December 23, 2024

Study the effect of friction between gears on gear strength


With the acceleration of the development of gear transmission to high speed and heavy load and the deepening of research, it has been found that the influence of friction between teeth on the strength of the gear cannot be easily ignored. In addition, in the design process of gear transmission, there are some uncertain phenomena, mainly manifested by the randomness and ambiguity of each design parameter. In the conventional design method, the randomness and ambiguity of each design parameter are often neglected, and all design parameters are considered as the determined quantity; therefore, the designed scheme is difficult to conform to the objective reality. That is to say, according to the law of biological evolution, a randomly generated population is propagated and naturally selected to make the fittest survive; so generations of circulation, so that the quality of the group and the individual quality of the group are constantly evolving, and through the diversity of individuals in the group Multiple points of the solution space are simultaneously searched, and finally effectively converge to the global optimal solution.
Based on the above factors, this paper combines engineering practice with a foreign-mechanical displacement helical gear transmission as the research object. By applying fuzzy reliable design theory, the genetic algorithm is used to blur the variable-angle helical gear transmission under the friction between teeth. Reliable optimization. The example shows that the effect is very good. Under the genetic algorithm, the fuzzy reliable optimization mathematical model is used to solve the membership function of the fuzzy constraint. The membership function in the fuzzy design theory is used to represent the intermediate transition process of the gear stress and other parameters from the full permit to the completely unallowable. The form of the membership function varies with the nature of the constraints. In engineering, according to the design requirements and the nature of the gear transmission constraints, the linear membership functions are used for each constraint fuzzy function. Genetic algorithm flow chart engineering example A single-stage closed involute helical gear reduction drive, known transmission power P1=10kW, drive wheel speed n1=970r/min, gear ratio u=4, inter-tooth friction factor f= 0.14, symmetric arrangement, one-way operation, three-shift operation, working life of 10 years, both sizes are 45 steel, both rounds are 8-level precision; the fuzzy reliability of gear transmission is R=0.978, small gear quenching and tempering The large gear is normalized and the hardness is HBS=162~217. The genetic algorithm is used to optimize the fuzzy reliability of the gear transmission.
According to the requirements of the topic, the method described in this paper is used to optimize the design. The objective function of the optimized design is established according to the formula. Determine the gear surface deformation coefficient xn1 and xn2, the normal modulus mn, the pinion gear z1, the tooth width coefficient d, and the helix angle as design variables. Considering the fuzzy factors such as design level, manufacturing level, materials used, importance, etc., the two-level fuzzy comprehensive evaluation method is used to determine the optimal level value and then transform the fuzzy optimization problem into the optimal horizontal cut-off by using the optimal horizontal cut-off method. On the non-fuzzy optimization problem, the genetic algorithm is used to optimize the solution. In view of the shortcomings and defects in the traditional gear strength theory, the calculation formula of the strength of the helical gear under the friction between teeth is given. A series of studies have shown that the effect of friction between teeth on the strength of the gear can not be ignored. This paper comprehensively considers the randomness and ambiguity of various factors affecting the helical gear transmission. Therefore, the established mathematical model and solution scheme are closer to objective reality. Since the genetic algorithm starts to search from multiple points at the same time, the solution process converges quickly and the global optimal solution of the whole optimization problem can be obtained.

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