A bearing single-point fault dynamics modeling method for a sugarcane leaf bundling machine

Abstract

This invention discloses a dynamic modeling method for single-point faults in a sugarcane baler bearing, comprising the following steps: Step (1) constructing a dynamic model of a sugarcane baler tapered roller bearing under healthy conditions; Step (2) constructing the time-varying displacement and contact force generated by the rolling elements of the sugarcane baler tapered roller bearing in the peeling fault area using piecewise functions; Step (3) constructing a dynamic model of the sugarcane baler tapered roller bearing with a single-point fault and a system vibration differential equation set; Step (4) solving the dynamic response characteristics of the sugarcane baler tapered roller bearing; The beneficial effect is that this method can effectively simulate the vibration response characteristics of the sugarcane baler tapered roller bearing when there is a single-point fault, which is of great value for fault diagnosis and feature extraction of the sugarcane baler tapered roller bearing.

Description

Technical Field

[0001] This invention relates to the field of bearing failure dynamics technology, and in particular to a method for dynamic modeling of single-point failures in a sugarcane leaf baler bearing. Background Technology

[0002] Tapered roller bearings, as a typical type of radial thrust bearing, possess significant advantages in agricultural machinery transmission systems due to their ability to simultaneously withstand radial and unidirectional axial loads. These advantages include high load-bearing capacity, good impact resistance, and suitability for heavy-duty conditions, making them widely used in the core transmission components of sugarcane balers. Sugarcane balers operate in complex field conditions, subjecting bearings to long-term alternating loads, dust erosion, and the coupled effects of mechanical vibration. This can lead to localized faults such as single-point spalling on the outer raceway, causing nonlinear vibrations in the bearing system. Consequently, this results in decreased transmission accuracy, increased operating noise, and a significant reduction in equipment reliability and efficiency. Therefore, effectively constructing a dynamic model of single-point faults in tapered roller bearings for sugarcane balers, and simulating the system vibration characteristics and dynamic response under fault conditions, can provide theoretical support for early diagnosis and warning of bearing faults and for the structural optimization design of sugarcane balers.

[0003] However, current traditional research on bearing dynamics modeling is mostly focused on the field of general machinery, without fully considering the actual working conditions of sugarcane balers. This makes it difficult to meet the actual engineering needs of sugarcane baler bearings and restricts the development of fault diagnosis technology for core components of agricultural machinery.

[0004] To address the aforementioned problems, this invention proposes a dynamic modeling method for single-point faults in sugarcane baler bearings. By constructing a bearing dynamic model and a system vibration differential equation set under single-point fault conditions, the dynamic response characteristics of the bearing under different operating conditions can be solved. This method can effectively simulate the vibration response characteristics of tapered roller bearings in sugarcane balers when a single-point fault exists, filling the technical gap in dynamic modeling of bearing faults in sugarcane balers. It provides a theoretical model for fault diagnosis of sugarcane baler bearings and is of great significance for improving the reliability and intelligence level of agricultural machinery. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies and fill related technological gaps, this invention provides a dynamic modeling method for single-point failure of a sugarcane leaf baler bearing. This method first constructs a multi-degree-of-freedom dynamic model of a tapered roller bearing under healthy conditions, then accurately characterizes the time-varying displacement and contact force of the fault region through piecewise functions, and then introduces fault excitation to construct a bearing dynamic model and a system vibration differential equation set under single-point failure. Finally, the vibration differential dynamic equation of the system is solved by numerical integration to obtain the bearing dynamic response characteristics under different working conditions. This method has a certain degree of universality.

[0006] The technical solution adopted by this invention to solve its technical problem is as follows: A dynamic modeling method for single-point failure of a sugarcane leaf baler bearing, characterized by comprising the following steps:

[0007] Step (1): Construct a dynamic model of the tapered roller bearing of the sugarcane leaf baler under healthy conditions. When the bearing is running, due to the rigid connection between the inner ring of the bearing and the shaft, and the outer ring being fixed on the bearing housing, the rotational angular velocity of the bearing cage is... Represented as:

[0008] ;

[0009] in, The average diameter of the rolling element. For bearing pitch diameter, The outer raceway contact angle. The rotational angular velocity of the shaft containing the bearing;

[0010] No. A rolling element in Rotation angle at time for:

[0011] ;

[0012] in, The number of rolling elements in the bearing. The initial angular position of the first rolling element. For time;

[0013] Ignoring the effects of centrifugal force and gyroscopic torque on the rolling elements, the rolling elements deform when the bearing is subjected to external force. Each rolling element and bearing outer ring in Total deformation along the contact normal at any moment for:

[0014] ;

[0015] in, For the rolling element in Deformation in the direction, For the rolling element in Deformation in the direction, For the rolling element in Deformation in the direction, For the first The radial clearance of each rolling element within the load area;

[0016] Therefore, the components of the load on the outer ring of the bearing in the three coordinate directions are as follows:

[0017] ;

[0018] in, For the outer ring of the bearing Load borne in the direction For the outer ring of the bearing Load borne in the direction For the outer ring of the bearing Load borne in the direction For bearing contact stiffness, It is a unit step function;

[0019] Construct a dynamic model of tapered roller bearings for a sugarcane leaf baler considering 9 degrees of freedom:

[0020] ;

[0021] in, , , The inner ring of the bearing is respectively , , Vibration displacement in three directions, , , The outer ring of the bearing is respectively , , Vibration displacement in three directions, , , The bearing housing is located at , , Vibration displacement in three directions;

[0022] Step (2): The time-varying displacement and contact force of the rolling elements of the tapered roller bearing in the sugarcane leaf baler in the peeling fault area are constructed using piecewise functions. The geometric parameters of the fault model are analyzed, and it can be seen that the fault area of ​​the outer raceway corresponds to half of the outer ring center arc in the circumferential direction. The maximum displacement increment of the rolling element in the fault region Represented as:

[0023] ;

[0024] in, For fault width, The outer raceway diameter;

[0025] Therefore, it can be concluded that during the entire interaction between the rolling element and the fault region, the displacement increment of the rolling element in the outer raceway spalling fault region is... Represented as:

[0026] ;

[0027] in, Let θ be the angular position of the outer raceway spalling fault area, and mod(∙) be the modulo operator;

[0028] When the rolling element passes through the fault area on the outer raceway surface of the bearing, it will collide with the edge of the fault area, causing a rapid change in its motion state and a sudden change in radial load, thus generating a significant impact force. At this time, the resultant contact force between the rolling element and the outer raceway of the bearing in the radial direction... Represented as:

[0029] ;

[0030] in, The impact force generated by the collision between the rolling element and the fault area. For impact force and The angle between directions This refers to the load borne by the rolling element when it rolls within the fault-free region.

[0031] Therefore, the time-varying contact force between the rolling element and the spalled area of ​​the outer raceway Represented as:

[0032] ;

[0033] in, This refers to the radial contact force generated between the rolling elements and the outer raceway of the bearing;

[0034] Step (3): Construct a dynamic model and a set of system vibration differential equations for the tapered roller bearing of a sugarcane baler with a single point of failure. Introduce the fault into the constructed dynamic model of the tapered roller bearing of the sugarcane baler under healthy conditions to obtain the comprehensive displacement excitation when the bearing has a single point of failure. for:

[0035] ;

[0036] in, The parameters used to determine whether a rolling element has passed through a spalling fault area can be expressed as:

[0037] ;

[0038] Therefore, when a single point of failure exists, the components of the load on the outer ring of the bearing in the three coordinate directions are as follows:

[0039] ;

[0040] From this, the vibration differential equation of the tapered roller bearing in a sugarcane leaf baler with a single point of failure can be derived:

[0041] The differential equations for the vibration of the bearing inner ring are as follows:

[0042] ;

[0043] in, For the mass of the bearing inner ring, , , The inner ring of the bearing is respectively , , Vibration velocities in three directions , , The inner ring of the bearing is respectively , , Vibration acceleration in three directions, , , The outer ring of the bearing is respectively , , Vibration velocities in three directions This serves as the support damping for the inner ring of the bearing. This refers to the contact damping between the inner and outer rings of the bearing. This refers to the support stiffness of the bearing inner ring. This refers to the radial preload applied to the inner ring of the bearing. It is the acceleration due to gravity;

[0044] The differential equations for the vibration of the bearing outer ring are as follows:

[0045] ;

[0046] in, For the mass of the bearing outer ring, , , The outer ring of the bearing is respectively , , Vibration acceleration in three directions, , , The bearing housing is located at , , Vibration velocities in three directions This refers to the contact damping between the bearing outer ring and the bearing housing. This refers to the contact stiffness between the outer ring of the bearing and the bearing housing.

[0047] The bearing housing vibration differential equations:

[0048] ;

[0049] in, For the quality of the bearing housing, , , The bearing housing is located at , , Vibration acceleration in three directions, For the support damping of the bearing housing, This refers to the support stiffness of the bearing housing;

[0050] Step (4): Solve the dynamic response characteristics of the tapered roller bearing of the sugarcane leaf baler. Taking into account the influence of multiple parameters such as contact damping, contact stiffness, time-varying contact force and radial preload in the system vibration differential equation set, analyze the vibration response behavior of the bearing under different conditions and reveal the influence law of the peeling fault on the dynamic response of the system under various working conditions.

[0051] Compared with existing technologies, the beneficial effects of this invention are as follows: By integrating key parameters such as contact stiffness, contact damping, time-varying contact force, radial preload, and geometric characteristics of the fault area, a 9-DOF dynamic model of the tapered roller bearing of a sugarcane baler under healthy conditions is first established. Then, fault excitation is introduced to construct a bearing dynamic model and a system vibration differential equation set under single-point spalling fault. The numerical integration method is used to solve the equation set to obtain the dynamic response characteristics of the bearing system under different speeds and different fault widths. This fills the technical gap in dynamic modeling of single-point faults in tapered roller bearings of sugarcane balers and provides theoretical models and data support for early diagnosis and online warning of single-point faults in sugarcane baler bearings. Attached Figure Description

[0052] Figure 1 This is a flowchart of the dynamic modeling method for single-point failure of tapered roller bearings in sugarcane leaf balers;

[0053] Figure 2 This is a diagram showing the bearing structural parameters and load distribution.

[0054] Figure 3 This is a structural diagram of the rolling element when it gets stuck in the fault area;

[0055] Figure 4 It is a dynamic model of a single-point failure of a tapered roller bearing in a sugarcane leaf baler;

[0056] Figure 5 These are vibration response diagrams of a single-point fault in a bearing at different rotational speeds. Detailed Implementation

[0057] Embodiments of the present invention will be described with reference to the accompanying drawings, which will be further described below. Figures 1-5 The specific embodiments of the present invention will be described in detail below.

[0058] Figure 1 A flowchart illustrating the dynamic modeling method for single-point failure of a sugarcane leaf baler bearing is provided, including the following steps:

[0059] Step (1): Construct a dynamic model of the tapered roller bearing of a sugarcane leaf baler under healthy conditions. Figure 2 This is a diagram showing the bearing's structural parameters and load distribution. When the bearing is running, due to the rigid connection between the inner ring and the shaft, and the outer ring being fixed to the bearing housing, the bearing cage rotates at an angular velocity... Represented as:

[0060] ;

[0061] in, The average diameter of the rolling element. For bearing pitch diameter, The outer raceway contact angle. The rotational angular velocity of the shaft containing the bearing;

[0062] No. A rolling element in Rotation angle at time and the Radial clearance of each rolling element within the load area for:

[0063] ;

[0064] in, The number of rolling elements in the bearing. The initial angular position of the first rolling element. For time, This refers to the radial clearance of the bearing;

[0065] Ignoring the effects of centrifugal force and gyroscopic torque on the rolling elements, the rolling elements deform when the bearing is subjected to external force. Each rolling element and bearing outer ring in Total deformation along the contact normal at any moment for:

[0066] ;

[0067] in, For the rolling element in Deformation in the direction, For the rolling element in Deformation in the direction, For the rolling element in Deformation in the direction;

[0068] Therefore, the components of the load on the outer ring of the bearing in the three coordinate directions are as follows:

[0069] ;

[0070] in, For the outer ring of the bearing Load borne in the direction For the outer ring of the bearing Load borne in the direction For the outer ring of the bearing Load borne in the direction For bearing contact stiffness, It is a unit step function;

[0071] Construct a dynamic model of tapered roller bearings for a sugarcane leaf baler considering 9 degrees of freedom:

[0072] ;

[0073] in, , , The inner ring of the bearing is respectively , , Vibration displacement in three directions, , , The outer ring of the bearing is respectively , , Vibration displacement in three directions, , , The bearing housing is located at , , Vibration displacement in three directions;

[0074] Step (2): Use piecewise functions to construct the time-varying displacement and contact force generated by the rolling elements of the tapered roller bearing in the peeling fault area of ​​the sugarcane leaf baler. Figure 3 This is a structural diagram of the rolling element when it is trapped in the fault location. Analyzing the geometric parameters of the fault model, it can be seen that the fault area of ​​the outer raceway corresponds to half the arc of the outer ring center in the circumferential direction. The maximum displacement increment of the rolling element in the fault region Represented as:

[0075] ;

[0076] in, For fault width, The outer raceway diameter;

[0077] Therefore, it can be concluded that during the entire interaction between the rolling element and the fault region, the displacement increment of the rolling element in the outer raceway spalling fault region is... Represented as:

[0078] ;

[0079] in, The angle position of the outer raceway spalling fault area is set here. mod(∙) is the modulo operator. The fault area of ​​the outer raceway is half the circumferential radius of the outer ring center. This represents the maximum displacement increment of the rolling element in the fault region;

[0080] When the rolling element passes through the fault area on the outer raceway surface of the bearing, it will collide with the edge of the fault area, causing a sharp change in its motion state and a sudden change in radial load, thus generating a significant impact force. Treating the bearing as a conservative system, assuming that mechanical energy is conserved during the impact, and that the cage and inner raceway speeds are not affected by the instantaneous speed change of the rolling element, we can conclude that:

[0081] ;

[0082] in, For the mass of the rolling element, For impact force and The angle between directions It is the acceleration due to gravity. This indicates the contact deformation between the rolling element and the raceway. and This indicates the linear velocity and angular velocity of the rolling element when it enters the fault zone. and This indicates the linear velocity and angular velocity of the rolling element when it collides with the trailing edge of the fault zone. This represents the moment of inertia of the rolling element as it enters the fault zone. This represents the moment of inertia of the rolling element when it collides with the trailing edge of the fault area.

[0083] Impact and Angle between directions Represented as:

[0084] ;

[0085] The linear velocity of the rolling element before entering the fault zone Represented as:

[0086] ;

[0087] Therefore, the linear velocity when the rolling element collides with the rear edge of the fault area is... Represented as:

[0088] ;

[0089] Analyzing the radial motion of the rolling element using the impulse theorem yields the following results:

[0090] ;

[0091] in, This indicates the speed at which the rolling element experiences an impact. Indicates the duration of the impact. The impact force generated by the collision between the rolling element and the fault area;

[0092] The impact force generated by the collision between the rolling element and the fault area can be calculated. for:

[0093] ;

[0094] At this time, the contact force generated radially between the rolling element and the outer raceway of the bearing Represented as:

[0095] ;

[0096] in, This refers to the load borne by the rolling element when it rolls within the fault-free region.

[0097] Therefore, the time-varying contact force between the rolling element and the spalled area of ​​the outer raceway Represented as:

[0098] ;

[0099] in, This refers to the radial contact force generated between the rolling elements and the outer raceway of the bearing;

[0100] Step (3): Construct a dynamic model and a set of system vibration differential equations for a tapered roller bearing in a sugarcane baler with a single point of failure. Figure 4 This is a dynamic model of a single-point fault in a tapered roller bearing of a sugarcane baler. By introducing the fault into the constructed dynamic model of the tapered roller bearing of the sugarcane baler under healthy conditions, the comprehensive displacement excitation when the bearing has a single-point fault can be obtained. for:

[0101] ;

[0102] in, The parameters used to determine whether a rolling element has passed through a spalling fault area can be expressed as:

[0103] ;

[0104] Calculate contact stiffness using a modified formula We can obtain:

[0105] ;

[0106] in, and These are the contact compliance coefficients of the inner and outer raceways of the bearing, respectively. It is half the cone apex angle of the rolling element. The contact angle between the rolling element and the inner ring raceway flange. The inner raceway contact angle;

[0107] Therefore, when a single point of failure exists, the load on the outer ring of the bearing in the three coordinate directions is as follows:

[0108] ;

[0109] From this, the vibration differential equation of the tapered roller bearing in a sugarcane leaf baler with a single point of failure can be derived:

[0110] The differential equations for the vibration of the bearing inner ring are as follows:

[0111] ;

[0112] in, For the mass of the bearing inner ring, , , The inner ring of the bearing is respectively , , Vibration velocities in three directions , , The inner ring of the bearing is respectively , , Vibration acceleration in three directions, , , The outer ring of the bearing is respectively , , Vibration velocities in three directions This serves as the support damping for the inner ring of the bearing. This refers to the contact damping between the inner and outer rings of the bearing. This refers to the support stiffness of the bearing inner ring. This refers to the radial preload applied to the inner ring of the bearing. It is the acceleration due to gravity;

[0113] The differential equations for the vibration of the bearing outer ring are as follows:

[0114] ;

[0115] in, For the mass of the bearing outer ring, , , The outer ring of the bearing is respectively , , Vibration acceleration in three directions, , , The bearing housing is located at , , Vibration velocities in three directions This refers to the contact damping between the bearing outer ring and the bearing housing. This refers to the contact stiffness between the outer ring of the bearing and the bearing housing.

[0116] The bearing housing vibration differential equations:

[0117] ;

[0118] in, For the quality of the bearing housing, , , The bearing housing is located at , , Vibration acceleration in three directions, For the support damping of the bearing housing, This refers to the support stiffness of the bearing housing;

[0119] Step (4): Solve the dynamic response characteristics of the tapered roller bearing of the sugarcane leaf baler. Taking into account the influence of multiple parameters such as contact damping, contact stiffness, time-varying contact force and radial preload in the system vibration differential equation set, analyze the vibration response behavior of the bearing under different speeds and different fault widths, and reveal the influence law of the peeling fault on the dynamic response of the system under various working conditions.

[0120] In the example, the parameters selected for the tapered roller bearing of the sugarcane leaf baler are shown in Table 1. The vibration differential equations of the tapered roller bearing of the sugarcane leaf baler are solved by programming to obtain the dynamic response characteristics of the bearing system under different speeds and different fault widths.

[0121] Table 1 Basic parameters of tapered roller bearings for sugarcane leaf balers

[0122] parameter numerical values Number of rolling elements 13 Bearing outer diameter (mm) 47 Bearing inner diameter (mm) 25 Bearing pitch diameter (mm) 34.78 Average diameter of rolling elements (mm) 7.31 Inner raceway diameter (mm) 27.5 Outer raceway diameter (mm) 42.1 Bearing clearance (mm) <![CDATA[1 10 -3 <!-- 10 -->]]> Outer raceway contact angle (°) 16

[0123] Figure 5 These are vibration response diagrams of single-point faults in bearings at different speeds. They show the vibration acceleration of the outer ring of the bearing as a function of time when the speed is 1000 r / min and 2000 r / min, respectively, revealing the influence of spalling faults on the dynamic response of the system under different operating conditions.

[0124] The above description is merely a preferred embodiment of the invention and does not constitute any limitation on the invention. Any modifications, alterations, or equivalent changes made to the above embodiments based on the essence of the invention shall still fall within the protection scope of the invention.

Claims

1. A dynamic modeling method for single-point failure of a sugarcane leaf baler bearing, characterized in that, Includes the following steps: Step (1): Construct a dynamic model of the tapered roller bearing of the sugarcane leaf baler under healthy conditions. When the bearing is running, since the inner ring of the bearing is rigidly connected to the shaft and the outer ring is fixed on the bearing housing, the first... A rolling element in Rotation angle at time for: ； in, The number of rolling elements in the bearing. The initial angular position of the first rolling element. The angular velocity of the bearing cage rotation. For time; Ignoring the effects of centrifugal force and gyroscopic torque on the rolling elements, the rolling elements deform when the bearing is subjected to external force. Each rolling element and bearing outer ring in Total deformation along the contact normal at any moment for: ； in, For the rolling element in Deformation in the direction, For the rolling element in Deformation in the direction, For the rolling element in Deformation in the direction, The outer raceway contact angle. For the first The radial clearance of each rolling element within the load area; Therefore, the components of the load on the outer ring of the bearing in the three coordinate directions are as follows: ； in, For the outer ring of the bearing Load borne in the direction For the outer ring of the bearing Load borne in the direction For the outer ring of the bearing Load borne in the direction For bearing contact stiffness, It is a unit step function; Construct a dynamic model of tapered roller bearings for a sugarcane leaf baler considering 9 degrees of freedom: ； in, , , The inner ring of the bearing is respectively , , Vibration displacement in three directions, , , The outer ring of the bearing is respectively , , Vibration displacement in three directions, , , The bearing housing is located at , , Vibration displacement in three directions; Step (2): Use piecewise functions to construct the time-varying displacement and contact force of the rolling elements of the tapered roller bearing in the peeling fault area of ​​the sugarcane leaf baler, and the displacement increment of the rolling elements in the peeling fault area of ​​the outer raceway. for: ； in, The angular position of the outer raceway spalling fault area is given by [reference], and mod(∙) is the modulo operator. The fault area of ​​the outer raceway is half the circumferential radius of the outer ring center. This represents the maximum displacement increment of the rolling element in the fault region; Time-varying contact force between rolling element and outer raceway spalling area Represented as: ； in, This refers to the radial contact force generated between the rolling elements and the outer raceway of the bearing. This refers to the load borne by the rolling element when it rolls within the fault-free region. Step (3): Construct a dynamic model and a set of system vibration differential equations for the tapered roller bearing of a sugarcane baler with a single point of failure. Introduce the fault into the constructed dynamic model of the tapered roller bearing of the sugarcane baler under healthy conditions to obtain the comprehensive displacement excitation when the bearing has a single point of failure. for: ； in, Parameters for determining whether the rolling element has passed through the spalling fault area; Therefore, when a single point of failure exists, the components of the load on the outer ring of the bearing in the three coordinate directions are as follows: ； From this, the vibration differential equation of the tapered roller bearing in a sugarcane leaf baler with a single point of failure can be derived: The differential equations for the vibration of the bearing inner ring are as follows: ； in, For the mass of the bearing inner ring, , , The inner ring of the bearing is respectively , , Vibration velocities in three directions , , The inner ring of the bearing is respectively , , Vibration acceleration in three directions, , , The outer ring of the bearing is respectively , , Vibration velocities in three directions This serves as the support damping for the inner ring of the bearing. This refers to the contact damping between the inner and outer rings of the bearing. This refers to the support stiffness of the bearing inner ring. This refers to the radial preload applied to the inner ring of the bearing. It is the acceleration due to gravity; The differential equations for the vibration of the bearing outer ring are as follows: ； in, For the mass of the bearing outer ring, , , The outer ring of the bearing is respectively , , Vibration acceleration in three directions, , , The bearing housing is located at , , Vibration velocities in three directions This refers to the contact damping between the bearing outer ring and the bearing housing. This refers to the contact stiffness between the outer ring of the bearing and the bearing housing. The bearing housing vibration differential equations: ； in, For the quality of the bearing housing, , , The bearing housing is located at , , Vibration acceleration in three directions, For the support damping of the bearing housing, This refers to the support stiffness of the bearing housing; Step (4): Solve the dynamic response characteristics of the tapered roller bearing of the sugarcane leaf baler, systematically analyze the vibration response behavior of the bearing under different conditions, and reveal the influence law of the peeling fault on the dynamic response of the system under various working conditions.

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