Statics Final Project

Contents

1 Problem Motivation 2

2 Problem specifications and Constraints 3

3 Analysis 4

3.1 Bucket Centroid 5

3.2 Beam and Arm Weight 6

3.3 Excavator Above Ground Level 7

3.31 Shear Force and Moment Diagrams 8

3.32 Pressure in Hydraulics 9

3.4 Excavator At Ground Level 10

3.41 Pressure in Hydraulics 13

3.5 Excavator Below Ground Level 14

3.51 Pressure in Hydraulics 17

4 Discussion 18

5 Conclusion 19

6 Works Cited 20

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1 Problem Motivation

During a makeup class session professor Sezen decided it would be beneficial for our studies to examine the two force members on a Bobcat skid steer. Upon examining the ISELF construction, it was obvious that heavy machinery was crucial to construction cost and efficiency. Heavy machinery such as skid steers, excavators and front end loaders are often present at sites of this magnitude. This sparked an interest to further study the structural mechanics behind the design of heavy machinery. After researching a variety of construction equipment throughout different companies, a conclusion was made that a mini excavator provided a minimal number of statically indeterminate situations. Thus, only a few assumptions and modifications to the current design were needed allowing more accurate calculations. Taking all this into consideration, a decision was made that a study of the internal and external forces applied on the two main members and the hydraulics actuators on a Bobcat M324 excavator (Fig. 1) would satisfy these desires.

Figure 1: Bobcat M324 Excavator

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2 Problem Specification and Constraints

After analyzing a few diagrams of the M324 it was clear that some initial simplifications and assumptions (referenced in Fig. 2 below) were going to be necessary to complete this problem. A decision was that joint J would be disregarded and it be assumed as an extension of the bucket. Member IH was also disregarded throughout the studies to simplify the main concern of the internal and external forces on the boom, arm and hydraulics. The weights of the three hydraulics and hardware were presumed negligible. Further assumptions of dimensions and angles were made accordingly, based on the specific position being analyzed. These values were estimated through scaling the few dimensions provided by Bobcat and some basic trigonometry (*Note – red underlined dimensions denote estimations). Unknowns for completing the force equilibrium problem include the following;

- Weight of the boom and arm- Reaction forces in the X and Y direction at pin joints A, F & K- Two force members (Hydraulics) FBC, FDE and FGH

- Calculations for the bucket centroid (not used in force equilibrium calculations)

Figure 3: Bobcat M324 excavator with denoted joints and members at ground level.

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Beam

Arm

Figure 2: Bobcat M324 dimensions that were referenced to determine necessary unknowns.

The study of the Bobcat M324 was completed with a specified load of sand at the following three positions; the bucket at ground level (Fig. 3), the bucket above ground level (Fig. 4) and the bucket below ground level (Fig. 5).

The free body diagram for the excavator at each position is delivered more effectively when each member is separately analyzed. These FBDs can be seen at the beginning of each analysis.

3 Analysis

The load that is being applied to the excavator (In all three positions) is 1 cubic foot of sand, weighing 100 lbs. To understand the reactive and reactant forces in the excavator in each position referenced it is best to study the system one component at a time. In each scenario it has been broken down into three separate FBDs. starting with where the load is applied, working towards the operator. The study includes calculations of internal and external forces along with determining the pressure each hydraulic needs to exert on the system to keep it at equilibrium. Calculations along with results for this system can be seen throughout the remaining sections of the analysis.

3.1 Bucket Centroid

Finding the Center of mass of the bucket was very important. Calculating the center of mass for the bucket is essential, determining how the weight is positioned affects whether the buckets hydraulic will apply or resist a force to keep the system at equilibrium. Although the exact coordinates were not used, a close estimate was obtained allowing for a more accurate solution when determining the

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Figure 4: Excavator with bucket below ground level.

Figure 5: Excavator with the bucket above ground level.

20" Trenching Bucket Operating Weight 92 lbs Length 15.5 in Width 20.25 in Height 13.4 in ISO Heaped Capacity 1.4 cubic ft ISO Struck Capacity 1 cubic ft Predrilled For Bolt-on Edges or Teeth

Bucket Specifications

Table 1: Dimensions for the excavator’s Bucket attachment.

forces.

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Figure Area Ẋ Ȳ1 25.765 11.45 4.052 49.395 9.6 6.6753 25.96 3.875 1.6754 32.25 5.6 6.68

Table 2: Results for the bucket's Centroid.

3.2 Beam and Arm Weight

In order to begin the study, an unknown weight of the excavator’s two main components (Beam & arm) needed to be determined. In order to calculate these weights as accurately as possible unknown dimensions were determined using existing dimensions provided. With these dimensions an area, followed by a volume for the beam and arm was acquired. With a known density of steel (0.28 lbs/in3), the ability to determine the weight of the beam and arm is possible.

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3.3 Bucket above Ground Level

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Figure 5: Excavator with the bucket above ground level.

3.31 Shear Force and Moment (*The horizontal force FDE applied to the arm is neglected due to insufficient knowledge)

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3.32 Pressure In Hydraulics

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3.4 Bucket at Ground Level

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Figure 3: Bobcat M324 excavator with denoted joints at ground level.

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3.41 Pressure In Hydraulics

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3.5 Excavator below Ground Level

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Figure 6: Excavator with bucket below ground level.

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3.51 Pressure In Hydraulics

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4 Discuss ion

Table 4 displays all calculated unknowns of the excavator at each position. Active forces (Weights and loads) are the forces creating the internal and reactive forces. The Reactive forces are the forces applied at each pin joint due to the active forces on the system. The internal forces (Hydraulics) are acting against the active forces, keeping the system at equilibrium. After analyzing the results of each hydraulic at all three positions the measured pressures make sense. The Hydraulic actuator in the bucket only needs to apply minimal force in each situation. Piston 1 only stabilized the bucket preventing it rotating about point K resulting in losing the load of sand. Piston 2 will need to apply a much greater force than Piston 1 due to the fact that it has to hold the bucket load and the arm at equilibrium. The arm is reaching out horizontally for the bucket above ground, explaining why piston 2 in the scenario is so much higher than the rest. Piston 3 requires the highest PSI in all three situations due to the nature of the excavators design. Piston 3 is required to hold the buckets load, the weight of the arm and the weight of the beam. The PSI in Piston 2 for the bucket below ground level is higher than anticipated. These values make sense, it was expected that the PSI in Piston 1 would be less than piston 2, and less than piston 3. Also, The fact that the pressures in each hydraulic for the bucket above ground are the highest. With the beam, arm and load extended out as far as possible, this will create a large moment near the joints connected to the cab.

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(PSI) Above Ground Ground Level Below GroundPiston 1 13.58 13.58 62.32Piston 2 524 25.76 748.11Piston 3 670.69 149.57 220.41

Pressure In Hydraulics

Table 3: Calculated PSI in each hydraulic at each position.

KX = 0 lbs KX = 0 lbs KX = 96.0 lbs

KY = 153.6 lbs KY = 288.0 lbs KY = 192.0 lbs

FX = 9080.7 lbs FX = 323.3 lbs FX = 5702.5 lbs

FY = 3590.2 lbs FY = 756.1 lbs FY = 4449.4 lbs

AX = 4180.2 lbs AX = 1769.7 lbs AX = 6172.3 lbs

AY = 2940.1 lbs AY = 181.5 lbs AY = 13452.8 lbs

FGH = 440.60 lbs FDE = 323.70 lbs FGH = 96.0 lbs

FDE = 9401.02 lbs FCB =2936.76 lbs FDE = 6584.72 lbs

FCB = 4327.68 lbs FCB = 13168.9 lbs

WBEAM = 663.0 lbs

WARM = 965.0 lbs

WBucket = 92.00 lbs

WSand = 100.00 lbs

Below Ground Level Ground Level Above Ground level

Internal Forces

Active Forces

Reactive Forces

Table 4: Calculated Internal and external and external forces of the systems.

5 Conclusion

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Works Cited

Meriam, J.L., and L.G. Kraige. Engineering Mechanics Statics. 7th. 1. Hoboken, New Jersey:

John Wiley & Sons, Inc, 2011. 109-333. Print.

Meriam, J.L., and L.G. Kraige. Engineering Mechanics Statics. 6th. 1. Hoboken, New Jersey:

John Wiley & Sons, Inc, 2010. 106-330. Print.

Weeder, Morris Rod. "324 Compact Excavator." Bobcat. Bobcat Company, 02/09/2007. Web. 27

Apr 2012.

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