The Vex forum has a thread about mixing 269 and 393 motors and most people are correct in saying that you should always make sure they are coupled 1:1. However, the motors will surely run with different gearing. At any given speed , the torques just sum and you get a combined motor that has the effective torque of two motors which have the average torque.
What happens is the free speeds of the combined motors will be higher than the lowest motor free speed when the torque resultant goes to zero so the slow motor will be fighting the fast motor. This results in loss of efficiency for sure.
I wrote an excel program that sums the speed/torque curves of two motors when plots them as a function of speed. This inverts the normal torque-speed curve so it might be a little confusing.
Here is a plot with a gearing of 3:1 on the second motor…. i.e. if motor 1 is disconnected, the common shaft will turn at 3 x the free speed of motor 1.
When the total torque is zero, the free_speed is 120 RPM and the total current is 3.5 amps instead of 2xi_free or .74 amps that you would get with two motors geared at 1:1. Motor 2 is forced to operate at a slower speed relative to its max and therefore has a higher current all the time. As shown in the figure the efficiency goes down to 18%.
If there is just a slight difference in gearing there would hardly be any noticeable change. I.e. last year we use the 393 high speed 160 rpm gearing coupled with a 5/3 gearing on a legacy motor running at 100 rpm. So we have a 160/167 difference or 4.5% difference. We saw some heating but it was caused by other factors… see post for picture of drive train, I ran the excel program with a gearing of 1.1 and the i_free increased from .74 to .8 amps. The peak efficiency dropped about .6 %.
Why do we see the weaker motors heating up when coupled with a 393??
Effect of backlash??: Could gear backlash cause extra heating if the weaker motor is directly coupled to the wheel axles. Every time a direction change is commanded, the weaker motor will see the full load until the 393 moves enough to take up the slop. Lets say that you have 1/4 turn slop in the drive train between the 393 and a 269. With no load on the 393 while its in the slop, it would take .15 seconds to take up the slop. Drivers that are very active with the stick essentially do a bang bang type of controlling. We know that this type of driving heats up motors… if this type of driving was done at a rate of six direction changes per 10 seconds the weaker motor would see full load 10% of the time. Hmmm something to think about. No conclusions here.