# Example and mathematical model of optimum design for minimum center distance of two stage spur gear

As shown in the figure, it is known that the input power P1 of the high-speed stage of the two-stage helical cylindrical gear reducer is 6.2kw, the speed n1 is 1450r / min, the total transmission ratio I is 31.5, the gear width coefficient is ψ d = 0.5, and the load coefficient K is 1.3. The gear material and heat treatment are as follows: big gear 45 steel, normalizing treatment, small gear 45 steel, quenching and tempering treatment. The surface hardening temperature is 45hrc. It is required to determine the gear transmission scheme according to the minimum total center distance.

Solution: according to the gear material and heat treatment specification, the calculation can get σ H = 518.75MPa, [σ F] 1.3 = 153.5mpa and [σ F] 2.4 = 141.6mpa. The relevant data are substituted into the strength calculation formula

High speed shaft torque T1 = 41690;

Intermediate shaft torque T2 = 40440;

High speed shaft gear load factor K1 = 1.225;

Low speed shaft gear load factor K1 = 1.204. 