Spring deflection load calculation for excavator

[robax25]

1. A hydraulic cylinder equipped with a helical coil compression spring(figure is attached). The oil pressure acts the spring and moves the boom from position 1 to position 2.

Maximum boom load in position 1 F1max= 16550N
Minimum boom load in position 2 F2min = 18550N

cylinder load Fcyl=19000N
Elastic modulus E= 206000N/mm^2
shear modulus G=80000N/mm^2

1)determine the springs Load Fs1 and Fs2 for the different boom positions.

Homework Equations

F=C/S C= spring constant, s= deflection of the spring

The Attempt at a Solution

Springs load Fs1 for the positions 1 Fs1=Fcylsin60° =16454.48N
spring load Fs2 for the position 2 Fs2 = Fclycos60°=9500N

 

[Dr.D]

What is the direction of gravity in this problem? Is it a factor? If so, do you have the weight of the boom? Is the shovel force constant in direction, fixed relative to the boom, or what? We seem to be missing some information here.

 

[robax25]

yes, shovel force is constant. All descriptions can be found in the figures which I uploaded.

 

[Dr.D]

yes, shovel force is constant. All descriptions can be found in the figures which I uploaded.

So the shovel force is constant in both magnitude and absolute direction, or constant in magnitude and constant in relative direction?

I saw no gravity vector, so does that mean that gravity, and consequently weight, is not a factor?

 

[robax25]

gravity is included. when it moves from neutral position it needs 19000 N force which is provided by hydraulic cylinder. In this case structure weight is neglected but shovel force has to be considered. from neutral position to position 1 is 30 degree and in this position shovel can take 16550N force(maximum) and when it moves back 30° from neutral position, it has minimum force 18550N.

 

[haruspex]

The oil pressure acts the spring and moves the boom from position 1 to position 2.

The oil pressure acting on the plate would move it from position 2 to position 1.

I don't understand how the oil pressure (F_cyl*area) can be constant. From an equilibrium state, it must increase to push on the plate.

I'm not sure in what sense the load forces are a max and a min. Max and min wrt what? Certainly not in respect of each other, since the min is greater than the max. Maybe just ignore those qualifiers and say those are the load forces at the two positions.
On that basis, and trusting the "constant F_cyl" statement, what is the corresponding spring force at each position?