1 Introduction to biomass dryers Drying equipment, also known as dryers and dryers, is used to carry out drying operations. The moisture in the material is vaporized by heating to obtain a solid material with a specified moisture content.
The dryer is generally composed of a cylinder, a rolling ring, a supporting device, a rotating device, a shirt in the cylinder, and a rotating drum. This design uses a type of dryer that directly transfers heat. The cylinder is in the form of a shirtless, lift-up copy board.
2 Finite element analysis of the dryer gear 2.1 Main parameters of the dryer The output speed of the motor selected in this design is 1500r/min, the gear material is 40Cr, the gear ratio of the ring gear and the gear is 7.35, the modulus is 10mm, and the number of teeth of the small gear is z1. =17, initial tooth width B = 100mm, the elastic modulus of the gear is 200GPa, the Poisson's ratio is 0.3, and the density is 7.8×103kgm-3.
It is calculated that the allowable stress of contact fatigue of the tooth surface is 495 MPa (take safety factor S=1), and the allowable stress of bending fatigue of the root is 306 MPa (take safety factor S=1.5).
2.2 Gear Modeling The transmission mode of the dryer is the gear ring gear transmission. The finite element analysis of the driving wheel (pinion gear) will be carried out here. This design adopts parametric modeling and uses the tooth width B as the design variable to facilitate the subsequent optimization design. The parametric geometry model is shown in 2, and the finite element model is shown in 3.
2.3 Finite Element Analysis of Gears After the parametric model of the drive wheels is built, loads and constraints are applied to them. The load is applied to the meshing area of ​​the teeth, and the constraint is applied to the nodes on the surface of the shaft hole. According to the design calculation, the normal force of the pinion is Fn=8451.65N, and the circumferential force is obtained after decomposition. The radial force is Fr=7941.17N.
After solving the solution by the finite element analysis software ANSYS, the joint stress cloud diagram (4) and displacement cloud map (5) of the gear finite element model under external load are obtained.
From the stress and deformation distribution under the meshing state of the gear teeth, the stress and deformation of the gear teeth are mainly distributed on the meshing tooth pairs, and on the gear teeth and gear bodies adjacent thereto, the meshing distance increases. Decrease rapidly. At the root of the meshing tooth pair, the stress value is maximized. On the pair of meshing teeth, the stress and deformation at the point of engagement are maximized. From the deformation of the meshing teeth, the deflection of the gear teeth is large, the contact deformation is second, and the deformation of the gear body is small.
After finite element analysis, the maximum stress value of the gear is 39.731 MPa, which occurs at the root of the meshing tooth pair, and its value is much smaller than the bending fatigue allowable stress of the root. The maximum strain value of the gear teeth is 0.619×10-7, and the deformation is not large. The bending stress of the tooth root dangerous section is σF=KFtYFaYSabm where: FFa is the tooth profile coefficient, which is related to the contour shape of the gear teeth; YSa is the stress correction coefficient; b is the tooth width; m is the modulus.
It can be seen from the calculation that σF=39.434 MPa, which is basically consistent with the maximum stress value.
It can be seen that the gear has a lot of optimization space and it is necessary to optimize it.
3 optimization design of the dryer gear The basic principle of the design is to optimize the model, use various optimization methods, and find the extreme value of the objective function by satisfying the design requirements, and obtain the optimal design. Before a design optimization work, you need to determine the design variables, state variables, and objective functions of the optimized design. In this design, the tooth width B is used as the design variable, the root bending stress is used as the state variable, and the weight of the gear is the objective function. The tooth width B can be calculated based on the contact strength:
BG≥4.29×109×N×η×Kj×Kdj(iG+1)df2×n[σj]2=64mm and the range of the tooth width coefficient Ψd=0.3～0.6, it can be determined that the width range of the pinion is 64mm≤B≤ 100mm.
Since the allowable stress of root bending is 306 MPa, the range of state variables is 0 ≤ σ ≤ 306 MPa.
From this, the mathematical model for its optimization can be determined as:
MinWT(B)B=[σ]0≤σ≤30664≤B≤100
STEP=1SUB=1SEQV(AVG)DMX=.619E-07SMN=.977E-03SMX=39.731NODALSOLUIIONSTEP-1SUB-1IIME=1USUM(AVG)RSYS=0DMX=.619E-08SMX=.619E-08
After the solution is solved, the corresponding design variables, state variables and objective functions are extracted, and the zero-order method is selected to optimize it. After 4 iterations, the optimization result is obtained as shown in Fig. 6. The optimized result is shown in Figure 1. Compared with the original scheme, the optimized gear width is greatly reduced, the gear weight is also reduced by 58.67%, and the maximum stress is increased, but within the allowable stress range. Does not affect the overall performance of the gear.
4 At the end of this paper, the finite element analysis and corresponding optimization design of the drive gear of the dryer are carried out. Through the finite element analysis of the gear, the stress distribution and displacement of the gear under load are obtained. Then the mathematical model is established and its structure is optimized. The quality of the gear is greatly reduced under the condition of ensuring reliable performance, which saves the material and makes the original design more scientific and reasonable.
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