P19432: Murphy's Stage
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# Preliminary Detailed Design

 Table of Contents 1 Team Vision for Preliminary Detailed Design Phase 2 Lift Assist Analysis 3 Platform Analysis and Simulation 4 Drawings, Schematics 5 Bill of Material (BOM) 6 Test Plans 7 Designs (CAD) 8 Risk Assessment 9 Plans for next phase

## Team Vision for Preliminary Detailed Design Phase

Team MUSIC's Preliminary Detailed Design Goals:

• Effectively design ~80% of the stage by the end of this phase (11/15/18)
• Preliminary design and analysis of subsystems
• Focus on the highest priority subsystems
• Lift assist
• Mounting to existing structures
• Platform design

## Lift Assist Analysis

In order to properly design the lift assist system a mathematical model was made using geometric relations and static forces varied over the duration of lifting and lowering of the stage. All analysis and simulations were done on the larger center section of the stage.

Assumptions:

1. Uniform weight distribution across stage surface
2. Neglect frictional effects
3. Modeled stage as 2 dimensional plane
4. Human force always acts perpendicular to surface

Listed below are the variables used to analyze the lift assist.

##### Lift Assist Symbols and Equations

Lift Assist Variables

Lift Assist Equations

#### Lift Assist Simulation 1: Required Lift Assist Force

After obtaining the necessary equations, a mathematical model was created to simulate various reactions of the lift assist system.. The first simulation run was the required lift assist force. Assumptions:

1. Human force always acts at the end of the stage (Extension pole used to reach heights beyond human reach)
2. Human force in accordance with Engineering Specification S6 of 31 lbs
3. Theta is varied between 0 and 90 degrees. (0 degrees is stage down position, 90 degrees is stage stow position)

Assumed Geometry for Simulations:

1. a = 9 in.
2. b = 1 in.
3. c = 4-(a+b)/2 = 3.5833 ft.
4. phi_0 = 0 deg.
5. W_f + W_b = 250 lbs. (Total weight of stage)

Required Lift Assist Force

The results show a maximum required force of 760 lbs and a minimum required force of -978 lbs. Notice the negative values of the force. As shown in the figure, there is a switch from positive to negative values of the required force at ~73 degrees. This means, with the applied human force acting, at 73 degrees between the stage platform and the horizontal the stage will begin to lift itself. In order to prepare for this switch in force, a pole with a with some sort of hook on the end will be used to allow the user to counter-act the change in force direction so the stage lift will not become uncontrollable.

#### Lift Assist Simulation 2: Required Human Force

Using the graph from simulation 1, gas spring sizes and quantities were researched to properly account for the necessary lift assist force. Another simulation was run to calculate the required applied human force given the properties of chosen gas spring as lift assist.

Assumptions:

1. Gas springs have different, but constant extension and compression forces
2. Same geometry as Simulation 1
3. Extension pole used for both lifting and lowering stage

Gas Spring Properties (McMaster Part #4138T635)

1. Extension force = 250 lbs.
2. Compression force = 340 lbs.
3. Compressed Length = 19.29 in.
4. Stroke Length = 16.14 in.
5. Number of gas springs = 3

Required Human Force

Because gas springs exhibit different forces during compression and extension, the required human forces will differ whether the stage is being raised or lowered. For this reason the simulation was run using the extension force to raise the stage, and the compressive force to lower the stage. Given our design this is how the lift assist will be reacting in real life.

Important Values from Simulation 2

1. Max Lift force during raising : 31.98 lbs
2. Min Lift force during raising : -23.80 lbs
3. Max Lift force during lowering : 3.72 lbs
4. Min Lift force during lowering : -32.36 lbs

It is important to note that any negative lifting forces would be considered a "pulling" force from the perspective of the user. It is also important to note that the magnitude of the maximum lifting forces exceeds the 31 lbs of engineering requirement S6. It may be necessary to revisit this requirement to allow more flexibility for the maximum lifting force. It may also be necessary to add a requirement that designates a maximum allowable pulling force, as this was previously not considered.

## Platform Analysis and Simulation

Structural analysis of the stage construction is important to verify that the stage will not fail under typical loading conditions. Failure can be described as either the stage deflecting too much under load or any material experiencing too much stress as to yield of break. For this analysis the critical loading condition which will be analyzed is the engineering requirement which states the stage much be able to support 150 pounds per square foot.

Hand Calculations: It is important to determine critical failure metrics using hand calcs. This serves as a check to make sure the computer simulation is correct and provides the ability to select material to perform more complex simulations with.

A simple hand calculation can be used to find the resulting shear stress in the pin on a hinge by dividing the resulting force by the cross sectional area. The loading diagram and stress equation can be seen in the schematic section. This equation allows us to pick the correct hinge, assuming the failure mode would be the pin.

This analysis is an very conservative, simulating an unrealistic worst case scenario of a 250 pound force is exerted at the center of one of the cross beams. As if a 250lb person was standing at the center of the beam and the beam was not supported by any other members except for the edges.

This analysis will be performed for a standard 2x4 as well as for 2x1 rectangular hollow aluminum tubing.

The figure below shows the calculations used to determine the deflection and stress in the beam.

Hand calc equations

Where: Force, P = 125lb Length, l = 54in These values are half the total since the deflection is being analyzed at the center of the beam, fixed at either end. A schematic of this simplification can be seen in the schematic section on this EDGE page.

The following figures show the calculated results for deflection and stress of the materials of interest.

Wood 2x4 Hand Calc Analysis

Hollow Aluminum Tube Hand Calc Analysis

Results: Wood 2x4: max deflection = 0.47 inches Aluminum tubing: max deflection = 1.76 inches

After some discussion, the decision was made to move forward with the aluminum tubing. The primary reason for this decision was to reduce stage weight. A lighter stage would simplify other areas of the Murphy Stage design and is also a conscious effort to improve safety. Using the aluminum also reduces the thickness dimension of the stage, producing more space for the lift assist system.

While it is important to remember this analysis is very conservative, however, in an effort to mitigate the stage deflection more aluminum members will be used, spaced every 12 inches.

Finite Element Simulation

After basic hand calculations were conducted, the stage construction was analyzed using ANSYS Workbench, a finite element software that can simulate complex geometries under loads to find values like resulting stress and deflection.

The image below shows the deformation plot of just the aluminum frame subjected to the static loading scenario.

Hollow Aluminum Tube Hand Calc Analysis

This simulation contains the aluminum stage frame as well as a plate mimicking the top stage surface.

The boundary conditions given to this simulation mimic the hinge and leg placement. At each of these locations, vertical displacement was fixed to zero to provide the support. A load of 150 lb/ft^2 was applied to the top stage surface, this pressure provided 13,500 pounds of vertical force spread over the entire stage surface.

Finite Element Deformation Plot

## Drawings, Schematics

Lift Assist Schematic (Stage Down)

Lift Assist Schematic (Mid Transition)

Gas Spring Length Schematic (Stage Down)

Gas Spring Length Schematic (Mid Transition)

Beam Bending Schematic

## Bill of Material (BOM)

The preliminary Bill of Materials and Cost Estimate for the stage can be found here.

Show below is the BOM for the center section of the stage as of 11/13/18:

Preliminary Bill of Materials for the Center Stage Section

## Test Plans

The tests planned span both semesters. One set is preliminary testing, to verify results from our engineering analysis. The second set is product testing, verifying that our product meets our engineering requirements.

The test plans can be found here.

#### Preliminary Testing

The preliminary testing involves verifying our analysis of the gas springs being used in the lift assist and the hinges being used to rotate the stage.

The gas springs are listed with constant values for specs, when in reality they vary in value with distance. The current assumption is that they do not vary significantly enough to impact setup and takedown forces. The test is intended to verify this by measuring the force it takes to move the spring at various positions.

The hinge testing is a tensile test intended to verify that the hinges should fail in tension along the flanges near the pin, not in shear through the pin, or in any other unexpected way, as well as to verify that the failure point is well outside intended loads.

#### Product Testing

The testing for MSD II is largely about verifying engineering requirements, but also for testing to make sure that in some use cases outside the bounds of our project, the stage does not fail.

One such expected case is if the operator applies too large a force too quickly when setting up and taking down the stage.

The analysis conducted on the platform configuration and lift assist were used to construct a CAD model.

The Murphy Stage in the Stowed Position, Viewed as if behind the stage

The Murphy Stage in the Deployed Position, Viewed as if in front of the stage

## Risk Assessment

Updated Risk Assessment located here.

Risk Analysis updated as of 11/14/2018

## Plans for next phase

Design Review Presentation can be found here.

Preliminary Gantt Chart for Next Phase

Links to individual 3 week plan: