Planetary gear complex working condition damage analysis method

Abstract

The invention discloses a planetary gear complex working condition damage analysis method, which mainly considers accumulated fatigue damage calculation of a planetary gear train under a complex working condition, and comprises the following steps of: establishing a multi-degree-of-freedom planetary gear train torsion nonlinear dynamic model, calculating meshing force, and calculating contact stress and bending stress of gear teeth based on the meshing force. Then, a rain flow counting method is adopted to conduct cycle counting on the tooth surface contact stress and tooth root bending stress time history of each stage of gear to obtain a gear stress spectrum, stress data is subjected to load grading and substituted into a Goodman equation, equivalent symmetric cyclic stress amplitude and frequency are obtained, and on the basis of a known material S-N curve, a gear stress spectrum is obtained; and performing damage calculation on the rotating part by using a Miner damage theory. According to the method, a rain flow counting method and a Goodman equation calculation method are combined, fatigue damage of planetary gear teeth under complex working conditions is analyzed, and planetary gear train fatigue damage prediction is achieved.

Description

Technical Field

[0001] The invention relates to a gear tooth damage analysis method, and in particular to a planetary gear tooth complex working condition damage analysis method. Background Art

[0002] The planetary gear reducer is an indispensable part of the electromechanical transmission system. It transmits power output during operation, and its performance directly affects the reliability, stability and other performance of the transmission system. Since the failure mode and damage type of typical components of the electromechanical transmission system are more complex under complex stress, it is crucial to analyze the damage of the planetary gears in the system.

[0003] The damage analysis of planetary gears under complex working conditions can be calculated using Miner theory, especially in the fatigue strength design of mechanical parts and structural components that are subjected to spectral loads. By calculating the Miner coefficient, the safety level, service life, or working load that a part can withstand can be predicted, thereby achieving the purpose of structural dimension design of the part. At present, there is no method for calculating the damage of planetary gears under complex working conditions in China, and the problem of damage calculation and analysis of planetary gears under complex working conditions needs to be solved urgently. Summary of the invention

[0004] The present invention provides a damage analysis method for planetary gears under complex working conditions. It aims to solve the problem that the cumulative damage of planetary gears under complex working conditions cannot be calculated by the lack of damage calculation method for planetary gears in electromechanical composite transmission systems, predicts the total damage of planetary gear components and analyzes the cumulative damage.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A complex working condition damage analysis method for planetary gears comprises the following steps:

[0007] Step 1: Establish a torsional nonlinear dynamic model of a multi-degree-of-freedom planetary gear train and calculate the meshing force;

[0008] Step 2: Calculate the contact stress and bending stress of the gear teeth based on the meshing force;

[0009] Step 3: Use the rain flow counting method to count the time history of the gear tooth surface contact stress and the tooth root bending stress of each level of gear to obtain the gear stress spectrum;

[0010] Step 4: Load grade the stress data and substitute it into the Goodman equation to obtain the equivalent symmetrical cyclic stress amplitude and frequency;

[0011] Step 5: Based on the known material SN curve, use Miner damage theory to calculate the damage of rotating parts.

[0012] The beneficial effects of the present invention are:

[0013] (1) The above damage calculation method can be used to predict the cumulative damage of planetary gear teeth under complex working conditions, and can predict in advance whether the components are about to fail due to fatigue, so that timely maintenance and replacement can be carried out, thereby improving safety and reliability.

[0014] (2) The proposed method can predict the cumulative damage of planetary gear teeth under complex working conditions and can be extended to other materials and other typical rotating components to realize the fatigue damage prediction and analysis of components under complex working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a flow chart of the present invention

[0016] Figure 2 This is a schematic diagram of the planetary gear train transmission of the present invention.

[0017] Figure 3 The sun gear speed of the present invention is 7138r / min; the torque is 406N·M, and the sun gear-planet gear double single double multi-cycle meshing stiffness is

[0018] Figure 4 The rain flow counting method program flow chart of the present invention is

[0019] Figure 5 The sun gear contact stress graded load spectrum and cumulative damage curve of the present invention are

[0020] Figure 6 The sun gear bending stress graded load spectrum and cumulative damage curve of the present invention are

[0021] Detailed description of the implementation plan

[0022] In order to make the technical means, creative features, objectives and effects achieved by the present invention easy to understand, the specific implementation methods of the present invention are described in detail below with reference to the accompanying drawings.

[0023] A complex working condition damage analysis method for planetary gears involves the following steps:

[0024] Step 1: The torsional nonlinear dynamic model of the multi-degree-of-freedom planetary gear system of the present invention is composed of basic components such as sun gears, planetary gears, inner gear rings, planet carriers, bearings, and housings. It includes 1 sun gear represented by s, N planetary gears (represented by P nRepresents the nth planetary gear), and the planetary gears are evenly installed on the planetary carrier, the planetary carrier is represented by c, the inner ring gear is represented by r and is fixed, the sun gear is used as the input end, the input end torque is Tin, the planetary carrier is used as the output end, and the output end torque is Tout. In order to establish the torsional nonlinear dynamic model of the multi-degree-of-freedom planetary gear train, the gears, transmission shafts and other components are assumed to be rigid bodies and the torsional stiffness is not considered during modeling, and the meshing process of the gear pair is simplified to a system composed of stiffness and damping elements, in which the meshing force acts along a specific meshing line direction. In this model, nonlinear factors such as time-varying meshing stiffness, tooth side clearance, comprehensive meshing error and meshing damping of the internal and external gear pairs in the planetary gear train are particularly considered. At the same time, in order to simplify the model, this model ignores factors such as the friction between the tooth surface and the bearing, the support stiffness of the bearing and the overall translation of the system.

[0025] Analysis of the internal excitation and meshing force calculation of the planetary gear train, based on Newton's law, can list N+2 vibration motion differential equations for the torsional nonlinear dynamics model of the planetary gear train:

[0026]

[0027] Where: I s Represents the sun gear moment of inertia; I pn Represents the moment of inertia of the nth planetary gear; I c Represents the moment of inertia of the planet carrier; the base circle radius of the planet carrier is I s ;I s is the meshing angle of the planetary gears; rc is the radius of the planet carrier; r i (i=s,pn,r) represent the base circle radius of the sun gear, planetary gear and inner ring gear respectively; m i (i=s,pn,r) is the mass; the time-varying meshing stiffness, meshing damping coefficient, meshing comprehensive error and half tooth side clearance of the sun gear and the nth planetary gear are expressed as K spn , C spn 、e spn 、b spn , similarly, K rpn , C rpn 、e rpn 、b rpn , represents the time-varying meshing stiffness, meshing damping coefficient, meshing comprehensive error and half tooth side clearance of the nth planetary gear meshing with the ring gear; the transmission diagram of the planetary gear train is as follows Figure 2 .

[0028] Step 2: The present invention takes the planetary gear at the output end of the motor in the electromechanical composite transmission system of the tracked vehicle as the research object, and uses MATLAB software to compile dynamic programs based on the multi-degree-of-freedom planetary dynamics mathematical model. The planetary gear system program uses the sun gear as input, the ring gear is fixed, and the planetary carrier is output. The meshing stiffness and vibration displacement of the gears under various working conditions can be intuitively analyzed through software analysis. Then the corresponding contact stress and bending stress are calculated based on the Hertz contact stiffness and bending stiffness. The meshing stiffness curve under the working conditions of the sun gear speed of 7138r / min and torque of 406N·M calculated by MATLAB is as follows Figure 3 .

[0029] Step 3: For the contact stress and bending stress data obtained in the previous step, the rain flow counting method is used to further process the data. The rain flow counting method is implemented using MATLAB software program, and mainly uses the four-peak valley comparison method. Since the four-peak valley comparison method uses two peak and two valley data, it does not need to reorder the data before counting. In the process of determining a load cycle Δp using the four-peak valley comparison method, first read four consecutive points p from the load history. i 、p i+1 、p i+2 、p i+3 When these four points satisfy the following relationship, it is recorded as a full load cycle.

[0030] Δp=|p i+2 -p i+1 |≤min(|p i+3 -p i+2 |、|p i+1 -p i |) (2)

[0031] The mean is:

[0032] The amplitude is:

[0033] After recording a load cycle, delete the two middle points from the load history, read two new peak-valley values ​​from the load history again, form four new peak-valley values, and continue to use the above load cycle conditions for judgment. If the above load cycle conditions are not met, discard the first point, read the fifth peak-valley value from the load history again, and continue to judge. This is the end of the counting. The remaining peak-valley values ​​that cannot form a full cycle form a residual half cycle. The program flow chart of the rain flow counting method is as follows: Figure 4 .

[0034] Step 4: Load grade the stress data processed by the rainflow counting method and substitute it into the Goodman equation to obtain the equivalent symmetrical cyclic stress amplitude and frequency.

[0035] Step 5: Miner theory In the case of multiple stress levels, the total damage D is the sum of the damage of each stress amplitude, that is:

[0036]

[0037] Among them, n i is the actual number of cycles under the i-th level stress amplitude, N i It indicates the allowable number of cycles until fatigue failure occurs at the i-th level stress amplitude, which can be obtained from the SN curve.

[0038] The sun gear with a sun gear speed of 7138 r / min and a torque of 406 N·M is taken as the research object. Based on Miner's linear cumulative damage theory, the damage accumulation curve is calculated through the SN curve. The sun gear contact stress graded load spectrum and the cumulative damage curve are shown in Figure 5 , the sun gear bending stress graded load spectrum and cumulative damage curve are as follows Figure 6 .

[0039] The parts not elaborated in detail in the present invention belong to the known technologies in the art. Any technical solutions formed by equivalent transformation or equivalent replacement shall fall within the protection scope of the present invention.

Claims

1. A complex working condition damage analysis method for planetary gears, characterized in that The fatigue damage of planetary gears is predicted by dynamic modeling, which includes the following steps: Step 1: Establish a torsional nonlinear dynamic model of a multi-degree-of-freedom planetary gear train and calculate the meshing force; Step 2: Calculate the contact stress and bending stress of the gear teeth based on the meshing force; Step 3: Use the rain flow counting method to count the time history of the gear tooth surface contact stress and the tooth root bending stress of each level of gear to obtain the gear stress spectrum; Step 4: Load grade the stress data and substitute it into the Goodman equation to obtain the equivalent symmetrical cyclic stress amplitude and frequency; Step 5: Based on the known material SN curve, use Miner damage theory to calculate the damage of rotating parts.

2. A planetary gear complex working condition damage analysis method as claimed in claim 1, characterized in that: The internal excitation and meshing force calculation of the planetary gear train are analyzed, and the meshing force is calculated based on the torsional nonlinear dynamic model of the multi-degree-of-freedom planetary gear train.

3. A planetary gear complex working condition damage analysis method as claimed in claim 1, characterized in that: In step 2, firstly, the Hertz contact stiffness k is calculated based on the meshing force obtained by deriving through mechanical formulas. h and bending stiffness U b , and then calculate the corresponding contact stress and bending stress based on the Hertz contact stiffness and bending stiffness.

4. A planetary gear complex working condition damage analysis method as claimed in claim 1, characterized in that: In step 3, the rain flow counting method converts the random load spectrum into a dual-parameter discrete load history with amplitude and mean, and writes a rain flow counting program in MATLAB to count the load-time signal.

5. A planetary gear complex working condition damage analysis method as claimed in claim 1, characterized in that: In step 4, the stress data is load graded and substituted into the Goodman equation to obtain the equivalent symmetrical cyclic stress amplitude and frequency.

6. A planetary gear complex working condition damage analysis method as claimed in claim 1, characterized in that: In step 5, Miner theory is used to estimate the cumulative damage of the planetary gear under different working conditions under cyclic loads based on the SN curve.

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