I've been studying this topic for a couple of days now. I started by asking some questions regarding output Torque and gear ratios relations. Now I came with the whole picture and some calculations that I been working on. My goal is to find out if I'm in the right direction, and also point-out relations between equations that I'm not sure of. To make this more clear and clean, I divide the system into three sections; A, T and B.
In section A its the electric motor and worm/spur torque transmission.
On another topic with a lot of help, I realise that the power provides by the motor is crucial to generate the output torque and angular velocity that your system requires. No matter the radius, ratios or N of teeth of the spur; if the power isn't enough, the gate won't move at the desired velocity.
So, the problem in question: My goal is to find out if this system will be able to move a gate of 600 kg with a velocity of 0.33 m/s, and how much time it will take to reach that velocity.
The technical data of the motor is:
P = 1/2 hp ; RPM = 1450 ; 220V/50Hz
P = 0.5 hp = 373 (kg * m2 /s3) Pin = Tin * win
win = 1450 rpm = 151.84 (rad/seg)
Tin = 373 (kg * m2 /s3) / 151.84 (rad/seg) = 2.456 N*m
This, of course, is in an ideal situation, without considering losses. (how can I add an estimation of electric motor losses?)
The worm/spur system has a gear ratio of 23:1.
Considering the efficiency of the system of 80%, we have:
Tout = 23 * (0.8 * Pin) / win = 45.2 N*m
Now, Tout also can be calculated by Tout = 0.8 * Pin / wout
angular velocity applied on the spur is: wout = (0.8 * Pin) / Tout
wout = 0.8 * 373 (kg * m2 /s3) / 45.2 N*m = 6.6 rad/sec --> 63 rpm
To consider real circumstances, its the moment of inertia has something to do within this case? I mean, is this Tout enough to accelerate the spur to 63 rpm??
In this section, I'm wondering what happens with force transmitted in the distance "d" to the pinion. I'm not sure if I need to consider losses in this section.
Here I have a lot of question about what's happening. The Pinion has 17 teeth and is module 4.
From gear design, I understand that module, and axial pitch determines the Lead and lead angle of the gear. This has a direct relation with the surface contact (involute) in the system and frictional forces.
Is the torque Tout the same as calculated for the worm/spur system? What about the radius of the pinion? If I increase the radius, the Torque will increase as well? The radius of the pinion is = 0.025 (m)
Tout = F * r
F = 45.2 N*m / 0.025 m = 1808 N
Does this mean that the force applied to the rack is 1808 N? Is this force enough to accelerate until 0.33 m/s?
F = m * a = 600 kg * 9.8 m/s2 = 5880 N ; here I need to consider a friction factor according to the wheels and ground. (0.1)
F = 5880 N * 0.1 = 588 N; this means that I need to generate 588 N force to move the gate, but what about the acceleration? if the gate has 4 m, how much time will take to reach the 0.33 m/s
I need a last push to understand this system entirely.