Gearbox size selection

For the correct selection of the gearbox and driving electric motor the following data must be known: Required total torque M ₂, gearbox output speed n₂, loading mode and corresponding operational coefficient S_m. On the basis of these values, it is then possible to fix the corresponding gearbox size, power and gear ratio "i".

Correlations for calculating the various magnitudes

Output torque M₂

Torque M₂depends on the required gearbox load and it may be expressed as the force F ₂, which actuates at certain distance on the arm r₂.

M₂[Nm] = F₂[N] x r₂ [m]

Operating coefficient S_m

In order to ensure the gearbox optimum service life at different operating load modes, when selecting the gearbox size, we use so called operating coefficient S _m, which is the product of partial factors, reflecting the individual conditions.

S_m= S₁x S₂x S₃ x S₄

S1- load factor
1,0	normal impact-free start, small accelerated mass (fans, gear pumps, mounting belts, conveyer worms, mixers of liquids, filling and packing machines)
1,25	start with moderate impacts, irregular operation, and medium accelerated mass (conveyer belts, elevators, winches, masticating mixing machines, wood-working, printing, and textile machines
1,5	irregular operation, heavy impacts, high accelerated mass (concrete mixers, suction pumps, compressors, machine hammers, roll stands, heavy goods transporters, bending and pressing machines, alternating-move machines)

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S2- factor of operation smoothness
S2	number of closings per hour
1,0	0 to 10
1,15	10 to 50
1,3	50 to 100
1,5	100 to 200

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S3- factor of operation time
S3	number of starts per day
0,8	0 to 4
1,0	4 to 8
1,2	8 to 16
1,3	16 to 24

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S4- factor of drive
S4	type of electric motor
1,0	electric motor without brake
1,2	electric motor with brake

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When selecting propre gearbox, it is cecessary to see that the operation factor S_m be smaller than service factor of gearbox S_f.

Service factor S_f

Gearbox service factor S_f determines the approximate ratio of the maximum torque at the gearbox output, which can permanently burden the gearbox, to the actual total torque, which the selected electric motor is able to provide.

M_2max
S_f= --------------------- [-]  
M₂

Maximum torque M_2maxis fixed for the operating coefficient S_m = 1, as specified in Table 5.1. Values of service factors for the various variants of sizes, gears, and assignment of electric motors are specified in Table 6.1.

Electric motor output P₁

For fixing the necessary output of the electric motor P₁the following relation shall be used:

M₂[Nm] x N₂[min^-1] x 100
P₁= ------------------------------------------------- [kW]
9550 x [%]

A portion of the output is consumed for overcoming the gearbox mechanical resistance. This ratio expresses the efficiency , which is the ratio of the power at the output P₂ to the power at the input P₁.

P₂
= -------------- x 100 [%]
P₁   

Gear ratio i

The gear ratio is the gearbox inlet-to-outlet speed ratio

n₁
i = ----------- [-]
n₂

n₁[min^-1] - electric motor nominal speed

n₂[min^-1] - gearbox outlet speed

Radial and axial load of the shaft

The spur bevel gearboxes KTM are furnished with output shaft with cylindrical pin fitted with a keyway. The values of admissible radial load values are specified in Table 6.1. The admissible shaft load is rated for inlet speed n ₁= 1400 [min^-1], for the given gear and motor output.

Radial load of the shaft

For determining this values, as the point of application of the radial force F_radthe shaft half-free end has been taken (see the following figure).

Fr[N]

- values of admissible radial load stated in Table 6.1.

Calculated F_rad may not exceed the maximum admissible radial load of the shaft specified in Table 6.1.

In case a pulley, chain wheel, toothed wheel and the like are put on the outlet shaft, the actual radial load can be calculated with the help of the following formula:

M₂x k x 2000
F_r= --------------------------- [N]
D

M2[Nm]	- output torque
D [mm]	- computing diameter (pitch circle) of the pulley (toothed wheel) at the output
k	- load factor
	1,10 chain wheels 1,25 spur gears 1,50 pulley

Axial load F_{a max.}with F_x= 0

The admissible axial load of a hollow shaft is determined with the relation

F_r
F_{a max.}= ---------------- [N]  
3

Fa max.[N]	- the maximum admissible force
Fr [N]	- value of the admissible radial load stated in Table.a 6.1.

The radial load of the shaft with the axial force actuating simultaneously

When actuating simultaneously, the axial and radial forces may not exceed the load of the shaft

F_ra= F _r- 3 x F_a [N]

Fa [N]	- the axial load of the shaft
Fr [N]	- values of the admissible radial load stated in Table 6.1.
Fra [N]	- the maximum admissible radial force with the axial force actuating simultaneously Fa [N]