By Chris Smith
Sometimes our designs call for certain common components to be used for correct operation. One of these components is springs.
Springs are a very useful component but can be difficult to size correctly, leading to unnecessary costs or even system failures. The Dynamic Simulation tool within Inventor can help quickly design the correct spring for the situation.
Creating a study
Our goal is to create a coil spring that will limit rotary movement to a maximum of 18 degrees between the leg carrier and the body, at a maximum load of 2000N, and a resting force on the spring of 1200N.
First, we need to open the assembly in the dynamic simulation environment. We can see from the image below that the assembly constraints have been automatically converted to simulation Joints.
Dynamic simulation likes there to be a limited range of freedom after the constraint has been converted or joints manually added. This is to limit the calculations required for the overall assembly. The assembly has been created in such a way as to aid in correct joint creation. Creating sub-assemblies of components that do not need to move in the simulation, like all the components that make up the leg carrier, means that the software will not add unnecessary joints.
We can check if the assembly joints are over constrained or under constrained by checking the Mechanism Status window. For best results you would constrain the model down to a single degree of mobility, as seen below. If your assembly has been constrained with dynamic simulation in mind, then the automatic conversion should try to limit the assembly to a single DOM.
Adding initial motion to the assembly
We already have some of the inputs we need to create our study so now we can add these figures into the simulation study.
Selecting revolution 4 from the model browser I can see from the glyph that this is the joint that we want to limit the rotation.
I can right click this Joint and select properties. Then select the Edit imposed motion option.
Then I can enable imposed motion, set the driving option to position, and then click the icon for the grapher in the box on the right. This will allow us to define motion over time instead of a fixed input.
In the grapher window we can add the final position at 1 second. Changing the Y2 value to 18 degrees.
Click ok and close the windows. You can click play on the simulation player to check the motion of the assembly but remember to set the player back to construction mode to make further changes.
Applying a force to the motion.
Next, we need to add a force to the motion we have just created in the simulation to represent working conditions.
Add a force from the Dynamic Simulation ribbon and select a point on the arm. For the location I will choose the point shown below.
The direction of the force will be the face shown here.
Make sure the direction of the force is pointing in the correct direction with the flip direction option. I am also going to set the magnitude direction to associative so that the force is always normal to the face, instead of a fixed direction, as well as changing the display scale to 0.001 so the force glyph does not fill the display window.
We now need to change the magnitude to input grapher so that we can associate our force with the imparted motion from the previous step.
In the output grapher window, I select the Reference option on the left and set the reference to position for the Revolution 4 joint. This will change the graph to force over position instead of force over time.
I will set the starting position at 0 degrees and a force of 1200N, which is our resting force, and the end position to 18 degrees and 2000N, which is our maximum position/force.
We can also see from the graph that the force does not represent a spring very well. It has an even force before and after 0 degrees. We can change this by selecting each sector using the sector selection buttons.
And setting the value to constant slope
This will give a better representation of the force acting on the spring.
Once the slope has been edited, I can close the grapher and click ok to accept the inputs for the force. We can also remove the motion we added earlier in the joint properties as the force we have just created will now impart motion. Remove the motion from the joint just deselect the Enable imposed motion check box.
Running the simulation at this point will give incorrect results as we have no opposing force to the force, we have just added so the arm will just spin around the rotation joint.
Creating a spring
The opposing force that we need in this system will be our spring. As we are trying to design a suitable spring for our design, this force will be unknown. We can simulate this using the unknown force option on the Dynamic Simulation ribbon.
As our force is representing a spring, which pushed equally in opposing directions, I will use the Jack option.
The location points for the force will be the top and bottom retainers, as shown below.
I will set the joint to revolution 4 and the final position to 18 degrees. I will also reduce the display glyph scale.
Clicking ok will run the study. When the study has completed, we should see a new column in the output grapher for our unknown force. The force is associated to the motion in Revolution 4.
Now we have our spring force, we need to determine a few more inputs before we can create our spring. We need to know the spring length. To do this we can use the trace function to map the positions of the top and bottom retainers throughout the study.
Selecting trace from the ribbon or grapher window, I select the trajectory option and use the same input locations that we used for the unknown force.
Running the simulation to create the trace values and opening the output grapher we should see the traces have been added to the tree on the left.
To determine the spring length, we can use the equation below.
Distance = √ ( (Xa – Xb)2 + (Ya – Yb)2 +(Za – Zb)2 )
By adding these traces, we will be creating the values for X, Y and Z for each end point (a & b) of our spring. We can also use a tool in Dynamic Simulation to create a graph curve to represent our spring length. We can use the New Curve option in the output grapher.
I can give the new curve a name, Spring Length and add the equation to the lower window.
To add the X, Y and Z values from the traces, expand the trace branches and select the appropriate box for the value you need. For example, the first value P[X] (Trace:2) is added by selecting the P[X] box in the Trace branch.
If the equation is valid there will be a message to confirm this. Click OK to accept the input. The graph will update with our new curve. Right clicking the curve header lets us search for maximum and minimum values.
Max distance = 312.64mm
Min distance = 265.59mm
We can also use the grapher to plot our length against other values. To do this, right click the new curve in the User Variables branch and select set as reference. The values will be added to the top view in the grapher. Selecting the Force option under the Unknown force branch will allow us to plot the force against length.
Force at max length = 2580.49N
Force at min length = 5665.82N
With these values we can calculate the required stiffness of our spring.
Stiffness = (Force Max – Force Min) / Change in length
(5665.82 – 2580.49) / (312.64 – 265.59)
3085.33 / 47.05
Stiffness = 65.57N/mm
Adding a Spring Joint
We should now have all the information we need to create our spring for our assembly. To create the spring representation, we need to add it as a joint. Select the insert joint option from the ribbon and select the Spring/Damper/Jack option from the drop-down menu. The component selections will the top and bottom retainers that we used in the previous section.
Click OK to create the spring. If the inputs were correct, we should get a new option in the model browser for Force Joints.
Double click (or right click and select properties) to edit the spring.
We have already calculated our stiffness. The free length of the spring can be calculated using the below equation.
(Preload / Stiffness) + Max length
The preload in our system will be the force at 0 degrees (or rest) which is our minimum force (2580.49N), and the maximum length (at rest) is 312.64mm.
(2580.49 / 65.57) + 312.64 = 351.99mm
Free length = 352mm
Damping for a spring is approximately 10% of the stiffness value, so I will set this to 6N/mm.
My spring needs to be 40mm diameter. Facets changes the display of the spring and turns is the number of coils in the spring.
Selecting OK will accept the inputs and we should now have a complete design. We can test this by applying different forces using the original force we created earlier.
Edit the force properties and change the force from the grapher to a fixed magnitude of 1200N and run the simulation. There should be no movement in the system.
Change the force magnitude to 2000N and the system should move. Changing the magnitude between 1200 and 2000N should give varying results.
After running the 2000N simulation I can open the output grapher and select the position for the Revolution 4 Joint and the Force from our external force. I can see that the maximum rotation angle at 2000N is 17.29 degrees, which is within our design limits.
Our study is now complete, and we can take the information from our study to create our required spring. Dynamic simulation will not create a spring model however so this will still have to be done manually.
I hope this demonstration helps in your design process. Please do not hesitate to contact Cadline for additional training on Dynamic Simulation.
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