A method for predicting the spline wear life of a wheel-side reducer of a mine dump truck

Abstract

This invention discloses a method for predicting the spline wear life of a mine dump truck wheel-side reducer, comprising the following steps: 1) statistically analyzing the measured load-time history data using the rainflow counting method to obtain a load spectrum suitable for spline life calculation; 2) calculating the compressive stress on the spline surface based on the motor torque value in the obtained load spectrum; 3) calculating the wear life coefficient value under the allowable compressive stress of the spline; 4) taking the logarithm of the cycle number of spline operation and the wear life coefficient based on the relationship between the cycle number and the wear life coefficient, and fitting a curve; 5) substituting the logarithm of the calculated spline life coefficient Lw as x into the fitted curve to calculate the allowable cycle number of spline wear under the substituted load, and calculating the spline operating time; 6) using the Palmgern-Miner linear damage accumulation theory to calculate the damage value of the design life and predict the life. This invention provides a solution for spline wear life, saving experimental costs.

Description

Technical Field

[0001] This invention relates to a method for predicting the wear life of splines in the wheel-side reducer of a mining dump truck, belonging to the field of mining dump trucks. Background Technology

[0002] The methods for calculating spline strength include Niemann and DIN 5466, but these only calculate the safety factor and lack relevant standards for design life calculation. This makes it impossible to predict lifespan in engineering applications and fails to meet the spare parts reserve requirements for maintenance cycles. Spline fretting wear is a complex chemical and mechanical process, and its mechanism analysis is currently mainly based on experimental research. Summary of the Invention

[0003] To address the problems existing in the prior art, this invention provides a method for predicting the spline wear life of a mine dump truck wheel-side reducer.

[0004] To achieve the above objectives, the present invention employs a method for predicting the spline wear life of a mine dump truck's wheel-side reducer, comprising the following steps:

[0005] S1. The measured load-time history data is statistically analyzed using the rainflow counting method to obtain the results, which are then summarized into a load spectrum that can be used for spline life calculation. This load spectrum includes the motor torque value.

[0006] S2. Calculate the compressive stress on the spline surface based on the motor torque value in the obtained load spectrum;

[0007] S3. Transform the calculation formula for allowable compressive stress on the spline surface to obtain the wear life coefficient value under allowable compressive stress of the spline;

[0008] S4. Based on the relationship between the number of cycles and the wear life coefficient of the spline operation, the logarithm of the number of cycles and the wear life coefficient is processed, and the least squares method is used to fit the curve of the number of cycles and the wear life coefficient.

[0009] The relationship between y (after taking the logarithm of the number of cycles) and x (after taking the logarithm of the wear life coefficient) is as follows:

[0010] y = -6.643511x + 7.987457, the accuracy of the fitted error is: R 2 =0.999480;

[0011] S5. Take the logarithm of the spline wear life coefficient Lw calculated in step S3 and substitute it as x into the curve fitted in step S4 to calculate y. Then take the antilogarithm to calculate the allowable number of spline wear cycles N' under the applied load. n ;

[0012] S6. Applying the Palmgren-Miner linear damage accumulation theory, divide the actual number of cycles under the load by the allowable number of cycles N' for spline wear under each load in step S5. n Calculate the damage value for the design life. When the damage value equals 1, fatigue failure is considered to have occurred, and the fatigue life is estimated.

[0013] In some embodiments, the formula for calculating the compressive stress on the spline surface in step S2 is:

[0014]

[0015] Where Sc is the surface compressive stress of the spline, MPa; T is the motor torque, Nm; D is the spline pitch circle diameter, m; Z is the number of spline teeth; Lg is the spline engagement length, mm; and H is the spline engagement height, mm.

[0016] In some embodiments, the formula for calculating the allowable compressive stress in step S3 is as follows:

[0017]

[0018] Formula for converting to wear life coefficient value:

[0019]

[0020] Where Sc is the surface compressive stress of the spline, MPa; Sac is the maximum allowable compressive stress, MPa; Lw is the wear life coefficient; Ko is the spline overload coefficient; and Km is the error coefficient.

[0021] In some embodiments, the value of Sac in step S3 is: 103.421 when the steel is carburized and Rc58; 82.737 when the steel is carburized and Rc555; and 103.421 when the steel is nitrided.

[0022] In some embodiments, the wear life coefficient Lw is taken as:

[0023] When the number of loops is 10 4 At that time, the wear life coefficient is 4; when the number of cycles is 10 5 At that time, the wear life coefficient was 2.8; when the number of cycles was 10... 6 At that time, the wear life coefficient is 2.0; when the number of cycles is 10... 7 At that time, the wear life coefficient is 1.4; when the number of cycles is 10... 8 At that time, the wear life coefficient is 1.0; when the number of cycles is 10... 9 At that time, the wear life coefficient was 0.7; when the number of cycles was 10... 10 At that time, the wear life coefficient was 0.5.

[0024] In some embodiments, the value of the spline overload factor Ko is:

[0025] When the input end of the prime mover is uniform and stable, and the output end of the driven machine is uniform, stable, slightly impacted, intermittently impacted, and severely impacted, the spline overload coefficients are 1.0, 1.2, 1.5, and 1.8, respectively.

[0026] When the input end of the prime mover experiences a slight impact, and the output end of the driven machine experiences uniform, stable, slight, intermittent, and severe impacts, the spline overload coefficients are 1.2, 1.2, 1.8, and 2.1, respectively.

[0027] When the input end of the prime mover experiences a moderate impact, and the output end of the driven machine experiences uniform, stable, slight, intermittent, and severe impacts, the spline overload coefficients are 2.0, 2.2, 2.4, and 2.8, respectively.

[0028] In some embodiments, the error coefficient Km is taken as:

[0029] When the error is 0.001 mm / mm, and the tooth surface widths are 12.7 mm, 25.4 mm, 50.8 mm, and 101.6 mm, the error coefficients are 1.0, 1.0, 1.0, and 1.5, respectively.

[0030] When the error is 0.002 mm / mm, and the tooth surface widths are 12.7 mm, 25.4 mm, 50.8 mm, and 101.6 mm, the error coefficients are 1.0, 1.0, 1.5, and 2.0, respectively.

[0031] When the error is 0.004 mm / mm, and the tooth surface widths are 12.7 mm, 25.4 mm, 50.8 mm, and 101.6 mm, the error coefficients are 1.0, 1.5, 2.0, and 2.5, respectively.

[0032] When the error is 0.008 mm / mm and the tooth surface widths are 12.7 mm, 25.4 mm, 50.8 mm, and 101.6 mm, the error coefficients are 1.5, 2.0, 2.5, and 3.0, respectively.

[0033] In some embodiments, in step S5, the working time of the spline is calculated using the following formula:

[0034]

[0035] In the formula, L n Let h be the working time of the spline in the nth working cycle; N' n R is the number of allowed loops in the nth working cycle; n The ratio of time spent in the nth work cycle to the total cycle time; nn The rotational speed (rpm) is the speed during the nth work cycle.

[0036] In some embodiments, in step S6, the damage value for the design life is calculated as follows:

[0037]

[0038] Fatigue failure is considered to have occurred when the damage value equals 1. Fatigue life prediction:

[0039]

[0040] In the formula, F is the damage value, 0≤F≤1; N 1、 N2…N n N' represents the actual number of cycles under each operating condition; 1、 N'2…N' n R1, R2, ..., R3 represent the allowable number of cycles under each operating condition; L represents the design life in hours; R1, R2, ..., R3 represent the allowable number of cycles under each operating condition. n The ratio of the time for each operating condition to the total cycle time; n1, n2…n n The speed is given in rpm for each operating condition.

[0041] Compared with existing technologies, the method for predicting the spline wear life of the wheel-side reducer of the mining dump truck of the present invention uses the measured load-time history data and the results of the rainflow counting method to summarize a load spectrum that can be used for spline life calculation. The surface compressive stress is calculated from the torque value in the load spectrum (this method is not limited to surface compressive stress). Then, the spline compressive stress life coefficient is calculated by transforming the spline allowable compressive stress calculation formula. By fitting the relationship between the life coefficient and the logarithm of the number of cycles into a curve, the damage value and life of a single cycle are calculated. Combined with the cumulative damage theory, the fatigue life under the load spectrum is predicted, providing an engineering solution for spline wear life, saving test costs and improving efficiency. Attached Figure Description

[0042] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0043] Figure 1 The curve of wear cycle number and wear life coefficient of spline surface compressive stress is fitted to the present invention. Detailed Implementation

[0044] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this application will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments of this application and the specific features in the embodiments are detailed descriptions of the technical solutions of this application, rather than limitations on the technical solutions of this application. In the absence of conflict, the embodiments of this application and the technical features in the embodiments can be combined with each other.

[0045] A method for predicting the wear life of splines in a mine dump truck wheel-side reducer includes the following steps:

[0046] S1. The measured load-time history data is statistically analyzed using the rainflow counting method to obtain the results, which are summarized into a load spectrum that can be used for spline life calculation. The load spectrum includes frequency value, motor speed value and motor torque value, as shown in Table 1.

[0047] Table 1 Load spectrum for spline life calculation

[0048] Serial Number frequency(%) Motor speed (rpm) Motor torque (Nm) 1 <![CDATA[R1]]> <![CDATA[n1]]> <![CDATA[T1]]> 2 <![CDATA[R2]]> <![CDATA[n2]]> <![CDATA[T2]]> … … … … n Rn nn Tn

[0049] S2. Calculate the compressive stress on the spline surface based on the motor torque value in the obtained load spectrum;

[0050] The formula for calculating the compressive stress on the spline surface is:

[0051]

[0052] Where Sc is the surface compressive stress of the spline, MPa; T is the motor torque, Nm; D is the spline pitch circle diameter, m; Z is the number of spline teeth; Lg is the spline engagement length, mm; H is the spline engagement height, mm;

[0053] S3. Transform the calculation formula for allowable compressive stress on the spline surface to obtain the wear life coefficient value under allowable compressive stress of the spline;

[0054] The formula for calculating allowable compressive stress is as follows:

[0055]

[0056] Formula for converting to wear life coefficient value:

[0057]

[0058] Where Sc is the surface compressive stress of the spline, MPa; Sac is the maximum allowable compressive stress, the values ​​of which are shown in Table 2; Lw is the wear life coefficient, the values ​​of which are shown in Table 3; Ko is the spline overload coefficient, the values ​​of which are shown in Table 4; Km is the error coefficient, the values ​​of which are shown in Table 5.

[0059] Table 2 Maximum allowable compressive stress, Sac (MPa)

[0060] steel Floating involute spline Carburizing, Rc58 103.421 Carburizing, Rc555 82.737 Nitriding 103.421 Quenching -

[0061] Table 3 Wear life coefficient, Lw

[0062]

[0063]

[0064] Table 4 Spline overload coefficient, Ko

[0065]

[0066] Table 5 Error coefficients, Km

[0067]

[0068] S4. Based on the relationship between the number of working cycles of the spline and the wear life coefficient (as shown in Table 3), the logarithm of the number of cycles and the wear life coefficient is processed (as shown in Table 6), and the least squares method is used to fit the curve of the number of cycles and the wear life coefficient.

[0069] Table 6 shows the spline wear life coefficient, calculated as Log(Lw).

[0070]

[0071]

[0072] The fitted curve and function relationship are as follows: Figure 1 As shown, the relationship between y (after taking the logarithm of the number of cycles) and x (after taking the logarithm of the wear life coefficient) is: y = -6.643511x + 7.987457, and the accuracy of the fitted error is: R. 2 =0.999480;

[0073] S5. Take the logarithm of the calculated spline life coefficient Lw and substitute it as x into the fitted equation: y = -6.643511x + 7.987457(R) 2 In the expression =0.9999480), calculate y and then take the antilogarithm;

[0074] The allowable number of cycles N' for spline wear under the applied load can then be calculated. n The working time of the spline can be calculated using the following formula:

[0075]

[0076] In the formula, L n Let h be the working time of the spline in the nth working cycle; N' n R is the number of allowed loops in the nth working cycle; nThe percentage of time spent in the nth work cycle to the total cycle time; n n The rotational speed, in rpm, is the rotational speed during the nth work cycle.

[0077] S6. Applying the Palmgern-Miner linear damage accumulation theory, under each stress application, the component's lifespan is subjected to a small amount of fatigue damage. When the fatigue damage accumulates to a certain extent and reaches the fatigue life limit, fatigue fracture occurs. Divide the actual number of load cycles by the allowable number of spline wear cycles N' under each load in step S5. n The damage value for the design life is calculated as follows:

[0078]

[0079] Fatigue failure is considered to have occurred when the damage value equals 1. Fatigue life prediction:

[0080]

[0081] In the formula, F is the damage value, 0≤F≤1; N 1、 N2…N n N' represents the actual number of cycles under each operating condition; 1、 N'2…N' n R1, R2, ..., R3 represent the allowable number of cycles under each operating condition; L represents the design life in hours; R1, R2, ..., R3 represent the allowable number of cycles under each operating condition. n The ratio of the time for each operating condition to the total cycle time; n1, n2…n n The speed is given in rpm for each operating condition.

[0082] Application Example 1

[0083] Taking an electric drive dump truck (using a motor + reducer transmission) as an example, the motor speed can reach 3500 rpm. The main damage form of the spline is tooth surface wear. The known spline parameters of the motor are Dp = 8 / 16, number of teeth Z = 35, pressure angle α = 30°, and meshing length Lg = 50 mm. The specific calculation parameters are shown in Table 7 below.

[0084] Table 7 Parameters of Electric Drive Dump Truck

[0085]

[0086]

[0087] Calculations show that the estimated lifespan of this spline is 8,126,933 hours.

[0088] The present invention provides a method for predicting the spline wear life of a mine dump truck wheel-side reducer. It uses measured load-time history data and statistical results obtained through rainflow counting to generate a load spectrum suitable for spline life calculation. The surface compressive stress is calculated from the torque values ​​in the load spectrum (this method is not limited to surface compressive stress). Then, by transforming the spline allowable compressive stress calculation formula, the spline compressive stress life coefficient is calculated. A curve is fitted to the relationship between the life coefficient and the logarithm of the number of cycles to calculate the damage value and life of a single cycle. Combined with cumulative damage theory, the fatigue life under the load spectrum is predicted, providing an engineering solution for spline wear life, saving testing costs, and improving efficiency.

[0089] Furthermore, those skilled in the art will understand that although some embodiments described herein include certain features found in other embodiments but not others, combinations of features from different embodiments are also within the scope of protection of this invention and form different embodiments. For example, in the embodiments described above, those skilled in the art can use them in combination based on known technical solutions and the technical problems to be solved by this application.

Claims

1. A method for predicting the wear life of splines in a mine dump truck wheel-side reducer, characterized in that, Includes the following steps: S1. The measured load-time history data is statistically analyzed using the rainflow counting method to obtain the results, which are then summarized into a load spectrum that can be used for spline life calculation. This load spectrum includes the motor torque value. S2. Calculate the compressive stress on the spline surface based on the motor torque value in the obtained load spectrum; S3. Transform the calculation formula for allowable compressive stress on the spline surface to obtain the wear life coefficient value under allowable compressive stress of the spline; S4. Based on the relationship between the number of cycles and the wear life coefficient of the spline operation, the logarithm of the number of cycles and the wear life coefficient is processed, and the least squares method is used to fit the curve of the number of cycles and the wear life coefficient. The relationship between y (after taking the logarithm of the number of cycles) and x (after taking the logarithm of the wear life coefficient) is as follows: y = -6.643511x + 7.987457, the accuracy of the fitted error is: R 2 =0.999480; S5. Take the logarithm of the spline wear life coefficient Lw calculated in step S3 and substitute it as x into the curve fitted in step S4 to calculate y. Then take the antilogarithm to calculate the allowable number of spline wear cycles N' under the applied load. n ; S6. Applying the Palmgren-Miner linear damage accumulation theory, divide the actual number of cycles under the load by the allowable number of cycles N' for spline wear under each load in step S5. n Calculate the damage value for the design life. When the damage value equals 1, fatigue failure is considered to have occurred, and the fatigue life is estimated.

2. The method for predicting the spline wear life of a mine dump truck wheel-side reducer according to claim 1, characterized in that, The formula for calculating the compressive stress on the spline surface in step S2 is as follows: Where Sc is the surface compressive stress of the spline, MPa; T is the motor torque, Nm; D is the spline pitch circle diameter, m; Z is the number of spline teeth; Lg is the spline engagement length, mm; and H is the spline engagement height, mm.

3. The method for predicting the spline wear life of a mine dump truck wheel-side reducer according to claim 1, characterized in that, The formula for calculating the allowable compressive stress in step S3 is as follows: Formula for converting to wear life coefficient value: Where Sc is the surface compressive stress of the spline, MPa; Sac is the maximum allowable compressive stress, MPa; Lw is the wear life coefficient; Ko is the spline overload coefficient; and Km is the error coefficient.

4. The method for predicting the spline wear life of a mine dump truck wheel-side reducer according to claim 3, characterized in that, In step S3, the value of Sac is as follows: when the steel is carburized and Rc is 58, Sac is 103.421; when the steel is carburized and Rc is 555, Sac is 82.737; when the steel is nitrided, Sac is 103.

421.

5. The method for predicting the spline wear life of a mine dump truck wheel-side reducer according to claim 3, characterized in that, The wear life coefficient Lw is taken as follows: when the number of cycles is 10 4 At that time, the wear life coefficient is 4; when the number of cycles is 10 5 At that time, the wear life coefficient was 2.8; when the number of cycles was 10... 6 At that time, the wear life coefficient is 2.0; when the number of cycles is 10... 7 At that time, the wear life coefficient is 1.4; when the number of cycles is 10... 8 At that time, the wear life coefficient is 1.0; when the number of cycles is 10... 9 At that time, the wear life coefficient was 0.7; when the number of cycles was 10... 10 At that time, the wear life coefficient was 0.

5.

6. The method for predicting the spline wear life of a mine dump truck wheel-side reducer according to claim 3, characterized in that, The value of the spline overload coefficient Ko is: When the input end of the prime mover is uniform and stable, and the output end of the working machine is uniform, stable, slightly impacted, intermittently impacted, and severely impacted, the spline overload coefficients are 1.0, 1.2, 1.5, and 1.8, respectively. When the input end of the prime mover experiences a slight impact, and the output end of the driven machine experiences uniform, stable, slight, intermittent, and severe impacts, the spline overload coefficients are 1.2, 1.2, 1.8, and 2.1, respectively. When the input end of the prime mover experiences a moderate impact, and the output end of the driven machine experiences uniform, stable, slight, intermittent, and severe impacts, the spline overload coefficients are 2.0, 2.2, 2.4, and 2.8, respectively.

7. The method for predicting the spline wear life of a mine dump truck wheel-side reducer according to claim 3, characterized in that, The error coefficient Km takes the following values: When the error is 0.001 mm / mm, and the tooth surface widths are 12.7 mm, 25.4 mm, 50.8 mm, and 101.6 mm, the error coefficients are 1.0, 1.0, 1.0, and 1.5, respectively. When the error is 0.002 mm / mm, and the tooth surface widths are 12.7 mm, 25.4 mm, 50.8 mm, and 101.6 mm, the error coefficients are 1.0, 1.0, 1.5, and 2.0, respectively. When the error is 0.004 mm / mm, and the tooth surface widths are 12.7 mm, 25.4 mm, 50.8 mm, and 101.6 mm, the error coefficients are 1.0, 1.5, 2.0, and 2.5, respectively. When the error is 0.008 mm / mm and the tooth surface widths are 12.7 mm, 25.4 mm, 50.8 mm, and 101.6 mm, the error coefficients are 1.5, 2.0, 2.5, and 3.0, respectively.

8. The method for predicting the spline wear life of a mine dump truck wheel-side reducer according to claim 1, characterized in that, In step S5, the working time of the spline is calculated using the following formula: In the formula, L n Let h be the working time of the spline in the nth working cycle; N' n R is the number of allowed loops in the nth working cycle; n The ratio of time spent in the nth work cycle to the total cycle time; n n The rotational speed (rpm) is the speed during the nth working cycle.

9. The method for predicting the spline wear life of a mine dump truck wheel-side reducer according to claim 1, characterized in that, In step S6, the damage value for the design life is calculated as follows: Fatigue failure is considered to have occurred when the damage value equals 1. Fatigue life prediction: In the formula, F is the damage value, 0≤F≤1; N 1、 N2…N n N' represents the actual number of cycles under each operating condition. 1、 N'2…N' n R1, R2, ..., R3 represent the allowable number of cycles under each operating condition; L represents the design life in hours; R1, R2, ..., R3 represent the allowable number of cycles under each operating condition. n The ratio of the time for each operating condition to the total cycle time; n1, n2…n n The speed is given in rpm for each operating condition.

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