The mathematical model of the optimized design of the reducer The establishment of the correct mathematical model is the key to the optimal design of the reducer. Therefore, the mathematical model of the optimized design of the reducer must be able to correctly express the design problem of the reducer, accurately and reliably ensure the purpose of the design of the reducer and various constraints.
Selection of design variables Generally, all independent design parameters of the gear reducer that affect the design quality, such as gear tooth number, modulus, helix angle, tooth width and displacement coefficient, and the center distance of each level should be used as design variables. .
However, too many design variables will increase the workload and difficulty of the calculation. Usually, the design parameters that are easy to control and have obvious influence on the optimization target are used as design variables.
Gear strength constraint The gear strength constraint refers to the tooth surface contact fatigue strength of the gear and the bending fatigue strength of the gear. These two calculations are carried out according to the method in the national standard GB3480-83. Whether the strength is sufficient or not, according to whether the actual safety factor meets or exceeds the predetermined safety factor.
Selection of optimization method From the mathematical model established above, the gear reducer optimization design is an optimization design problem with a single objective function with multiple inequality constraints, discrete design variables and continuous design variables. The solution must use discrete variable optimization methods, such as stochastic grid search method, discrete penalty function method, discrete complex method. At present, the more commonly used method is the discrete complex method [3].

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BPS and BPF have been detected in many everyday products, such as personal care products (e.g., body wash, hair care products, makeup, lotions, toothpaste), paper products (e.g., currency, flyers, tickets, mailing envelopes, airplane boarding passes), and food (e.g., dairy products, meat and meat products, vegetables, canned foods, cereals). BPS, BPF, and BPA have been detected in indoor dust at the following concentrations: BPS, 0.34 μg/g; BPF, 0.054 μg/g; BPA, 1.33 μg/g . BPS and BPF have also been detected in surface water, sediment, and sewage effluent, generally at lower concentrations than BPA, but in the same order of magnitude . In humans, BPS and BPF have been detected in urine at concentrations and frequencies comparable to BPA. In urine samples from 100 American, nonoccupationally exposed adults, found BPF in 55% of samples at concentrations up to 212 ng/mL, and BPS in 78% of samples at concentrations up to 12.3 ng/mL. BPA was found in 95% of the samples, with concentrations up to 37.7 ng/mL.

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