A method for calculating the dynamic response of a ball bearing with local raceway fault

Abstract

The present invention proposes a method for calculating the dynamic response of a ball bearing with a local fault in the raceway, obtaining the basic parameters and fault parameters of the rolling bearing; calculating the fault span angle and the additional clearance caused by the local fault; calculating the angle difference between the center of the rolling element and the center of the local fault, and determining the deformation of the rolling element and the raceway after the fault occurs in combination with whether the rolling element is located in the fault area; establishing a dynamic model of a ball bearing with a local fault in the raceway; using the 4th-order Runge-Kutta method to solve the dynamic equation of the ball bearing with a local fault in the raceway, obtaining the radial displacement of the ball bearing in the vertical and horizontal directions, and completing the calculation of the dynamic response of the ball bearing with a local fault in the raceway. The present invention can simulate a variety of local fault conditions, systematically and efficiently calculate the dynamic response of a ball bearing with a local fault in the raceway, and has important value for the fault diagnosis of ball bearings.

Description

Technical Field

[0001] The invention relates to the field of solving the dynamic response of a faulty ball bearing, and in particular to a method for calculating the dynamic response of a ball bearing with a local raceway fault. Background Art

[0002] Ball bearings contain multiple nonlinear factors such as bearing variable stiffness, Hertzian contact and bearing clearance, which will lead to complex dynamic behavior of ball bearings (Zhang Zhiyong, 2015). Pitting, spalling, cracking and wear faults of ball bearings are the most common forms of raceway faults, which can be simplified as local faults (Wei Xunkai, 2014). After a local fault occurs in a ball bearing, nonlinear factors increase, making the dynamic response of the ball bearing more complex. Tandon and Choudhury believe that the impact generated by a local fault in a bearing has a duration. They use three common pulses, rectangular, triangular and semi-sinusoidal, to characterize the impact generated by the fault. The final impact force is equal to the impact function multiplied by the contact force at the fault (Tandon N et al. 1997). When Tadina and Boltezar modeled the faulty bearing system, they combined the multi-body dynamics method with the finite element method to obtain the control equation of the system and considered the influence of different boundary properties on the contact stiffness (Tadina M, Boltezar M. 2011). In the above studies on local faults of ball bearings, the former simulates local faults by using different impact force sequences, but its disadvantage is that the magnitude of the impact force cannot be directly obtained and the local fault cannot be quantitatively described; the latter uses the finite element method to simulate local faults, but its disadvantage is that the dynamic behavior of the faulty ball bearing cannot be simulated. The present invention overcomes the above disadvantages, uses the additional clearance caused by the local fault to describe the impact caused by the local fault, and can simulate a variety of local fault conditions (including fault type, fault size and fault location), and systematically and efficiently calculates the dynamic response of the ball bearing with local raceway fault. Summary of the invention

[0003] The object of the present invention is to provide a method for calculating the dynamic response of a ball bearing with a local raceway fault.

[0004] The technical solution to achieve the purpose of the present invention is: a method for calculating the dynamic response of a ball bearing with a local raceway fault, comprising the following steps:

[0005] Step 1, obtaining basic parameters and fault parameters of rolling bearings;

[0006] Step 2: Calculate the fault span angle and the additional gap caused by the local fault;

[0007] Step 3: Calculate the angle difference between the center of the rolling element and the center of the local fault, and determine the deformation of the rolling element and the raceway after the fault occurs, based on whether the rolling element is located in the fault area.

[0008] Step 4, substituting the basic parameters and fault parameters of the rolling bearing in step 1 and the fault span angle and the additional clearance caused by the local fault in step 2, and combining whether the rolling element is located in the fault area, a dynamic model of the ball bearing with local raceway fault is established;

[0009] Step 5: Use the 4th-order Runge-Kutta method to solve the dynamic equation of the ball bearing with local raceway fault, obtain the radial displacement of the ball bearing in the vertical and horizontal directions, and complete the calculation of the dynamic response of the ball bearing with local raceway fault.

[0010] Further, step 1, obtain the basic parameters and fault parameters of the rolling bearing, wherein:

[0011] The basic parameters include geometric dimensions, number of balls, contact stiffness, bearing clearance and equivalent damping;

[0012] The fault parameters include fault type, fault size and fault location;

[0013] The fault types include inner ring raceway fault and outer ring raceway fault.

[0014] Furthermore, in step 2, the fault span angle and the additional gap caused by the local fault are calculated, and the specific method is as follows:

[0015] Step 2.1: Calculate the fault span angle θ e :

[0016]

[0017] Step 2.2: Calculate the angle between the rolling element and the local fault

[0018]

[0019] Step 2.3, calculate the additional gap Δh caused by local fault:

[0020]

[0021] In equations (1) to (3), d is the local fault size; d i d o They are the raceway diameters of the inner and outer rings of the bearing respectively; D is the rolling element diameter.

[0022] Further, in step 3, the angle difference between the center of the rolling element and the center of the local fault is calculated, and the deformation of the rolling element and the raceway after the fault occurs is determined in combination with whether the rolling element is located in the fault area. The specific method is:

[0023] Step 3.1: Calculate the angle difference θ between the center of each rolling element and the center of the local faultbd :

[0024]

[0025] Step 3.2: If the rolling element is located in the fault area, the deformation of the rolling element and the normal raceway needs to be reduced by the additional clearance caused by the local fault, otherwise it remains unchanged:

[0026]

[0027] In equations (4) to (5), mod(·) is the remainder function; ω c and ω s are the angular velocity of the cage and the angular velocity of the shaft respectively; t is the time independent variable; is the outer ring fault position angle; δ i is the deformation of the rolling element and the normal raceway, δ i * The deformation of the rolling elements and raceways after a fault occurs.

[0028] Furthermore, the basic parameters and fault parameters of the rolling bearing in step 1 and the fault span angle and the additional clearance caused by the local fault in step 2 are substituted, and the dynamic model of the ball bearing with local raceway fault is established in combination with whether the rolling element is located in the fault area. The specific method is as follows:

[0029]

[0030] and

[0031]

[0032]

[0033] θ i =2π(i-1) / N b +ω c t (9)

[0034] δ i =xcosθ i +ysinθ i -δ 0 (10)

[0035]

[0036] In equations (6) to (11), x and y are the radial displacements of the ball bearing in the vertical and horizontal directions; F x 、F y is the ball bearing reaction force in the x and y directions; m is the equivalent mass of the ball bearing; c is the equivalent damping; W is the ball bearing gravity; θ i is the instantaneous angular position of the i-th rolling element; 2δ0 F is the radial working clearance of the bearing; i * is the Hertz contact force between the rolling element and the raceway, K is the Hertz contact stiffness; G(·) is the Heaviside function that represents the contact condition, describing the contact between the rolling element and the raceway. The G(·) value is 1 when contact occurs and 0 when contact is lost; N b is the number of rolling elements.

[0037] A system for calculating the dynamic response of a ball bearing with a local raceway fault completes the calculation of the dynamic response of a ball bearing with a local raceway fault based on the method for calculating the dynamic response of a ball bearing with a local raceway fault.

[0038] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the calculation of the dynamic response of a ball bearing with a local raceway fault is completed based on the method for calculating the dynamic response of a ball bearing with a local raceway fault.

[0039] A computer-readable storage medium stores a computer program, which, when executed by a processor, completes the calculation of the dynamic response of a ball bearing with a local raceway fault based on the method for calculating the dynamic response of a ball bearing with a local raceway fault.

[0040] Compared with the prior art, the present invention has the following significant advantages: 1) the height of the rolling body center dropped in the fault area is used to represent the additional clearance caused by the local fault, thereby overcoming the adverse effect of the additional clearance specified by humans on the model; 2) a variety of fault parameters such as local faults (fault type, fault size and fault location) are included, which greatly facilitates the study of the dynamic response of ball bearings under different fault conditions; 3) the 4th-order Runge-Kutta method is used to solve the dynamic equation of the ball bearing with local raceway fault, and the dynamic response of the ball bearing with local raceway fault is calculated systematically and efficiently, which can calculate not only the steady-state response but also the transient response. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a schematic diagram of local failure of the inner ring and outer ring raceways of a bearing according to an embodiment of the present invention.

[0042] Figure 2 Schematic diagram of additional gap geometry change caused by local fault in an embodiment of the present invention, (a) is a schematic diagram of outer ring fault, (b) is a schematic diagram of inner ring fault.

[0043] Figure 3 1 is a model diagram of a ball bearing according to an embodiment of the present invention, (a) is a cross-sectional diagram of the ball bearing, and (b) is a dynamic principle diagram.

[0044] Figure 41 and 1 are acceleration response diagrams of the outer ring local fault system of an embodiment of the present invention, (a) is the acceleration response diagram in the horizontal direction, and (b) is the acceleration response diagram in the vertical direction.

[0045] Figure 5 1 and 1 are acceleration response diagrams of the inner ring local fault system according to an embodiment of the present invention, wherein (a) is the acceleration response diagram in the horizontal direction, and (b) is the acceleration response diagram in the vertical direction.

[0046] Figure 6 1 is an acceleration response diagram of the system after the outer ring fault position angle is changed according to an embodiment of the present invention, (a) is an acceleration response diagram in the horizontal direction, and (b) is an acceleration response diagram in the vertical direction.

[0047] Figure 7 It is a flow chart of the method for calculating the dynamic response of a ball bearing with a local raceway fault according to the present invention. DETAILED DESCRIPTION

[0048] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0049] like Figure 7 As shown, a method for calculating the dynamic response of a ball bearing with a local raceway fault comprises the following steps:

[0050] Step 1, input the basic parameters of the rolling bearing (geometric dimensions, number of balls, contact stiffness, bearing clearance, equivalent damping) and fault parameters (inner ring or outer ring fault, fault size, fault location);

[0051] Step 2: Calculate the fault span angle and the additional clearance caused by the local fault according to the basic parameters and fault parameters of the rolling bearing provided in step 1. The specific method is as follows:

[0052] Step 2.1, calculate the fault span angle θ e :

[0053]

[0054] Step 2.2, calculate the angle between the rolling element and the local fault

[0055]

[0056] Step 2.3, calculate the additional gap Δh caused by local fault:

[0057]

[0058] In equations (1) to (3), d is the local fault size; d i d o They are the raceway diameters of the inner and outer rings of the bearing respectively; D is the rolling element diameter.

[0059] In step 3, the angle difference between the center of each rolling element and the center of the local fault is calculated, and it is determined whether the rolling element is located in the fault area. If it is located in the fault area, the deformation of the rolling element and the raceway is reduced by the additional gap, otherwise it remains unchanged. The specific method is:

[0060] Step 3.1, calculate the angle difference θ between the center of each rolling element and the center of the local fault bd :

[0061]

[0062] Step 3.2, determine whether the rolling element is located in the fault area. If the rolling element is located in the fault area, the deformation of the rolling element and the normal raceway needs to be reduced by the additional gap caused by the local fault, otherwise it remains unchanged:

[0063]

[0064] In equations (4) to (5), mod(·) is the remainder function; ω c and ω s are the angular velocity of the cage and the angular velocity of the shaft respectively; t is the time independent variable; is the outer ring fault position angle; δ i is the deformation of the rolling element and the normal raceway, δ i * The deformation of the rolling elements and raceways after a fault occurs.

[0065] Step 4: Substitute the basic parameters and fault parameters of the rolling bearing in step 1 and the fault span angle and additional clearance caused by the local fault in step 2, and combine the determination of whether the rolling element is located in the fault area in step 3 to establish the dynamic model of the ball bearing with local raceway fault:

[0066]

[0067] and

[0068]

[0069]

[0070] θ i =2π(i-1) / N b +ω c t (9)

[0071] δ i =xcosθ i+ysinθ i -δ 0 (10)

[0072]

[0073] In equations (6) to (11), x and y are the radial displacements of the ball bearing in the vertical and horizontal directions; F x 、F y is the ball bearing reaction force in the x and y directions; m is the equivalent mass of the ball bearing; c is the equivalent damping; W is the ball bearing gravity; θ i is the instantaneous angular position of the i-th rolling element; 2δ 0 F is the radial working clearance of the bearing; i * is the Hertz contact force between the rolling element and the raceway, K is the Hertz contact stiffness; G(·) is the Heaviside function that represents the contact condition, describing the contact between the rolling element and the raceway (the G(·) value is 1 when contact occurs and 0 when contact is lost); N b is the number of rolling elements.

[0074] Step 5, using the 4th-order Runge-Kutta method to solve the dynamic equation of the ball bearing with local raceway fault in step 4, obtain the radial displacement of the ball bearing in the vertical and horizontal directions, and complete the calculation of the dynamic response of the ball bearing with local raceway fault.

[0075] The present invention also proposes a system for calculating the dynamic response of a ball bearing with a local raceway fault. Based on the method for calculating the dynamic response of a ball bearing with a local raceway fault, the calculation of the dynamic response of a ball bearing with a local raceway fault is completed.

[0076] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the calculation of the dynamic response of a ball bearing with a local raceway fault is completed based on the method for calculating the dynamic response of a ball bearing with a local raceway fault.

[0077] A computer-readable storage medium stores a computer program, which, when executed by a processor, completes the calculation of the dynamic response of a ball bearing with a local raceway fault based on the method for calculating the dynamic response of a ball bearing with a local raceway fault.

[0078] Example

[0079] In order to verify the effectiveness of the method of the present invention, the following simulation is performed: Given the geometric parameters of the deep groove ball bearing 6308 as shown in Table 1, the local fault parameters as shown in Table 2.

[0080] Table 1 Geometric parameters of deep groove ball bearing 6308

[0081]

[0082] Table 2 Local fault parameters

[0083]

[0084] For Figure 1 The local fault distribution diagram shown in the figure shows that the fault span angles of the outer ring and inner ring are 0.0175 and 0.02 respectively. Figure 2 The geometric position relationship between the center of the rolling element and the fault area, the fault angles of the local faults of the outer and inner raceways are calculated to be 0.0933 and 0.0666 respectively, and the additional clearances caused by the local faults of the outer and inner raceways are calculated to be 7.9μm and 4.1μm respectively. The angle difference between the center of the rolling element and the center of the local fault is calculated to determine whether the rolling element is located in the fault area. Figure 3 The cross-section diagram and dynamic principle diagram of the ball bearing are shown in Figure 2. Substituting the basic parameters and fault parameters of the rolling bearing, as well as the fault span angle and the additional clearance caused by the local fault, the fourth-order Runge-Kutta method is used to solve the dynamic equation of the ball bearing with local raceway fault, and the dynamic response of the ball bearing with local raceway fault is obtained, where Figure 4 It is the dynamic response of outer race fault, and the acceleration presents regular impact; Figure 5 is the dynamic response of the inner ring fault, and the acceleration amplitude changes with time. By changing the outer ring fault position angle to π / 60, the dynamic response of the system under this fault condition can be calculated, such as Figure 6 As shown, the vertical acceleration increases and the horizontal acceleration decreases.

[0085] In summary, the present invention overcomes the adverse effects of the additional clearance caused by subjective local faults on the model, and includes a variety of fault parameters such as local faults (fault type, fault size and fault location). It can systematically and efficiently calculate the steady-state response and transient response of ball bearings with local raceway faults, which is of great value to the fault diagnosis of ball bearings.

[0086] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0087] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

Claims

1. A method for calculating the dynamic response of a ball bearing with a local raceway fault. It is characterized in that The following steps are involved: Step 1, obtaining basic parameters and fault parameters of rolling bearings; Step 2: Calculate the fault span angle and the additional gap caused by the local fault; Step 3: Calculate the angle difference between the center of the rolling element and the center of the local fault, and determine the deformation of the rolling element and the raceway after the fault occurs, based on whether the rolling element is located in the fault area. Step 4, substituting the basic parameters and fault parameters of the rolling bearing in step 1 and the fault span angle and the additional clearance caused by the local fault in step 2, and combining whether the rolling element is located in the fault area, a dynamic model of the ball bearing with local raceway fault is established; Step 5, using the 4th-order Runge-Kutta method to solve the dynamic equation of the ball bearing with local raceway fault, obtain the radial displacement of the ball bearing in the vertical and horizontal directions, and complete the calculation of the dynamic response of the ball bearing with local raceway fault; Step 1, obtaining basic parameters and fault parameters of the rolling bearing, where: The basic parameters include geometric dimensions, number of balls, contact stiffness, bearing clearance and equivalent damping; The fault parameters include fault type, fault size and fault location; The fault types include inner ring raceway fault and outer ring raceway fault; Step 4: Substitute the basic parameters and fault parameters of the rolling bearing in step 1 and the fault span angle and the additional clearance caused by the local fault in step 2, and establish a dynamic model of the ball bearing with local raceway fault in combination with whether the rolling element is located in the fault area. The specific method is as follows: and i i =2π(i-1) / N b +oh c t (9) d i =xcosθ i +ysinθ i -d 0 (10) In equations (6) to (11), x and y are the radial displacements of the ball bearing in the vertical and horizontal directions; F x 、F y is the ball bearing reaction force in the x and y directions; m is the equivalent mass of the ball bearing; c is the equivalent damping; W is the ball bearing gravity; θ i is the instantaneous angular position of the i-th rolling element; δ 0 Half of the radial working clearance of the bearing; F i * is the Hertz contact force between the rolling element and the raceway, K is the Hertz contact stiffness; G(·) is the Heaviside function that represents the contact condition, describing the contact between the rolling element and the raceway. When contact occurs, the G(·) value is 1, and when contact is lost, the value is 0. N b is the number of rolling elements; δ i * The deformation of the rolling element and raceway after the fault occurs; t is the time independent variable.

2. The method for calculating the dynamic response of a ball bearing with a local raceway fault according to claim 1, It is characterized in that Step 2: Calculate the fault span angle and the additional gap caused by the local fault. The specific method is: Step 2.1: Calculate the fault span angle θ e : Step 2.2: Calculate the angle between the rolling element and the local fault Step 2.3, calculate the additional gap Δh caused by local fault: In equations (1) to (3), d is the local fault size; d i d o They are the raceway diameters of the inner and outer rings of the bearing respectively; D is the rolling element diameter.

3. The method for calculating the dynamic response of a ball bearing with a local raceway fault according to claim 1, It is characterized in that Step 3: Calculate the angle difference between the center of the rolling element and the center of the local fault, and determine the deformation of the rolling element and the raceway after the fault occurs, based on whether the rolling element is located in the fault area. The specific method is as follows: Step 3.1: Calculate the angle difference θ between the center of each rolling element and the center of the local fault bd : Step 3.2: If the rolling element is located in the fault area, the deformation of the rolling element and the normal raceway needs to be reduced by the additional clearance caused by the local fault, otherwise it remains unchanged: In equations (4) to (5), mod(·) is the remainder function; ω c and ω s are the cage angular velocity and the shaft angular velocity respectively; is the outer ring fault position angle; δ i is the deformation of the rolling element and the normal raceway.

4. A system for calculating the dynamic response of a ball bearing with a local raceway fault, It is characterized in that Based on the method for calculating the dynamic response of a ball bearing with a local raceway fault as described in any one of claims 1 to 3, the calculation of the dynamic response of a ball bearing with a local raceway fault is completed.

5. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the calculation of the dynamic response of a ball bearing with a local raceway fault is completed based on the method for calculating the dynamic response of a ball bearing with a local raceway fault as described in any one of claims 1 to 3.

6. A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the calculation of the dynamic response of a ball bearing with a local raceway fault is completed based on the method for calculating the dynamic response of a ball bearing with a local raceway fault as described in any one of claims 1 to 3.

Images