Design of helical gear transmission based on MATLAB

1.The establishment of the mathematical model of gear transmission design generally includes three parts: (1) design variables: the basic geometric parameters or performance parameters of gear transmission generally include: number of teeth, normal pressure angle, normal module, tooth top height coefficient, top clearance coefficient, shaft intersection angle, etc. (2) Objective function: common objective functions include minimum volume (or mass), maximum bearing capacity, longest working life, minimum vibration, etc. (3) Constraint conditions: the general conditions are to meet the contact fatigue strength, bending fatigue strength, the number of teeth not less than the minimum number of teeth where undercutting occurs, the modulus of the gear transmitting power not less than 2mm, the tooth width not to cause excessive uneven load distribution, the transmission ratio error not greater than the given error design requirements, etc.

In the helical gear drive, the main parameters are module, number of teeth, tooth width coefficient, helix angle, etc. Among these important variables, the module determines the size and strength of the gear. When the module is fixed, the number of teeth determines the size of the graduation circle. The helix angle is also an important parameter, which directly affects the shape of the gear, the size and size of the force. Therefore, in the design of gear transmission, the selection of module, the number of pinion teeth, helix angle and tooth width coefficient will directly affect the outline size and transmission quality of the transmission device. Therefore, module, number of teeth, helix angle and tooth width coefficient are selected as design variables.

2.Tooth contact fatigue strength condition

When calculating the contact stress of helical gear drive, its characteristics shall be considered:

(1) The contact line of meshing is inclined, which is helpful to improve the contact strength. The coefficient of helix angle Z βis introduced;

(2) The curvature radius of the joint is calculated according to the normal plane;

(3) Large coincidence and stable transmission.

It can be considered that the meshing of a pair of helical gears is equivalent to the meshing of their equivalent spur gears, so the strength calculation of helical gears can be transformed into the strength calculation of the equivalent spur gears.

Like the spur gear, the condition of tooth surface contact fatigue strength of helical cylindrical gear is obtained by using Hertz formula and substituting the relevant parameters of equivalent spur gear

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