Gear on fixed rack, force analysis

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In summary, "Gear on fixed rack, force analysis" examines the forces acting on equipment mounted on a stationary rack. It evaluates the static and dynamic loads, considering factors such as weight distribution, friction, and structural integrity of the rack. The analysis aims to ensure safe operation and optimal performance of the gear while identifying potential failure points under various conditions.
  • #1
Emilio_2004
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TL;DR Summary
I want to build a monorack system but i struggle to understand the mechanical basics. What forces and torques act on a gear on a fixed rack
I am confused cause in my diagram for the sake of simplicity i ignore gravity and friction. But the net torque on the gear is zero? How can that be? I am sorry if thats a stupid question but i am just a bit confused and honestly stuck since days on that.

F react. Is the force that causes the gear to move forward cause on the free body diagram of the gear thats the net force. We apply a torque to the gear. This will result in a tangential force at the point of contact. Of course we need to also consider the pressure angle of the mashing, thats why i drew a force pointing upwards on from bearing of the gear to account for that (same for the rack) The force from the gear is the same as the one that will be acting on the rack (actio reactio).

The rack experiences a net force of zero as its fixed into place. But my free body diagram as it is now doesn’t make sense cause of what i already said regarding the net torque. I already was on Reddit and i got a response stating that the normal force on the gear/ the reaction force gets smaller by time, but I honestly dont get it, i hope someone can help me out. I also apologize if i am a bit unclear with what i wrote so far.
IMG_1378.jpeg
 
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  • #2
Welcome to PF.

Emilio_2004 said:
TL;DR Summary: I want to build a monorack system but i struggle to understand the mechanical basics. What forces and torques act on a gear on a fixed rack

But my free body diagram as it is now doesn’t make sense
Yeah, I'm not understanding it either. How is the gear suspended/supported below the beam? How is it driven? Directly by a motor shaft, or indirectly by another gear?

Are you thinking of something like this...?



1715968921849.png
 

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  • #3
I wrote that haha. But i simplified it and got here to understand it haha. The geer would be suspended by a wheel above the rail, supporting it, but i already accounted for that by drawing in force B. The gear would have an applied torque coming from a motor
 
  • #4
What is missing from your free body diagram are the accelerations.

So, summation of forces along the x-axis:
$$F_x = ma$$
Summation of moments:
$$M_1 - F_x r = I\alpha$$
And the accelerations are linked together by:
$$a= \alpha r$$
3 equations, 3 unknowns: ##a, \alpha, F_x##

Simplifying, we get:
$$M_1 - m(\alpha r) r = I\alpha$$
$$M_1 = (I + mr^2)\alpha$$
and
$$F_x = \frac{^{M_1} /_r}{\left(1+ \frac{I}{mr^2}\right)}$$
There is a force ##F_x## only if there is an acceleration. If there is a moment ##M_1##, there is an acceleration. Otherwise, the velocity is constant, and ##M_1 = F_x = 0##. This is true because we haven't included any resistance, which has to exist in a real mechanism.

Yep, a wheel - once launched - will never stop rolling if there is nothing to slow it down. Any input force will only accelerate or decelerate it.
 
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  • #5
Thank you so much, but if there were resistance where and how would it act?
 
  • #6
Emilio_2004 said:
Thank you so much, but if there were resistance where and how would it act?
The bearings that support the motor shaft, gears and the trolley guide wheels, will have some friction.
 
  • #7
Baluncore said:
The bearings that support the motor shaft, gears and the trolley guide wheels, will have some friction.
Thank you! This Makes sense. I have one last question. When i asked on reddit a couple of days ago i got a reply: „The forces on the gear are going to accelerate it, and this will mean that the normal force on the rack and the reaction on the gear goes down.“ What did he/she mean by that?
 
  • #8
Emilio_2004 said:
What did he/she mean by that?
If we assume an electric motor that runs at a set speed. It will take time to accelerate the trolley to match the speed of the motor through the gear train. From that time on, the only torque needed from the motor will be that needed to overcome friction, so the electric motor torque and current will fall when it reaches synchronous speed.

If the motor is supplied with a fixed current, then the motor torque will be constant, so the system will accelerate continuously to the limiting speed of the motor and supply voltage.
 
  • #9
Baluncore said:
If we assume an electric motor that runs at a set speed. It will take time to accelerate the trolley to match the speed of the motor through the gear train. From that time on, the only torque needed from the motor will be that needed to overcome friction, so the electric motor torque and current will fall when it reaches synchronous speed.

If the motor is supplied with a fixed current, then the motor torque will be constant, so the system will accelerate continuously to the limiting speed of the motor and supply voltage.
Oh i understand. And if we assume no friction or terminal speed there will be always be the same normal/reaction force?
 
  • #10
Emilio_2004 said:
Oh i understand. And if we assume no friction or terminal speed there will be always be the same normal/reaction force?
That will depend on the motor and motor controls.
In reality, it cannot accelerate forever.
 
  • #11
Of course, but if we assume ideal conditions which are impossible in reality, will the resulting force on the teeth be constant if we apply a constant torque to the motor/a constant current, and it will accelerate into infinity?
 
  • #12
If the motor torque could remain constant, the force on the teeth would remain constant. The system will then accelerate towards infinity.
 
  • #13
Emilio_2004 said:
.. The geer would be suspended by a wheel above the rail, supporting it, but i already accounted for that by drawing in force B. The gear would have an applied torque coming from a motor
Welcome, Emilio!

What are you trying to move with that apparatus?

You will need two wheels above the rail, …or two rails and four wheels, if you need to balance the lateral weight of the motor.
 
  • #14
What type of motor are you using to drive the gear? Each of these are controlled differently, and load the gear differently. This would help us to interpret what you were told on Reddit.

1) A small servo typically controlled by an Arduino?
2) An industrial servo motor?
3) An induction motor?

We also need to know about the load and the motion profile:

1) What is the total moving mass?
2) What is the maximum acceleration?
3) What is the maximum velocity during the move?
4) What is the maximum move distance?
 

FAQ: Gear on fixed rack, force analysis

What is a fixed rack in the context of gear systems?

A fixed rack is a linear component used in gear systems that provides a straight path for the movement of a pinion gear. It is typically stationary and serves as the reference point against which the pinion rotates, converting rotational motion into linear motion.

How does force analysis apply to gears on a fixed rack?

Force analysis in gears on a fixed rack involves evaluating the forces acting on the gear system, including the input torque, the load on the pinion, and the reactions at the fixed rack. This analysis helps in understanding how forces are transmitted through the system and in determining the mechanical advantage and efficiency of the gear arrangement.

What factors influence the forces in a gear system with a fixed rack?

Several factors influence the forces in a gear system with a fixed rack, including the size and shape of the gears, the material properties, the angle of engagement, the load applied to the system, and the friction between the gear components. Additionally, the arrangement and alignment of the gears can also impact the force distribution.

How can I calculate the force exerted by the pinion on the fixed rack?

The force exerted by the pinion on the fixed rack can be calculated using the formula: F = T / r, where F is the force, T is the torque applied to the pinion, and r is the radius of the pinion. This calculation helps in determining the load that the rack will experience due to the pinion's rotation.

What are common applications of gear systems with fixed racks?

Common applications of gear systems with fixed racks include linear actuators, steering mechanisms in vehicles, automated machinery, and various types of material handling equipment. These systems are favored for their ability to convert rotary motion into precise linear movement efficiently.

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