CN113392525B - Load distribution calculation method for angular contact ball bearing - Google Patents
Load distribution calculation method for angular contact ball bearing Download PDFInfo
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Abstract
The invention discloses a load distribution calculation method of an angular contact ball bearing, which comprises the following steps: obtaining a load solving method and a contact deformation solving method of rolling bodies in the angular contact ball bearing; along the radial load acting line direction borne by the bearing, the rolling bodies are grouped into team_1 to team_N; setting a value of N, and calculating deformation of the team_n to the team_N in a trial mode; and checking whether the contact deformation quantity of the team_n to the team_N has a negative value, if so, adjusting the value of N, and then re-executing the trial calculation step, otherwise, solving the load distribution solving method of the team_n to the team_N to obtain the load distribution of the angular contact ball bearing. The technical effect of the method provided by the disclosure is that the calculation result can ensure the mathematical convergence requirement and the physical rationality requirement. Here, physical rationality means that the contact deformation between the rolling elements and the raceways of the angular ball bearing calculated by this method is only compressive deformation, and no tensile deformation occurs.
Description
Technical Field
The disclosure belongs to the field of bearing load calculation, and particularly relates to an angular contact ball bearing load distribution calculation method.
Background
Angular contact ball bearings are a type of support member widely used in the field of rotary machines. The main components of the bearing comprise: an inner race, an outer race, rolling elements, a cage, etc. The bearing realizes the connection between a static part and a moving part of a rotary mechanical system or the connection between different moving parts by utilizing the movement of rolling bodies along an inner raceway and an outer raceway. For angular contact ball bearings, the contact between the rolling elements and the inner and outer raceways belongs to point contact.
The load distribution solving purpose of the angular contact ball bearing is as follows: under certain working conditions, the displacement of the bearing, the contact deformation and the contact load between the rolling bodies and the inner raceway and the outer raceway respectively are obtained through calculation. Regarding the problem of load distribution of angular contact ball bearings, there have been studies conducted by researchers historically, and several methods have been proposed. These methods fall into two main categories: experimental formula based methods and mathematical methods based on iterative calculations.
The experimental formula method based on the test is only suitable for calculating the load distribution problem with simple working conditions, and more importantly, the experimental formula method has lower calculation accuracy, can only be used for rough estimation, and can not meet engineering requirements in many times. The mathematical method based on iterative computation is presented after the empirical formula. Compared with an empirical formula method, the method has greatly improved calculation accuracy, but because the method does not fully consider the physical background of the load distribution problem of the angular contact ball bearing, the solved result has the condition of no physical meaning, the initial value of iterative calculation needs to be repeatedly adjusted until a reasonable result is obtained, the trial calculation process is sometimes longer, the real load distribution result is difficult to obtain under individual conditions, and the engineering requirement cannot be met in the aspect of calculation efficiency.
Disclosure of Invention
In order to solve at least one of the above technical problems, an object of the present disclosure is to provide a method for calculating load distribution of an angular contact ball bearing, which not only can obtain a mathematical solution of a mechanical problem, but also can further obtain a final object understanding through judging the obtained mathematical solution.
In order to achieve the purpose of the disclosure, the technical scheme adopted by the disclosure is as follows:
a load distribution calculation method of an angular contact ball bearing comprises the following steps:
establishing a load distribution model of the angular contact ball bearing, and forming a load solving method and a contact deformation solving method of rolling bodies in the angular contact ball bearing;
arranging all rolling bodies along the direction of a radial load acting line borne by the bearing to form a rolling body group, wherein the rolling body group comprises team_1 to team_N;
And (3) trial calculation: setting a value of N, wherein N is more than or equal to 1 and less than or equal to N, and calculating contact deformation of the team_n to the team_N according to a contact deformation solving method when the team_n to the team_N are in a contact state and the rest rolling body groups are in a non-contact state;
And checking whether the contact deformation quantity of the team_n to the team_N has a negative value, if so, adjusting the value of N, and then, recalculating, otherwise, solving the load distribution solving method of the team_n to the team_N to obtain the load distribution of the angular contact ball bearing.
Optionally, the load solving method of the rolling body is to analyze load distribution before and after deformation of the angular contact ball bearing to form a nonlinear algebraic equation set of the load distribution, wherein the value obtained by solving the nonlinear algebraic equation set of the load distribution is the load distribution of the rolling body;
The method for solving the contact deformation of the rolling element is to analyze load distribution before and after deformation of the angular contact ball bearing to form a contact deformation algebraic equation set, and the value obtained by solving the contact deformation algebraic equation set is the contact deformation of the rolling element.
Alternatively, the system of nonlinear algebraic equations of the load distribution employs the following system of equations:
Qij-Qoj＝0
Wherein, F a represents the axial force born by the bearing, F r represents the radial force born by the bearing, M represents the external torque born by the bearing, z represents the number of rolling elements in the bearing, Q ij represents the contact force between the jth rolling element and the inner raceway, Q oj represents the contact force between the jth rolling element and the outer raceway, delta ij represents the contact deformation between the jth rolling element and the inner raceway, delta oj represents the contact deformation between the jth rolling element and the outer raceway, and the coefficient H j is used for identifying the contact state of the jth rolling element;
if the j-th rolling element is in a contact state, H j is equal to 1;
If the j-th rolling element is in a non-contact state, H j is equal to 0.
Optionally, the algebraic system of contact deformation comprises a nonlinear algebraic system of equations of the load distribution, further comprising the following system of equations:
Δj＝δij+δoj
Wherein Delta j represents the total contact deformation of the jth rolling element, delta a represents the axial displacement of the bearing inner ring, delta r represents the radial displacement of the bearing inner ring, alpha j represents the contact angle of the jth rolling element, The j-th rolling element position angle is represented by θ, the deflection angular displacement of the bearing is represented by θ, and the pitch circle radius of the bearing is represented by R.
Optionally, the contact angle α j of the jth rolling element is solved in conjunction with the following system of equations:
S1j＝rij+roj-Dj
Wherein S 1j represents the distance between the center of curvature of the outer raceway groove and the center of curvature of the inner raceway groove before deformation, S 2j represents the distance between the center of curvature of the outer raceway groove and the center of curvature of the inner raceway groove after deformation, D j represents the diameter of the jth rolling element, r ij represents the radius of curvature of the inner raceway groove at the jth rolling element, r oj represents the radius of curvature of the outer raceway groove at the jth rolling element, and α represents the nominal contact angle of the bearing.
Alternatively, when the number of rolling elements is an odd number, the rolling element group team_1 or team_n includes 1 rolling element, and each of the remaining rolling element groups includes a pair of two rolling elements symmetrical along a radial load acting line to which the bearing is subjected.
Alternatively, when the number of rolling elements is even, each of the rolling element groups team_1 and team_n includes 1 rolling element, and each of the remaining rolling element groups includes a pair of two rolling elements symmetrical along a radial load acting line to which the bearing is subjected.
Alternatively, after each calculation of any one of the deformation results in the rolling element group, it is checked whether the contact deformation obtained by trial is a negative value.
Alternatively, the amounts of deformation of the rolling element groups team_n to team_n are tried from N equal to 1, and when the contact deformation obtained by the trial is a negative value, n+1 is then tried again.
In the method, a load distribution model of the angular contact ball bearing is established through mechanical analysis, a load solving method and a contact deformation solving method for solving the rolling bodies are formed, the load distribution of the angular contact ball bearing under a given working condition is calculated, then the rolling bodies are grouped along the direction of a radial load acting line borne by the bearing, the stress conditions of the same group of rolling bodies are the same, and the stress conditions of different groups of rolling bodies are different; for rolling elements, only compression deformation at the time of contact or no deformation at the time of no contact is possible; setting a value of N, and calculating deformation of the team_n to the team_N according to a contact deformation solving method when the team_n to the team_N are in a contact state and the rest rolling body groups are in a non-contact state; at most, N cases need to be calculated, solutions of all contact cases can be calculated in trial, but negative numbers can appear when the contact deformation is calculated, the conclusion is impossible in physical situations, only mathematical solutions are adopted, the contact cases of the negative number solutions are eliminated, and when the results of all Team calculation do not have the negative number solutions, the solutions are the same as the actual situations. The solution of the load distribution solving method in the current state is the load distribution of the angular contact ball bearing.
The method has the advantages that the technical effect of the method provided by the disclosure is reflected in that the calculation result can ensure the mathematical convergence requirement and the physical rationality requirement. Here, physical rationality means that the contact deformation between the rolling elements and the raceways of the angular ball bearing calculated by this method is only compressive deformation, and no tensile deformation occurs.
Drawings
The accompanying drawings, which are included to provide a further understanding of the disclosure and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the disclosure and together with the description serve to explain the principles of the disclosure.
FIG. 1 is a flow chart of a method of the angular contact ball bearing of the present disclosure;
FIG. 2 is a force-bearing front-rear deformation cooperative graph of the angular contact ball bearing of the present disclosure;
FIG. 3 is a grouping schematic diagram of a grouping of rolling elements when the rolling elements are even in number in the present disclosure;
fig. 4 is a grouping schematic diagram of a grouping of rolling elements when the rolling elements are odd in the present disclosure.
Detailed Description
The present disclosure is described in further detail below with reference to the drawings and the embodiments. It is to be understood that the specific embodiments described herein are merely illustrative of the relevant content and not limiting of the present disclosure. It should be further noted that, for convenience of description, only a portion relevant to the present disclosure is shown in the drawings.
In addition, embodiments of the present disclosure and features of the embodiments may be combined with each other without conflict. The present disclosure will be described in detail below with reference to the accompanying drawings in conjunction with embodiments.
Example 1
Referring to fig. 1, a method for calculating load distribution of an angular contact ball bearing includes:
establishing a load distribution model of the angular contact ball bearing, namely carrying out stress analysis before and after deformation on the angular contact ball bearing to form a load solving method and a contact deformation solving method for solving rolling bodies in the angular contact ball bearing;
The load distribution solving method is used for calculating load distribution in the angular contact ball bearing; the load solving method of the rolling body specifically comprises the steps of analyzing load distribution before and after deformation of the angular contact ball bearing to form a nonlinear algebraic equation set of the load distribution, wherein the value obtained by the nonlinear algebraic equation set is the load distribution of the rolling body in the angular contact ball bearing;
The contact deformation solving method is used for calculating the deformation of each rolling body in the angular contact ball bearing; the method for solving the contact deformation of the rolling body specifically comprises the steps of analyzing load distribution before and after deformation of the angular contact ball bearing to form a contact deformation algebraic equation set, and solving the contact deformation algebraic equation set to obtain a value which is the deformation of the rolling body;
referring to fig. 3 and 4, all rolling elements are arranged along the radial load acting line direction borne by the bearing to form a rolling element group, wherein the rolling element group comprises team_1 to team_n; the method comprises the steps of dividing a pair of rolling bodies with symmetrical radial load acting line positions into two groups, wherein the rolling bodies with different stress and deformation amounts are divided into one group by the same group, and the stress and deformation amounts of each group can be independently analyzed; when the angular contact ball bearing is stressed, part of the rolling bodies can be free from pressure, and can be defined as a non-contact state, and when the rolling bodies are stressed, the rolling bodies can be defined as a contact state.
When the angular contact ball bearing is stressed, various conditions can occur; for example, it may be that no rolling bodies are in a non-contact state, i.e., team_1 to team_n are all in a contact state; as another example, it may be that the rolling elements in team_1 are in a non-contact state, and team_2 to team_n are in a contact state; for another example, it may be that the rolling elements in team_1 to team_2 are in a non-contact state, and team_3 to team_n are in a contact state; by so doing analysis; a total of n+1 cases can be analyzed, the rolling elements in the Team in the non-contact state are not stressed, the load distribution is 0, calculation is not needed, and the load distribution and the contact deformation are calculated for the rolling elements in the Team in the contact state through the load distribution solving method and the contact deformation solving method; however, negative numbers may appear as a result of calculation, but in practice, rolling elements are not deformed in tension, and negative solution is not a true solution for an angular ball bearing, when the contact deformation amounts in all teams of a certain contact state are positive solutions after excluding this case, such contact state, load distribution, and contact deformation amounts are true solutions for angular ball bearings.
Therefore, when solving, a trial calculation step is performed, the trial calculation step being: setting a value of N, wherein N is more than or equal to 1and less than or equal to N, and calculating contact deformation of the team_n to the team_N according to a contact deformation solving method when the team_n to the team_N are in a contact state and the rest rolling body groups are in a non-contact state;
And checking whether the contact deformation of all the team_n to the team_N has a negative value in the current state, if so, adjusting the value of N, and then carrying out a trial calculation step again, otherwise, solving the load distribution solving method of the team_n to the team_N to obtain the load distribution of the angular contact ball bearing, wherein the load distribution of other rolling bodies is 0. Preferably, each time a result of any one of the deformation amounts in the rolling element group is calculated, it is checked whether or not the contact deformation amount obtained by trial calculation is a negative value. The calculation of the results of grouping the rolling elements into the Team is not needed, whether the contact deformation is negative is detected after each calculation of the contact deformation of the Team, and if the contact deformation is negative, the calculation is carried out from the new calculation after the value of n is newly set, so that the calculation amount can be greatly reduced.
The method for setting the n value can be as follows:
The amounts of deformation of the rolling element groups team_n to team_n are tried from N equal to 1, and when the contact deformation obtained by the trial is a negative value, n+1 is then tried again.
Example two
In the present embodiment, the load solving method and the contact deformation solving method for solving the rolling elements are calculated by a nonlinear algebraic equation set and a contact deformation algebraic equation set of the load distribution.
In order to calculate the load distribution of the angular contact ball bearing, a load distribution model of the angular contact ball bearing needs to be established first to quantitatively describe the behavior of the angular contact ball bearing under the action of load. Referring to fig. 2, the change of the relative geometric positions of the bearing assembly, i.e. the inner ring, the rolling bodies and the outer ring of the angular contact ball bearing before and after loading is shown, and it should be noted that fig. 2 shows the relative geometric position relationship between the jth rolling body and the inner ring and the outer ring contacted with the jth rolling body obtained by cutting the bearing through a radial plane passing through the axis of the bearing. Wherein O-xyz is a fixed coordinate system, and the Oz axis is along the axial direction of the bearing. O bj,Oej and O ij represent the center of sphere, the center of curvature of the outer raceway groove, and the center of curvature of the inner raceway groove, respectively, of the jth rolling element. To analyze the change in the relative geometric positions of the components, it is assumed here that the outer race of the bearing is stationary, and thus the position of the outer raceway groove center of curvature O ej is unchanged, and the positions of the ball center O bj of the rolling element and the inner raceway groove center of curvature O ij change after the bearing is stressed, their new positions being shown by O 'bj and O' ij, respectively. In addition, δ a and δ r represent the axial displacement and the radial displacement of the bearing inner ring, that is, the axial displacement and the radial displacement of the bearing, respectively.
The deformation coordination of the inner ring, the rolling elements and the outer ring of the bearing can be obtained with reference to fig. 2. First, when the bearing is not loaded, the distance between the outer raceway groove center of curvature and the inner raceway groove center of curvature can be expressed as:
Where r ij and r oj denote the inner raceway groove radius of curvature and the outer raceway groove radius of curvature, respectively, at the jth rolling element, and D j denotes the diameter of the jth rolling element. After the bearing is loaded, the inner raceway groove center of curvature moves from point O ij to point O' ij, at which point the distance between the outer raceway groove center of curvature and the inner raceway groove center of curvature becomes:
Where θ represents the deflection angular displacement of the bearing, R represents the pitch radius of the bearing, or the distance from the center of the bearing to the center of the rolling element, phi j represents the position angle of the jth rolling element, and α represents the nominal contact angle of the bearing. After the bearing is loaded, the contact angles of all the rolling bodies change, and the contact angle of the jth rolling body is denoted by a j after the change is assumed to be
When the bearing is in a mechanical balance state, the contact force between the rolling bodies and the inner and outer raceways is equal, namely
Qij-Qoj＝0 (4)
Wherein, Q ij and Q oj are the contact forces between the jth rolling element and the inner and outer raceways, respectively, and according to the Hertz contact theory, they can be expressed as:
wherein, K ij and K oj are respectively the contact stiffness coefficients between the jth rolling element and the inner and outer raceways. Delta ij and delta oj represent contact deformations between the jth rolling element and the inner and outer raceways, respectively. Considering the external force and the external moment acting on the bearing, the balance equation of the bearing inner ring is:
where F a and F r represent the axial and radial forces, respectively, experienced by the bearing, and M represents the external moment experienced by the bearing. z represents the number of rolling elements in the bearing. The coefficient H j is used to identify the contact state of the jth rolling element, and is specifically defined as:
The load distribution can be calculated only by determining the value of H j, but the contact state of the rolling element cannot be accurately known before the load distribution is calculated, and thus the value of H j cannot be determined. Obviously, this is a problem that needs to be solved by "hypothesis, iteration, test hypothesis", and the processing method of H j is the core gist of the method proposed by the present application.
For rolling elements in contact, there is a quantitative relationship between the total contact deformation and the bearing displacement, and assuming that the j-th rolling element is in contact, this quantitative relationship can be expressed as:
Where Δ j represents the total contact deformation of the jth rolling element, which can be expressed as:
Δj＝δij+δoj (12)
Equations (4) - (12) form a nonlinear algebraic equation set for solving the load distribution of the angular contact ball bearing and a contact deformation algebraic equation set, and theoretically, the load distribution of the angular contact ball bearing can be obtained by solving the load distribution by adopting an iterative algorithm, but the load distribution is not the same. The iterative algorithm can only obtain a solution in mathematical sense, and further, the solution at the moment meets the requirement of convergence in mathematical sense, but does not necessarily have physical meaning. In particular, to the calculation of the load distribution problem of the angular ball bearing, there may be a problem in that the contact deformation solved by the iterative mathematical method may have both positive and negative values, the positive value representing compression deformation, and the negative value representing tension deformation, corresponding thereto. It is apparent that the contact between the rolling elements and the raceways can only be compressive deformation or zero deformation, and not tensile deformation. The solution found by the iterative algorithm is a mathematical motionless point, and the iterative algorithm stops calculating when the motionless point is found, so that only the iteration initial value can be changed when the situation is met, the calculation is performed again, and the reciprocating attempt is performed until a true solution which meets the mathematical requirement and has physical significance is found.
The load distribution of the angular contact ball bearing can be calculated by the equation set in this embodiment in combination with the method in the first embodiment.
Example III
Referring to fig. 3, this embodiment is used to analyze the load distribution of an angular ball bearing when the number of rolling elements is even, where each of the rolling element groups team_1 and team_n includes 1 rolling element, and each of the remaining rolling element groups includes a pair of two rolling elements symmetrical along the radial load acting line applied to the bearing, and the exemplary calculation method is the same when the number of rolling elements is 16, and when the number of rolling elements is other even.
Table 1 below shows the grouping when the number of rolling elements is 16
| Group of | Numbering of rolling elements included |
| Team_1 | 9 |
| Team_2 | 8,10 |
| Team_3 | 7,11 |
| Team_4 | 6,12 |
| Team_5 | 5,13 |
| Team_6 | 4,14 |
| Team_7 | 3,15 |
| Team_8 | 2,16 |
| Team_9 | 1 |
Table 2 below shows a trial calculation process for a number of rolling elements of 16
Step 1: as shown in tables 1 and 2, the 1 st trial was performed, and at this time, all the rolling elements in the nine groups team_1 to team_9 were in contact, and all H j (j=1, 2, …, 16) were equal to 1 according to the correspondence between the rolling elements and the groups. After the value of H j is determined, a nonlinear algebraic equation set composed of equations (4) - (12) is solved, and whether the solved contact deformation has a negative value is checked. If the negative value does not exist, ending trial calculation, and obtaining a result by solving at the moment, namely the load distribution of the angular contact ball bearing; otherwise, step 2 is performed.
Step 2: the 2 nd trial calculation was performed in combination with tables 1 and 2, at which the rolling elements in the eight groups team_2 to team_9 were in contact, and H 9 was equal to 0 and the remaining H j (j=1, 2, …,8,10, …, 16) were all equal to 1, as understood from the correspondence between the rolling elements and the groups. After the value of H j is determined, a nonlinear algebraic equation set composed of equations (4) - (12) is solved, and whether the solved contact deformation has a negative value is checked. If the negative value does not exist, ending trial calculation, and obtaining a result by solving at the moment, namely the load distribution of the angular contact ball bearing; otherwise, step 3 is executed.
Step 3: a 3 rd trial was performed in combination with tables 1 and2, at which time the rolling elements in the seven groups team_3 to team_9 were in contact, and H 8,H9 and H 10 were equal to 0 and the rest of H j (j=1, 2, …,7,11, …, 16) were all equal to 1, as seen from the correspondence between the rolling elements and the groups. After the value of H j is determined, a nonlinear algebraic equation set composed of equations (4) - (12) is solved, and whether the solved contact deformation has a negative value is checked. If the negative value does not exist, ending trial calculation, and obtaining a result by solving at the moment, namely the load distribution of the angular contact ball bearing; otherwise, in combination with the sequence in table 2, the value of H j is redetermined according to the 4 th trial run, and a trial run is performed, and it is determined whether to perform the next trial run according to the solved contact deformation condition.
According to the trial calculation mode provided by the steps, the calculation is sequentially carried out until the solved contact deformation is non-negative, and the final load distribution of the angular contact ball bearing is obtained. It is particularly pointed out that. Once the contact deformation obtained by a certain trial calculation is non-negative, the calculation is terminated, and the obtained result is the real load distribution of the angular contact ball bearing, so that the next trial calculation can not be performed.
Example IV
Referring to fig. 4, this embodiment is used to analyze the load distribution of an angular ball bearing when the number of rolling elements is an odd number, the rolling element group team_1 or team_n includes 1 rolling element, each of the remaining rolling element groups includes a pair of two rolling elements symmetrical along the radial load acting line applied to the bearing, and the exemplary calculation method is the same when the number of rolling elements is 15 and when the number of rolling elements is other odd number.
Table 3 below shows the grouping for 16 rolling elements
| Group of | Numbering of rolling elements included |
| Team_1 | 8,9 |
| Team_2 | 7,10 |
| Team_3 | 6,11 |
| Team_4 | 5,12 |
| Team_5 | 4,13 |
| Team_6 | 3,14 |
| Team_7 | 2,15 |
| Team_8 | 1 |
| Group of | Numbering of rolling elements included |
Table 4 below shows a trial calculation process for 16 rolling elements
Step 1: as shown in tables 3 and 4, the 1 st trial was performed, and at this time, all the rolling elements in the eight groups team_1 to team_8 were in contact, and all H j (j=1, 2, …, 15) were equal to 1 according to the correspondence of the rolling elements and the groups. After the value of H j is determined, a nonlinear algebraic equation set composed of equations (4) - (12) is solved, and whether the solved contact deformation has a negative value is checked. If the negative value does not exist, ending trial calculation, and obtaining a result by solving at the moment, namely the load distribution of the angular contact ball bearing; otherwise, step 2 is performed.
Step 2: the 2 nd trial calculation was performed in combination with tables 3 and 4, at this time, the rolling elements in the seven groups team_2 to team_8 were in contact, and as is known from the correspondence between the rolling elements and the groups, H 8 and H 9 were equal to 0, and the remaining H j (j=1, 2, …,7,10, …, 15) were all equal to 1. After the value of H j is determined, a nonlinear algebraic equation set composed of equations (4) - (12) is solved, and whether the solved contact deformation has a negative value is checked. If the negative value does not exist, ending trial calculation, and obtaining a result by solving at the moment, namely the load distribution of the angular contact ball bearing; otherwise, step 3 is executed.
Step 3: a 3 rd trial was performed in combination with tables 3 and 4, at this time, the rolling elements in the seven groups team_3 to team_8 were in contact, and H 7、H8、H9 and H 10 were equal to 0, and the remaining H j (j=1, 2, …,6,11, …, 15) were all equal to 1, as understood from the correspondence between the rolling elements and the groups. After the value of H j is determined, a nonlinear algebraic equation set composed of equations (4) - (12) is solved, and whether the solved contact deformation has a negative value is checked. If the negative value does not exist, ending trial calculation, and obtaining a result by solving at the moment, namely the load distribution of the angular contact ball bearing; otherwise, in combination with the sequence in table 4, the value of H j is redetermined according to the 4 th trial run, and the trial run is performed, and whether the next trial run is performed is determined according to the solved contact deformation condition.
According to the trial calculation mode provided by the steps, the calculation is sequentially carried out until the solved contact deformation is non-negative, and the final load distribution of the angular contact ball bearing is obtained. It is particularly pointed out that. Once the contact deformation obtained by a certain trial calculation is non-negative, the calculation is terminated, and the obtained result is the real load distribution of the angular contact ball bearing, so that the next trial calculation can not be performed.
In the description of the present specification, reference to the terms "one embodiment/manner," "some embodiments/manner," "example," "a particular example," "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment/manner or example is included in at least one embodiment/manner or example of the application. In this specification, the schematic representations of the above terms are not necessarily for the same embodiment/manner or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments/modes or examples. Furthermore, the various embodiments/modes or examples described in this specification and the features of the various embodiments/modes or examples can be combined and combined by persons skilled in the art without contradiction.
Furthermore, the terms "first," "second," and the like, are used for descriptive purposes only and are not to be construed as indicating or implying a relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defining "a first" or "a second" may explicitly or implicitly include at least one such feature. In the description of the present application, the meaning of "plurality" means at least two, for example, two, three, etc., unless specifically defined otherwise.
It will be appreciated by those skilled in the art that the above-described embodiments are merely for clarity of illustration of the disclosure, and are not intended to limit the scope of the disclosure. Other variations or modifications will be apparent to persons skilled in the art from the foregoing disclosure, and such variations or modifications are intended to be within the scope of the present disclosure.
Claims (7)
1. The method for calculating the load distribution of the angular contact ball bearing is characterized by comprising the following steps of:
establishing a load distribution model of the angular contact ball bearing, and forming a load solving method and a contact deformation solving method of rolling bodies in the angular contact ball bearing;
arranging all rolling bodies along the direction of a radial load acting line borne by the bearing to form a rolling body group, wherein the rolling body group comprises team_1 to team_N;
And (3) trial calculation: setting a value of N, wherein N is more than or equal to 1 and less than or equal to N, and calculating contact deformation of the team_n to the team_N according to a contact deformation solving method when the team_n to the team_N are in a contact state and the rest rolling body groups are in a non-contact state;
Checking whether the contact deformation quantity from the team_n to the team_N has a negative value, if so, adjusting the value of N, and then re-trial calculating, otherwise, solving the load distribution solving method from the team_n to the team_N to obtain the load distribution of the angular contact ball bearing;
The load solving method of the rolling body is that a nonlinear algebraic equation set of the load distribution is formed by analyzing the load distribution before and after deformation of the angular contact ball bearing, and the value obtained by solving the nonlinear algebraic equation set of the load distribution is the load distribution of the rolling body;
the method for solving the contact deformation of the rolling body is to analyze load distribution before and after deformation of the angular contact ball bearing to form a contact deformation algebraic equation set, and solve the obtained value through the contact deformation algebraic equation set to be the contact deformation of the rolling body;
the nonlinear algebraic equation set of the load distribution uses the following equation set:
Qij-Qoj＝0
Wherein, F a represents the axial force born by the bearing, F r represents the radial force born by the bearing, M represents the external torque born by the bearing, z represents the number of rolling elements in the bearing, Q ij represents the contact force between the jth rolling element and the inner raceway, Q oj represents the contact force between the jth rolling element and the outer raceway, delta ij represents the contact deformation between the jth rolling element and the inner raceway, delta oj represents the contact deformation between the jth rolling element and the outer raceway, and the coefficient H j is used for identifying the contact state of the jth rolling element;
if the j-th rolling element is in a contact state, H j is equal to 1;
If the j-th rolling element is in a non-contact state, H j is equal to 0.
2. The angular contact ball bearing load distribution calculation method according to claim 1, wherein: the algebraic equation set of contact deformation includes a nonlinear algebraic equation set of load distribution, and further includes the following equation set:
Δj＝δij+δoj
Wherein Delta j represents the total contact deformation of the jth rolling element, delta a represents the axial displacement of the bearing inner ring, delta r represents the radial displacement of the bearing inner ring, alpha j represents the contact angle of the jth rolling element, The j-th rolling element position angle is represented by θ, the deflection angular displacement of the bearing is represented by θ, and the pitch circle radius of the bearing is represented by R.
3. The angular contact ball bearing load distribution calculation method according to claim 2, wherein: the contact angle α j of the jth rolling element is solved in conjunction with the following equation set:
S1j＝rij+roj-Dj
Wherein S 1j represents the distance between the center of curvature of the outer raceway groove and the center of curvature of the inner raceway groove before deformation, S 2j represents the distance between the center of curvature of the outer raceway groove and the center of curvature of the inner raceway groove after deformation, D j represents the diameter of the jth rolling element, r ij represents the radius of curvature of the inner raceway groove at the jth rolling element, r oj represents the radius of curvature of the outer raceway groove at the jth rolling element, and α represents the nominal contact angle of the bearing.
4. The angular contact ball bearing load distribution calculation method according to claim 1, wherein: when the number of rolling elements is an odd number, the rolling element group team_1 or team_n includes 1 rolling element, and each of the remaining rolling element groups includes a pair of two rolling elements symmetrical along a radial load acting line to which the bearing is subjected.
5. The angular contact ball bearing load distribution calculation method according to claim 1, wherein: when the number of rolling elements is even, each of the rolling element groups team_1 and team_n includes 1 rolling element, and each of the remaining rolling element groups includes a pair of two rolling elements symmetrical along a radial load acting line to which the bearing is subjected.
6. The angular contact ball bearing load distribution calculation method according to claim 1, wherein: after each calculation of any one of the deformation results in the rolling element group, it is checked whether the contact deformation obtained by trial calculation is a negative value.
7. The angular contact ball bearing load distribution calculation method according to claim 1, wherein: the deformation amounts of the rolling element groups team_n to team_n are tried from N equal to 1, and when the contact deformation amount obtained by the trial has a negative value, N is added with 1 and then the trial is carried out again.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| RU2141582C1 (en) * | 1998-09-25 | 1999-11-20 | Акционерное общество "АО ВНИПП" | Method for making up set of parts at selective assembling of radial ball thrust bearings |
| JP2003050169A (en) * | 2001-05-17 | 2003-02-21 | Ntn Corp | Real-time bearing load sensing |
| CN108228991A (en) * | 2017-12-26 | 2018-06-29 | 三门峡职业技术学院 | A kind of method for solving high-speed angular contact ball bearing numerical value |
| CN110674577A (en) * | 2019-09-23 | 2020-01-10 | 武汉理工大学 | New energy automobile high-rotating-speed bearing dynamic parameter acquisition method |
| CN111159880A (en) * | 2019-12-26 | 2020-05-15 | 熵智科技(深圳)有限公司 | Ball bearing contact stiffness calculation method |
-
2021
- 2021-06-15 CN CN202110662281.7A patent/CN113392525B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| RU2141582C1 (en) * | 1998-09-25 | 1999-11-20 | Акционерное общество "АО ВНИПП" | Method for making up set of parts at selective assembling of radial ball thrust bearings |
| JP2003050169A (en) * | 2001-05-17 | 2003-02-21 | Ntn Corp | Real-time bearing load sensing |
| CN108228991A (en) * | 2017-12-26 | 2018-06-29 | 三门峡职业技术学院 | A kind of method for solving high-speed angular contact ball bearing numerical value |
| CN110674577A (en) * | 2019-09-23 | 2020-01-10 | 武汉理工大学 | New energy automobile high-rotating-speed bearing dynamic parameter acquisition method |
| CN111159880A (en) * | 2019-12-26 | 2020-05-15 | 熵智科技(深圳)有限公司 | Ball bearing contact stiffness calculation method |
Non-Patent Citations (2)
| Title |
|---|
| 基于球-滚道非完全接触状态下的球轴承载荷分布计算及刚度特性研究;张进华;方斌;朱永生;闫柯;洪军;;机械工程学报(09);全文 * |
| 联合载荷作用下高速角接触球轴承快速计算方法及接触角分析;方斌;张进华;洪军;朱永生;;西安交通大学学报(06);全文 * |
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