Understanding of Geared Motors

Not exactly cheap, but affordable, when I can manage with gears for a motor which costs 0.5 dollar why buy something expensive

If I need 900 g cm torque would that be fine with gears? Its around 2.5 times the stall torque.

The stall torque is not a good place to base your calculations on. It is the maximum torque produced by a motor: when it has not started rotating but the power has just been applied.
Almost every motor will burn out if operated at the stall torque for any length of time. The data sheet graph does not even extend to the stall parameters! They have just typed in those numbers in the graph.
Efficiency is terrible at that part of the curve.

I did a search on AliExpress for dc gear motor and found this motor
JGA25-370 Geared motor DC motor 6V 12V 24V electric gear motor high torque 5/10/15/30/60/100/150/200/300/400/500/1000/1200 rpm

One of the choices is 12V, 1000 rpm for $2.23.
The only torque they list is 9 kg.cm. This is undoubtedly the stall torque. But even if you de-rate it considerably, it should meet your needs.

They'd have to be suitable gears!

Although the principles are all identical, The gears in an automobile gearbox are not going to be the same as the gears in a cheap plastic car!

As with anything, cheap gears aren't going to get far!

Thank you but unfortunately the length would be too large for fitting. This type of motors will need a gear bending the torque force by 90 degree to fit.

Will try to find good gears. Thanks !

I am not a motor expert but looking at the curve if you use a 15:1 gear ratio you would have 1875 g-cm of torque at 1000 rpm. First you said you needed 1500 g-cm then it became 900 g-cm so both are satisfied. I started with a motor speed of 15000 rpm, at that speed the T is about 125 g-cm.
Operating at max efficiency and a 20:1 gear ratio you'll have a speed of 1000 rpm and T=800 g-cm.
If I am out in left field on this someone let me know.

Thanks for the math, now all thats left is finding these parts.

How did you get 800g-cm?

at 20,000 rpm the torque is about 40 g-cm so if the gear ratio is 20:1 the torque should increase
by 20 so 40 x 20 = 800 g-cm.

According to the data sheet max efficiency occures at 18960 rpm with a torque of 69.5 g-cm

You asked how I got 800 g-cm so I don't really know what your telling me.

Max efficiency is at 69.5 g-cm NOT 40 g-cm

If I use maximum efficiency it will be around 13:1, better to use 15:1 to be on the safe side and also 15 is more easily available. And I had another question, suppose I buy those small plastic gears, and it's labelled as 'x' teeth, does that mean that the diameter of the gear piece is 'x' mm? (For spiral gears).And if I use a bigger motor like the RS-555 and use bevel gears to rotate it by 90 degree will that work well? In theory if I do that all my requirements are sufficiently met

Thanks for schooling me Jim.

That depends on the pitch or module (metric).

Metric:
gear diameter = z * module
So, for a 30 tooth gear of module 0.5, the diameter is 15 mm.

Imperial"
D = z/pitch
A 20 tooth gear of 40 tpi will have a diameter of 0.5"

You may need to clarify what you mean by "spiral" gears. I assume you mean helical gears.

I am sorry, I mean spur gears like the ones normally available when you search gear set of 78 pieces or 54 pieces. Thanks for the info

I did some math and came to the conclusion, the Power of the motor remains constant, and not following SI units I will describe Power = RPM x Torque in (g-cm). So it comes to Power = 475vw. Where v is my intended speed in m/s for my project and w is the weight of my car in gram.

Now I put in v=6 and w=600. This leads to P= 1,710,000. Now, in similar kind of units, RS-385 gives 657,685. RS-555 gives 880,000. RS-775 gives 2,437,500. All calculated at maximum efficiency. So I have come to the conclusion that 775 is more befitting for my project.

And for the gearbox, the motor gives 650 g-cm and I will need 900 g-cm, so a 3:2 gear will be suitable.

Please tell me if there are any flaws in my conclusion or will this work fine.

The flaw is assuming perfectly cut gears. If gear teeth are perfectly cut for the pitch, they will ROLL against each other as they mesh. Imperfect gears will SLIDE together and SLIDE apart. Friction will greatly reduce your computed efficiency.
Almost all cheap gears will slid against the mating gear, so don't count on 100% efficiency with gears. Each gear set will reduce efficiency of the whole.

I think you are getting there.
What we don't know is what is the efficiency of your car as a whole. There are losses all the way from the battery to the motor to the gears to the transmission to the wheels.
We also don't know its size and weight.

One simplified way of looking at this would be to look at existing examples. Look for RC cars and see what sort of motors they use. My guess is that a small RC car probably uses an "RS 550" size motor, and a buggy may use a 775 size.
And more expensive ones use brushless motors.