In the field of mechanical design, there are many uncertain phenomena. One of its main manifestations is ambiguity. Ambiguity is an objective attribute of things. In design, the ambiguity of various factors affecting design is considered, so that the design scheme Better conforming to objective reality is an important issue facing our mechanical design workers.
In recent years, domestic and foreign scientific and technological workers have done a lot of research on the optimization of gear reducers, and established some available optimization mathematical models and design procedures. However, the previous work did not take into account the ambiguity affecting the various factors of the work of the reducer, so that the design is difficult to better meet the objective reality. Taking the mechanized production line of casting workshop and the belt conveyor commonly used in engineering as an example, considering the ambiguity of all constraints and the ambiguity of various factors affecting gear transmission, the fuzzy optimization mathematical model is established and the fuzzy optimization design is carried out. Very obvious.
This kind of reducer is widely used in engineering, and the annual output is quite large. Therefore, it is of great practical significance to carry out fuzzy optimization design.
The relevant parameters of the belt conveyor are shown as the transmission system diagram of the belt conveyor. Power transmission is driven by the motor through a V-belt and a single-stage spur gear reducer.
It is known that the design parameters of a belt conveyor are: the power required by the active drum is 7=11, the drum shaft speed is “7=57 rpm, the gear ratio is /=4.2, the transmission efficiency of the triangular belt is still 0.994, gear meshing The efficiency is still = 0.97, the rolling bearing efficiency is = 0.99, the sliding bearing efficiency is 0.996, the pinion material is 45 steel, the quenching and tempering is HBi=230~280, and the large gear material is 45 steel. The original conventional design scheme is: small Gear tooth number zi=21, mode m=7, tooth width B=130mm. 2 Mathematical model of fuzzy optimization design Under the condition of the same transmission power, the reducer's small size and light weight will bring us many benefits. Therefore, we carry out fuzzy optimization design with the goal of minimum volume.
2.1 Determining the design variable The gear modulus m directly affects the size and strength of the gear. The modulus m and the number of gear teeth are discrete values, the modulus is fixed, the number of teeth will determine the diameter of the gear index circle, and the tooth width factor % directly determines the width of the gear. Therefore, the pinion tooth number zi, the modulus m, and the tooth width coefficient are taken as design variables.
2.2 Establishing the objective function 2 Journal of Sichuan University of Science and Technology (Natural Science Edition) October 2006 ~~ The volume of the reducer mainly depends on the gear diameter circle diameter and gear width in the reducer. The smaller the gear volume, the smaller the cabinet size. The lighter the weight. Therefore, the sum of the volumes of the pinion 1 and the large gear 2 is taken as the objective function.
K = m3Zl3 (1 + i) 2 (F is the sum of the volumes of gear 1 and gear 2) ... objective function Txj = 2.3 establish fuzzy constraints 4 constraints have two main aspects: performance constraints and geometric constraints. Performance constraints such as stress should take into account the intermediate process from full allowable to completely unacceptable. For geometric constraints, the ambiguity of the boundary should be considered. We consider these constraints as fuzzy subsets in the design space, and establish the constraints as follows: 2.3.1 Contact stress constraints The upper limit of the allowable contact stress with ambiguity. ~ 2.3.2 Bending stress constraint: 2kT1Z1Y: upper limit of allowable bending stress with ambiguity 2.3.3 upper and lower limit of tooth width 2.3.4 upper and lower limit of design variable constraint m above the symbol "" With fuzzyness, in summary, the fuzzy optimization model of the problem can be expressed as: Seeking: X=T variable constraint: (/3 fuzzy constraint membership function and non-fuzzy optimization model membership function of each fuzzy constraint, should be based on constraints The nature and design requirements are determined. Here we use linear membership functions for both performance constraints and geometric constraints. As shown in the figure, the membership of the stress on the allowable values ​​is the geometric constraint pair. The membership of the allowed value.
(Other cases) Corresponding can be constrained (a):
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