Electric drive reduction gearbox lubrication test method and system

By calculating and generating multiple lubrication test conditions and test samples, simulating real driving scenarios, lubrication tests and quantitative evaluations of the gearbox, solving the problems of low lubrication test efficiency and inaccurate results in the existing technology, and achieving more efficient and accurate lubrication tests.

CN119574105AActive Publication Date: 2025-03-07ZHIXIN TECH CO LTD
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Patent Information

Application Number
CN202411618379.2
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-13
Publication Date
2025-03-07
Estimated Expiration
2044-11-13

AI Technical Summary

Technical Problem

In the prior art, the gearbox lubrication test is inefficient and the results are inaccurate, making it difficult to truly simulate the working conditions of the gearbox during actual driving.

Method used

By calculating and generating the working condition characteristic parameters and the maximum rotation speed of the differential wheel end under multiple lubrication test conditions based on the preset vehicle parameters and electric drive parameters, multiple different test samples are generated, including the refueling volume parameters, the working condition characteristic parameters and the rotation speed of the differential wheel end. Then, the gearbox on the test bench was lubricated, and the real-time image at the bearing was collected, and the ratio of the lubricating oil area to the total bearing area was obtained through image recognition, and the lubricating results were quantified.

Benefits of technology

Scientifically and comprehensively simulate real driving scenarios, improve the comprehensiveness and accuracy of gearbox lubrication tests, and quantitative evaluation results improve objectivity and accuracy.

✦ Generated by Eureka AI based on patent content.

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Patent Text Reader

Abstract

A lubrication test method and system for an electrically driven reduction gearbox belongs to the technical field of development of electrically driven reduction gears.The lubrication test method comprises the steps that working condition characteristic parameters under multiple lubrication test working conditions and / or the maximum rotation speed of the wheel end of a differential in the reduction gearbox are / is obtained through calculation according to preset whole vehicle parameters and electrically driven parameters; aiming at each lubrication test working condition, generating a plurality of different test samples; each test sample comprises a refueling quantity parameter, a working condition characteristic parameter and a differential wheel end rotating speed; and carrying out a lubrication test according to each test sample, and collecting real-time images of each bearing in the reduction gearbox in the test process to carry out image recognition to obtain a ratio of the lubricating oil area to the total area of the bearings and a corresponding test result. According to the method, related sample data of various lubrication test working conditions are calculated through the whole vehicle parameters and the electric driving parameters, so that lubrication test samples under all working conditions are scientifically and comprehensively generated, test result analysis is performed through image recognition, and the evaluation accuracy is improved.
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Description

Technical Field

[0001] The present application relates to the technical field of electric drive reduction gearbox development, and in particular to a lubrication test method and system for an electric drive reduction gearbox. Background Art

[0002] With the development of electrification in the automotive industry, more and more models are switching their powertrains from traditional fuel-driven to electric-driven. The normal operation and reliability of electric drive cannot be achieved without good lubrication. How to determine the minimum refueling amount of the gearbox while ensuring that all its components can have good lubrication effects under various working conditions is the key to the development of gearbox oil.

[0003] Therefore, the lubrication test of the gearbox system is the basis for oil quantity confirmation and subsequent test development. The existing related technologies are limited to improving the tooling structure in the gearbox lubrication test, for example, improving the design of the lubrication oil channel in the gearbox. There is a lack of systematic definition and detailed description of the generation method of the lubrication working condition and the evaluation method of the test results. It is difficult to associate with the actual use of the vehicle and the electric drive system (referred to as electric drive), and it is difficult to truly simulate the working conditions of the gearbox in actual driving.

[0004] Specifically, the generation of existing lubrication conditions is mostly based on project experience and has a certain degree of randomness, while the existing evaluation methods rely on manual visual inspection and make evaluations based on subjective evaluations, which easily ignores relevant data in the lubrication process, resulting in low reliability of lubrication effect evaluation results. Summary of the invention

[0005] The present application provides a lubrication test method and system for an electric drive reduction gearbox, which can solve the technical problems of low lubrication test efficiency and inaccurate results in the prior art.

[0006] In a first aspect, an embodiment of the present application provides a method for testing lubrication of an electric drive reduction gearbox, the method comprising:

[0007] Calculation is performed based on preset vehicle parameters and electric drive parameters to obtain operating condition characteristic parameters under multiple lubrication test conditions and / or the maximum wheel end speed of the differential in the reduction box; the multiple lubrication test conditions include flat ground driving conditions, ramp driving conditions, acceleration and deceleration driving conditions, roll driving conditions, and ramp and roll combined driving conditions, and the operating condition characteristic parameters are used to describe the characteristics of the lubrication test conditions;

[0008] For each lubrication test condition, multiple different test samples are generated; each test sample includes oil filling quantity parameters, working condition characteristic parameters, and differential wheel end speed;

[0009] The reduction gearbox on the test bench is lubricated according to each test sample, and real-time images of each bearing in the reduction gearbox are collected during the test. Image recognition is performed on the real-time images to obtain the ratio of the lubricating oil area to the total bearing area, and the lubrication results are quantitatively evaluated based on the ratio.

[0010] In conjunction with the first aspect, in one implementation, the method includes:

[0011] For the flat ground driving condition, the maximum forward speed of the vehicle when moving forward and the maximum reverse speed of the vehicle when moving backward are calculated based on the vehicle parameters and electric drive parameters;

[0012] The maximum rotation speed of the wheel end of the differential when the vehicle is moving forward is calculated according to the maximum forward speed; the maximum rotation speed of the wheel end of the differential when the vehicle is moving backward is calculated according to the maximum backward speed;

[0013] Different fueling amount parameters, different operating condition characteristic parameters, and different differential wheel end speeds are combined to obtain a plurality of different test samples under flat ground driving conditions; the operating condition characteristic parameters of the flat ground driving conditions are used to describe the forward movement and backward movement of the vehicle.

[0014] In combination with the first aspect, in one implementation, the maximum forward vehicle speed is calculated using the following formula:

[0015]

[0016] in,

[0017] P m Indicates the working condition requirement of the drive motor, in kw;

[0018] V max1 Indicates the maximum forward speed in km / h;

[0019] η t Indicates the transmission system efficiency;

[0020] m represents the vehicle mass in kg;

[0021] g represents the acceleration due to gravity, g = 9.8 m / s 2 ;

[0022] f represents the rolling resistance coefficient of the vehicle;

[0023] C D Indicates the drag coefficient;

[0024] A represents the windward area, in m 2 ;

[0025] m, g, f, C D, and A are vehicle parameters, P m and η t Electric drive parameters.

[0026] In combination with the first aspect, in one implementation, the maximum wheel end speed of the differential when the vehicle is moving forward is calculated using the following formula:

[0027]

[0028] in,

[0029] n dri Indicates the maximum speed of the wheel end of the differential when the vehicle is moving forward, in r / min;

[0030] V max1 Indicates the maximum forward speed in km / h;

[0031] r represents the wheel diameter in meters.

[0032] The maximum speed of the wheel end of the differential when the vehicle is moving backward is calculated using the following formula:

[0033]

[0034] in,

[0035] n rev Indicates the maximum speed of the wheel end of the differential when the vehicle moves backward, in r / min;

[0036] V max2 Indicates the maximum reverse speed in km / h;

[0037] r represents the wheel diameter in meters.

[0038] In conjunction with the first aspect, in one implementation, the method includes:

[0039] For ramp driving conditions, the maximum climbing gradient when the vehicle is going uphill and the maximum descending gradient when the vehicle is going downhill are calculated based on the vehicle parameters and electric drive parameters;

[0040] Calculate the maximum wheel speed of the differential when the vehicle is going uphill and the maximum wheel speed of the differential when the vehicle is going downhill according to the preset coefficient and the maximum wheel speed of the differential when the vehicle is moving forward;

[0041] Different refueling parameters, different operating characteristic parameters, and different differential wheel end speeds are combined to obtain a plurality of different test samples under a slope driving condition; the operating characteristic parameters of the slope driving condition are used to describe the climbing gradient of the vehicle and the descending gradient of the vehicle.

[0042] In conjunction with the first aspect, in one implementation, the method includes:

[0043] For acceleration and deceleration driving conditions, calculations are performed based on vehicle parameters and electric drive parameters to obtain the maximum acceleration liquid level inclination in the reduction box when the vehicle is accelerating and the maximum deceleration liquid level inclination in the reduction box when the vehicle is decelerating;

[0044] The maximum wheel speed of the differential when the vehicle is accelerating is obtained by calculating the wheel speed at the inflection point of the external characteristic curve and the speed ratio of the reduction gearbox;

[0045] The maximum rotation speed of the wheel end of the differential when the vehicle is moving forward is used as the maximum rotation speed of the wheel end of the differential when the vehicle is decelerating;

[0046] Different refueling amount parameters, different operating condition characteristic parameters, and different differential wheel end speeds are combined to obtain multiple different test samples under acceleration and deceleration driving conditions; the operating condition characteristic parameters of the acceleration and deceleration driving conditions are used to describe the inclination of the acceleration fluid level in the reduction box when the vehicle accelerates and the inclination of the deceleration fluid level in the reduction box when the vehicle decelerates.

[0047] In conjunction with the first aspect, in one implementation, the method includes:

[0048] For the rolling driving condition, the maximum left tilt inclination in the reduction gearbox when the vehicle tilts to the left and the maximum right tilt inclination in the reduction gearbox when the vehicle tilts to the right are calculated based on the vehicle parameters and the electric drive parameters;

[0049] Calculate the maximum wheel end speed of the differential when the vehicle is leaning to the left and the maximum wheel end speed of the differential when the vehicle is leaning to the right according to the preset coefficient and the maximum wheel end speed of the differential when the vehicle is moving forward;

[0050] Different refueling parameters, different operating characteristic parameters, and different differential wheel end speeds are combined to obtain multiple different test samples under the rolling driving condition; the operating characteristic parameters of the rolling driving condition are used to describe the left inclination of the vehicle when it leans to the left and the right inclination of the vehicle when it leans to the right.

[0051] In conjunction with the first aspect, in one implementation, the method includes:

[0052] For the ramp and roll combined driving condition, multiple test samples of the ramp driving condition are combined with multiple test samples of the roll driving condition to obtain test samples of the ramp and roll combined driving condition; the operating condition characteristic parameters of the ramp and roll combined driving condition are used to describe the climbing grade of the vehicle climbing, the descending grade of the vehicle descending, the left inclination of the vehicle leaning to the left, and the right inclination of the vehicle leaning to the right.

[0053] In conjunction with the first aspect, in one implementation, the method includes:

[0054] After the reduction gearbox is installed on the test bench, the differential in the reduction gearbox is driven to rotate through the tooling shaft of the test bench. The rotation speed of the tooling shaft is consistent with the rotation speed of the differential wheel end in the test sample. The position and movement of the test bench are consistent with the refueling parameters and operating condition characteristic parameters in the test sample.

[0055] In a second aspect, an embodiment of the present application provides an electric drive reduction gearbox lubrication test system, the system comprising:

[0056] A preprocessing module, which is used to calculate according to preset vehicle parameters and electric drive parameters to obtain operating condition characteristic parameters under multiple lubrication test conditions and / or the maximum wheel end speed of the differential in the reduction box; the multiple lubrication test conditions include flat ground driving conditions, ramp driving conditions, acceleration and deceleration driving conditions, roll driving conditions, and ramp and roll combined driving conditions, and the operating condition characteristic parameters are used to describe the characteristics of the lubrication test conditions;

[0057] A sample generation module, which is used to generate a plurality of different test samples for each lubrication test condition; each test sample includes a refueling amount parameter, a working condition characteristic parameter, and a differential wheel end speed;

[0058] The test module is used to perform lubrication tests on the reduction box on the test bench according to each test sample, and collect real-time images of each bearing in the reduction box during the test; perform image recognition on the real-time images to obtain the ratio of the lubricating oil area to the total bearing area, and quantitatively evaluate the lubrication results based on the ratio.

[0059] The beneficial effects brought by the technical solution provided in the embodiments of the present application include:

[0060] Taking into account the vehicle parameters and electric drive parameters, lubrication test samples under various lubrication test conditions are generated through calculation. Different lubrication test samples include refueling quantity parameters, operating condition characteristic parameters, and differential wheel end speed. It can scientifically and comprehensively simulate real driving scenarios and improve the comprehensiveness and accuracy of lubrication testing of reduction gearboxes.

[0061] During the test, real-time images of each bearing in the reduction gearbox are collected and image recognition is performed on the real-time images to obtain the ratio of the lubricating oil area to the total bearing area. The test results are obtained based on the ratio, and the objectivity and accuracy of the test evaluation results are improved in a quantitative evaluation manner. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 This is a flow chart of an embodiment of the electric drive reduction gearbox lubrication test method of the present application;

[0063] Figure 2This is a flow chart of an embodiment of a lubrication test method for an electric drive reduction gearbox of the present application;

[0064] Figure 3 This is a schematic diagram of the functional modules of an embodiment of the electric drive reduction gearbox lubrication test system of the present application. DETAILED DESCRIPTION

[0065] In order to enable those skilled in the art to better understand the solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0066] In order to make the objectives, technical solutions and advantages of the present application clearer, the implementation methods of the present application will be further described in detail below with reference to the accompanying drawings.

[0067] In a first aspect, an embodiment of the present application provides a lubrication test method for an electric drive reduction gearbox.

[0068] In one embodiment, referring to Figure 1 and Figure 2 , Figure 1 This is a flow chart of an embodiment of the electric drive reduction gearbox lubrication test method of the present application. Figure 2 This is a flow chart of an embodiment of the electric drive reduction gearbox lubrication test method of the present application. Figure 1 and Figure 2 As shown, the electric drive reduction gearbox lubrication test method includes:

[0069] Step S1: Calculate according to preset vehicle parameters and electric drive parameters to obtain operating condition characteristic parameters under multiple lubrication test conditions and / or the maximum wheel end speed of the differential in the reduction box. The multiple lubrication test conditions include flat ground driving conditions, ramp driving conditions, acceleration and deceleration driving conditions, roll driving conditions, and ramp and roll combined driving conditions. The operating condition characteristic parameters are used to describe the characteristics of the lubrication test conditions.

[0070] Step S2: for each lubrication test condition, generate a plurality of different test samples, each of which includes a refueling amount parameter, a condition characteristic parameter, and a differential wheel end speed.

[0071] Step S3: performing lubrication tests on the reduction box on the test bench according to each test sample, and collecting real-time images of each bearing in the reduction box during the test.

[0072] Step S4: Perform image recognition on the real-time image to obtain the ratio of the lubricating oil area to the total bearing area, and perform quantitative evaluation on the lubrication result according to the ratio.

[0073] The existing technology has the technical problems of inaccurate evaluation of the actual lubrication effect of the lubricating oil in the reduction gearbox and over-reliance on subjective evaluation, resulting in low evaluation quality. In addition, in the actual driving process of the whole vehicle, there are ups and downslopes, acceleration and deceleration, left and right tilt, and the combination of ups and downslopes and left and right tilts, which will affect the actual lubrication effect. The existing lubrication test lacks improvement in lubrication conditions.

[0074] In this embodiment, for the generation and evaluation of lubrication test conditions, the vehicle parameters and electric drive parameters are taken into consideration, and lubrication test samples under various lubrication test conditions are generated by calculation. Different lubrication test samples include refueling quantity parameters, operating condition characteristic parameters, and differential wheel end speed, which can scientifically and comprehensively simulate real driving scenarios and improve the comprehensiveness and accuracy of lubrication testing of the reduction gearbox.

[0075] During the test, real-time images of each bearing in the reduction gearbox are collected and image recognition is performed on the real-time images to obtain the ratio of the lubricating oil area to the total bearing area. The test results are obtained based on the ratio, and the objectivity and accuracy of the test evaluation results are improved in a quantitative evaluation manner.

[0076] Furthermore, in one embodiment, the method includes:

[0077] For flat ground driving conditions, the maximum forward speed of the vehicle when it is moving forward and the maximum reverse speed of the vehicle when it is moving backward are calculated based on the vehicle parameters and electric drive parameters.

[0078] The maximum rotation speed of the wheel end of the differential when the vehicle is moving forward is calculated based on the maximum forward speed. The maximum rotation speed of the wheel end of the differential when the vehicle is moving backward is calculated based on the maximum backward speed.

[0079] Different fueling amount parameters, different operating condition characteristic parameters, and different differential wheel end speeds are combined to obtain multiple different test samples under flat ground driving conditions. The operating condition characteristic parameters of the flat ground driving condition are used to describe the forward movement and backward movement of the vehicle.

[0080] In this embodiment, the flat ground driving condition is the basis of the lubrication test and is generally tested and evaluated first. The lubrication performance of the reduction gearbox under the flat ground driving condition mainly depends on the differential wheel end speed corresponding to the maximum vehicle speed when the vehicle is moving forward, and the maximum differential wheel end speed corresponding to the maximum vehicle speed when the vehicle is reversing.

[0081] Furthermore, in one embodiment, the maximum forward vehicle speed is calculated using the following formula (1):

[0082]

[0083] Among them, P m Indicates the working condition requirement of the drive motor, in kw. V max1 Indicates the maximum forward speed, in km / h. t Indicates the efficiency of the transmission system. m indicates the mass of the vehicle, in kg. g indicates the acceleration due to gravity, g = 9.8 m / s 2 . f represents the rolling resistance coefficient of the vehicle. C D Indicates the drag coefficient. A indicates the windward area, in m 2 m, g, f, C D , and A are vehicle parameters, P m and η t Electric drive parameters.

[0084] In this embodiment, the vehicle speed when moving forward is generally not limited in advance, while the maximum vehicle speed when moving backward generally needs to be determined according to a preset reverse speed limit strategy.

[0085] Furthermore, in one embodiment, the maximum wheel end speed of the differential when the vehicle is moving forward is calculated using the following formula (2):

[0086]

[0087] Among them, n dri Indicates the maximum speed of the wheel end of the differential when the vehicle is moving forward, in r / min. max1 Indicates the maximum forward speed in km / h. r indicates the wheel diameter in m.

[0088] The maximum wheel speed when the vehicle moves backward is calculated using the following formula (3):

[0089]

[0090] Among them, n rev Indicates the maximum speed of the wheel end of the differential when the vehicle is moving backward, in r / min. max2 Indicates the maximum reverse speed in km / h. r indicates the wheel diameter in m.

[0091] In this embodiment, after the maximum forward vehicle speed and the maximum reverse vehicle speed are converted, the maximum rotational speed of the wheel end of the differential is converted using the above formula (2) and formula (3).

[0092] In a specific embodiment, taking the flat ground driving condition of a newly developed electric drive vehicle as an example, the maximum wheel end speed of the differential when the vehicle is moving forward is calculated to be 1100 rpm through the vehicle parameters and the electric drive parameters, and the maximum wheel end speed of the differential when the vehicle is moving backward is 400 rpm. The differential wheel end speed when the vehicle is moving forward is represented by a positive value, and the differential wheel end speed when the vehicle is moving backward is represented by a negative value. The test sample set of the flat ground driving condition is shown in Table 1 below, which includes 13 test sample working condition points, wherein the working condition to be processed is marked with a circle (○):

[0093] Table 1 Test sample set of flat ground driving condition

[0094]

[0095]

[0096] In this embodiment, when conducting a lubrication test, the reduction gearbox is installed on a test bench, the differential in the reduction gearbox is controlled to rotate according to the differential wheel end speed in the test sample, and the test bench is controlled to move according to the operating characteristic parameters in the test sample, that is, the vehicle moving forward and the vehicle moving backward, so that the reduction gearbox simulates being in the vehicle moving forward scenario and the vehicle moving backward scenario.

[0097] Furthermore, in one embodiment, the method includes:

[0098] For the slope driving condition, the maximum climbing gradient of the vehicle when going uphill and the maximum descending gradient of the vehicle when going downhill are calculated based on the vehicle parameters and electric drive parameters.

[0099] The maximum rotational speed of the wheel end of the differential when the vehicle is moving forward is calculated based on the preset coefficient, and the maximum rotational speed of the wheel end of the differential when the vehicle is going uphill and the maximum rotational speed of the wheel end of the differential when the vehicle is going downhill are obtained.

[0100] Different fueling parameters, different operating characteristic parameters, and different differential wheel end speeds are combined to obtain multiple different test samples under the ramp driving condition. The operating characteristic parameters of the ramp driving condition are used to describe the climbing grade of the vehicle and the descending grade of the vehicle.

[0101] In this embodiment, the lubrication performance of the reduction gearbox under the ramp driving condition mainly depends on the maximum climbing grade and the maximum descending grade.

[0102] The differential wheel end speed corresponding to the maximum vehicle speed when moving forward, and the maximum differential wheel end speed corresponding to the maximum vehicle speed when the vehicle is reversing.

[0103] According to automobile theory, the slope angle and climbing grade are calculated using the following formula (4) and formula (5) respectively:

[0104]

[0105] i=tanα (5)

[0106] Where, α represents the maximum climbing angle. i represents the maximum climbing grade. t Indicates the maximum driving force of the motor, in N. F f Indicates the rolling resistance of the vehicle, in N. F w Represents air resistance in N. G represents the gross weight of the vehicle in N.

[0107] For the maximum climbing angle α, the corresponding climbing angle i1 = tanα, and the corresponding maximum speed of the differential wheel end is 0.2×n dri , n dri It is the maximum speed of the wheel end of the differential when the vehicle is moving forward under flat driving conditions.

[0108] For a medium climbing angle α / 2, the corresponding climbing angle i2 = tan(α / 2), and the corresponding maximum speed of the differential wheel end is 0.4×n dri .

[0109] For the maximum downhill angle -α, the corresponding climbing angle i3 = tan(-α), and the corresponding maximum speed of the differential wheel end is 0.2×n dri .

[0110] For a moderate downhill slope angle of -α / 2, the corresponding climbing angle i2 = tan(-α / 2), and the corresponding maximum speed of the differential wheel end is 0.4×n dri .

[0111] In a specific embodiment, taking the ramp driving condition of a newly developed electric drive vehicle as an example, the vehicle's extreme climbing grade is calculated by the vehicle parameters and the electric drive parameters to be i1=40%, and the maximum wheel end speed of the differential is 200 rpm during the extreme climbing. The medium climbing grade of the vehicle is i2=25%, and the maximum wheel end speed of the differential is 400 rpm during the medium climbing. The differential wheel end speed when the vehicle is climbing is represented by a positive value, and the differential wheel end speed when the vehicle is going downhill is represented by a negative value. The test sample set of the ramp driving condition is shown in Table 2 below, which includes 12 test sample working condition points, wherein the working condition to be processed is marked with a circle (○):

[0112] Table 2 Test sample set of ramp driving condition

[0113] slope 100 200 300 400 Moderate climbing 25% ○ ○ ○ ○ Maximum climbing grade 40% ○ ○ Moderate downhill -25% ○ ○ ○ ○ Extreme downhill slope -40% ○ ○

[0114] Furthermore, in one embodiment, the method includes:

[0115] For acceleration and deceleration driving conditions, calculations are performed based on vehicle parameters and electric drive parameters to obtain the maximum acceleration fluid level inclination in the reduction box when the vehicle accelerates and the maximum deceleration fluid level inclination in the reduction box when the vehicle decelerates.

[0116] The maximum speed of the wheel end of the differential when the vehicle accelerates is obtained by calculating the wheel speed at the inflection point of the external characteristic curve and the speed ratio of the reduction gearbox.

[0117] The maximum rotational speed of the wheel end of the differential when the vehicle is moving forward is used as the maximum rotational speed of the wheel end of the differential when the vehicle is decelerating.

[0118] Different refueling parameters, different operating characteristic parameters, and different differential wheel end speeds are combined to obtain multiple different test samples under acceleration and deceleration driving conditions. The operating characteristic parameters of the acceleration and deceleration driving conditions are used to describe the acceleration fluid level inclination in the reduction box when the vehicle accelerates and the deceleration fluid level inclination in the reduction box when the vehicle decelerates.

[0119] In this embodiment, due to inertia, when the vehicle is in extreme acceleration and extreme braking conditions, the liquid level in the reduction box will produce a corresponding liquid level angle, and the angle has a corresponding conversion relationship with the acceleration and deceleration of the whole vehicle. The conversion formula (6) of the maximum liquid level inclination angle of acceleration and the conversion formula (7) of the maximum liquid level inclination angle of deceleration are as follows:

[0120] Q = arctan(a / g) (6)

[0121] P = arctan(b / g) (7)

[0122] Among them, Q represents the maximum liquid surface inclination angle of acceleration, a represents the vehicle's limit acceleration, and the unit is m / s 2 , the corresponding maximum liquid surface inclination is (a / g)×%.

[0123] P represents the maximum liquid level inclination angle for deceleration, and b represents the vehicle's limit deceleration, in m / s 2 , the corresponding maximum liquid level inclination during deceleration is (b / g)×%.

[0124] Since the limit acceleration drops significantly after passing the inflection point of the external characteristic (before this point, the acceleration of the whole vehicle is the maximum, and then it drops), the maximum vehicle speed corresponding to the limit acceleration condition is the maximum vehicle speed corresponding to the inflection point of the motor external characteristic curve, and the maximum speed of the differential wheel end corresponding to the limit acceleration condition is the wheel end speed corresponding to the maximum speed. The maximum speed of the differential wheel end when the vehicle accelerates is obtained by dividing the wheel speed at the inflection point of the external characteristic curve by the speed ratio of the reduction box.

[0125] In a specific embodiment, taking the ramp driving condition of a newly developed electric drive vehicle as an example, the maximum liquid level inclination corresponding to the extreme acceleration is calculated by the vehicle parameters and the electric drive parameters to be 45%, the maximum wheel end speed corresponding to the extreme acceleration is 400rpm, the maximum liquid level inclination corresponding to the extreme braking is -60%, and the maximum wheel end speed corresponding to the extreme acceleration is 1100rpm. The differential wheel end speed when the vehicle accelerates is represented by a positive value, and the differential wheel end speed when the vehicle brakes is represented by a negative value. The test sample set of the acceleration and deceleration driving condition is shown in Table 3 below, which includes 13 test sample working condition points, wherein the working condition to be processed is marked with a circle (O):

[0126] Table 3 Test sample set of acceleration and deceleration driving conditions

[0127]

[0128] Furthermore, in one embodiment, the method includes:

[0129] For the rolling driving condition, calculation is performed based on the vehicle parameters and the electric drive parameters to obtain the maximum left tilt inclination in the reduction box when the vehicle tilts to the left and the maximum right tilt in the reduction box when the vehicle tilts to the right.

[0130] The maximum wheel end speed of the differential when the vehicle is leaning to the left and the maximum wheel end speed of the differential when the vehicle is leaning to the right are calculated based on the preset coefficient and the maximum wheel end speed of the differential when the vehicle is leaning to the right.

[0131] Different fueling parameters, different operating condition characteristic parameters, and different differential wheel end speeds are combined to obtain multiple different test samples under the rolling driving condition. The operating condition characteristic parameters of the rolling driving condition are used to describe the leftward inclination of the vehicle when it is tilted to the left and the rightward inclination of the vehicle when it is tilted to the right.

[0132] In this embodiment, the maximum tilt angle is when the vehicle is driving or turning, causing the left and right wheels of the vehicle to deflect to different degrees, and the maximum deflection angle is the maximum roll angle. Calculating the maximum roll angle plays a vital role in the formulation of lubrication conditions. The lubrication test of the maximum tilt angle can effectively evaluate the lubrication risk of the vehicle under the condition of tilting driving. The maximum tilt angle calculation formula (8) is as follows:

[0133]

[0134] Where β is the maximum roll angle, m is the vehicle mass, in kg. H is the height of the vehicle center of mass, in m. z It represents the vertical load of the tire in N. c represents the wheelbase in m.

[0135] At the medium left-leaning liquid level angle, the maximum vehicle speed corresponding to the platform tilt angle β / 2 is 80% of the maximum vehicle speed on flat ground. At the extreme left-leaning liquid level angle, the maximum vehicle speed corresponding to the platform tilt angle β is 20% of the maximum vehicle speed on flat ground.

[0136] In a specific embodiment, taking the ramp driving condition of a newly developed electric drive vehicle as an example, the vehicle parameters and the electric drive parameters are used to calculate that the limit tilt angle is 20°, the limit tilt is 36%, and the maximum wheel end speed at the limit tilt is 200 rpm. The test sample set of the roll driving condition is shown in Table 4 below, which includes 24 test sample working condition points, wherein the working condition to be processed is marked with a circle (○):

[0137] Table 4 Test sample set of roll driving condition

[0138] 100 200 300 400 … 900 Medium left tilt level, bench tilt 18% ○ ○ ○ ○ ○ ○ Extreme left tilt level, platform tilt 36% ○ ○ Medium right tilt level, platform tilt 18% ○ ○ ○ ○ ○ ○ Limit right tilt level, platform tilt 36% ○ ○

[0139] Furthermore, in one embodiment, the method includes:

[0140] For the ramp and roll combined driving condition, multiple test samples of the ramp driving condition are combined with multiple test samples of the roll driving condition to obtain the test samples of the ramp and roll combined driving condition. The condition characteristic parameters of the ramp and roll combined driving condition are used to describe the climbing grade of the vehicle climbing, the descending grade of the vehicle descending, the left inclination of the vehicle leaning to the left, and the right inclination of the vehicle leaning to the right.

[0141] In this embodiment, uphill, downhill, left lean, and right lean are combined respectively to obtain four groups of test postures, and the specific rotation speed is the intersection of the ramp and tilt postures.

[0142] The maximum wheel speed of the corresponding combined working condition is 0.4×n dri .

[0143] In a specific embodiment, taking the flat ground driving condition of a newly developed electric drive vehicle as an example, the medium inclination angle is 10°, the medium inclination is 18%, the medium climbing grade is 25%, and the maximum wheel end speed of the medium climbing grade is 40 rpm through calculations based on the vehicle parameters and the electric drive parameters. The test sample set of the ramp and roll combined driving condition is shown in Table 5 below, which includes 16 test sample condition points, wherein the condition to be processed is marked with a circle (○):

[0144] Table 5 Test sample set of ramp and roll combined driving conditions

[0145]

[0146]

[0147] Furthermore, in one embodiment, the method includes:

[0148] After the reduction gearbox is installed on the test bench, the differential in the reduction gearbox is driven to rotate through the tooling shaft of the test bench. The rotation speed of the tooling shaft is consistent with the rotation speed of the differential wheel end in the test sample. The position and movement of the test bench are consistent with the refueling parameters and operating condition characteristic parameters in the test sample.

[0149] In this embodiment, the various lubrication test conditions generated according to the above steps are summarized into a matrix of the overall lubrication conditions, and repeated tests are performed according to three refueling amounts, namely, the lower limit, the middle value and the upper limit of the refueling amount.

[0150] Specifically, the reducer is installed in the specified direction. When the vehicle moves forward, the rotation direction of the reducer input shaft is forward. The reducer is installed in the specified direction. When the vehicle moves backward, the rotation direction of the reducer input shaft is reverse. The temperature measured by the temperature sensor at the reducer oil drain hole bolt.

[0151] The lubrication matrix of the entire working condition is input to the test bench for the execution of the lubrication test. The gearbox lubrication transparent prototype is fixed on the lubrication bench through the tooling. The bench motor drives the gearbox to rotate through the tooling shaft at the differential end (belonging to the bench, driving the differential to drive the gearbox to rotate), and the input shaft end of the gearbox (normally the input shaft drives the gearbox to rotate by driving the differential) is unloaded. An oil temperature sensor is arranged at the bottom of the gearbox to detect the temperature of the lubricating liquid.

[0152] During the entire test process, only the differential wheel end speed is loaded. The running time of each speed condition is 3 minutes, and the speed increase and decrease rate is unified to the wheel end speed 10rpm / s. For each running condition, the corresponding lubrication video is recorded by the camera. The main observation objects are the six bearings of the reduction box, and there are six cameras corresponding to each. During the operation, the lubricating fluid temperature is maintained between 60℃ and 80℃.

[0153] Documentation before the test: 1) Lubricant type. 2) Lubricant filling amount and residual oil amount.

[0154] Test operation process documentation: 1) Test bench input speed, torque (liquid resistance to the tooling axis). 2) Test bench flip angle. 3) Oil pan temperature.

[0155] Post-test documentation: 1) Subjective evaluation score sheet of lubrication results for each lubrication part. 2) Video file of lubricating oil flow under each working condition.

[0156] The gearbox lubrication test focuses on the bearing parts, and each bearing position has a corresponding camera to record the lubrication conditions. After the video is recorded, the lubrication conditions of different bearing positions in each condition are image recognized. The lubricating liquid is displayed in red. After importing the pictures of the lubrication conditions, the Python algorithm is used to distinguish and identify the area S of the lubricating liquid. red .

[0157] The specific steps of using Python code to calculate the area of ​​lubricant in the image include: loading the image, color space conversion, color threshold segmentation, and area statistics. Among them, an important step is to use the color threshold segmentation technique, which involves separating pixels of a specific color or color range in the image. Commonly used processing libraries such as OpenCV provide powerful functions to implement color detection and area calculation.

[0158] First, you need to load the image and preprocess it. Preprocessing usually includes grayscale conversion, noise removal, etc. The specific steps include image preprocessing, color threshold segmentation, and calculation of the lubricant area. Image preprocessing converts the BGR image to the HSV color space. Color threshold segmentation segments the image based on the color threshold, which involves setting the minimum and maximum thresholds of the color in the HSV color space and extracting the corresponding color area through these thresholds. This step is completed by the inRange() function of OpenCV.

[0159] #Define the minimum and maximum thresholds of the color (taking red as an example)

[0160] lower_red=np.array([0,120,70])

[0161] upper_red=np.array([10,255,255])

[0162] Get the mask of the corresponding color area according to the threshold

[0163] mask=cv2.inRange(hsv_image,lower_blue,upper_blue)

[0164] Perform AND operation on the mask and the original image to extract the colored part

[0165] color_segment=cv2.bitwise_and(image,image,mask=mask)

[0166] Calculate the area of ​​the lubricating fluid (red)

[0167] After obtaining the color mask, the steps to calculate the color area are as follows:

[0168] #Calculate the number of red pixels in the mask, which is the area of ​​the color area (in pixels)

[0169] lower_red=np.array([0,120,70])

[0170] upper_red=np.array([10,255,255])

[0171] red_area=calculate_area_of_color(hsv_image,lower_red,upper_red)

[0172] The value of red_area is the area S where the lubricant is identified. red .

[0173] The amount of lubricating fluid is quantitatively scored. Taking the input shaft bearing as an example, the area of ​​the bearing seat is taken as the benchmark S base , Proportion = S red / S base ×100%, objectively score the lubrication results according to the gradient of area ratio. The specific scoring table is shown in Table 6 below:

[0174] Table 6 Lubrication test result scoring table

[0175] Proportion of lubricating fluid and base area Objective Rating Point Subjective evaluation >60% 4 Fully lubricated >40% and <60% 3 Good lubrication >20% and <40% 2 Fully lubricated >0% and <20% 1 Light lubrication =0% 0 No lubrication

[0176] For the prototype state corresponding to a single speed lubrication condition, customer scores are given to bearings in different parts. Taking the condition of flat driving, where the differential wheel end speed is 1000rpm and the oiling amount is the median value, as an example, the specific lubrication test score record table is shown in Table 7 below:

[0177] Table 7 Lubrication test result score table for flat driving condition

[0178] Operating speed (median fueling amount at 1000rpm on flat driving wheel end) Objective scoring Input shaft bearing A 3 Input shaft bearing B 2 Intermediate shaft bearing C 2 Intermediate shaft bearing D 2 Differential bearing E 1 Differential bearing F 1

[0179] For the series of working conditions, the scores are recorded. For example, the lubrication test results of the vehicle moving forward and the vehicle moving backward under the flat ground driving condition are scored. The summary table is shown in Table 8 below:

[0180] Table 8 Summary of the lubrication test results for forward and reverse vehicle travel on flat ground

[0181]

[0182]

[0183] All working conditions are scored and recorded, and all lubrication working condition scores are weighted and risk assessed.

[0184] After the three oiling amounts corresponding to all working conditions are completed, all working conditions corresponding to each bearing are weightedly scored, and risk warnings are given for working conditions and bearing numbers with a score less than or equal to 1.

[0185] Based on the above lubrication result matrix, the oil filling amount is evaluated and the oil passages of the bearing accessories with lubrication risks are optimized accordingly.

[0186] The present invention generates corresponding lubrication conditions according to the vehicle and electric drive parameters, and uses a customer quantitative evaluation method to analyze and evaluate the lubrication results. This patent proposes a generation system and quantitative evaluation method for the lubrication conditions of an electric drive reducer, so as to take reasonable lubrication conditions to assess the electric drive reducer, so as to save the number of samples and test costs. The objective evaluation method can avoid the errors and non-repeatability of human subjective evaluation.

[0187] In a second aspect, an embodiment of the present application also provides an electric drive reduction gearbox lubrication test system.

[0188] In one embodiment, referring to Figure 3 , Figure 3 This is a functional module diagram of an embodiment of the electric drive reduction gearbox lubrication test system of the present application. Figure 3 As shown, the electric drive reduction gearbox lubrication test system includes:

[0189] The preprocessing module 1 is used to calculate according to the preset vehicle parameters and electric drive parameters to obtain the operating condition characteristic parameters under each lubrication test condition and / or the maximum wheel end speed of the differential in the reduction box. The above-mentioned multiple lubrication test conditions include flat ground driving conditions, ramp driving conditions, acceleration and deceleration driving conditions, roll driving conditions, and ramp and roll combined driving conditions. The above-mentioned operating condition characteristic parameters are used to describe the characteristics of the lubrication test conditions.

[0190] The sample generation module 2 is used to generate a plurality of different test samples for each lubrication test condition. Each test sample includes a refueling amount parameter, a condition characteristic parameter, and a differential wheel end speed.

[0191] The test module 3 is used to perform lubrication tests on the reduction box on the test bench according to each test sample, and collect real-time images of each bearing in the reduction box during the test. The real-time images are image recognized to obtain the ratio of the lubricating oil area to the total bearing area, and the lubrication results are quantitatively evaluated based on the ratio.

[0192] In this embodiment, the vehicle parameters and electric drive parameters are taken into consideration, and lubrication test samples under various lubrication test conditions are generated by calculation. Different lubrication test samples include refueling quantity parameters, operating condition characteristic parameters, and differential wheel end speed, which can scientifically and comprehensively simulate real driving scenarios and improve the comprehensiveness and accuracy of lubrication testing of the reduction gearbox.

[0193] During the test, real-time images of each bearing in the reduction gearbox are collected and image recognition is performed on the real-time images to obtain the ratio of the lubricating oil area to the total bearing area. The test results are obtained based on the ratio, and the objectivity and accuracy of the test evaluation results are improved in a quantitative evaluation manner.

[0194] Among them, the functional implementation of each module in the above-mentioned electric drive reducer lubrication test system corresponds to the various steps in the above-mentioned electric drive reducer lubrication test method embodiment, and its functions and implementation processes will not be repeated here one by one.

[0195] It should be noted that the serial numbers of the above-mentioned embodiments of the present application are only for description and do not represent the advantages or disadvantages of the embodiments.

[0196] The terms "including" and "having" and any variations thereof in the specification and claims of this application and the above-mentioned drawings are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not limited to the listed steps or units, but optionally includes steps or units that are not listed, or optionally includes other steps or units inherent to these processes, methods, products or devices. The terms "first", "second" and "third" are used to distinguish different objects, etc., and do not represent a sequence, nor do they limit "first", "second" and "third" to different types.

[0197] In the description of the embodiments of the present application, "exemplary", "for example" or "for example" are used to indicate examples, illustrations or descriptions. Any embodiment or design described as "exemplary", "for example" or "for example" in the embodiments of the present application should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplary", "for example" or "for example" is intended to present related concepts in a specific way.

[0198] In the description of the embodiments of the present application, unless otherwise specified, " / " means or, for example, A / B can mean A or B. "And / or" in the text is only a description of the association relationship of associated objects, indicating that three relationships can exist. For example, A and / or B can mean: A exists alone, A and B exist at the same time, and B exists alone. In addition, in the description of the embodiments of the present application, "multiple" means two or more than two.

[0199] In some processes described in the embodiments of the present application, multiple operations or steps that appear in a specific order are included, but it should be understood that these operations or steps may not be executed in the order in which they appear in the embodiments of the present application or in parallel, and the sequence number of the operation is only used to distinguish the different operations, and the sequence number itself does not represent any execution order. In addition, these processes may include more or fewer operations, and these operations or steps may be executed in sequence or in parallel, and these operations or steps may be combined.

[0200] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus a necessary general hardware platform, and of course by hardware, but in many cases the former is a better implementation method. Based on such an understanding, the technical solution of the present application is essentially or the part that contributes to the prior art can be embodied in the form of a software product, which is stored in a storage medium (such as ROM / RAM, disk, CD) as described above, and includes a number of instructions for a terminal device to execute the methods described in each embodiment of the present application.

[0201] The above are only preferred embodiments of the present application, and are not intended to limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made using the contents of the present application specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present application.

Claims

1. A method for testing the lubrication of an electric drive reduction gearbox, characterized in that: The method comprises: Calculation is performed based on preset vehicle parameters and electric drive parameters to obtain operating condition characteristic parameters under multiple lubrication test conditions and / or the maximum wheel end speed of the differential in the reduction box; the multiple lubrication test conditions include flat ground driving conditions, ramp driving conditions, acceleration and deceleration driving conditions, roll driving conditions, and ramp and roll combined driving conditions, and the operating condition characteristic parameters are used to describe the characteristics of the lubrication test conditions; For each lubrication test condition, multiple different test samples are generated; each test sample includes oil filling quantity parameters, working condition characteristic parameters, and differential wheel end speed; The reduction gearbox on the test bench is lubricated according to each test sample, and real-time images of each bearing in the reduction gearbox are collected during the test. Image recognition is performed on the real-time images to obtain the ratio of the lubricating oil area to the total bearing area, and the lubrication results are quantitatively evaluated based on the ratio.

2. The electric drive reduction gearbox lubrication test method according to claim 1, characterized in that: The method comprises: For the flat ground driving condition, the maximum forward speed of the vehicle when moving forward and the maximum reverse speed of the vehicle when moving backward are calculated based on the vehicle parameters and electric drive parameters; The maximum rotation speed of the wheel end of the differential when the vehicle is moving forward is calculated according to the maximum forward speed; the maximum rotation speed of the wheel end of the differential when the vehicle is moving backward is calculated according to the maximum backward speed; Different fueling amount parameters, different operating condition characteristic parameters, and different differential wheel end speeds are combined to obtain a plurality of different test samples under flat ground driving conditions; the operating condition characteristic parameters of the flat ground driving conditions are used to describe the forward movement and backward movement of the vehicle.

3. The electric drive reduction gearbox lubrication test method according to claim 1, characterized in that: The maximum forward speed is calculated using the following formula: Among them, P m Indicates the working condition requirement of the drive motor, in kw; V max1 Indicates the maximum forward speed, in km / h; η t Indicates the efficiency of the transmission system; m indicates the mass of the vehicle, in kg; g indicates the acceleration due to gravity, g = 9.8 m / s 2 ; f represents the rolling resistance coefficient of the vehicle; C D Indicates the drag coefficient; A indicates the windward area, in m 2 ; m, g, f, C D , and A are vehicle parameters, P m and η t Electric drive parameters.

4. The electric drive reduction gearbox lubrication test method according to claim 2, characterized in that: When the vehicle is moving forward, the maximum speed of the wheel end of the differential is calculated using the following formula: Among them, n dri Indicates the maximum speed of the wheel end of the differential when the vehicle is moving forward, in r / min; V max1 represents the maximum forward speed in km / h; r represents the wheel diameter in m; the maximum wheel speed of the differential when the vehicle is moving backward is calculated using the following formula: Among them, n rev Indicates the maximum speed of the wheel end of the differential when the vehicle is moving backward, in r / min; V max2 It indicates the maximum reverse speed in km / h; r indicates the wheel diameter in m.

5. The electric drive reduction gearbox lubrication test method according to claim 1, characterized in that: The method comprises: For ramp driving conditions, the maximum climbing gradient when the vehicle is going uphill and the maximum descending gradient when the vehicle is going downhill are calculated based on the vehicle parameters and electric drive parameters; Calculate the maximum wheel speed of the differential when the vehicle is going uphill and the maximum wheel speed of the differential when the vehicle is going downhill according to the preset coefficient and the maximum wheel speed of the differential when the vehicle is moving forward; Different refueling parameters, different operating characteristic parameters, and different differential wheel end speeds are combined to obtain a plurality of different test samples under a slope driving condition; the operating characteristic parameters of the slope driving condition are used to describe the climbing gradient of the vehicle and the descending gradient of the vehicle.

6. The electric drive reduction gearbox lubrication test method according to claim 1, characterized in that: The method comprises: For acceleration and deceleration driving conditions, calculations are performed based on vehicle parameters and electric drive parameters to obtain the maximum acceleration liquid level inclination in the reduction box when the vehicle is accelerating and the maximum deceleration liquid level inclination in the reduction box when the vehicle is decelerating; The maximum wheel speed of the differential when the vehicle is accelerating is obtained by calculating the wheel speed at the inflection point of the external characteristic curve and the speed ratio of the reduction gearbox; The maximum rotation speed of the wheel end of the differential when the vehicle is moving forward is used as the maximum rotation speed of the wheel end of the differential when the vehicle is decelerating; Different refueling amount parameters, different operating condition characteristic parameters, and different differential wheel end speeds are combined to obtain multiple different test samples under acceleration and deceleration driving conditions; the operating condition characteristic parameters of the acceleration and deceleration driving conditions are used to describe the inclination of the acceleration fluid level in the reduction box when the vehicle accelerates and the inclination of the deceleration fluid level in the reduction box when the vehicle decelerates.

7. The electric drive reduction gearbox lubrication test method according to claim 1, characterized in that: The method comprises: For the rolling driving condition, the maximum left tilt inclination in the reduction gearbox when the vehicle tilts to the left and the maximum right tilt inclination in the reduction gearbox when the vehicle tilts to the right are calculated based on the vehicle parameters and the electric drive parameters; Calculate the maximum wheel end speed of the differential when the vehicle is leaning to the left and the maximum wheel end speed of the differential when the vehicle is leaning to the right according to the preset coefficient and the maximum wheel end speed of the differential when the vehicle is moving forward; Different refueling parameters, different operating characteristic parameters, and different differential wheel end speeds are combined to obtain multiple different test samples under the rolling driving condition; the operating characteristic parameters of the rolling driving condition are used to describe the left inclination of the vehicle when it leans to the left and the right inclination of the vehicle when it leans to the right.

8. The electric drive reduction gearbox lubrication test method according to claim 1, characterized in that: The method comprises: For the ramp and roll combined driving condition, multiple test samples of the ramp driving condition are combined with multiple test samples of the roll driving condition to obtain test samples of the ramp and roll combined driving condition; the operating condition characteristic parameters of the ramp and roll combined driving condition are used to describe the climbing grade of the vehicle climbing, the descending grade of the vehicle descending, the left inclination of the vehicle leaning to the left, and the right inclination of the vehicle leaning to the right.

9. The electric drive reduction gearbox lubrication test method according to claim 1, characterized in that: The method comprises: After the reduction gearbox is installed on the test bench, the differential in the reduction gearbox is driven to rotate through the tooling shaft of the test bench. The rotation speed of the tooling shaft is consistent with the rotation speed of the differential wheel end in the test sample. The position and movement of the test bench are consistent with the refueling parameters and operating condition characteristic parameters in the test sample.

10. An electric drive reduction gearbox lubrication test system, characterized in that: The system comprises: A preprocessing module, which is used to calculate according to preset vehicle parameters and electric drive parameters to obtain operating condition characteristic parameters under multiple lubrication test conditions and / or the maximum wheel end speed of the differential in the reduction box; the multiple lubrication test conditions include flat ground driving conditions, ramp driving conditions, acceleration and deceleration driving conditions, roll driving conditions, and ramp and roll combined driving conditions, and the operating condition characteristic parameters are used to describe the characteristics of the lubrication test conditions; A sample generation module, which is used to generate a plurality of different test samples for each lubrication test condition; each test sample includes a refueling amount parameter, a working condition characteristic parameter, and a differential wheel end speed; The test module is used to perform lubrication tests on the reduction box on the test bench according to each test sample, and collect real-time images of each bearing in the reduction box during the test; perform image recognition on the real-time images to obtain the ratio of the lubricating oil area to the total bearing area, and quantitatively evaluate the lubrication results based on the ratio.

Citation Information

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