The main form of gear failure is bending fatigue failure. According to the failure physical stress intensity model, it is assumed that the strength degradation amount ad under different failure modes follows the normal distribution, and the mathematical relationship corresponding to bending fatigue failure is as follows:
The function corresponding to contact fatigue failure is:
The random variables in the above two formulas are interrelated, which leads to the conclusion that the two failure stresses are related. According to the full probability formula, considering the failure related joint distribution of strength degradation, the gear reliability model is:
Where N, CF and CH are respectively:
Where: δ F is gear bending fatigue strength; Δ DF is the degradation of gear bending fatigue strength; Ka is the service factor; KV is the dynamic load coefficient; KH β Tooth load distribution coefficient for calculating contact strength; KH α Load distribution coefficient between teeth for calculating contact strength; δ H is gear contact fatigue strength; Δ DH is the degradation of gear contact fatigue strength; FI is the nominal tangential force on the indexing circle in the gear end face; B is the working tooth width; H is the tooth height; M is gear modulus; YF α Is the tooth profile coefficient when the load acts on the tooth top; YS α Is the stress correction coefficient when the load acts on the tooth top; Y ε Coincidence coefficient calculated for bending strength; Y β Helix angle coefficient calculated for bending strength; ZH is the node area coefficient; Ze is the elastic coefficient; Ｚ β Helix angle coefficient calculated for contact strength; Z ε The coincidence coefficient calculated for the contact strength; D1 is the indexing circle diameter of the gear; μ Is the tooth ratio.
Through bending fatigue test and corresponding numerical simulation, it is found that the fracture of tooth root is the main factor affecting the bending fatigue life of gear. The crack on the tooth root will experience a stable propagation zone from initiation to fracture, and the crack will show a certain propagation law in the stable propagation zone. It is of great significance to study the propagation law of crack in the propagation zone by using the propagation finite element method for the prediction of gear life.
The bending fatigue strength of gear can be determined by the following two methods: 1) gear bench operation test (hereinafter referred to as “a test method”); 2) Pulse loading test of gear teeth (hereinafter referred to as “B test method”).
A test method: the specific test is to install the gear pair w used for testing on the gear testing machine for load. If the following two conditions occur, the test will stop: first, the gear has bending fatigue fault; Second, when the number of tooth root stress cycles reaches the specified cycle base n without failure (hereinafter referred to as “overrun”). Through this method, the life data of gear teeth under the action of test stress can be obtained. If there is no problem with the setting of test device and the test process is normal, the obtained data can usually be called “test point”.
B test method: in the pulse fatigue test, select the gear without meshing and at least one tooth away from the load gear (including support teeth), and apply the pulse load only to the test gear. The pulse is loaded by a special fixture, and the life data of the gear is obtained when the bending fatigue failure of the gear occurs. Take several test points on each test gear.