Modeling piston/crank with position loop equation, excel plot

In summary, the conversation is about a student seeking help with their work on solving for the constant angular velocity of a graphed sinusoidal motion. They are unsure about the correctness of their geometry work and have provided images for reference. Another user suggests simplifying the variables and provides a solution for finding the constant angular velocity. The student thanks them and confirms that their graph looks similar to the one provided.
  • #1
DarksideEE7
1
0

Homework Statement



attachment.php?attachmentid=27075&stc=1&d=1279734347.jpg


Homework Equations


I would like to know if my work is correct. I thought that the graph would be a sinusoidal, but there is a small irregularity in the middle.

Am I correct in using θAC = 90 deg and θAB = 36.8699 deg in solving for the constant angular velocity?

I attached the scratch paper portion because that contains my geometry work for determining the θAB value beyond the symbolic part, and I'm unsure if that's correct.

I've set up the position, velocity, and acceleration loop equations symbolically as shown below.

What concerned me about using θAC = 90 deg is that it causes θ'AB = 0 due to the cos term. This ends up making the max angular velocity -60 rad/s...

The Attempt at a Solution



[PLAIN]http://img203.imageshack.us/img203/4069/piston2.jpg
attachment.php?attachmentid=27077&stc=1&d=1279734347.jpg


Scratch paper

[PLAIN]http://img827.imageshack.us/img827/9174/pistonscratchpaper.jpg

https://www.physicsforums.com/attachment.php?attachmentid=27079&stc=1&d=1279735274

[PLAIN]http://img408.imageshack.us/img408/2493/pistongraph.jpg


Thanks in advance for helping out a clueless EE student!

EDIT:

Resized images...can resize further if the res is too big for your monitor. Also fixed broken link. Still missing the scratch paper image because I'm away from home. I'll upload when I get home...but hopefully this should be enough for someone to check my basic equations and graph.
 

Attachments

  • Problem.jpg
    Problem.jpg
    30.8 KB · Views: 548
  • piston1.jpg
    piston1.jpg
    35.8 KB · Views: 391
  • piston2.jpg
    piston2.jpg
    21.1 KB · Views: 497
Last edited by a moderator:
Physics news on Phys.org
  • #2
It's pretty difficult to follow your steps, so I cannot comment in detail on your work. I think we need not use so many variables (please excuse me if I misunderstand something). Two coordinates are enough: [tex]\phi[/tex] (angle between AC and AB) and x.

The only geometric condition relating the coordinates is: [tex]b^2=a^2+x^2-2axcos\phi[/tex]

Plug a=3 and b=5 in, then solve for x (x>0 as the origin is at A): [tex]x=\sqrt{9cos^2\phi +16}+3cos\phi[/tex]

Thus: [tex]\dot{x}=-(\frac{9sin\phi cos\phi}{\sqrt{9cos^2\phi +16}}+3sin\phi)\dot{\phi}[/tex]

From here, we can find the constant angular velocity of AC in the range [tex]0<\phi <\pi[/tex] and [tex]\dot{x}<180 in/s[/tex]. Then the rest is simple. The graph I obtained looks akin to yours.
 

Related to Modeling piston/crank with position loop equation, excel plot

1. What is the purpose of modeling a piston/crank with a position loop equation?

The purpose of modeling a piston/crank system with a position loop equation is to simulate the movement and behavior of the system in order to predict its performance and make any necessary adjustments before physically building it. This helps to save time and resources during the design and testing process.

2. How do you create a position loop equation for a piston/crank system?

To create a position loop equation for a piston/crank system, you will need to first determine the position of the piston and crank at any given time. This can be done by using trigonometric functions and the dimensions of the system. Then, you can create a mathematical equation that relates the position of the piston to the position of the crank and the time.

3. What is the significance of using an excel plot in modeling a piston/crank system?

An excel plot allows you to visualize the data and results from the position loop equation in a graphical format. This makes it easier to identify any patterns or trends and make adjustments to the model as needed. It also allows for easy comparison between different scenarios or variations of the system.

4. What are some common challenges when modeling a piston/crank system?

One common challenge when modeling a piston/crank system is accurately representing the actual behavior of the system. This may require adjusting the model parameters or accounting for external factors such as friction or varying loads. Another challenge is choosing the appropriate level of complexity for the model, as too much complexity can lead to computational difficulties while too little may result in inaccurate predictions.

5. How can the position loop equation and excel plot be used to improve the design of a piston/crank system?

The position loop equation and excel plot can be used to test different design variations and optimize the system for maximum efficiency and performance. By manipulating the model parameters and observing the results on the excel plot, engineers can make informed decisions about the design of the system and make any necessary improvements before constructing the physical prototype.

Hot Threads

Recent Insights

Back
Top