# Traditional calculation and check of spiral bevel gear planetary reducer

The main failure modes of gear transmission are tooth surface pitting and tooth fracture. The working time of the reducer is short, and the pitting on the tooth surface is not considered, so only the bending strength of the tooth root is checked. There are many gears in the planetary gear train, so the load can be shared, so only the center wheel 3 with large force needs to be checked.

Strength check of center wheel

Firstly, the bending strength of the tooth root of the center wheel gear 3 is checked, and the formula is shown in Table 1.

The circumferential force of gear 3: ft21 = 2t3 / 4D3, D3 is the diameter of dividing circle. The torque of gear 3: T3 = Th / i3h η, planetary gear train i3h = 4.67, transmission efficiency η = 0.9.

According to the working environment and consulting the mechanical design manual, the load factor, stress correction factor and other parameters are substituted into the root bending strength checking formula.

The minimum safety factor is 2. According to the calculation results, the center wheel 3 meets the strength requirements.

Strength check of bevel gear

The strength checking formula of bevel gear is shown in Table 2.

Under the rated working condition, the calculated bending stress of tooth root σ f = 105.37 MPa, taking sflim = 2, σ ‘flim = 399.5 MPa. The bending strength of tooth root is satisfied when σ f ≤ σ ‘flim.

Under the condition of emergency stop, the calculated stress of tooth root bending σ f = 316.12 MPa and sflim = 2 can also obtain σ f ≤ σ ‘flim, which meets the bending strength of tooth root.

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