Design method of thermal grid model and thermal transfer equation of multistage series rolling bearing

Abstract

The invention discloses a design method of a thermal grid model and a thermal transfer equation of a multi-stage series rolling bearing, and relates to the field of engineering heat transfer science, the multi-stage rolling bearing comprises a first-stage bearing, a second-stage bearing and a third-stage bearing, the first-stage bearing and the third-stage bearing are composed of balls, an inner ring and an outer ring, the second-stage bearing is composed of a special bionic roller, a first-stage bearing outer ring and a third-stage bearing inner ring, a retainer is further arranged in the second-stage bearing, and the special bionic roller is movably embedded into the retainer. The invention provides a design method of a heat grid model and a heat transfer equation of a multistage series rolling bearing. The design method comprises the following steps: dividing temperature nodes; setting parameter codes; analyzing a heat transfer path in the bearing; constructing a multi-stage series rolling bearing thermal grid model; and establishing a heat transfer equation according to the heat grid model. The method is provided for the first time on the basis of a novel multi-stage series rolling bearing structure, and theoretical and engineering practice basis is provided for a novel multi-stage bearing heat grid model and a heat transfer equation design method.

Description

Technical Field

[0001] The present invention relates to the field of engineering heat transfer, and specifically relates to a design method for a thermal grid model and a heat transfer equation of a multi-stage series rolling bearing. Background Art

[0002] For working conditions with high rotational speed, high temperature, and high stress, a two-stage series bearing has been proposed. Compared with the traditional single-stage bearing, the two-stage series bearing has a certain improvement in rotational speed. From a kinematic perspective, the middle ring of the two-stage series bearing shares a certain rotational speed, and the rotating middle ring distributes the rotational speed to the outer bearing, thus achieving the distribution of rotational speed, making the two-stage series bearing have the advantages of low rolling element movement speed and high bearing limiting speed, and being applicable to high-speed occasions.

[0003] Since the two-stage series bearing has one more stage of bearing and an adapter ring compared with the traditional single-stage bearing, its mass increases, which in turn causes an increase in rotational inertia, a decrease in system response speed, an increase in machine load, and the bearing requires more energy to overcome the friction and inertial forces caused by its own weight, restricting its application range.

[0004] With the development of technology, the requirements for various performance aspects of bearings are getting higher and higher. Since the performances of bearings are interrelated, the current two-stage bearing is suitable for high-speed occasions, but due to the increase in its mass, the friction increases and the natural working temperature also rises. Therefore, the research on the thermal characteristics of bearings has become an urgent task to promote the development of bearings. As an advanced form of rolling bearings, multi-stage rolling bearings involve more parameters and factors in their design, and advanced design concepts and methods need to be comprehensively applied. However, the domestic research in this area is not yet mature. Therefore, the thermal grid model and heat transfer calculation design of multi-stage bearings are an important direction to promote the development of rolling bearing design technology.

[0005] Therefore, it is necessary to propose a design method for a thermal grid model and heat transfer calculation of a new type of multi-stage rolling bearing, based on the new type of multi-stage bearing structure, to reveal its heat transfer mechanism and provide a theoretical basis and technical support for the thermal research of the new type of multi-stage bearing. Summary of the Invention

[0006] The purpose of the present invention is to provide a design method for a thermal grid model and a heat transfer equation of a multi-stage series rolling bearing to promote the development of rolling bearing design technology. Based on the multi-stage series rolling bearing structure, the present invention reveals its heat transfer mechanism and provides an idea for the thermal grid model and heat transfer calculation design method of the multi-stage series bearing.

[0007] The present invention specifically adopts the following technical solutions to achieve the above purpose: A design method for a thermal grid model and a heat transfer equation of a multi-stage series rolling bearing, comprising: S1. Divide several temperature nodes based on the bearing structure of a multi - stage series rolling bearing. Among them, the multi - stage series rolling bearing is composed of a first - stage bearing in the inner layer, a second - stage bearing in the middle layer, and a third - stage bearing in the outer layer connected in series. The first - stage bearing and the third - stage bearing are ball bearings, the second - stage bearing is a roller bearing, and a cage is also arranged in the raceway of the second - stage bearing. Each roller of the second - stage bearing is movably embedded in the cage, and when the roller rotates, it drives the cage to rotate synchronously in the raceway. The several temperature nodes include the inner - ring temperature, outer - ring temperature, rolling - element temperature, lubricant temperature, and cage temperature of each stage of the bearing. S2. Set the heat - flow rate generated at each temperature node, each friction point, and the parameter codes of the internal thermal resistance of the bearing. S3. Based on the heat - transfer theory, analyze the internal heat - transfer path of the bearing. The heat - transfer path is divided into two forms: heat conduction and heat convection. Among them, the heat - transfer mode of the lubricant between the bearing rolling elements and the raceway and the lubricant between the bearing rolling elements and the cage is heat - convection transfer. The heat conduction between the bearing rolling elements and the raceway is negligible, and the heat is indirectly transferred by the lubricant. The heat - transfer path is set as the heat generated by friction at the friction - heat - generation temperature node is transferred to the lubricant around the friction - heat - generation temperature node, and then transferred to the bearing rolling elements, the inner and outer rings of the bearing, and the bearing cage. S4. Based on the set temperature nodes and the internal heat - transfer path of the bearing, combined with the bearing structure, construct a thermal grid model of the multi - stage series rolling bearing. The thermal grid model abstracts each part of the bearing into thermal nodes and is connected by thermal resistances to reflect the internal heat - transfer relationship of the bearing. S5. According to the thermal grid model, use the set parameter codes to establish heat - transfer equations in sequence from the inner ring of the first - stage bearing to the outer ring of the third - stage bearing of the multi - stage series rolling bearing. The heat - transfer equation is the mathematical expression of the law of conservation of energy in the heat - transfer process and is used to describe the internal heat - transfer law of the bearing.

[0008] Optionally, S1 includes: Based on the axisymmetric structure of the multi - stage series rolling bearing, establish a two - dimensional coordinate system with the center of symmetry of the bearing as the origin, divide the bearing into four parts, and then take the cross - section of any one of the four parts on the coordinate axis. Divide the temperature nodes from the inner ring to the outer ring on this cross - section, and set temperature nodes at the inner ring of the first - stage bearing, the lubricant outside the inner ring of the first - stage bearing, the balls of the first - stage bearing, the lubricant inside the outer ring of the first - stage bearing, the outer ring of the first - stage bearing, the lubricant outside the inner ring of the second - stage bearing, the rolling elements of the second - stage bearing, the cage of the second - stage bearing, the lubricant on the surface of the cage of the second - stage bearing, the lubricant inside the outer ring of the second - stage bearing, the outer ring of the second - stage bearing, the lubricant inside the inner ring of the third - stage bearing, the rolling elements of the third - stage bearing, the lubricant inside the outer ring of the third - stage bearing, and the outer ring of the third - stage bearing.

[0009] Optionally, S2 includes: Set are the temperatures of the inner rings of the first-level bearings, the inner rings of the second-level bearings, and the inner rings of the third-level bearings; are the temperatures of the outer rings of the first-level bearings, the outer rings of the second-level bearings, and the outer rings of the third-level bearings; are the temperatures of the rolling elements of the first-level bearings, the rolling elements of the second-level bearings, and the rolling elements of the third-level bearings; is the temperature of the cage; is the temperature of the lubricant on the surface of the cage; are the temperatures of the lubricants on the outer surfaces of the inner rings of the first-level bearings, the lubricants on the inner surfaces of the outer rings of the first-level bearings, the lubricants on the outer surfaces of the inner rings of the second-level bearings, the lubricants on the inner surfaces of the outer rings of the second-level bearings, the lubricants on the outer surfaces of the inner rings of the third-level bearings, and the lubricants on the inner surfaces of the outer rings of the third-level bearings; are the heat generated by friction between the rolling elements of the first-level bearings and the inner rings of the first-level bearings, the heat generated by friction between the rolling elements of the first-level bearings and the outer rings of the first-level bearings, the heat generated by friction between the rolling elements of the second-level bearings and the inner rings of the second-level bearings, the heat generated by friction between the rolling elements of the second-level bearings and the outer rings of the second-level bearings, the heat generated by friction between the rolling elements of the second-level bearings and the cage of the second-level bearings, the heat generated by friction between the rolling elements of the third-level bearings and the inner rings of the third-level bearings, and the heat generated by friction between the rolling elements of the third-level bearings and the outer rings of the third-level bearings; are the radial heat convection thermal resistances on the outer surfaces of the inner rings of the first-level bearings, the radial heat convection thermal resistances on the outer surfaces of the rolling elements of the first-level bearings, the radial heat convection thermal resistances on the inner surfaces of the outer rings of the first-level bearings, the radial heat conduction thermal resistances of the rolling elements of the first-level bearings, the radial heat convection thermal resistances on the outer surfaces of the inner rings of the second-level bearings, the radial heat convection thermal resistances on the outer surfaces of the rolling elements of the second-level bearings, the radial heat conduction thermal resistances of the rolling elements of the second-level bearings, the axial heat convection thermal resistances at the ends of the rolling elements of the cage of the second-level bearings, the axial heat convection thermal resistances between the cage of the second-level bearings and the lubricant on its surface, the radial heat convection thermal resistances on the inner surfaces of the outer rings of the second-level bearings, the radial heat convection thermal resistances on the outer surfaces of the inner rings of the third-level bearings, the radial heat convection thermal resistances on the outer surfaces of the rolling elements of the third-level bearings, the radial heat conduction thermal resistances of the rolling elements of the third-level bearings, and the radial heat convection thermal resistances on the inner surfaces of the outer rings of the third-level bearings.

[0010] Optionally, the S5 includes: For each temperature node, the heat input and output are equal, i.e., Q input , ouput , input , ouput , , , ,

[0010] +Q ouput = 0, where Q input represents the heat input to the temperature node, Q ouput represents the heat output from the temperature node. The heat is transferred through the thermal resistance, and the heat is represented by dividing the temperature by the thermal resistance, thereby obtaining the heat transfer equation for each temperature node, where the heat transfer equation at the contact between the rolling element of the first-level bearing and the inner ring of the first-level bearing is: ; In the formula, is the total thermal resistance of the lubricant on the surface of the rolling elements of the first-stage bearing and half of the rolling elements of the first-stage bearing; ; The heat transfer equation at the rolling elements of the first-stage bearing is: ; The heat transfer equation at the contact between the rolling elements of the first-stage bearing and the outer ring of the first-stage bearing is: ; The heat transfer equation of the outer ring of the first-stage bearing is: ; The heat transfer equation at the contact between the rolling elements of the second-stage bearing and the inner ring of the second-stage bearing is: ; In the formula, is the total thermal resistance of the lubricant on the surface of the rolling elements of the second-stage bearing and half of the rolling elements of the second-stage bearing; ; The heat transfer equation at the rolling elements of the second-stage bearing is: ; The heat transfer equation at the contact between the rolling elements of the second-stage bearing and the cage is: ; The heat transfer equation at the contact between the rolling elements of the second-stage bearing and the outer ring of the second-stage bearing is: ; The heat transfer equation of the outer ring of the second-stage bearing is: ; The heat transfer equation at the contact between the rolling elements of the third-stage bearing and the inner ring of the third-stage bearing is: ; In the formula, is the total thermal resistance of the lubricant on the surface of the rolling elements of the third stage and half of the rolling elements of the third-stage bearing; ; The heat transfer equation at the rolling elements of the third-stage bearing is: ; The heat transfer equation at the contact between the rolling elements of the third-stage bearing and the outer ring of the third-stage bearing is: .

[0011] Optionally, the first-level bearing is a deep groove ball bearing, including a first-level bearing inner ring, a first-level bearing outer ring, and first-level balls, wherein the first-level balls roll in a raceway formed by the first-level bearing inner ring and the first-level bearing outer ring, and there are 10 first-level balls in total.

[0012] Optionally, the secondary bearing includes a primary bearing outer ring, a tertiary bearing inner ring, a special bionic roller and a retaining frame; wherein, the special bionic roller is designed to imitate the morphology of skeletal muscle, is cylindrical, and a circular hole is provided in the center of the cylinder, and with the central circular hole as the center of the circle, four fan-shaped arc holes are distributed equidistantly in a circular pattern on the cylinder wall.

[0013] Optionally, the three-stage bearing includes a three-stage bearing inner ring, a three-stage bearing outer ring and three-stage balls, and the number of the three-stage balls is 29 in total.

[0014] Optionally, the retaining frame consists of a first ring body, a second ring body and sixteen beam bodies equidistantly distributed circumferentially; wherein the beam body is connected between the first ring body and the second ring body; each of the special bionic rollers is embedded in the space enclosed by two adjacent beam bodies, the first ring body and the second ring body.

[0015] Optionally, both side end faces of the inner ring of the third-stage bearing are provided with raceway grooves; wherein, the end face grooves facing inward constitute the roller raceway of the second-stage bearing, and the end face grooves facing outward constitute the ball raceway of the third-stage bearing.

[0016] The beneficial effects of the present invention are as follows: The present invention provides a design method for a thermal grid model and a heat transfer equation of a multi-stage tandem rolling bearing. Compared with a two-stage bearing, the multi-stage tandem rolling bearing has an additional layer of special bearing inside, i.e., a three-layer rolling bearing. The multi-stage tandem rolling bearing has no adapter ring structure. The new layer of special bearing replaces the adapter ring structure in the two-stage tandem bearing. Due to its special structure, it obtains better speed transmission and load-bearing capacity on the basis of the performance of the two-stage tandem bearing. However, the thermal characteristics of the bearing are also one of the key performances of the bearing. The study of the thermal performance of the new multi-stage tandem bearing is an important part of the study of the performance of the multi-stage tandem bearing. Therefore, the present invention designs a thermal model and heat transfer calculation for the bearing, and proposes a thermal grid model and heat transfer calculation method for the multi-stage tandem rolling bearing. First, the special structure of the bearing is analyzed, and then a thermal grid model of the multi-stage tandem bearing is established based on its special structure and heat transfer theory. Finally, a corresponding heat transfer calculation equation is designed based on the established thermal grid model, thereby providing theoretical support for the thermal grid model and heat transfer calculation of the multi-stage rolling bearing, so that future research on the thermal characteristics of the multi-stage tandem bearing can be traced, which is helpful to optimize the design parameters and performance indicators of the bearing. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the structure and technical solution of the present invention, the drawings required for the present invention will be briefly introduced below.

[0018] Figure 1 It is the overall schematic diagram of the multi-stage series rolling bearing in the present invention; Figure 2 It is the front view of the multi-stage series rolling bearing in the present invention; Figure 3 It is the overall schematic diagram of the first-stage bearing; Figure 4 It is the overall schematic diagram of the second-stage bearing; Figure 5 It is the overall schematic diagram of the special bionic drum of the second-stage bearing; Figure 6 It is the overall schematic diagram of the third-stage bearing; Figure 7 It is the overall schematic diagram of the outer ring of the second-stage bearing; Figure 8 It is the overall schematic diagram of the cage of the second-stage bearing; Figure 9 It is the flow schematic diagram of the design method of the thermal grid model and heat transfer equation of a multi-stage series rolling bearing in the present invention; Figure 10 It is the schematic diagram of the thermal grid model of the multi-stage series bearing in the present invention; In the figure: 1. First-stage bearing; 2. Second-stage bearing; 3. Third-stage bearing; 11. First-stage balls; 12. Inner ring of the first-stage bearing; 13. Outer ring of the first-stage bearing; 21. Inner ring of the second-stage bearing; 22. Outer ring of the second-stage bearing; 23. Special bionic drum; 24. Cage; 31. Inner ring of the third-stage bearing; 32. Third-stage balls; 33. Outer ring of the third-stage bearing; 231. Circular hole; 232. Sector arc hole; 241. First ring; 242. Second ring; 243. Beam body; 311. Drum raceway of the second-stage bearing; 312. Ball raceway of the third-stage bearing. Detailed implementation manners

[0019] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0020] An embodiment of the present invention provides a design method for a thermal grid model and a heat transfer equation of a multi-stage tandem rolling bearing. Its innovation lies in that, compared with the traditional thermal grid model and heat transfer equation design method of a two-stage tandem bearing, this thermal grid model and heat transfer equation design method is based on the multi-stage tandem rolling bearing structure, which provides certain theoretical guidance for the thermal research of multi-stage tandem bearings.

[0021] Specifically, refer to Figures 1 to 2 The multi-stage tandem rolling bearing is mainly composed of an inner first-stage bearing 1, a middle second-stage bearing 2 and an outer third-stage bearing 3 connected in series. The first-level bearing 1 is the innermost bearing in the entire bearing system and is designed as a ball bearing. The first-level bearing is connected to the rotating shaft when in use. Figure 3 The primary bearing 1 includes a primary ball 11, a primary bearing inner ring 12, and a primary bearing outer ring 13. The primary ball 11 rolls in the raceways of the primary bearing inner ring 12 and the primary bearing outer ring 13 to achieve rolling of the bearing.

[0022] The secondary bearing 2 is the middle layer bearing in the entire bearing system, that is, between the primary bearing 1 and the tertiary bearing 3. Figure 4 , designed as a roller bearing (drum bearing), including a secondary bearing inner ring 21, a secondary bearing outer ring 22 and a special bionic roller 23. Figure 5 The special bionic roller is designed based on the microscopic morphology of skeletal muscle and is cylindrical in shape. Four fan-shaped arc holes 232 are distributed in a circular shape around the central circular hole 231 at equal distances.

[0023] The third-level bearing 3 is the outermost bearing in the entire bearing system. It is usually installed on the bearing seat when in use. It is a ball bearing like the first-level bearing. Figure 6 The three-stage bearing 3 includes a three-stage bearing inner ring 31, three-stage balls 32 and a three-stage bearing outer ring 33.

[0024] The first-stage bearing outer ring 13 and the third-stage bearing inner ring 31 together constitute the inner ring and outer ring of the second-stage bearing, that is, the first-stage bearing outer ring 13 is shared by the second-stage bearing inner ring 21, and the third-stage bearing inner ring 31 is shared by the second-stage bearing outer ring 22.

[0025] Reference Figure 7 , Figure 7This is an overall schematic diagram of the inner ring 31 of the three-stage bearing of the present invention (i.e., the outer ring 22 of the two-stage bearing). As shown in the figure, functional raceway grooves are machined on both sides of the inner ring 31 of the three-stage bearing. The inner end face groove forms the drum raceway 311 of the two-stage bearing, and its contour curve is precisely matched with the geometric shape of the special bionic drum 23, which is used to limit and support the rolling of the cylinder in the two-stage bearing raceway. The outer end face groove forms the ball raceway 312 of the three-stage bearing, and the groove curvature radius thereof is adapted to the diameter of the three-stage balls 32, which is used to guide and carry the rotational movement of the three-stage balls 32 in the three-stage bearing raceway.

[0026] In addition, a cage 24 is provided in the raceway of the two-stage bearing 2, which is used for circumferential positioning and radial support of the special bionic drum 23. As Figure 8 shown, the structure of the cage 24 includes: a first ring 241 and a second ring 242 arranged coaxially; sixteen connecting beam bodies 243 evenly distributed circumferentially. The two ends of the beam bodies 243 are respectively fixed between the two rings to form a rigid frame structure. Each special bionic drum 23 is installed in the rectangular pane space defined by two adjacent beam bodies 243, the first ring 241, and the second ring 242. When the cylinder rolls, the cage 24 is driven to rotate synchronously through the contact transmission of the beam bodies 243. This structure can ensure the equidistant distribution of the rolling elements and effectively inhibit the collision between the rolling elements and the rolling friction loss of the rolling elements.

[0027] Referring to Figure 9 , Figure 9 This is a schematic flow diagram of the design method of the thermal grid model and heat transfer equation of a multi-stage series rolling bearing in an embodiment of the present invention, which is applied to the above multi-stage series rolling bearing. As Figure 9 shown, the method includes the following steps: S1, dividing a number of temperature nodes based on the bearing structure of the multi-stage series rolling bearing; The number of temperature nodes includes the inner ring temperature, outer ring temperature, rolling element temperature, lubricant temperature, and cage temperature of each stage of the bearing. Since the multi-stage series rolling bearing is an axisymmetric structure, a two-dimensional coordinate system is established with the bearing symmetry center as the origin, and the bearing is divided into four parts. Then, any cross-section of the four parts on the coordinate axis is taken, and the temperature nodes are divided from the inner ring to the outer ring on this cross-section. Temperature nodes are respectively set at the inner ring of the first-stage bearing, the lubricant outside the inner ring of the first-stage bearing, the balls of the first-stage bearing, the lubricant inside the outer ring of the first-stage bearing, the outer ring of the first-stage bearing, the lubricant outside the inner ring of the second-stage bearing, the rolling elements of the second-stage bearing, the cage of the second-stage bearing, the lubricant on the surface of the cage of the second-stage bearing, the lubricant inside the outer ring of the second-stage bearing, the outer ring of the second-stage bearing, the lubricant inside the inner ring of the third-stage bearing, the rolling elements of the third-stage bearing, the lubricant inside the outer ring of the third-stage bearing, and the outer ring of the third-stage bearing.

[0028] S2. Set the heat flow generated at each temperature node and each friction point, and the parameter codes of the internal thermal resistance of the bearing; Specifically, set as the temperatures of the inner rings of the first-level, second-level, and third-level bearings; as the temperatures of the outer rings of the first-level, second-level, and third-level bearings; as the temperatures of the rolling elements of the first-level, second-level, and third-level bearings; as the temperature of the cage; as the temperature of the lubricant on the surface of the cage; as the temperatures of the lubricants on the outer surfaces of the inner rings of the first-level bearing, the inner surfaces of the outer rings of the first-level bearing, the outer surfaces of the inner rings of the second-level bearing, the inner surfaces of the outer rings of the second-level bearing, the outer surfaces of the inner rings of the third-level bearing, and the inner surfaces of the outer rings of the third-level bearing; as the heat generated by the friction between the rolling elements and the inner ring of the first-level bearing, the heat generated by the friction between the rolling elements and the outer ring of the first-level bearing, the heat generated by the friction between the rolling elements and the inner ring of the second-level bearing, the heat generated by the friction between the rolling elements and the outer ring of the second-level bearing, the heat generated by the friction between the rolling elements and the cage of the second-level bearing, the heat generated by the friction between the rolling elements and the inner ring of the third-level bearing, and the heat generated by the friction between the rolling elements and the outer ring of the third-level bearing; as the radial heat convection resistances on the outer surfaces of the inner rings of the first-level bearing, the radial heat convection resistances on the outer surfaces of the rolling elements of the first-level bearing, the radial heat convection resistances on the inner surfaces of the outer rings of the first-level bearing, the radial heat conduction resistances of the rolling elements of the first-level bearing, the radial heat convection resistances on the outer surfaces of the inner rings of the second-level bearing, the radial heat convection resistances on the outer surfaces of the rolling elements of the second-level bearing, the radial heat conduction resistances of the rolling elements of the second-level bearing, the axial heat convection resistances at the rolling element ends of the cage of the second-level bearing, the axial heat convection resistances between the cage of the second-level bearing and the lubricant on its surface, the radial heat convection resistances on the inner surfaces of the outer rings of the second-level bearing, the radial heat convection resistances on the outer surfaces of the inner rings of the third-level bearing, the radial heat convection resistances on the outer surfaces of the rolling elements of the third-level bearing, the radial heat conduction resistances of the rolling elements of the third-level bearing, and the radial heat convection resistances on the inner surfaces of the outer rings of the third-level bearing.

[0029] S3. Analyze the internal heat transfer path of the bearing based on the theory of heat transfer; Since the thermal property parameters of the two parts of the contact area are the same, it is assumed that the heat generated at the contact is evenly distributed to the two parts in contact with each other. The actual heat transfer is three-dimensional, but due to the bearing being an axisymmetric rotating body, ignoring the radial and torque loads, the frictional heat of the inner and outer rings is invariant circumferentially, and the heat transfer models of the balls at any azimuth angle are similar. Therefore, the heat transfer situation inside the bearing can be approximately described by a one-dimensional model. In heat transfer, it is considered that as long as there is a temperature difference in one medium or between two media, heat transfer will inevitably occur. According to different heat transfer modes, the heat transfer process can be divided into three basic forms: heat conduction, heat convection, and heat radiation. However, for the multi-stage series rolling bearing of the present invention, heat radiation is temporarily ignored, and the main heat transfer paths are heat conduction and heat convection. It is also assumed that the lubricant between the rolling elements and raceways of the bearing mainly transfers heat by convection to each part, and the heat conduction between the rolling elements and raceways of the bearing is ignored. Since heat is continuously generated by high-speed rotation and friction inside the bearing, and the rolling elements and raceways of the bearing are not in direct contact but are separated by lubricant, assuming that the lubricant is evenly distributed on the surface of the rolling elements of the bearing, the heat generated by friction between the rolling elements and raceways of the bearing is indirectly transferred by the lubricant. Based on the above assumptions, the general heat transfer path is: the temperature node of heat generation by friction → the temperature node of the lubricant around the temperature node of heat generation by friction → the temperature nodes of the rolling elements, inner and outer rings, and cage of the bearing.

[0030] S4. Based on the set temperature nodes and the heat transfer path inside the bearing, combined with the bearing structure, construct the thermal grid model of the multi-stage series rolling bearing; The thermal grid model abstracts each part of the bearing into thermal nodes, which are connected by thermal resistances and are used to reflect the heat transfer relationship inside the bearing. As Figure 10 , Figure 10 is a schematic diagram of the thermal grid model of the multi-stage series rolling bearing of the present invention, Figure 10 which describes the positions and heat transfer relationships between each temperature node, transfer thermal resistance, and heat source point. From the overall heat generation situation of the multi-stage bearing, it can be divided into 7 heat sources, namely, the frictional heat generation of the lubricant at the contact points between the balls and the inner and outer raceways of the first-stage bearing, the frictional heat generation of the lubricant at the contact points between the rollers and the inner and outer raceways and the cage of the second-stage bearing, and the frictional heat generation of the lubricant at the contact points between the balls and the inner and outer raceways of the third-stage bearing. Each heat source inputs heat to the bearing structures in the radial or axial directions respectively.

[0031] S5. According to the thermal grid model, establish heat transfer equations in sequence from the inner ring of the first-stage bearing to the outer ring of the third-stage bearing of the multi-stage series rolling bearing using the set parameter codes to describe the heat transfer law inside the bearing.

[0032] When the steady-state operation reaches thermal equilibrium, for each temperature node, the heat entering and leaving the temperature node is equal, that is, Q input +Q ouput=0, Q input , Q ouput are the heat of the incoming and outgoing temperature nodes respectively, and the representation of heat can be analogous to the representation of current. Current can be expressed as voltage divided by resistance. Here, heat can be expressed as temperature divided by thermal resistance. Based on this, a heat transfer equation can be established according to the established heat grid model.

[0033] The established heat transfer equation is as follows: The heat transfer equation at the contact between the rolling element of the first-stage bearing and the inner ring of the first-stage bearing is: ; In the formula, is the total thermal resistance of the lubricant on the surface of the rolling element of the first-stage bearing and half of the rolling element of the first-stage bearing; ; The heat transfer equation at the rolling element of the first-stage bearing is: ; The heat transfer equation at the contact between the rolling element of the first-stage bearing and the outer ring of the first-stage bearing is: ; The heat transfer equation of the outer ring of the first-stage bearing is: ; The heat transfer equation at the contact between the rolling element of the second-stage bearing and the inner ring of the second-stage bearing is: ; In the formula, is the total thermal resistance of the lubricant on the surface of the rolling element of the second-stage bearing and half of the rolling element of the second-stage bearing; ; The heat transfer equation at the rolling element of the second-stage bearing is: ; The heat transfer equation at the contact between the rolling element of the second-stage bearing and the cage is: ; The heat transfer equation at the contact between the rolling element of the second-stage bearing and the outer ring of the second-stage bearing is: ; The heat transfer equation of the outer ring of the second-stage bearing is: ; The heat transfer equation at the contact between the rolling element of the third-stage bearing and the inner ring of the third-stage bearing is: ; In the formula, is the total thermal resistance of the lubricant on the surface of the third-stage rolling element and half of the rolling element of the third-stage bearing; ; The heat transfer equation at the rolling element of the third-stage bearing is: ; The heat transfer equation at the contact between the rolling element of the third-stage bearing and the outer ring of the third-stage bearing is: .

[0034] The above heat transfer equation describes the heat transfer equation based on the above heat transfer assumptions and theoretical supports such as "the heat entering and leaving the temperature nodes is equal". The equation represents the heat transfer law of the heat generated by the heat source in the medium in the radial direction or the axial direction respectively. Its core essence is the mathematical expression of the law of conservation of energy in the heat transfer process.

[0035] The present invention provides a design method for a thermal grid model and a heat transfer equation of a multi-stage series rolling bearing. First, analyze its special bearing structure. Secondly, establish a thermal grid model for the new multi-stage series bearing according to its special structure and heat transfer theory. Finally, design a corresponding heat transfer calculation equation based on the established thermal grid model, so that the future research on the thermal characteristics of the multi-stage series bearing can be traced and provide research ideas for it.

[0036] The above is only a preferred embodiment of the present invention and is not intended to limit the present invention. The patent protection scope of the present invention is subject to the claims. Any equivalent structural changes made by using the description and drawings of the present invention should be included in the protection scope of the present invention by the same token.

Claims

1. A design method for the thermal grid model and heat transfer equation of a multi-stage series rolling bearing, characterized in that, Including: S1, dividing several temperature nodes based on the bearing structure of a multi-stage series rolling bearing. Among them, the multi-stage series rolling bearing is composed of a first-stage bearing in the inner layer, a second-stage bearing in the middle layer, and a third-stage bearing in the outer layer connected in series. The first-stage bearing and the third-stage bearing are ball bearings, the second-stage bearing is a roller bearing, and a cage is also arranged in the raceway of the second-stage bearing. Each roller of the second-stage bearing is movably embedded in the cage, and when the roller rotates, it drives the cage to rotate synchronously in the raceway. The several temperature nodes include the inner ring temperature, outer ring temperature, rolling element temperature, lubricant temperature, and cage temperature of each stage of the bearing; S2, setting the heat flux generated at each temperature node and each friction point and the parameter codes of the internal thermal resistance of the bearing; S3, based on the heat transfer theory, analyzing the internal heat transfer path of the bearing, and dividing the heat transfer path into two forms: heat conduction and heat convection. Among them, the heat transfer mode of the lubricant between the bearing rolling element and the raceway and the lubricant between the bearing rolling element and the cage is heat convection transfer. The heat conduction between the bearing rolling element and the raceway is negligible, and the heat is indirectly transferred by the lubricant. The heat transfer path is set as the heat generated by friction at the temperature node is transferred to the lubricant around the friction-generated heat temperature node, and then transferred to the bearing rolling element, the inner and outer rings of the bearing, and the bearing cage; S4, based on the set temperature nodes and the internal heat transfer path of the bearing, combined with the bearing structure, constructing a thermal grid model of the multi-stage series rolling bearing. The thermal grid model abstracts each part of the bearing into thermal nodes and is connected by thermal resistance to reflect the internal heat transfer relationship of the bearing; S5, according to the thermal grid model, establishing heat transfer equations in sequence from the inner ring of the first-stage bearing to the outer ring of the third-stage bearing of the multi-stage series rolling bearing using the set parameter codes. The heat transfer equation is the mathematical expression of the law of conservation of energy in the heat transfer process and is used to describe the internal heat transfer law of the bearing.

2. The design method of the thermal grid model and heat transfer equation of the multi-stage series rolling bearing according to claim 1, characterized in that, The said S1 includes: Based on the axisymmetric structure of the multi-stage series rolling bearing, a two-dimensional coordinate system is established with the center of symmetry of the bearing as the origin, the bearing is divided into four parts, and then the cross-section of any one of the four parts on the coordinate axis is taken, and the temperature nodes are divided from the inner ring to the outer ring on this cross-section. Temperature nodes are set at the inner ring of the first-stage bearing, the lubricant outside the inner ring of the first-stage bearing, the balls of the first-stage bearing, the lubricant inside the outer ring of the first-stage bearing, the outer ring of the first-stage bearing, the lubricant outside the inner ring of the second-stage bearing, the rolling elements of the second-stage bearing, the cage of the second-stage bearing, the lubricant on the surface of the cage of the second-stage bearing, the lubricant inside the outer ring of the second-stage bearing, the outer ring of the second-stage bearing, the lubricant inside the inner ring of the third-stage bearing, the rolling elements of the third-stage bearing, the lubricant inside the outer ring of the third-stage bearing, and the outer ring of the third-stage bearing.

3. The design method of the thermal grid model and heat transfer equation of the multi-stage series rolling bearing according to claim 1, characterized in that, The said S2 includes: Settings are the temperatures of the inner rings of the first-level bearing, the second-level bearing, and the third-level bearing; are the temperatures of the outer rings of the first-level bearings, the second-level bearings, and the third-level bearings; are the temperatures of the rolling elements of the first-stage bearing, the second-stage bearing, and the third-stage bearing; is the cage temperature; is the temperature of the lubricant on the cage surface; are the temperatures of the lubricants on the outer surface of the inner ring of the first-stage bearing, the lubricants on the inner surface of the outer ring of the first-stage bearing, the lubricants on the outer surface of the inner ring of the second-stage bearing, the lubricants on the inner surface of the outer ring of the second-stage bearing, the lubricants on the outer surface of the inner ring of the third-stage bearing, and the lubricants on the inner surface of the outer ring of the third-stage bearing; The heat generated by friction between the rolling elements and the inner ring of the first-level bearing, the heat generated by friction between the rolling elements and the outer ring of the first-level bearing, the heat generated by friction between the rolling elements and the inner ring of the second-level bearing, the heat generated by friction between the rolling elements and the outer ring of the second-level bearing, the heat generated by friction between the rolling elements and the rolling element cage of the second-level bearing, the heat generated by friction between the rolling elements and the inner ring of the third-level bearing, and the heat generated by friction between the rolling elements and the outer ring of the third-level bearing; The radial thermal convection thermal resistance of the outer surface of the inner ring of the first-stage bearing, the radial thermal convection thermal resistance of the outer surface of the rolling elements of the first-stage bearing, the radial thermal convection thermal resistance of the inner surface of the outer ring of the first-stage bearing, the radial heat conduction thermal resistance of the rolling elements of the first-stage bearing, the radial thermal convection thermal resistance of the outer surface of the inner ring of the second-stage bearing, the radial thermal convection thermal resistance of the outer surface of the rolling elements of the second-stage bearing, the radial heat conduction thermal resistance of the rolling elements of the second-stage bearing, the axial thermal convection thermal resistance at the rolling element end of the cage of the second-stage bearing, the axial thermal convection thermal resistance between the cage of the second-stage bearing and the lubricant on its surface, the radial thermal convection thermal resistance of the inner surface of the outer ring of the second-stage bearing, the radial thermal convection thermal resistance of the outer surface of the inner ring of the third-stage bearing, the radial thermal convection thermal resistance of the outer surface of the rolling elements of the third-stage bearing, the radial heat conduction thermal resistance of the rolling elements of the third-stage bearing, the radial thermal convection thermal resistance of the inner surface of the outer ring of the third-stage bearing.

4. The design method of the thermal grid model and heat transfer equation of the multi-stage series rolling bearing according to claim 3, characterized in that, The said S5 includes: For each temperature node, the heat input and output are equal, i.e., Q input +Q ouput = 0, where Q input represents the heat input to the temperature node, and Q ouput represents the heat output from the temperature node. The heat is transferred through the thermal resistance, and the heat is expressed by dividing the temperature by the thermal resistance, so as to obtain the heat transfer equation of each temperature node. Among them, The heat transfer equation at the contact between the rolling element of the first-stage bearing and the inner ring of the first-stage bearing is: ； In the formula, is the total thermal resistance of the lubricant on the surface of the rolling elements of the first-stage bearing and half of the rolling elements of the first-stage bearing; ； The heat transfer equation at the rolling element of the first-stage bearing is: ； The heat transfer equation at the contact between the rolling element of the first-stage bearing and the outer ring of the first-stage bearing is: ； The heat transfer equation of the outer ring of the first-stage bearing is: ； The heat transfer equation at the contact between the rolling element of the second-stage bearing and the inner ring of the second-stage bearing is: ； In the formula, is the total thermal resistance of the lubricant on the surface of the rolling elements of the secondary bearing and half of the rolling elements of the secondary bearing; ； The heat transfer equation at the rolling element of the second-stage bearing is: ； The heat transfer equation at the contact between the secondary bearing rolling element and the cage is: ； The heat transfer equation at the contact point between the secondary bearing rolling element and the secondary bearing outer ring is: ； The heat transfer equation of the secondary bearing outer ring is: ； The heat transfer equation at the contact between the rolling element of the third-stage bearing and the inner ring of the third-stage bearing is: ； Wherein, is the total thermal resistance of the lubricant on the surface of the third-stage rolling elements and half of the third-stage bearing rolling elements; ； The heat transfer equation at the rolling element of the third-stage bearing is: ； The heat transfer equation at the contact between the rolling element of the third-stage bearing and the outer ring of the third-stage bearing is: 。 5. The design method of the thermal grid model and heat transfer equation of the multi-stage series rolling bearing according to claim 1, characterized in that, The first-level bearing is a deep groove ball bearing, which includes a first-level bearing inner ring, a first-level bearing outer ring, and first-level balls. The first-level balls roll in a raceway formed by the first-level bearing inner ring and the first-level bearing outer ring, and there are 10 first-level balls in total.

6. The design method of the thermal grid model and heat transfer equation of the multi-stage series rolling bearing according to claim 5, characterized in that, The secondary bearing includes a primary bearing outer ring, a tertiary bearing inner ring, a special bionic roller and a retaining frame; wherein, the special bionic roller is designed based on the morphology of skeletal muscle, is cylindrical, has a circular hole in the center of the cylinder, and with the central circular hole as the center of the circle, four fan-shaped arc holes are distributed equidistantly in a circular pattern on the cylinder wall.

7. The design method of the thermal grid model and heat transfer equation of the multi-stage series rolling bearing according to claim 6, characterized in that The three-stage bearing includes a three-stage bearing inner ring, a three-stage bearing outer ring and three-stage balls, and the number of the three-stage balls is 29 in total.

8. The design method of the thermal grid model and heat transfer equation of the multi-stage series rolling bearing according to claim 7, characterized in that The retaining frame consists of a first ring body, a second ring body and sixteen beam bodies distributed equidistantly in the circumference; wherein the beam body is connected between the first ring body and the second ring body; each of the special bionic rollers is embedded in the space enclosed by two adjacent beam bodies, the first ring body and the second ring body.

9. The design method of the thermal grid model and heat transfer equation of the multi-stage series rolling bearing according to claim 8, characterized in that, Both side end faces of the inner ring of the three-stage bearing are provided with raceway grooves; wherein, the end face grooves facing inward constitute the roller raceway of the second-stage bearing, and the end face grooves facing outward constitute the ball raceway of the three-stage bearing.

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