Mathematical model of a two wheel drive tractor using Lagrange mechanics

[faisalmatar]

Homework Statement

Hello all,

I am currently working on designing a controller for a two-wheeled pushed tractor. As part of this process, I need to develop a mathematical model of the tractor. I have been using Lagrange mechanics to build the model, but I find it becoming very complicated, and the problem is turning highly nonlinear.

Has anyone worked on similar models or encountered a similar challenge? Any help or guidance would be greatly appreciated.

Thanks!

Relevant Equations

Lagrange mechanics

obtaining a mathematical model for a two wheels pushed tractor

 

[berkeman]

Welcome to PF.

Can you show us your work so far? That will help us make some suggestions. Also, what-all do you need to model? Just the suspension, or driving in a straight line over rough dirt, or including turns on rough dirt? Does your tractor have a rear differential or a straight shaft?

 

[vela]

I don't even know what a two-wheeled pushed tractor is.

 

[berkeman]

I don't even know what a two-wheeled pushed tractor is.

I fixed it to two wheel drive in the thread title, but not in the post. I'm pretty sure that's what they mean, as opposed to a 4WD tractor (if those exist).

 

[Lnewqban]

I don't even know what a two-wheeled pushed tractor is.

Perhaps an engine with only two parallel driving wheels?

https://en.wikipedia.org/wiki/Two-wheel_tractor

The operator is not "pushing" the thing, only steering it via individual hand brakes.

 

[vela]

I fixed it to two wheel drive in the thread title, but not in the post. I'm pretty sure that's what they mean, as opposed to a 4WD tractor (if those exist).

That makes sense. I was thinking, "Hmm, a two-wheeled tractor isn't going to be very stable in a field."

 

[vela]

Perhaps an engine with only two parallel driving wheels?

https://en.wikipedia.org/wiki/Two-wheel_tractor

The operator is not "pushing" the thing, only steering it via individual hand brakes.

Oh no! That makes sense too, except for the "pushed" part. I will await the OP to clarify.

 

[faisalmatar]

Welcome to PF.

Can you show us your work so far? That will help us make some suggestions. Also, what-all do you need to model? Just the suspension, or driving in a straight line over rough dirt, or including turns on rough dirt? Does your tractor have a rear differential or a straight shaft?

I made my work on papers now it needs sometime to transfer it to a document. firstly, the purpose of developing a model is to design a controller after getting the mathematical model of the tractor. what i need to control is the speed of the tractor and its stability during ploughing process with the assist of human force involvement (semi-autonomous) . so I'm imagining a two wheel tractor with a plough on the rear and a chassis just above the wheels and extended a little to the front, and with handle to make the human able to control it. The forces that interact with the systems are traction force on the wheels, rolling resistance, plough draft force (with the soil) and the human with hand force. i need to driving it a straight level over soil and assume a straight shaft.

 

[berkeman]

so I'm imagining a two wheel tractor with a plough on the rear and a chassis just above the wheels and extended a little to the front, and with handle to make the human able to control it.

Sorry, do you mean something like this?

https://www.abposters.com/work-with...home-farm-plow-the-soil-for-sowing-f429511102

 

[faisalmatar]

yes, but it has a wheels and a plough not only the helical plough, like this:

so i need to make the model taking into account all exerting forces, can you please help?

 

[berkeman]

so i need to make the model taking into account all exerting forces, can you please help?

Sure. So show us your work so far, especially how you plan to involve Lagrange mechanics in the modeling. We cannot offer tutorial help until you show significant effort on your own. That is in the PF rules (see INFO at the top of the page).

 

[faisalmatar]

I understand. I started by defining all the forces exerted on the system for every part(body, wheels, plough, handle) and the kinematics of the system assuming a movement in the x-direction and an up angle that is a result of the downward force applied by the human on the handle when starting ploughing.