Multi-stage inclined cylindrical gear transmission

The strength constraint design requires that the gear contact fatigue strength reliability RHj and the fatigue strength reliability RFk are both >0.99, ie: RHj0.99j=1, 2, 3RFk0.99R=1, 2,, 6 where: RHj (j=1 , 2, 3) are the reliability of contact fatigue strength of high-speed, medium-speed and low-speed gears respectively; RFk (k = 1, 2, 6,) are the reliability of bending fatigue strength of gears 1, 2, and 6, respectively .
The geometrically constrained gear 4 does not interfere with the high speed shaft (d5 d6)/2-d4/21 where: 1 is the sum of the high speed shaft radius, the amount of clearance between the tooth tip of the gear 4 and the shaft diameter; d4, d5, d6 are They are the graduation circle diameters of the gears 4, 5, and 6, respectively.
Reducer outer diameter DD0 (d1 d2) / 2 d2 2D0 / 2 where: 2 is the sum of the tooth tip height of the gear, the gap between the tooth tip and the inner wall of the reducer, and the wall thickness of the reducer; d1, d2 are gears The index circle diameter of 1, 2 . The radius of the projection at the reducer gear 4 is RR0 (d5 d6)/2 d4/2 3R0 where: 3 is the sum of the height of the tooth tip of the gear 4, the gap between the tooth tip and the inner wall of the reducer, and the deceleration thickness.
Gear Strength Reliability Calculation Based on theoretical analysis and related test reports, lognormal distribution is used as a probabilistic model of gear stress and strength. When the stress and strength are log-normal distribution, the reliability coefficient is equal to 2.326, then the contact fatigue limit mean and coefficient of variation of the test gear are as follows: the log contact fatigue limit mean can be used to find the tooth surface contact stress of the three-stage gear and The mean value and coefficient of variation of the root bending stress are then the logarithmic normal distribution simultaneous equations, and the reliability coefficients uHR and uFK of the contact fatigue strength and bending fatigue strength can be obtained: uHR=ln (F will be the strength The reliability RHj and RFK of the contact fatigue strength and the bending fatigue strength in the constraint are expressed by the corresponding reliability coefficients uHR and uFK, and the transformation and calculation of the gear strength constraint are realized.
The fuzzy reliability optimization model is solved by the optimal horizontal cut-off method, and the second-level fuzzy comprehensive evaluation method is used to determine the optimal level value. The fuzzy optimization model is transformed into a conventional optimization design on the optimal horizontal cutoff. According to the nature of the variables and constraints and the design requirements, for the convenience of the solution, the linear membership function is adopted, and the fuzzy distribution of the reliability is a semi-trapezoidal distribution; the fuzzy distribution of the stress of the gear 2 is a semi-trapezoidal distribution; the fuzzy distribution of other variables or constraints is adopted. Trapezoidal distribution.
The set of factors U={u1, u2,, un} each element ui represents each influencing factor. There are many influencing factors to be considered in the design, and there are layers between the factors. For this purpose, a two-level fuzzy comprehensive evaluation is adopted. First, the influencing factors are divided into six categories of elements; each element is divided into five factor levels.
Influencing factors, factors, factors, factors, factors, level 12,345, design level, high, high, low, high, high, high, low, high, low, high, low, good, good, good, good, good, good, good, good, good, good, good, poor, Importantly less important Generally more important Important less maintenance costs Generally larger Large 3.2 Establishing an evaluation set The evaluation set is a collection of various general evaluation results as elemental composition. The evaluation object of this example is the cut-off level, and its value range is [0,1]. According to the design conditions and requirements, the evaluation set is:={0.30, 0.40, 0.50, 0.60, 0.65, 0.70, 0.75, 0.80, 0.85, 0.90}3.3 Establishing weight set In order to reflect the influence of each influencing factor and factor level on the evaluation object, the weighting sets A and Ai of each influencing factor and factor level should be given. According to the design conditions, the weighting set of influencing factors is determined as: A = (0.25, 0.25, 0.15, 0.10, 0.10, 0.15) The factor level weight set is (take the factor as the design level as an example) Ai = (0.3478, 0.43478, 0.21739, 0, 0) 3.4 for fuzzy comprehensive evaluation 3.4.1 The first-level fuzzy comprehensive evaluation deals with the ambiguity of factors by integrating the influence of each factor level of an influencing factor on the value of the evaluation object. Firstly, the evaluation is based on the order of each factor of the individual influencing factors. According to the influence of the ranking order of each influencing factor on the evaluation object, the ranking evaluation matrix Ri(i=1, 2,, 6) of each factor is determined (taking the design level as an example). ):Ri=1.00.90.70.50.30.10.00.00.30.70.91.00.90.70.50.30.10.00.00.30.50.70.91.00.90.70.50.30.10.00.10.30.50.70.91.00.90.70.50.00.00.10.30.50. 750.850.90.951.0 When the design level is high, the cut-off level takes a low value, which means that the membership degree of the evaluation object is from large to small, that is, the allowable range of design parameters can be slightly larger; otherwise, the design level is low, and the cut-off set Take the high value horizontally. The first-order comprehensive evaluation of the i-th factor is carried out, and the first-level fuzzy comprehensive evaluation set is obtained: Bi=AiRi is composed of Bi(i=1, 2, 6) to form the second-level fuzzy comprehensive evaluation matrix R.
The symbol in the formula represents the fuzzy product of the fuzzy matrix, which means that the j-th element of the fuzzy matrix Bi is equal to the element of Ai and the corresponding element of the j-th column of Ri is taken as the smaller one, and then the larger of the obtained results .
The second-level fuzzy comprehensive evaluation is comprehensively considered, and the two-level fuzzy comprehensive evaluation set is obtained by fuzzy transformation: the evaluation result is determined by the maximum membership principle, and the evaluation corresponding to the maximum evaluation index of 0.9266 in the second-level fuzzy comprehensive evaluation set B is obtained. The concentrated element 0.80 is used as the evaluation result, that is, the optimal cut-off level is 0.80, thereby transforming the fuzzy optimization into a conventional optimization problem.
The selection and solution of the conventional optimization method Because the design scale is large, the calculation method of the grid method is too large, so the composite method is adopted. The modulus and the number of teeth are calculated according to the continuous variable, and the optimization result is obtained and then rounded (the number of teeth is rounded, and the modulus meets the recommended series).
The relevant parameters of a coaxial three-stage helical gear reducer are known as follows: input power P=3kW, input speed n1=2830r/min, total gear ratio i=114.18. Gear materials are 20CrMnTi alloy steel, After carburizing and quenching, the hardness of the tooth surface is 5962HRC, and the accuracy of the gear is 8-7-7. The radial dimension D0 of the reducer box is not more than 300mm, and the radius R0 of the gear at the gear 4 is not more than 180mm.

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