Me 356 Car Frame Design Write Up

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Group 14, Team GMBalsa Wood Car Frame Design

ME 356/ Professor Chung



1.0 Introduction & Engineering Description of “Crash & Eject”

In order to gain experience with the engineering design process, our team designed a balsa wood

car frame for “clients” and our sponsor, Professor Jae-Hyun Chung. Several criteria were

outlined in the context of developing a car frame. Constraints on dimensions, materials, and the

boundary conditions for a collision were given. The objective was to communicate with theclient and develop a car frame that satisfies all of his needs.

Balsa wood was given as the material for the car frame. The sponsor chose this material because

although balsa wood is soft and light weight, it is strong. Twenty sticks measuring 0.25” X

0.25” X 3’ were given, and additional materials were not allowed to be used. Although all of thesticks could be used in the design, the client expressed the desire to have a high specific strength,

or strength to weight ratio. Gorilla glue was provided to join frame members together. Wood

glue was also allowed for use in combining members but according to prior tests ran by theclient, connections made using the gorilla glue created a better bond between pieces of balsa

wood. No other materials were allowed during construction.

Several constraints were given for the dimensions of the structure. The car frame must consist of

three sections: a passenger space (100x200x300 mm), trunk space (70x150x150 mm), and an

engine room (70x70x150 mm) in which an aluminum engine block must fit. Also, the passenger

space had to be identified by 12 pieces of balsa wood, and span the entire width of the structure.Figure 1 illustrates the required dimensions.

Figure 1: Required Dimensions of Car Frame as Specified by Sponsor



Constraints were also placed on the gluing of members, and the total allowable overlap area

between two members. For any connection of members, the total allowable cross-sectional areawas defined as ¼ x ½ inch.

Most importantly, several loading criteria had to be fulfilled during a “collision”. The car frame

was tested using an Instron machine in conjunction with a compression plate. In order to passthe collision test, the frame must support a preload of 100 N without significant deformation

(<5mm). After the initial preloading, the structure must withstand at least 600 N before failure.

Failure was defined as fracture occurring in any of the members that comprise the passengerarea. In addition to the load requirement, the compression plate must move 130mm downward

without fracturing any part of the passenger space.

Once our team considered all of the design specifications and constraints, we formulated the

“crash and eject” failure sequence. The “crash and eject” failure sequence occurs in three stepsto prevent passenger-space damage. The first part relies on failure due to buckling. By

intentionally elongating one of the members in the trunk area, failure is expected to occur in this

area at a load in excess of 600N. Axisymmetric failure will cause the load plate to tilt, whichwould introduce a horizontal force component against the car frame. The overall strategy behind

the “crash and eject” failure sequence is to use this horizontal force to move the car frame out of the danger zone.

Because the engine block “holds down” the car frame, deep-notch stress concentrators are added

on both sides of the engine support members. Step two of the “crash and eject” sequence is thepredicted failure at the deep-notch concentration sites around the engine. These notches are so

severe that a small bending force on the car will cause fracture, leaving the engine grounded and

the car frame free to tilt. Step three of the “crash and eject” failure mechanism is the ejection of

the car frame out from under the load plate. Overall, our team’s goal is to implement the “crash

and eject” failure sequence to protect the passenger space and, consequently, satisfy the clientsand sponsor. Figures 2 & 3 illustrate the failure sequence.

Figure 2: Step One, Buckling at Intentionally Elongated

Column

Figure 3: Step Two, Fracture at Supports Around Engine. Once

Fractured, Frame is Free to Leave Platform



2.0 Analysis & Results

Our “crash and eject” failure sequence is wholly dependent on (1) buckling at an intentionallyelongated member and (2) fracture due to deep notches surrounding the engine compartment. To

support these failure mechanisms, our team has turned to engineering analysis that can be found

in the appendices of this report.

2.1 Loads Experienced During the Failure Sequence

1. Intentionally elongated member: Our design features an intentionally elongated member

whose length has been calculated in Appendix A. Our team utilized Euler’s slender beam

formula to determine that the optimal length of a column that buckles at 1000N is 155mm.As a result of uncertainty in the load factor, C, as well as manufacturing tolerances, our team

believes that the intentionally elongated beam will fail within the range of 600-1000N.

SolidWorks analysis suggests that at 600N the elongated beam is not predicted to fail.

2. Tilt of Load Plate & Estimated Force Component: The intentional failure of the elongated

beam is intended to cause the load plate to tilt at an appreciable angle. Our teamapproximates an oblique face to be created; contact with the face will split the applied load

into a vertical and a horizontal component (see Figure 4). It is our hope that the horizontal

force component is sufficient to break the car frame away from the motor and out of thetesting platform. To better predict if this is possible, it is important to estimate the horizontal

force that might be generated. To do this, a number of assumptions must be made.

Elongated beam fully collapses 150mm.

Oblique plane creates 45-degree angle as shown. No other members fail due to the force on the oblique plane

Analyze situation when 600N is applied normal to the oblique surface.

Figure 4: Schematic of Oblique Face Created when Column Buckles



Trigonometry dictates that the magnitude of the horizontal force is:

(2.1.1)

The horizontal force acts into the corner of the car frame. Only a portion of the force bends the

engine mounts by pure bending. Let’s assume that the horizontal force intersects the corner at 45degrees. Then,

(2.1.2)

As an aside, a force balance along the oblique plane will determine if the car frame will be able

to overcome static friction and slide along the tilt plate while being tilted out of the way.

(2.1.3)

(2.1.4)

where the coefficient of friction was determined between wood and steel1. It is apparent that

static friction will not keep the frame in the path of the load plate. Instead, the frame is free to

move out of the way in this analysis.

3. Bending About the Engine & Notch-Induced Fracture: The horizontal, pure-bending force

component is intended to pitch the car frame about the engine as it sits on two balsa wood

members. The stress concentration for a deep notch in the engine mounts is determined inAppendix B. A moment will occur as a result of the horizontal force component calculated inthe previous step:

(2.1.5)

where the force is expected to act a maximum of 450mm from the engine mounts. Let’s supposethat the moment is concentrated at the deep-notch stress concentrator shown in Appendix B. The

maximum stress at this location can then be roughly approximated as:

( )

(2.1.6)

(2.1.7)



A value of 13 GPa exceeds the maximum bending strength of 39 MPa obtained from MATWEB(Figure 5). Although this analysis involved several greatly simplified assumptions, our team

believes that it validates the concept that a sufficiently deep notch stress-concentrator can induce

failure at the engine. We are confident that a deep-stress concentration factor can generate a

stress that exceeds the bending strength of the material by at least ten times. Once the enginemounts fracture, the car frame is likely to pivot over the engine and fall out of the loading

apparatus.

Figure 5: Material Properties of Balsa Wood Used in Analysis

2.2 Critical Load Locations

In order for our team’s design to work, all of the structural members must withstand a load of at

least 600N before the buckling member fails. As a result, our team conducted severalSolidWorks analyses to determine the critical stress locations at 600N applied force. The

following figures illustrate the important findings.

As intended by design, the location of the critical points experiencing maximum stress are along

two main beams located on the bottom of car frame — one of these beams has been intentionally

elongated. After modeling and designing the car frame in SolidWorks, it was possible to simulatethe response of the car frame under a specified load condition of 600N. The von Mises stress

distribution was modeled by fixing the bottom of the car frame and applying the load to the top

of the frame. The result is shown in Figure 6.



Figure 6: von Mises Stress Distribution in Tested Car Frame. Notice a Maximum Stress at approximately 8.5 MPa along

the Bottom Rails of the Frame.

According to the color definition on the right side of Figure 6, it is clear that the greatest stressoccurs along the two main beams. The overall maximum stress location is highlighted in Figure

6 and it is located on the top-side of the beam. For a more exact location of the maximum stress

location, ISO metering has been used to remove the color of the lower stresses. Figure 7 shows

the result of ISO metering.

From the results generated by SolidWorks shown in Figure 7, these three points are the only

locations where stress reaches more than 7 MPa. Maximum stress is also shown to be about 8.5

MPa. According to equation 2.2.1, where and represents yielding stress, and

is maximum stress, the minimum factor of safety (FOS) for this load is . This FOS is alsoconsistent with the minimum FOS generated by simulation in SolidWorks.



⁄ (2.2.1)

Although maximum stress location is not exactly located on the beam that is designed to buckle

first, it is not a major concern. The SolidWorks simulation excludes the possibility of bucklingwhile calculating stress distribution, therefore buckling is not considered. A separate simulation

was performed for buckling analysis (See Figure 8). This figure shows that even though

maximum stress is not located on the buckling beam, buckling occurs at the designed location.

This happens because all other members are significantly shorter than the beam that is intendedto buckle.

Another important highly-stressed location on our car frame are located on the engine block

supporting members. Figure 3 shows the two members notched in four locations. As mentionedin the failure analysis section, these notches must act as stress concentrators. Although it is

difficult to calculate an exact stress concentrating factor for a hand-crafted notch, it was

possible to find a value based on some assumptions. was found to be to approximately

4.1 — all the calculations for value are shown in Appendix B.

Figure 7: ISO Metering Used to Identify Location of Greatest Stress



Figure 8: Buckling Analysis w/ ISO Metering to Show Maximum Buckling

4.0 Engineering Description of Failure Experienced in Testing

Although the SolidWorks simulation predicted failure in the elongated member, this did nothappen when the actual test was run. Instead, failure occurred behind the passenger

compartment on top of the trunk space. This failure was not due to buckling as expected but

appeared to be due to shear failure occurring in the glue joints. Shear failure could haveoccurred as a result of modeling and manufacturing errors.

When modeling the car frame in SolidWorks, our team may have not considered the various“end joint” geometries carefully enough. The car frame was modeled as a single part inSolidWorks as opposed to several individual components. As a result, our SolidWorks

simulations could not consider the unique stress situations that occur at the connections between

members. Several two-dimensional, 1:1 side views of the car frame were used as the basis for

construction. The side views did not specify member connections as a result of our model beingone-part rather than individual members. Without specifying member connections, each

individual team member was free to connect members as they felt necessary.



In addition to this, our team did not have a reliable way to clamp members during construction.The result of these imperfections were that air gaps existed in many of the glue joints between

members. This reduced area causes a greater stress concentration than expected. This certain

area of the trunk space that failed included a butt end joint, which was not originally considered.

It is very possible that this made shear a much bigger factor, compared to an angled joint. Afterthis key member failed, the remaining members could not hold the load and the structure

collapsed.

5.0 Improvements Made to the Car Frame

Errors made during the construction of the car frame were the principal reasons for premature

failure. Specifically the region of failure was a set of five beams that met at odd angles. Due to

imperfections in this region there was a gap filled with glue between the beams that went over

the passenger compartment and the main frame. Figure 9 shows the frame modeled with this

imperfection undergoing the stresses of the test.

Figure 9: Stress Analysis of Frame w/ Manufacturing Errors Modeled In



Figure 10: Factor of Safety Plot of Frame w/ Manufacturing Errors. Minimum FOS of 0.54, which corresponds closely

with a failure load of approximately 300N.

It is clear from these figures that the manufacturing errors predicated the type of failure thatoccurred during the compression test, as this model fails at the same places as occurred in the

test.

This problem has been addressed in our updated frame, in which the stresses caused by the

manufacturing errors are not as severe. In the updated frame manufacturing has been simplified

by removing complicated connecting angles and replacing them with butted-end joints. The

modifications require the members around the passenger space to be re-positioned therebyavoiding angled connections where glue gaps may occur. This change also makes it possible to

clamp the connections during construction because butted-end joints are far easier to fixture thanodd angles. A downside of this modification is a slight addition of weight. The frame gains

approximately 5.85 grams. This modification is worth the added weight as the frame will beeasier to manufacture and thus safer.

Another major improvement to the frame was the lengthening of the buckling beam. The framesupported 281 N during the compression test and by reviewing the video the buckling beam does

not deflect significantly. It is therefore safe to lengthen the beam closer to the limit of length thatshould buckle under the 600N load (Appendix A). This change will decrease the load that therest of the frame must support, and make it more likely to succeed in supporting the 600N load

despite any further manufacturing difficulties. We increased the length of the buckling beam

from 132mm to 149, or from 87.4 % of the predicted bucking length to 98.6%.

A third improvement was the removal of several beams that were unstressed. These beams were

inserted for cross bracing to combat bucking. Under further analysis a single corner beam

performed just as well as any of the double cross-braced sections of the model. Through the

removal of these excess beams the volume of the balsa in the model was reduced by 8.90 %,which translates to an equal reduction in weight. This reduction in weight was achieved despite

the addition of members described in the first section of improvements.



Figure 11: Factor of Safety Plot for Updated Frame. Minimum FOS of 3.49

Through these improvements the factor of safety of the frame was increased 69.6%,

manufacturing errors have been avoided, and weight was reduced by 8.90%. The improvements

in factor of safety can clearly be seen in Figures 11 and 12, which show the factor of safety andstress analysis of the updated frame.

Figure 12: von Mises Stress Distribution Plot for Updated Frame.



5.0 ConclusionsAfter our team received request to design a car frame from Balsa wood along with all the

geometrical constrains and specifications, an concentrated design process has been started. Firstpart of the process was to learn all the rules and obligations placed by the customer, as well as to

understand the customer’s specific desires about the project outcome. After multiple meetings

and effective communications with the customer our team went into the second process of thedesign. Generating multiple conceptual frames and evaluating each of them in order to choose

the best and final frame. Chosen conceptual frame was called “crash and eject” frame. Chosen

frame was then modeled in SolidWorks and analyzed for performance simulating the load

condition by SolidWorks. After multiple iterations of improvements final design was presentedto the sponsor for approval. After approval was received team has moved into the manufacturing

phase of frame development followed by physical testing. Although presented design showed

reasonable factor of safety guaranteeing the safety of frame, actual frame has not followed the

predictions and failed at the unexpected location. This encouraged one more iteration forimproving chosen design; now considering the manufacturing aspect of the design as well

increasing stress factor of safety.

Design was called “crash and eject” because failure was designed to happen in three steps whereframe would be “ejected” after the “crash”. Crash is represented by the first step of the failure.Applied load would buckle the intended member until the fracture of it. Second step is the

detachment of the engine. Tilted plate will generate bending force to the frame, which will cause

the severely notched members to fracture and disconnect the car from the heave engine block.And the third step is removal of the frame from under the continuously lowering force plate. Tilt

of the top load plate would push the frame to the side while it is being lowered, which will cause

the frame to slide or tilt to the side from under the loading plate.This design is simple and failure methods are predictable, therefore with the consideration of

manufacturing and other suggested improvements mention in report, frame will be safe. It will

pass the inspections and the testing successfully, this will satisfying the customer and the

sponsor, as was planned since beginning.



Appendix A: Calculating the Length of a Slender Beam to Fail @ 1000N

The success of our car frame design is dependent on the controlled buckling of a single balsasection. The goal is to buckle the column when a load of 1000N is applied to the car frame

without sustaining damage in any other member. The material properties used were:

Four columns will share an applied load of 1000N. First, let’s assume that the slenderness ratioof the column justifies the use of Euler’s equation— this assumption will be verified later. Also,

let’s assume that the glued joints of the column have fixed-fixed boundary conditions. This

assumption is reasonable because the glued joints prevent rotation. The equation used is,

The recommended value of C for fixed-fixed boundary conditions is given in Table 4-2 as equal

to 1.2.

The slenderness ratio that defines the boundary for the application of Euler’s equation is givenas:

The slenderness ratio for our calculated length is evaluated as:



Since our calculated slenderness ratio is larger than (l/k)1 we conclude that Euler’s equation isvalid as assumed in the beginning of the analysis. The calculated length of 151mm was

considered when designing our prototype.

Appendix B: Deep-Notch Stress Concentration Factor for Motor Beams

The motor rests on two balsa wood columns and the safety of our passenger compartment relies

on the car frame breaking from these columns. To ensure that the car frame breaks away fromthe motor, notches 0.125 in. thick or greater will be put into the balsa wood columns on theimmediate outside edges of the motor.

From Peterson’s Stress Concentration Factors, 3rd

edition, the stress concentration of a deep

groove in a tensioned member is given by the following figure and equation:

where “d” is the distance between the notch and the far edge of the column and “r” is the radiusof the notch. We will be cutting a V-shaped notch so we can assume that “r” is very small. Areasonable approximation is that “r” is at least ten times smaller than “d”.



Plugging these values into the above expression gives a stress concentration factor of at least

4.075. This should be a sufficient minimum to overcome any uncertainties in manufacturing orassembly.

References

[1] Carbide Depot. “Coefficient for Static Friction of Steel.”http://www.carbidedepot.com/formulas-frictioncoefficient.htm.

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Me 356 Car Frame Design Write Up