Gear transmission has the advantages of smooth transmission, compact structure and strong carrying capacity, so it is widely used in machines. How to obtain a reasonable involute profile and make the gear transmission have a longer service life is a problem that engineers and technicians are constantly exploring. In this paper, MAT2LAB software is used to optimize the open gear transmission of a mechanical mill BMΦ3×7 ball mill, and the involute tooth profile with the smallest tooth surface wear is obtained, which improves the service life of the gear.
1 measures to improve the service life of open gears The main failure modes of gear transmission are gear tooth fracture and tooth surface damage. There are four types of tooth surface damage, such as eclipse, gluing, abrasive wear and plastic flow. Among them, abrasive wear is the main failure mode of open gear transmission. Therefore, the life of an open gear transmission depends mainly on the wear thickness of the tooth surface. Increasing the service life of the open gear can be considered from the following aspects: 1) designing a reasonable involute tooth profile to reduce the friction length; 2) selecting a material with a small elastic modulus and a large friction fatigue strength; 3) adopting Appropriate heat treatment measures to improve the hardness of the tooth surface; 4) Select the appropriate processing method to reduce the surface roughness; 5) Select a suitable lubricant to reduce the friction factor.
It can be seen that when the material of the gear, the heat treatment measures, the processing method and the lubricant are all determined, the gear is optimized, and the involute tooth profile with the smallest tooth surface wear is the key to improve the service life of the open gear.
2 Mathematical model of gear optimization design When using MATLAB software to solve an actual optimization problem, we must first turn this problem into a mathematical problem, that is, to establish a mathematical model. The mathematical model includes three elements: design variables, objective functions, and constraints.
2.1 Design variables When the modulus, number of teeth, pressure angle and tooth width of the gear are fixed, the shape of the tooth profile depends only on the displacement coefficient x2 and x1 of the large and small gears, so the design variable is: x=[x1,x2] The target function of T2.2 is the most serious wear of the tooth root and the tooth tip during the transmission process. If the total wear of the tooth root and the tooth top of the large and small gears can be minimized, the service life of the open gear can be improved. The sliding coefficients of the root and the tip of the large and small gears are: λ21, λ22, λ11, λ12, and the radius of curvature of the root and the tip of the large and small gears are: Ï21, Ï22, Ï11, Ï12, then the total The wear amount H is [3]: H = CÏ11Ï22Ï11 Ï22 / cosα'12 (λ11μ λ22) Ï12Ï21Ï12 Ï21 / cosα'12 (λ12μ λ21) where C is a constant. The wear characteristic parameters of the root and the tip of the large and small gears are t21, t22, t11, t12, respectively, and t21=Ï12Ï21Ï12 Ï21/cosα'12λ21t22=Ï11Ï22Ï11 Ï22/cosα'12λ22t11=Ï11Ï22Ï11 Ï22/cosα'12λ11μt12=Ï12Ï21Ï12 Ï21 /cosα'12λ12μ is: H=C∑2j=1∑2i=1tij Since C is a constant, H depends on ∑2j=1∑2i=1tij, that is, depending on the displacement coefficient x1, x2, ie the objective function It is: F(x)=∑2j=1∑2i=1tij2.3 Constraints The constraints of gear design include the following aspects: 1) Avoiding the undercut phenomenon in gear machining pinion g1(x)=x1 z12sin2α≥ 0 large gear g2(x)=x2 z2sin2α≥02) limitation of gear transmission coincidence degree g3(x)=12Ï€[z1(tanαa1-tanα') z2(tanαa2tanα')]-[ε]≥03) Limit pinion g4(x)=da1015Ï€ 2x1tanαz1-InVda1 InVd-[Sa]≥0 large gear g5(x)=da2015Ï€ 2x2tanαz2-InVda2 InVd-[Sa]≥04) Gear excess curve without interference condition limiting pinion g6 ( x)=4(h3a-x1)z1sin2α tanα'-tanα-z2z1(tanαa2-tanα')≥0 large gear g7(x)=4(h3a-x2)z2 Sin2α tanα'-tanα-z1z2(tanαa1-tanα')≥05) Restriction of gear strength conditions Tooth surface contact strength g8(x)=SH1-[SH]≥0g9(x)=SH2-[SH]≥0 tooth root Bending strength g10(x)=SF1-[SF]≥0g11(x)=SF2-[SF]≥0 where α is the indexing circle pressure angle; α′ is the meshing angle; αa2, αa1 are large and small respectively Gear tip pressure angle; z2, z1 are the number of teeth of the large and small gears; da2, da1 are the diameter of the top and bottom of the large and small gears respectively; [ε] is the allowable coincidence value; [Sa] is the allowable top Thickness value; [SH] is the allowable contact strength safety factor; [SF] is the allowable bending strength safety factor; SH2 and SH1 are the large and small gear contact strength safety factors; SF2 and SF1 are the large and small gear bending strength respectively. Safety factor.
3 Example calculation analysis BMΦ3×7 ball mill open gear transmission parameters are: number of teeth z1=30, z2=196; modulus m=26; tooth width b=500; index circle pressure angle α=20°; transfer power P =900kW; pinion speed n1=135r/min.
The above parameters and related parameters calculated by the above parameters are brought into the objective function and constraints, and solved by MAT2LAB615 software on the microcomputer to obtain the minimum value of the total wear thickness of the tooth tips and roots of the large and small gears and their displacements. If the coefficient is x2=x1=0, the total wear thickness of the tooth tips and roots of the large and small gears can be obtained by using MAT2LAB615 software. Table 2 shows the large and small gears when the displacement coefficient is zero. Tooth top, root wear thickness μmx2x1t21t22t11t12∑2j=1∑2i=1tij012192619716017359116239179 The optimized design of the displacement gear can greatly reduce the total wear of the tooth root and the tooth top of the large and small gears, and obtain the involute opening with the smallest amount of tooth wear. Line profile, which increases the life of the gear. Practice has shown that the displacement gear with optimized design is 118 to 215 times the service life of the invariant gear.
4 Conclusion How to improve the service life of gears is a problem that engineers and technicians are constantly exploring. In this paper, MATLAB software is used to optimize the design of an open gear transmission, and the design variables, objective functions and constraints are determined. The appropriate mathematical model is established. The involute profile with the smallest tooth surface wear is obtained through analysis and calculation. Increases the service life of the gears. The method described in this paper can be extended to the optimal design of other gears, sprockets, worm gears and worms.
Thermal Oil,Heat Transfer Fluid Terminal,Industrial Heat Transfer Oil,Industrial Heat Conducting Oil
LIAONING ARMCO TECHNICAL LUBRICANTS CO., LTD. , https://www.armcoltherm.com