, otherwise, applying a temperature solving result in the last sub-step of the temperature solving cycle as the temperature load condition, and outputting the result by taking the heat generation rate as the result in the magnetic field solving.
And S82, reading the temperature field physical environment, and applying and solving the load by using the magnetic field solving output result.
S83, judging whether the sub-loop is finished, if yes, finishing the sub-loop and executing the step S9; otherwise, the process returns to step S7 to perform the solution calculation again.
And solving the scanning heating of the rack by the inductor in the sub-circulation along the designated profiling path by the rack finite element simulation model, and optimizing the distribution of the temperature field after the rack is heated by adjusting the relative movement speed of the inductor and the rack.
S9, judging whether the rack heating process is finished or not, if so, finishing the cycle, completing the whole simulation process, and outputting a numerical simulation map of the large-modulus rack induction heating process; otherwise, the procedure returns to step S2 to repeat the above steps.
According to the basic principle of electromagnetic induction heating, alternating current passing through an inductor is the only external load for realizing rack heating, therefore, an electric field generated by the alternating current in the inductor is called a source electric field, and in the moving process of the inductor, as the structure of the inductor does not change and the electrical parameter passing through the inductor is a constant value, the source electric field can be regarded as a stable state in the whole heating process. Therefore, when the rack is subjected to scanning type induction heating, the distribution change of the rack temperature field is influenced by the geometric characteristics of the rack and is independent of the source electric field. Based on the above analysis, the inductor is used as a carrier of the source electric field, and the position change of the inductor does not affect the distribution form of the temperature field after the rack is heated, so that the dynamic simulation of the rack scanning type induction heating can be realized by a method of continuously transferring the load, which is the principle of a load transfer cycle solution. In addition, the method can perform dynamic numerical simulation based on ANSYS software.
The present invention will be described in further detail with reference to specific examples.
In the present embodiment, a rack with a modulus of 25mm is selected as a research object, and the structural dimensions are shown in table 1.
TABLE 1
The material used by the rack is 42CrMo, and the change curve of the resistivity, the relative permeability, the thermal conductivity and the specific heat capacity of the material along with the temperature is shown in the attached figure 2.
As shown in fig. 3, in this embodiment, a BC segment is taken as an example, XOY is taken as a global coordinate system, and a local coordinate system xo is activated in the BC segment1y, at this time, the included angle between the positive direction of the X axis of the activated coordinate system and the positive direction of the X axis of the global coordinate system is zero, the heated area is judged to be the tooth top area, and the ordinate of the origin of coordinates o is greater than zero, so that the tooth top load migration speed v is selected to be v ═ v3As shown in FIG. 4a, a geometric model of the inductor is established based on the heating position, the lower right endpoint of the inductor and the origin o of the local coordinate system1And (4) overlapping.
Activating local coordinate system xo while heating CD segments2y, at the moment, the included angle between the positive direction of the X axis of the activated coordinate system and the positive direction of the X axis of the global coordinate system is negative, the heating area is judged to be an area between the tooth crest and the tooth root, and the load transfer speed v ═ v is selected at the position above the pitch circle2When moving below the pitch circle, the load transfer speed becomes v ═ v1As shown in FIG. 4b, a geometric model of the inductor is created based on the heating position, the lower left endpoint of the inductor and the origin o of the local coordinate system2And (4) overlapping.
And moving the inductor according to the load transfer speed and the time sub-step length, taking DE section heating as an example, wherein the load moving speed v is 1mm/s, the time sub-step length is 0.1s, 2 times are calculated in each sub-cycle, and the length of each step of the inductor is 0.2mm until the DE section heating is finished.
Since the rack geometry is repetitive, the heating is completed and the process exits with ABCDE in fig. 3 as one heating cycle. Fig. 5 is a cloud chart of rack temperature field distribution during heating.
As shown in fig. 6, a temperature measurement point A, B, C, D is defined on the rack. Fig. 7 is a temperature change curve chart in the heating process of the temperature measuring points, and it can be seen from the graph that the temperature of each point after heating reaches more than 800 ℃, and the temperature uniformity of each point is good, so as to meet the requirement of rack heat treatment, and illustrate the theoretical correctness and the result reliability of the numerical simulation method provided by the invention.
According to the numerical simulation method for the induction heating process of the large-modulus rack, the problem of inconsistent magnetic field distribution form caused by the change of the geometric characteristics of the rack when an inductor and the rack move relatively is considered, the temperature field distribution of the rack in the tooth profile direction after induction heating is further caused to be uneven, and different speeds are adopted for scanning so as to effectively improve the problem; the electromagnetic-thermal-motion multi-field coupling problem in the rack scanning type induction heating process is solved, compared with static simulation, the result is more accurate and reliable, and the method has guiding significance for actual production.
Finally, it should be noted that: although the present invention has been described in detail with reference to the above embodiments, it should be understood by those skilled in the art that: modifications and equivalents may be made thereto without departing from the spirit and scope of the invention and it is intended to cover in the claims the invention as defined in the appended claims.