阅读说明：本技术 一种基于刚度的空间精密轴系预紧力的测量方法 (Method for measuring pretightening force of space precision shafting based on rigidity ) 是由 谢友金 陈晓东 郝伟 李治国 崔凯 高雄 于 2021-06-21 设计创作，主要内容包括：本发明涉及轴系预紧力测量技术,具体涉及一种基于刚度的空间精密轴系预紧力的测量方法,以解决目前在轴系预紧力测量过程中,需要对轴系进行拆装、操作复杂、工作效率低,存在准确性低的问题。本发明所采用的技术方案包括以下步骤：步骤1)选取轴系实体装置中的组配轴承,该组配轴承的初始预紧力为F-0；在预紧力5/6F-0～5/3F-0内选取一组组配轴承的等差实验预紧力F-i；根据轴承刚度计算公式,得到每个等差实验预紧力F-i对应的轴承刚度；步骤2)建立轴系实体装置的有限元仿真模型,将每个等差实验预紧力F-i对应的轴承刚度代入有限元仿真模型,仿真计算出轴系实体装置每个等差实验预紧力F-i下对应的前k阶固有频率。(The invention relates to a shafting pretightening force measuring technology, in particular to a method for measuring the pretightening force of a spatial precision shafting based on rigidity, which aims to solve the problems of the prior shafting pretightening force measuring process that the shafting needs to be disassembled and assembled, the operation is complex, the working efficiency is low and the accuracy is low. The technical scheme adopted by the invention comprises the following steps: step 1) selecting a matched bearing in a shafting solid device, wherein the initial pretightening force of the matched bearing is F 0 (ii) a Under the pre-tension of 5/6F 0 ～5/3F 0 Equal difference experiment pretightening force F of internally selected group of assembled bearings i (ii) a Obtaining the pretightening force F of each equal difference experiment according to a bearing rigidity calculation formula i A corresponding bearing stiffness; step 2) establishing a finite element simulation model of the shafting solid device, and pre-tightening force F of each equal difference experiment i Substituting the corresponding bearing rigidity into a finite element simulation model, and simulating and calculating each equal difference experiment of the shafting entity deviceTension F i The lower corresponding first k natural frequencies.)

1. A method for measuring the pretightening force of a spatial precision shafting based on rigidity is characterized by comprising the following steps:

step 1) selecting a matched bearing in a shafting solid device, wherein the initial pretightening force of the matched bearing is F₀(ii) a Under the pre-tension of 5/6F₀～5/3F₀Within the range of (1), selecting a group of assembled bearings to obtain the pretightening force F of the equal difference experiment_i1, 2, 3, n, wherein n is not less than 3;

obtaining the pretightening force F of each equal difference experiment according to a bearing rigidity calculation formula_iCorresponding bearing stiffness (K)_xi、K_yi、K_zi)，K_xi、K_yiShowing the corresponding radial stiffness, K, of the assembled bearing under the pretightening force of the ith equal difference experiment_ziRepresenting the corresponding axial stiffness of the assembled bearing under the pre-tightening force of the ith equal difference experiment;

step 2) establishingA finite element simulation model of a shafting entity device, and pre-tightening force F of each equal difference experiment_iCorresponding bearing stiffness (K)_xi、K_yi、K_zi) Substituting the finite element simulation model into the finite element simulation model, and calculating each equal difference experiment pretightening force F of the shafting entity device through simulation_iLower corresponding front k natural frequency f_i1、f_i2、f_i3，…，f_ikWherein k is more than or equal to 1;

step 3) measuring the front k-order natural frequency f of the shafting entity device_1′、f_2′、f_3′、......，f_k′；

Step 4) searching each equal difference experiment pretightening force F of shafting entity device in the finite element simulation model by a difference method_iLower corresponding front k natural frequency f_i1、f_i2、f_i3，…，f_ikFront k order natural frequency f measured by shafting solid device_1′、f_2′、f_3′、......，f_k′Experiment pretightening force F with minimum error_aThe experimental pretightening force F_aThe actual pre-tightening force of the shafting is obtained.

2. The method for measuring the pretightening force of the spatial precision shafting based on the rigidity as claimed in claim 1, wherein the method comprises the following steps:

in the step 1), the pretightening force F of two adjacent equal difference experiments_iIs less than 0.1F₀。

3. The method for measuring the pretightening force of the spatial precision shafting based on the rigidity as claimed in claim 1 or 2, wherein the method comprises the following steps:

in step 2), k takes the value of 5.

4. The method for measuring the pretightening force of the spatial precision shafting based on the rigidity as claimed in claim 3, wherein the method comprises the following steps:

in the step 3), the first 5-order natural frequency of the shafting entity device is measured by a modal tester.

5. The method for measuring the pretightening force of the spatial precision shafting based on the rigidity as claimed in claim 4, wherein the method comprises the following steps:

in the step 1), axial rigidity K corresponding to pretightening force Fi of each equal difference experiment_ziThe radial stiffness K is calculated according to the following formula (1)_xi、K_yiCalculated according to the following formula (2):

wherein: d_wIs the diameter of the ball;

z is the number of balls;

f is a pretightening force;

and alpha is the actual contact angle of the bearing.

6. The method for measuring the pretightening force of the spatial precision shafting based on the rigidity as claimed in claim 5, wherein the method comprises the following steps: n is 11.

Technical Field

The invention relates to a shafting pretightening force measuring technology, in particular to a method for measuring the pretightening force of a spatial precision shafting based on rigidity.

Background

The pre-tightening of the bearing means that a certain pre-deformation is generated between the rolling bodies of the bearing and the inner and outer races by adopting a proper method so as to keep the inner and outer races of the bearing in a compact state. The proper bearing pretightening force can increase the rigidity of the bearing, improve the rotation precision of the shaft, reduce the vibration and noise of the shaft and prolong the service life of the bearing.

The use of the bearing can be influenced by overlarge or undersize pretightening force of the bearing. The excessive pretightening force can increase the contact stress between the ball and the inner and outer ring channels, so as to intensify the friction in the bearing, reduce the service life of the bearing and increase the thermal deformation of a shafting, and meanwhile, the excessive pretightening force can damage the state of a solid lubricating film on the surface of the bearing to influence the lubricating life of the space bearing; the pretightening force is too small to achieve the expected use rigidity and precision, the use effect is influenced, and when a shafting runs, the rolling bodies of the bearing are separated from the inner ring channel and the outer ring channel due to the centrifugal force or the influence of the bearing clearance, so that the bearing is damaged.

After the bearing is assembled in the shaft system, the initial loading pretightening force of the bearing is changed, and the pretightening force is related to the integral structure of the shaft system, the weight and the form of the loaded bearing, the change of temperature and other factors, so that the actual pretightening force of the shaft system cannot be directly measured. The magnitude of the pre-tightening force of the shaft system determines the magnitude of the contact stress between the bearing and the inner and outer ring raceways, and the contact stress is a key factor influencing the service life of the space solid lubrication bearing, so that the measurement of the actual pre-tightening force of the shaft system is very necessary.

The prior art generally adopts the following method for evaluating the actual pre-tightening force of a shafting:

(1) the hand feeling method comprises the following steps: and directly rotating the pre-tightened shaft system by hand, and judging whether the pre-tightening force of the bearing meets the design requirement by using experience. This method is relatively crude and cannot be evaluated quantitatively.

(2) Measuring the friction torque of a shafting: the method for measuring the friction torque of the shafting needs to use the contact friction coefficient of the steel ball and the raceway, the value of the friction coefficient is related to various factors such as the rotating speed, the working load, the temperature and the like, the value cannot be accurately determined, and the repeatability is poor.

(3) Axial deformation method: because the product shafting usually does not have the condition of directly applying pressure to measure the deformation, the shafting needs to be disassembled and assembled by the axial deformation measuring method, the axial deformation is completed by means of an external tool, the working efficiency is low, the operation repeatability is poor, the operation link is complex, and certain limitation is realized.

Disclosure of Invention

The invention provides a method for measuring the pre-tightening force of a space precision shafting based on rigidity, and aims to solve the problems that in the process of measuring the pre-tightening force of the shafting, the shafting needs to be disassembled and assembled, the operation is complex, the working efficiency is low, and the accuracy is low.

The technical scheme adopted by the invention is as follows:

a method for measuring the pretightening force of a space precision shafting based on rigidity is characterized by comprising the following steps:

step 1) selecting a matched bearing in a shafting solid device, wherein the initial pretightening force of the matched bearing is F₀(ii) a Under the pre-tension of 5/6F₀～5/3F₀Within the range of (1), selecting a group of assembled bearings to obtain the pretightening force F of the equal difference experiment_i1, 2, 3, n, wherein n is not less than 3;

obtaining the pretightening force F of each equal difference experiment according to a bearing rigidity calculation formula_iCorresponding bearing stiffness (K)_xi、K_yi、K_zi)，K_xi、K_yiShowing the corresponding radial stiffness, K, of the assembled bearing under the pretightening force of the ith equal difference experiment_ziRepresenting the corresponding axial stiffness of the assembled bearing under the pre-tightening force of the ith equal difference experiment;

step 2) establishing a finite element simulation model of the shafting solid device, and pre-tightening force F of each equal difference experiment_iCorresponding bearing stiffness (K)_xi、K_yi、K_zi) Substituting the finite element simulation model into the finite element simulation model, and calculating the shafting entity by simulationSetting each equal difference experiment pretightening force F_iLower corresponding front k natural frequency f_i1、f_i2、f_i3，…，f_ikWherein k is more than or equal to 1;

step 3) measuring the front k-order natural frequency f of the shafting entity device_1′、f_2′、f_3′、......，f_k′；

Step 4) searching the corresponding front k-order natural frequency f under each equal difference experiment pretightening force Fi of the shafting entity device in the finite element simulation model by a difference method_i1、f_i2、f_i3，…，f_ikFront k-order natural frequency f of physical device of measurement axis_1′、f_2′、f_3′、......，f_k′Experiment pretightening force F with minimum error_aThe experimental pretightening force F_aThe actual pre-tightening force of the shafting is obtained.

Further, in the step 1), the pretightening force F of two adjacent equal difference experiments_oIs less than 0.1F₀。

Further, in step 2), k is 5.

Further, in step 3), the first 5 th order natural frequency of the shafting entity device is measured by using a modal tester.

Further, in the step 1), each equal difference experiment pretightening force F_iCorresponding axial stiffness K_ziThe radial stiffness K is calculated according to the following formula (1)_xi、K_yiCalculated according to the following formula (2):

wherein: d_wIs the diameter of the ball;

z is the number of balls;

f is a pretightening force;

and alpha is the actual contact angle of the bearing.

Further, n is 11.

Compared with the prior art, the invention has the following beneficial effects.

The invention adopts a method for measuring the pretightening force of a space precision shafting based on rigidity, which comprises the steps of establishing a bearing pretightening force-rigidity mathematical model; and substituting the rigidity data calculated theoretically into the finite element model, and simulating to obtain the natural frequency of the finite element model of the corresponding shafting entity device under different experimental pretightening forces. And in an experimental state, a shafting entity device of the pretightening force to be tested is utilized to complete the inherent frequency test. And then comparing the multi-order natural frequency of finite element simulation and shafting entity device test, and obtaining a group of corresponding rigidity and pretightening force with the minimum natural frequency error result by using a difference method.

The method for measuring the pre-tightening force of the spatial precision shafting based on the rigidity does not need to disassemble and assemble the shafting, is high in working efficiency, evaluates the actual pre-tightening force of the shafting by utilizing the relation between the rigidity and the inherent frequency, establishes a finite element simulation model, and obtains the actual pre-tightening force of the shafting by mutually verifying the experiment result, so that the multi-order (especially the first five-order) inherent frequency is matched, the measuring accuracy is high, the reliability is higher, the operation repeatability is good, and the working efficiency of bearing pre-tightening force evaluation is improved.

Drawings

FIG. 1 is a finite element model diagram of a shafting entity device in the method for measuring the pre-tightening force of a spatial precision shafting based on rigidity.

FIG. 2 is a bearing model in the method for measuring the pre-tightening force of the spatial precision shafting based on the rigidity.

FIG. 3 is a cross-sectional view of a shafting solid device in the method for measuring the pre-tightening force of the spatial precision shafting based on the rigidity.

FIG. 4 is a flowchart of a method for measuring the pre-tightening force of a spatial precision shafting based on rigidity.

In the figure:

1-load shafting base, 2-shafting model, 21-first bearing, 22-second bearing and 3-load.

Detailed Description

The technical solution of the present invention will be clearly and completely described below with reference to the embodiments of the present invention and the accompanying drawings, and it is obvious that the described embodiments do not limit the present invention.

In this embodiment, a method for measuring the pretightening force of the spatial precision shafting based on the rigidity includes the following steps:

step 1) selecting a matched bearing in a shafting solid device, wherein the initial pretightening force of the matched bearing is 600N; selecting a group of assembled bearing equal difference experiment pretightening force F within the range of the pretightening force of 500N to 1000N_i1, 2, 3, 11, two adjacent equal difference experiment pretightening forces F_iThe difference of (a) is 50N;

obtaining the pretightening force F of each equal difference experiment according to a bearing rigidity calculation formula_iCorresponding bearing stiffness (K)_xi、K_yi、K_zi)，K_xi、K_yiShowing the corresponding radial stiffness, K, of the assembled bearing under the pretightening force of the ith equal difference experiment_ziRepresenting the corresponding axial stiffness of the assembled bearing under the pre-tightening force of the ith equal difference experiment;

pretightening force F of each equal difference experiment_iCorresponding axial stiffness K_ziThe radial stiffness K is calculated according to the following formula (1)_xi、K_yiCalculated according to the following formula (2):

wherein: d_wIs the diameter of the ball;

z is the number of balls;

f is an axial force;

and alpha is the actual contact angle of the bearing.

Step 2) establishing a finite element simulation model of the shafting solid device, and pre-tightening force F of each equal difference experiment_iCorresponding bearing stiffness (K)_xi、K_yi、K_zi) Substituting the obtained value into a finite element simulation model, and calculating the pretightening force F of each equal difference experiment through simulation_iLower corresponding natural frequency f of the first 5 th order_i1、f_i2、f_i3、f_i4、f_i5. The method comprises the following specific steps:

as shown in fig. 1, the finite element simulation model of the shafting physical device includes a load shafting base 1, a shafting model 2 and a load 3, the shafting model 2 of the pre-tightening force to be evaluated is assembled on the load shafting base 1, the load 3 is installed on the shafting model 2, and the finite element model of the whole shafting physical device is established by a method from a single part to a whole, wherein the shafting model 2 is as shown in fig. 2. The simulation of the bearing is a key part of finite element modeling of the shafting, and the method for simulating the bearing by using the MPC is adopted in the embodiment. Specifically, in ANSYS, each part is subjected to grid division and material setting independently, then screw holes connected among the parts, a bearing outer ring and a bearing sleeve are connected, an inner ring and a shaft are connected by adopting a constraint unit, and all the parts are assembled into a whole. The bottom surface of the load shafting base 1 is used for restraining the translational freedom degrees of all load shafting and is used for simulating the connection between the load shafting base and the test bed in the axial entity device.

The load 3 can be a stainless steel load, and the specific parameters are as follows:

TABLE 1

The contact angle and the rigidity of a group of angular contact bearings in a shafting corresponding to the load 3 are selected and are shown in the following table 2.

TABLE 2

Pre-tightening force F of shafting entity device in each equal difference experiment_iThe corresponding natural frequency finite element simulation results are shown in table 3 below.

TABLE 3

Step 3), measuring the first 5-order natural frequencies f1 ', f2 ', f3 ', f4 ' and f5 ' of the shafting entity device by using a modal tester, as shown in the following table 4:

TABLE 4

Order of the scale	1	2	3	4	5
						Natural frequency	75.687	78.684	178.535	540.605	598.696

Step 4) searching each equal difference experiment pretightening force F in the finite element simulation model by a difference method_iLower corresponding front k natural frequency f_i1、f_i2、f_i3，…，f_ikFirst 5 order natural frequency f of physical device of measuring shaft system_1′、f_2′、f_3′、f_4′、f_5′Experiment pretightening force F with minimum error_aThe experimental pretightening force F_aThe actual pre-tightening force of the shafting is obtained. Specifically, finite element simulation data is matched with experimental results. The most similar group of test results is found, and the results are shown in table 5 below, and it can be seen that the error of the natural frequency of the shafting entity device corresponding to the pretightening force 745N between 700N and 750N obtained by the difference method is the smallest.

TABLE 5

Therefore, the actual pretightening force of the bearing corresponding to the finite element result of the shafting solid device can be obtained as F_aIs 745N.

The above description is only an embodiment of the present invention, and is not intended to limit the scope of the present invention, and all equivalent structural changes made by using the contents of the present specification and the drawings, or applied directly or indirectly to other related technical fields, are included in the scope of the present invention.