# Gearbox Calculations

Hey, I am having a hard time determining output speed and torque from the CIM-U-LATOR gearbox using the 2 RS-550 banebots motors. Can anyone explain what formulas I need to determine this? All help is appreciated.

First step is to count teeth.

I haven’t used or seen a Cim-u-lator, but looking at the Banebots website it states that it has a 2.7:1 gear reduction. With a 10 tooth pinion on the motors driving a 27 tooth gear on the output shaft.

If the tooth counts match what the website says then you can use the following formula to determine the output speed.

Ratio=# Teeth in Gear/# Teeth in Pinion

Output Shaft Speed=Motor Speed/Ratio

Output Torque=Motor TorqueRatio(Number of Motors)

Single Reduction gearboxes spur gearboxes are relatively efficient so you can probably neglect any losses from the gears in your calculations.

It is probably worth stating that the motor speed is very dependent on load and so I typically suggest using a timing light to actually measure output speed. The formulas will usually get you in the ball park.

Banebots 550-12:

19,300 rpm free speed

70.5 ozin stall torque

85 stall amps

CIM-U-LATOR:

Gear reduction is 2.7:1

… so 2 550’s on a CIM-U-LATOR would be

free speed = 19,300/2.7 = 7148 rpm*

stall torque = 270.52.7 = 381 ozin*

stall amps = 2*85 = 170 amps

Is that what you were asking?

• neglecting gearbox efficiency losses

Yes, thanks for the help

You can enter those numbers:

stall torque = 270.52.7 = 381 ozin*

free speed = 19,300/2.7 = 7148 rpm*

stall amps = 2*85 = 170 amps

free amps = 2.8 amps

… into the motor calculator using option “u” (UserDefined motor):

``````Motor Calculator  build MCALC32ae 2/21/2012 117am

Select motor:
1)CIM      6)FP0673   d)FP2719   f)FP9012    g)FP9015    h)FP9013
a)am-0912  b)am-0914  7)DensoL   8)DensoR    c)Denso0160 u)UserDefined
2)RS395    3)RS540    4)RS550    e)RS775-12  5)RS775-18  x)exit u

Enter the following motor specs in the order and units indicated,
separated by spaces or tabs:
volts   stall_ozin      free_rpm        stall_amps      free_amps
12      **381 **            **7148**            **170**             **2.8**

UserDefined-> 12.0 381.0  7148 170.0  2.8 @ 12.00 volts:

oz-in      Nm     rpm    rpm%    amps   watts out  watts heat    eff%
0.0   0.000    7148   100.0     2.8         0.0        33.6     0.0

@ stall:
oz-in      Nm     rpm    rpm%    amps   watts out  watts heat    eff%
381.0   2.690       0     0.0   170.0         0.0      2040.0     0.0

@ max power:
oz-in      Nm     rpm    rpm%    amps   watts out  watts heat    eff%
190.5   1.345    3574    50.0    86.4       503.5       533.3    48.6

@ max efficiency:
oz-in      Nm     rpm    rpm%    amps   watts out  watts heat    eff%
43.3   0.306    6335    88.6    21.8       203.0        58.8    77.5

Select input:
1)oz-in  7)watts_in    3)rpm    5)amps   8)eff%
2)Nm     6)watts_out   4)rpm%   9)volts  a)rpm&ozin   b)rpm&amps
``````

… and then you can do calculations to determine the operating point under various conditions of speed, load , or applied voltage.