Thermal grid model and heat transfer equation design method for multi-stage tandem rolling bearings

Abstract

The present invention discloses a design method for a thermal grid model and a heat transfer equation of a multi-stage tandem rolling bearing, which relates to the field of engineering heat transfer. The multi-stage rolling bearing includes 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 and inner and outer rings. The second-stage bearing is composed of a special bionic roller, a first-stage bearing outer ring, and a third-stage bearing inner ring. The second-stage bearing is also provided with a retaining frame, and the special bionic roller is movably embedded in the retaining frame. Based on this, the present invention proposes a design method for a thermal grid model and a heat transfer equation of a multi-stage tandem rolling bearing, which includes: dividing temperature nodes; setting parameter codes; analyzing the heat transfer path inside the bearing; constructing a thermal grid model of a multi-stage tandem rolling bearing; and establishing a heat transfer equation based on the thermal grid model. The method of the present invention is the first proposed method based on the structure of a new multi-stage tandem rolling bearing, and provides a theoretical and engineering practice basis for the design method of a thermal grid model and a heat transfer equation of a new multi-stage bearing.

Description

Technical Field

[0001] The present invention relates to the field of engineering heat transfer, and in particular 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 high-speed, high-temperature, and high-stress operating environments, a two-stage tandem bearing has been proposed. Compared to traditional single-stage bearings, this bearing offers a significant improvement in speed. From a kinematic perspective, the middle ring of the two-stage tandem bearing shares a certain amount of speed, and the rotating middle ring distributes the speed to the outer bearings, thus achieving speed distribution. This gives the two-stage tandem bearing the advantages of low rolling element motion speed and high bearing limit speed, making it suitable for high-speed applications.

[0003] Because the two-stage tandem bearing has an additional first-stage bearing and adapter ring compared to the traditional single-stage bearing, its mass increases, which in turn increases the rotational inertia, reduces the system response speed, and increases the machine load. The bearing requires more energy to overcome the friction and inertia caused by its own weight, which limits its application range.

[0004] With the advancement of technology, the requirements for various bearing performance aspects are becoming increasingly stringent. Due to the interdependent relationship between various bearing performance characteristics, two-stage bearings are currently suitable for high-speed applications. However, their increased mass leads to increased friction, which naturally increases operating temperature. Therefore, research on the thermal properties of bearings has become a top priority in promoting bearing development. As an advanced form of rolling bearing, the design of multi-stage rolling bearings involves more parameters and factors, requiring the comprehensive application of advanced design concepts and methods. However, domestic research in this area is not yet mature. Therefore, the thermal grid model and heat transfer calculation design of multi-stage bearings are important directions for promoting the development of rolling bearing design technology.

[0005] Therefore, a new thermal grid model and heat transfer calculation design method for multi-stage rolling bearings are proposed. Based on the new multi-stage bearing structure, its heat transfer mechanism is revealed, which is very necessary to provide a theoretical basis and technical support for the thermal research of new multi-stage bearings. Summary of the Invention

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

[0007] In order to achieve the above-mentioned purpose, the present invention specifically adopts the following technical solutions:

[0008] A design method for a thermal grid model and heat transfer equation of a multi-stage tandem rolling bearing, comprising:

[0009] S1. Divide a plurality of temperature nodes based on the bearing structure of a multi-stage tandem rolling bearing, wherein the multi-stage tandem rolling bearing is composed of an inner-layer primary bearing, a middle-layer secondary bearing, and an outer-layer tertiary bearing connected in series, wherein the primary and tertiary bearings are ball bearings, and the secondary bearing is a roller bearing. A retainer is further provided in the raceway of the secondary bearing, and each roller of the secondary bearing is movably embedded in the retainer. When the roller rotates, the retainer is driven to rotate synchronously in the raceway; the plurality of temperature nodes include the inner ring temperature, outer ring temperature, rolling element temperature, lubricant temperature, and retainer temperature of each bearing;

[0010] S2, set the heat flux generated by each temperature node and each friction point and the thermal resistance parameter code of the bearing;

[0011] S3, based on heat transfer theory, analyzes the internal heat transfer path of the bearing and divides the heat transfer path into two forms: heat conduction and heat convection. The heat transfer mode between the lubricant between the bearing rolling elements and the raceways and between the bearing rolling elements and the cage is heat convection. Heat conduction between the bearing rolling elements and the raceways is negligible, and heat is indirectly transferred by the lubricant. The heat transfer path is set as heat transfer from the friction heat generation temperature node to the lubricant around the friction heat generation temperature node, and then transferred to the bearing rolling elements, bearing inner and outer rings, and bearing cage;

[0012] S4, based on the set temperature nodes, the internal heat transfer path of the bearing, and the bearing structure, constructing a thermal grid model of the multi-stage tandem rolling bearing. The thermal grid model abstracts various parts of the bearing as thermal nodes, which are connected by thermal resistances to reflect the heat transfer relationship within the bearing;

[0013] S5. According to the thermal grid model, heat transfer equations are established in sequence from the inner ring of the first-stage bearing to the outer ring of the third-stage bearing of the multi-stage tandem rolling bearing using set parameter codes. The heat transfer equation is a mathematical expression of the law of conservation of energy in the heat transfer process, and is used to describe the heat transfer law inside the bearing.

[0014] Optionally, S1 includes: based on the axially symmetrical structure of the multi-stage series rolling bearing, establishing a two-dimensional coordinate system with the bearing symmetry center as the origin, dividing the bearing into four parts, and then taking the cross-section of any part of the four parts on the coordinate axis, dividing the temperature nodes from the inner ring to the outer ring on the cross-section, and establishing temperature nodes at the first-level bearing inner ring, the first-level bearing inner ring external lubricant, the first-level bearing ball, the first-level bearing outer ring internal lubricant, the first-level bearing outer ring, the second-level bearing inner ring external lubricant, the second-level bearing rolling element, the second-level bearing retainer, the second-level bearing retainer surface lubricant, the second-level bearing outer ring internal lubricant, the second-level bearing outer ring, the third-level bearing inner ring internal lubricant, the third-level bearing rolling element, the third-level bearing outer ring internal lubricant and the third-level bearing outer ring.

[0015] Optionally, the S2 includes:

[0016] set up The temperature of the inner ring of the first-stage bearing, the inner ring of the second-stage bearing and the inner ring of the third-stage bearing;

[0017] The temperature of the outer ring of the first-level bearing, the outer ring of the second-level bearing and the outer ring of the third-level bearing;

[0018] The temperatures of the first-stage bearing rolling elements, the second-stage bearing rolling elements and the third-stage bearing rolling elements;

[0019] is the cage temperature; is the temperature of the lubricant on the cage surface;

[0020] The lubricant on the outer surface of the first-stage bearing inner ring, the lubricant on the inner surface of the first-stage bearing outer ring, the lubricant on the outer surface of the second-stage bearing inner ring, the lubricant on the inner surface of the second-stage bearing outer ring, the lubricant on the outer surface of the third-stage bearing inner ring, and the temperature of the lubricant on the inner surface of the third-stage bearing outer ring;

[0021] The friction heat generated by the rolling elements of the first-level bearing and the inner ring of the first-level bearing, the friction heat generated by the rolling elements of the first-level bearing and the outer ring of the first-level bearing, the friction heat generated by the rolling elements of the second-level bearing and the inner ring of the second-level bearing, the friction heat generated by the rolling elements of the second-level bearing and the outer ring of the second-level bearing, the friction heat generated by the rolling elements of the second-level bearing and the rolling element cage of the second-level bearing, the friction heat generated by the rolling elements of the third-level bearing and the inner ring of the third-level bearing, and the friction heat generated by the rolling elements of the third-level bearing and the outer ring of the third-level bearing;

[0022] It is the radial thermal convection resistance of the outer surface of the inner ring of the first-level bearing, the radial thermal convection resistance of the outer surface of the rolling element of the first-level bearing, the radial thermal convection resistance of the inner surface of the outer ring of the first-level bearing, the radial thermal conduction resistance of the rolling element of the first-level bearing, the radial thermal convection resistance of the outer surface of the inner ring of the second-level bearing, the radial thermal convection resistance of the outer surface of the rolling element of the second-level bearing, the radial thermal conduction resistance of the rolling element of the second-level bearing, the axial thermal convection resistance of the rolling element end of the second-level bearing cage, the axial thermal convection resistance of the second-level bearing cage and its surface lubricant, the radial thermal convection resistance of the inner surface of the second-level bearing outer ring, the radial thermal convection resistance of the outer surface of the third-level bearing inner ring, the radial thermal convection resistance of the outer surface of the third-level bearing rolling element, the radial thermal conduction resistance of the third-level bearing rolling element, and the radial thermal convection resistance of the inner surface of the outer ring of the third-level bearing.

[0023] Optionally, the S5 includes:

[0024] For each temperature node, the heat input and output are equal, that is, Q input +Q ouput =0, where Q input represents the heat input to the temperature node, Q ouput Represents the heat transferred from the temperature node. Heat is transferred through thermal resistance. The heat is expressed by dividing the temperature by the thermal resistance, thus obtaining the heat transfer equation for each temperature node, where:

[0025] The heat transfer equation at the contact point between the primary bearing rolling element and the primary bearing inner ring is:

[0026] ;

[0027] Where, It is the total thermal resistance of the first-stage bearing rolling element surface lubricant and half of the first-stage bearing rolling element;

[0028] ;

[0029] The heat transfer equation at the rolling element of the primary bearing is:

[0030] ;

[0031] The heat transfer equation at the contact point between the primary bearing rolling element and the primary bearing outer ring is:

[0032] ;

[0033] The heat transfer equation of the outer ring of the first-stage bearing is:

[0034] ;

[0035] The heat transfer equation at the contact point between the secondary bearing rolling element and the secondary bearing inner ring is:

[0036] ;

[0037] Where, is the total thermal resistance of the secondary bearing rolling element surface lubricant and one-half of the secondary bearing rolling element;

[0038] ;

[0039] The heat transfer equation at the rolling element of the secondary bearing is:

[0040] ;

[0041] The heat transfer equation at the contact between the secondary bearing rolling element and the cage is:

[0042] ;

[0043] The heat transfer equation at the contact point between the secondary bearing rolling element and the secondary bearing outer ring is:

[0044] ;

[0045] The heat transfer equation of the secondary bearing outer ring is:

[0046] ;

[0047] 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:

[0048] ;

[0049] Where, is the total thermal resistance of the third-grade rolling element surface lubricant and one-half of the third-grade bearing rolling elements;

[0050] ;

[0051] The heat transfer equation at the rolling element of the third-stage bearing is:

[0052] ;

[0053] 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:

[0054] .

[0055] 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.

[0056] 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.

[0057] 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.

[0058] 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.

[0059] 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.

[0060] The beneficial effects of the present invention are as follows:

[0061] 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

[0062] In order to more clearly illustrate the structure and technical solutions implemented in the present invention, the following briefly introduces the drawings required for the present invention.

[0063] Figure 1 This is an overall schematic diagram of the multi-stage tandem rolling bearing in the present invention;

[0064] Figure 2 This is a front view of the multi-stage tandem rolling bearing of the present invention;

[0065] Figure 3 This is the overall schematic diagram of the first-level bearing;

[0066] Figure 4 This is the overall schematic diagram of the secondary bearing;

[0067] Figure 5 This is the overall schematic diagram of the special bionic roller of the secondary bearing;

[0068] Figure 6 This is the overall schematic diagram of the three-stage bearing;

[0069] Figure 7 This is the overall schematic diagram of the secondary bearing outer ring;

[0070] Figure 8 It is the overall schematic diagram of the secondary bearing cage;

[0071] Figure 9 Schematic diagram of a flow chart of a design method for a thermal grid model and heat transfer equation of a multi-stage tandem rolling bearing in the present invention;

[0072] Figure 10 Schematic diagram of the multi-stage tandem bearing thermal grid model of the present invention;

[0073] In the figure: 1. First-level bearing; 2. Second-level bearing; 3. Third-level bearing; 11. First-level ball; 12. First-level bearing inner ring; 13. First-level bearing outer ring; 21. Second-level bearing inner ring; 22. Second-level bearing outer ring; 23. Special bionic roller; 24. Cage; 31. Third-level bearing inner ring; 32. Third-level ball; 33. Third-level bearing outer ring; 231. Circular hole; 232. Fan-shaped arc hole; 241. First circular ring; 242. Second circular ring; 243. Beam; 311. Roller raceway of second-level bearing; 312. Ball raceway of third-level bearing. DETAILED DESCRIPTION

[0074] The following will provide a clear and complete description of the technical solutions in the embodiments of the present invention, in conjunction with the accompanying drawings. Obviously, the described embodiments are only a portion of the embodiments of the present invention, not all of them. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are intended to fall within the scope of protection of the present invention.

[0075] 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.

[0076] 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.

[0077] 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.

[0078] 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.

[0079] 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.

[0080] 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.

[0081] Reference Figure 7 , Figure 7This is an overall schematic diagram of the tertiary bearing inner ring 31 (also known as the secondary bearing outer ring 22) of the present invention. As shown in the figure, functional raceway grooves are machined on both sides of the tertiary bearing inner ring 31. The inner end face groove forms the roller raceway 311 of the secondary bearing, and its contour curve accurately matches the geometric shape of the special bionic roller 23, which is used to limit and support the rolling of the cylinder in the secondary bearing raceway; the outer end face groove forms the ball raceway 312 of the tertiary bearing, and its channel curvature radius is adapted to the diameter of the tertiary ball 32, which is used to guide and carry the rotational movement of the tertiary ball 32 in the tertiary bearing raceway.

[0082] In addition, a retainer 24 is provided in the raceway of the secondary bearing 2 to provide circumferential positioning and radial support for the special bionic roller 23. Figure 8 As shown, the structure of the retainer 24 comprises a coaxially arranged first ring 241 and a second ring 242; sixteen circumferentially equidistant connecting beams 243, each secured between the two rings to form a rigid frame. Each specialized bionic roller 23 is embedded within a rectangular window defined by two adjacent beams 243, the first ring 241, and the second ring 242. As the rollers roll, the contact transmission of the beams 243 drives the retainer 24 to rotate synchronously. This structure ensures equidistant distribution of the rolling elements, effectively preventing collisions and rolling friction losses.

[0083] Reference Figure 9 , Figure 9 FIG. 1 is a flow chart of a design method for a thermal grid model and heat transfer equation of a multi-stage tandem rolling bearing according to an embodiment of the present invention, which is applied to the multi-stage tandem rolling bearing. Figure 9 As shown, the method includes the following steps:

[0084] S1, divides several temperature nodes based on the bearing structure of multi-stage tandem rolling bearing;

[0085] The temperature nodes include the temperature of the inner ring, outer ring, rolling element, lubricant, and cage of each bearing. Since the multi-stage tandem rolling bearing is an axisymmetric structure, a two-dimensional coordinate system is established with the bearing's center of symmetry as the origin, dividing the bearing into four parts. A cross-section of any of the four parts on the coordinate axis is then taken, and temperature nodes are divided from the inner ring to the outer ring on that cross-section. Temperature nodes are established at the first-stage bearing inner ring, the first-stage bearing inner ring external lubricant, the first-stage bearing balls, the first-stage bearing outer ring internal lubricant, the first-stage bearing outer ring, the second-stage bearing inner ring external lubricant, the second-stage bearing rolling elements, the second-stage bearing cage, the second-stage bearing cage surface lubricant, the second-stage bearing outer ring internal lubricant, the second-stage bearing outer ring, the third-stage bearing inner ring internal lubricant, the third-stage bearing rolling elements, the third-stage bearing outer ring internal lubricant, and the third-stage bearing outer ring.

[0086] S2, set the heat flux generated by each temperature node and each friction point and the thermal resistance parameter code of the bearing;

[0087] Specifically, set The temperature of the inner ring of the first-stage bearing, the inner ring of the second-stage bearing and the inner ring of the third-stage bearing;

[0088] The temperature of the outer ring of the first-level bearing, the outer ring of the second-level bearing and the outer ring of the third-level bearing;

[0089] The temperature of the first-stage bearing rolling element, the second-stage bearing rolling element and the third-stage bearing rolling element;

[0090] is the cage temperature; is the temperature of the lubricant on the cage surface;

[0091] The lubricant on the outer surface of the first-stage bearing inner ring, the lubricant on the inner surface of the first-stage bearing outer ring, the lubricant on the outer surface of the second-stage bearing inner ring, the lubricant on the inner surface of the second-stage bearing outer ring, the lubricant on the outer surface of the third-stage bearing inner ring, and the temperature of the lubricant on the inner surface of the third-stage bearing outer ring;

[0092] The friction heat generated by the rolling elements of the first-level bearing and the inner ring of the first-level bearing, the friction heat generated by the rolling elements of the first-level bearing and the outer ring of the first-level bearing, the friction heat generated by the rolling elements of the second-level bearing and the inner ring of the second-level bearing, the friction heat generated by the rolling elements of the second-level bearing and the outer ring of the second-level bearing, the friction heat generated by the rolling elements of the second-level bearing and the rolling element cage of the second-level bearing, the friction heat generated by the rolling elements of the third-level bearing and the inner ring of the third-level bearing, and the friction heat generated by the rolling elements of the third-level bearing and the outer ring of the third-level bearing;

[0093] It is the radial thermal convection resistance of the outer surface of the inner ring of the first-level bearing, the radial thermal convection resistance of the outer surface of the rolling element of the first-level bearing, the radial thermal convection resistance of the inner surface of the outer ring of the first-level bearing, the radial thermal conduction resistance of the rolling element of the first-level bearing, the radial thermal convection resistance of the outer surface of the inner ring of the second-level bearing, the radial thermal convection resistance of the outer surface of the rolling element of the second-level bearing, the radial thermal conduction resistance of the rolling element of the second-level bearing, the axial thermal convection resistance of the rolling element end of the second-level bearing cage, the axial thermal convection resistance of the second-level bearing cage and its surface lubricant, the radial thermal convection resistance of the inner surface of the second-level bearing outer ring, the radial thermal convection resistance of the outer surface of the third-level bearing inner ring, the radial thermal convection resistance of the outer surface of the third-level bearing rolling element, the radial thermal conduction resistance of the third-level bearing rolling element, and the radial thermal convection resistance of the inner surface of the outer ring of the third-level bearing.

[0094] S3, based on heat transfer theory, analyze the heat transfer path inside the bearing;

[0095] Since the thermal characteristic parameters of the two parts in the contact area are the same, assuming that the heat generated at the contact point is evenly distributed between the two parts in contact, the actual heat transfer is three-dimensional. However, since the bearing is an axisymmetric rotating body, ignoring radial and moment loads, the friction heat of the inner and outer rings remains constant along the circumferential direction, and the heat transfer model of the sphere at any azimuth angle is similar. Therefore, a one-dimensional model can be used to approximately describe the heat transfer inside the bearing. In heat transfer, it is believed that as long as there is a temperature difference between one medium or 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 bearing rolling elements and the raceway and each part is mainly transferred by heat convection, and heat conduction between the bearing rolling elements and the raceway is negligible. Because the bearing's internal friction generates heat from continuous high-speed rotation, and the bearing's rolling elements and raceways are not in direct contact, separated by lubricant, and assuming the lubricant is evenly distributed on the surface of the bearing's rolling elements, the heat generated by friction between the bearing's rolling elements and raceways is indirectly transferred by the lubricant. Based on these assumptions, the approximate heat transfer path is: friction-generating temperature node → temperature node of the lubricant surrounding the friction-generating temperature node → temperature node of the bearing's rolling elements, inner and outer rings, and cage.

[0096] S4, constructing a thermal grid model of the multi-stage tandem rolling bearing based on the set temperature nodes, the internal heat transfer path of the bearing, and the bearing structure;

[0097] The thermal grid model abstracts the various parts of the bearing into thermal nodes, which are connected by thermal resistance to reflect the heat transfer relationship inside the bearing. Figure 10 , Figure 10 This is a schematic diagram of the thermal grid model of the multi-stage tandem rolling bearing of the present invention. Figure 10 The article describes the position and heat transfer relationship between each temperature node, transfer thermal resistance and heat source point. From the perspective of the overall heat generation of multi-stage bearings, it can be divided into 7 heat sources, namely the friction heat generated by the lubricant at the contact point between the first-stage bearing ball and the inner and outer raceways, the friction heat generated by the lubricant at the contact point between the second-stage bearing roller and the inner and outer raceways and cage, and the friction heat generated by the lubricant at the contact point between the third-stage bearing ball and the inner and outer raceways. Each heat source inputs heat into the radial or axial direction of each bearing structure.

[0098] S5, according to the thermal grid model, using set parameter codes, sequentially establish heat transfer equations from the inner ring of the first-stage bearing to the outer ring of the third-stage bearing of the multi-stage tandem rolling bearing to describe the heat transfer law inside the bearing.

[0099] When steady-state operation reaches thermal equilibrium, for each temperature node, the heat input and output of the temperature node are equal, that is, Q input+Q ouput =0, Q input , Q ouput They are the heat transferred into and out of the temperature node respectively, and the representation of heat can be analogous to the representation of current. Current can be expressed as voltage divided by resistance, and here heat can be expressed as temperature divided by thermal resistance. In this way, the heat transfer equation can be established according to the established thermal grid model.

[0100] The heat transfer equation is established as follows:

[0101] The heat transfer equation at the contact point between the primary bearing rolling element and the primary bearing inner ring is: ;

[0102] Where, It is the total thermal resistance of the first-stage bearing rolling element surface lubricant and half of the first-stage bearing rolling element; ;

[0103] The heat transfer equation at the rolling element of the primary bearing is: ;

[0104] The heat transfer equation at the contact point between the primary bearing rolling element and the primary bearing outer ring is: ;

[0105] The heat transfer equation of the outer ring of the first-stage bearing is: ;

[0106] The heat transfer equation at the contact point between the secondary bearing rolling element and the secondary bearing inner ring is: ;

[0107] Where, is the total thermal resistance of the secondary bearing rolling element surface lubricant and one-half of the secondary bearing rolling element; ;

[0108] The heat transfer equation at the rolling element of the secondary bearing is: ;

[0109] The heat transfer equation at the contact between the secondary bearing rolling element and the cage is: ;

[0110] The heat transfer equation at the contact point between the secondary bearing rolling element and the secondary bearing outer ring is: ;

[0111] The heat transfer equation of the secondary bearing outer ring is: ;

[0112] 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: ;

[0113] Where, is the total thermal resistance of the third-grade rolling element surface lubricant and one-half of the third-grade bearing rolling elements; ;

[0114] The heat transfer equation at the rolling element of the third-stage bearing is: ;

[0115] 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: .

[0116] The above heat transfer equation describes the heat transfer equation based on the above heat transfer assumptions and the theory that "the heat entering and leaving the temperature node is equal". The equation expresses the heat transfer law generated by the heat source in the medium in the radial direction or axial direction respectively. Its core essence is the mathematical expression of the law of conservation of energy in the heat transfer process.

[0117] The present invention provides a design method for a thermal grid model and heat transfer equation of a multi-stage tandem rolling bearing. First, the special structure of the bearing is analyzed. Second, a thermal grid model of the novel multi-stage tandem bearing is established based on the special structure and heat transfer theory. Finally, a corresponding heat transfer calculation equation is designed based on the established thermal grid model. This provides a clear path for future research on the thermal characteristics of multi-stage tandem bearings and provides research ideas for them.

[0118] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. The scope of patent protection of the present invention shall be based on the claims. Any equivalent structural changes made using the contents of the description and drawings of the present invention should also be included in the scope of protection of the present invention.

Claims

1. A design method for a thermal grid model and heat transfer equation of a multi-stage tandem rolling bearing, characterized in that: include: S1. Divide a plurality of temperature nodes based on the bearing structure of a multi-stage tandem rolling bearing, wherein the multi-stage tandem rolling bearing is composed of an inner-layer primary bearing, a middle-layer secondary bearing, and an outer-layer tertiary bearing connected in series, wherein the primary and tertiary bearings are ball bearings, and the secondary bearing is a roller bearing. A retainer is further provided in the raceway of the secondary bearing, and each roller of the secondary bearing is movably embedded in the retainer. When the roller rotates, the retainer is driven to rotate synchronously in the raceway; the plurality of temperature nodes include the inner ring temperature, outer ring temperature, rolling element temperature, lubricant temperature, and retainer temperature of each bearing; S2, set the heat flux generated by each temperature node and each friction point and the thermal resistance parameter code of the bearing; S3, based on heat transfer theory, analyzes the internal heat transfer path of the bearing and divides the heat transfer path into two forms: heat conduction and heat convection. The heat transfer mode between the lubricant between the bearing rolling elements and the raceways and between the bearing rolling elements and the cage is heat convection. Heat conduction between the bearing rolling elements and the raceways is negligible, and heat is indirectly transferred by the lubricant. The heat transfer path is set as heat transfer from the friction heat generation temperature node to the lubricant around the friction heat generation temperature node, and then transferred to the bearing rolling elements, bearing inner and outer rings, and bearing cage; S4, based on the set temperature nodes, the internal heat transfer path of the bearing, and the bearing structure, constructing a thermal grid model of the multi-stage tandem rolling bearing. The thermal grid model abstracts various parts of the bearing as thermal nodes, which are connected by thermal resistances to reflect the heat transfer relationship within the bearing; S5. According to the thermal grid model, heat transfer equations are established in sequence from the inner ring of the first-stage bearing to the outer ring of the third-stage bearing of the multi-stage tandem rolling bearing using set parameter codes. The heat transfer equation is a mathematical expression of the law of conservation of energy in the heat transfer process, and is used to describe the heat transfer law inside the bearing.

2. The method for designing a thermal grid model and heat transfer equation for a multi-stage tandem rolling bearing according to claim 1, characterized in that: Said S1 comprises: Based on the axisymmetric structure of the multi-stage tandem rolling bearing, a two-dimensional coordinate system is established with the bearing symmetry center as the origin, and the bearing is divided into four parts. Then, the cross-section of any part 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 the cross-section. Temperature nodes are established at the first-level bearing inner ring, the first-level bearing inner ring external lubricant, the first-level bearing ball, the first-level bearing outer ring internal lubricant, the first-level bearing outer ring, the second-level bearing inner ring external lubricant, the second-level bearing rolling element, the second-level bearing retainer, the second-level bearing retainer surface lubricant, the second-level bearing outer ring internal lubricant, the second-level bearing outer ring, the third-level bearing inner ring internal lubricant, the third-level bearing rolling element, the third-level bearing outer ring internal lubricant and the third-level bearing outer ring.

3. The method for designing a thermal grid model and heat transfer equation for a multi-stage tandem rolling bearing according to claim 1, characterized in that: The S2 includes: set up The temperature of the inner ring of the first-stage bearing, the inner ring of the second-stage bearing and the inner ring of the third-stage bearing; The temperature of the outer ring of the first-level bearing, the outer ring of the second-level bearing and the outer ring of the third-level bearing; The temperatures of the first-stage bearing rolling elements, the second-stage bearing rolling elements and the third-stage bearing rolling elements; is the cage temperature; is the temperature of the lubricant on the cage surface; The lubricant on the outer surface of the first-stage bearing inner ring, the lubricant on the inner surface of the first-stage bearing outer ring, the lubricant on the outer surface of the second-stage bearing inner ring, the lubricant on the inner surface of the second-stage bearing outer ring, the lubricant on the outer surface of the third-stage bearing inner ring, and the temperature of the lubricant on the inner surface of the third-stage bearing outer ring; The friction heat generated by the rolling elements of the first-level bearing and the inner ring of the first-level bearing, the friction heat generated by the rolling elements of the first-level bearing and the outer ring of the first-level bearing, the friction heat generated by the rolling elements of the second-level bearing and the inner ring of the second-level bearing, the friction heat generated by the rolling elements of the second-level bearing and the outer ring of the second-level bearing, the friction heat generated by the rolling elements of the second-level bearing and the rolling element cage of the second-level bearing, the friction heat generated by the rolling elements of the third-level bearing and the inner ring of the third-level bearing, and the friction heat generated by the rolling elements of the third-level bearing and the outer ring of the third-level bearing; It is the radial thermal convection resistance of the outer surface of the inner ring of the first-level bearing, the radial thermal convection resistance of the outer surface of the rolling element of the first-level bearing, the radial thermal convection resistance of the inner surface of the outer ring of the first-level bearing, the radial thermal conduction resistance of the rolling element of the first-level bearing, the radial thermal convection resistance of the outer surface of the inner ring of the second-level bearing, the radial thermal convection resistance of the outer surface of the rolling element of the second-level bearing, the radial thermal conduction resistance of the rolling element of the second-level bearing, the axial thermal convection resistance of the rolling element end of the second-level bearing cage, the axial thermal convection resistance of the second-level bearing cage and its surface lubricant, the radial thermal convection resistance of the inner surface of the second-level bearing outer ring, the radial thermal convection resistance of the outer surface of the third-level bearing inner ring, the radial thermal convection resistance of the outer surface of the third-level bearing rolling element, the radial thermal conduction resistance of the third-level bearing rolling element, and the radial thermal convection resistance of the inner surface of the outer ring of the third-level bearing.

4. The method for designing a thermal grid model and heat transfer equation for a multi-stage tandem rolling bearing according to claim 3, characterized in that: The S5 includes: For each temperature node, the heat input and output are equal, that is, Q input +Q ouput =0, where Q input represents the heat input to the temperature node, Q ouput Represents the heat transferred from the temperature node. Heat is transferred through thermal resistance. The heat is expressed by dividing the temperature by the thermal resistance, thus obtaining the heat transfer equation for each temperature node, where: The heat transfer equation at the contact point between the primary bearing rolling element and the primary bearing inner ring is: ； Where, It is the total thermal resistance of the first-stage bearing rolling element surface lubricant and half of the first-stage bearing rolling element; ； The heat transfer equation at the rolling element of the primary bearing is: ； The heat transfer equation at the contact point between the primary bearing rolling element and the primary bearing outer ring is: ； The heat transfer equation of the outer ring of the first-stage bearing is: ； The heat transfer equation at the contact point between the secondary bearing rolling element and the secondary bearing inner ring is: ； Where, is the total thermal resistance of the secondary bearing rolling element surface lubricant and half of the secondary bearing rolling element; ； The heat transfer equation at the rolling element of the secondary 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: ； Where, is the total thermal resistance of the third-grade rolling element surface lubricant and one-half of the third-grade 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 method for designing a thermal grid model and heat transfer equation for a multi-stage tandem 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 method for designing a thermal grid model and heat transfer equation for a multi-stage tandem 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 method for designing a thermal grid model and heat transfer equation for a multi-stage tandem 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 method for designing a thermal grid model and heat transfer equation for a multi-stage tandem 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 method for designing a thermal grid model and heat transfer equation for a multi-stage tandem 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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