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Finite element analysis of fatigue life of engineering plastic gears

1 fatigue failure of gears

fatigue is a very interesting phenomenon. When the material or structure is subjected to repeated changes of load, although the stress value always does not exceed the strength limit of the material, Failure may occur even when it is lower than the yield limit. This failure phenomenon of materials or structures under repeated alternating loads is called fatigue failure

as shown in Figure 1, f represents the force acting on the gear during gear meshing. The gear teeth mesh once every revolution of the gear. When engaging, f rapidly increases from zero to the maximum value, and then decreases to zero. Therefore, the bending stress or at the root of the tooth also increases rapidly from zero to a maximum value and then decreases to zero. This process is repeated with the rotation of the gear. The change curve of stress or with time t is shown in Figure 2

Fig. 1 stress condition of gears during meshing

Fig. 2 tooth root stress versus time curve

in modern industry, many parts and components are subjected to alternating loads, and engineering plastic gears are typical parts. Engineering plastic gears are widely used in light industrial machinery with moderate transmission load, such as textile, printing and dyeing, papermaking and food, because of their advantages of low quality, self lubrication, good vibration absorption and low noise

there are many obvious essential differences between fatigue failure and traditional static failure:

1) static failure is the failure under a maximum load; Fatigue failure is the failure caused by repeated loads. It does not happen in a short time, but takes a certain time

2) when the static stress is less than the yield limit or strength limit, the static failure will not occur; When the alternating stress is far less than the static strength limit, or even less than the yield limit, fatigue failure may occur

3) static failure usually has obvious plastic deformation; Fatigue failure usually has no external macroscopic significant plastic deformation signs, which is not easy to detect in advance, which indicates that fatigue failure is more dangerous

The fatigue life of engineering plastic gears is a subject of great concern to designers, and it is also closely related to actual production. However, the calculation of fatigue life under fatigue load is very complex. Because to calculate fatigue life, there must be accurate load spectrum, material properties or S-N curve of components, appropriate cumulative damage theory, appropriate crack growth theory, etc. The ultimate purpose of fatigue analysis of engineering plastic gears in this paper is to determine their fatigue life under various quality conditions. It has certain engineering value to analyze and study the fatigue life of engineering plastic gears by using finite element method and CAE software2 determination of engineering plastic gear material

ultra high molecular weight polyethylene (UHMWPE) is a new thermoplastic engineering plastic with excellent comprehensive properties. Its molecular structure is exactly the same as that of ordinary polyethylene (PE), but its relative molecular weight can reach (1 ~ 4) × 106。 With the substantial increase of relative molecular weight, UHMWPE shows excellent properties that ordinary PE does not have, such as wear resistance, impact resistance, low friction coefficient, chemical resistance and noise attenuation

uhmwpe ranks first among engineering plastics in terms of wear resistance, which is 4 times higher than nylon 66 (PA66) and 7-8 times higher than carbon steel and stainless steel. The friction coefficient is only 0.07 ~ 0.11, with self lubrication and non adhesion. Therefore, UHMWPE is selected as the engineering plastic gear material for research in this paper. See Table 1 for UHMWPE performance

due to the poor thermal conductivity of UHMWPE, the gears meshed with UHMWPE are made of steel. In this way, it has good thermal conductivity and small friction loss, and can make up for the low accuracy of engineering plastic gears. 2. The meshing gears are standard spur gears. The parameters are: UHMWPE gear has 30 teeth, steel gear has 20 teeth, and the modulus is 4mm, so that the engineers and manufacturers can access it easily. The tooth width is 20mm, and the pressure angle is taken as 20 °. Table 1 performance of UHMWPE

3 establishment of fatigue analysis model of UHMWPE gear

during gear meshing, the gear teeth are like cantilever beams under line load, and the bending moment at the root of the tooth is the largest, so the bending fatigue strength at the root of the tooth is the weakest. When the gear teeth mesh at the top of the tooth, they are in the meshing area of double pairs of teeth. At this time, although the force arm of the bending moment is the largest, the force is not the largest, so the bending moment is not the largest. According to the analysis, the maximum bending moment of the tooth root can be divided into: when the gear meshing point is at the highest point of the single pair of teeth meshing area, the ultra nano friction and wear testing machine can be divided according to the load range. Therefore, when establishing the fatigue analysis model of UHMWPE gear, the highest point of the load acting on the meshing area of a single pair of teeth should be established

according to the analysis method of continuous transmission conditions of involute gears based on mechanical principle, the highest point of single pair of gears can be obtained. Then the fatigue analysis model of UHMWPE gear is established by using the gear modeling function and data conversion function of CAXA software, as shown in Figure 3

Figure 3 fatigue analysis model of UHMWPE gear

4 analyze the fatigue life of UHMWPE gear with ANSYS

ansys is a large general CAE software based on finite element analysis, and it is the first finite element analysis software approved by IS09001 in the world. Therefore, by accurately establishing the model, reasonable lattice division, load application and boundary condition setting, we can get reliable calculation results

for engineering plastic gears, because the mechanical properties and thermal properties of their materials are very different from those of metal materials, their failure forms and failure mechanisms are also very different from those of metal gears. Due to the low elastic modulus of plastic gears, the Hertz contact area is large and the contact stress is small during the meshing process with steel gears. Generally, surface failures such as pitting corrosion will not occur. Therefore, fatigue fracture or fracture of gear teeth under the action of bending stress is the main failure form of plastic gears. Therefore, the fatigue life of UHMWPE gears in three cases is mainly analyzed

4.1 fatigue life analysis of gears made of UHMWPE materials without defects

before using ANSYS to carry out fatigue analysis of gears, it is necessary to carry out contact analysis of 2 meshing gears. According to the actual contact situation analyzed above, the position of the highest point of the single tooth meshing area of the 2 gear is determined, and the contact type is defined as the face-to-face contact of the flexible body

take the steel gear meshing surface as the target surface, which is defined by the unit targel69, and take the UHMWPE gear meshing surface as the contact surface, which is determined by the unit contal71. You can enter the contact wizard from the menu (Main Menu> preprocessor> modeling> create> contact pair) to establish a "contact pair" of the contact surface of the target surface. It is also possible to adopt basic skin care formula. Relevant products have non transfer characteristics and establish contact pairs through other ways, which belongs to the basic operation of ANSYS and will not be detailed in this article

after the contact pair is established, enter the static strength solution process. The driving gear is a steel gear, and the transmission torque is 6N · M. the stress at the tooth root of UHMWPE material gear calculated by ANSYS is shown in Figure 4. From the stress nephogram, it can be seen that the maximum stress occurs at the gear root of UHMWPE material, the node number is 2279, and the stress value is 32.1mpa

Figure 4 stress nephogram at the root of UHMWPE gear

the steps of ANSYS fatigue analysis of engineering plastic gears are as follows: first enter post-processing POST1, restore the database, then extract the node stress at the maximum bending stress of the root of the gear and store it, and determine the number of repetitions. Finally, use miner fatigue accumulation theory to calculate the fatigue life and check the results

uhmwpe gear fatigue life prediction requires a more critical fatigue property is the S-N curve of the material. The S-N curve of the studied UHMWPE material is shown in Figure 5

Fig. 5 S-N curve of UHMWPE material

fatigue analysis results are shown in Fig. 6. It can be seen that under the working load set in the paper, the fatigue life of the UHMWPE gear teeth is 132800 times, and the cumulative fatigue coefficient is 0.75301

Figure 6 fatigue calculation results of flawless UHMWPE gear

4.2 fatigue life analysis of UHMWPE gear when there are weld marks on the tooth flank

uhmwpe gear injection molding process is complex. Improper process control is easy to produce welding lines and other injection defects. Therefore, by analyzing UHMWPE gears with weld line defects, the influence of different positions of the defects on the fatigue failure of gears can be determined. This has certain guiding significance for the injection molding process of engineering plastic gears, gate location arrangement, etc

when using ANSYS to analyze engineering plastic gears with weld line defects, the weld line is equivalent to the problem of type I crack, and kscon (Main Menu> preprocessor> meshshape&size> concentrate KPS create) is used to make ANSYS automatically generate singular elements around the key points at the tip of the weld line, and then analyze and solve. Suppose there is a 1.5mm long weld line between the two wheel teeth, and the position and size of the weld line are shown in Figure 7

Figure 7 size of weld line between teeth

fatigue analysis results show that under the condition of small weld line defects between teeth, the fatigue life of UHMWPE gear teeth is 124600 times, and the cumulative fatigue coefficient is 0.80257. The location of fatigue is not yet at the root of the tooth. It can be seen that in the case of small weld line defects between teeth, the defects have no great impact on the fatigue life of UHMWPE gears

4.3 fatigue life analysis of UHMWPE gear when there is a weld line at the root of the tooth

it is assumed that there is a weld line with a length of 1.5 mm at the root of the tooth, and the location and size of the weld line are shown in Figure 9

Figure 9 root weld line size

fatigue analysis results: fatigue failure occurs at the tip of the weld line, as shown in Figure 10. The fatigue life of gear teeth is only 5631 times. It can be seen that under the condition that there is a small weld mark defect at the tooth root, the gear will quickly fatigue and fracture

figure l0 location of fatigue failure

5 conclusion and outlook

1) the fatigue problem under complex boundary conditions can be calculated by using ANSYS finite element technology, which is of certain value to determine the fatigue life of engineering plastic gears

2) through ANSYS analysis, it is concluded that the fatigue life of the studied UHMWPE gear without defects is much higher than that of the gear with weld lines at the root

3) when the weld line is close to the gear root of UHMWPE material, the gear tooth will quickly fatigue and fracture after loading, so it is necessary to optimize the injection molding process to avoid weld lines at the gear root

4) many engineering plastics with excellent performance can be used as gear materials with medium load, such as POM, PA66, etc. checking their fatigue life by finite element method will speed up the design speed and improve the reliability at the same time. (end)

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