lifter kinematics for loading, Assignments of Mechanical Engineering

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Contents

Figure 3-49 r

• 1.0 ABSTRACT
• 2.0 KINEMATIC ANALYSIS AND CALCULATIONS
  • 2.1 Container loading and unloading paths
  • 2.2 Calculations
    • 2.2.1 Cylinder Force Calculation
    • 2.2.2 Reaction Forces at Joints Calculation
    • 2.2.3 Stabilizer Calculation
    • 2.2.4 Bending moment calculation
    • 2.2.5 Pin Calculation
• 3.0 CALCULATION RESULTS AND DISCUSSION
  • 3.1 Static Force Analysis
    • 3.1.1 Path
    • 3.1.2 Path
    • 3.1.3 Path
    • 3.1.4 Path 4, 5 and
  • 3.2 Bending Moment Calculation Results
    • 3.2.1 Boom Bending Moment
    • 3.2.1 V Rod Bending Moment
  • 3.3 Pin Calculation Results
  • 3.4 Stabilizer Calculation Results
  • 3.5 Material Selection and Factor of Safety
• 4.0 FEA ANALYSIS AND TOPOLOGY OPTIMIZATION
  • 4.1 FEA analysis of V Rod
  • 4.2 FEA analysis of Boom
  • 4.3 FEA analysis of Stabilizer Arm
  • 4.4 FEA analysis of Base
• 5.0 Summery
  • 5.1 Key Design Decisions and assumptions made through Solution Synthesis
  • 5.2 Final Model
    • 5.2.1 Components
    • 5.2.2 Assembly
    • 5.2.3 Working Dimensions
• 6.0 APPENDIXES
  • Appendix A
  • Appendix B
  • Appendix C
  • Appendix D
  • Appendix E
  • Appendix F
  • Appendix G
  • Appendix H
  • Appendix I
  • Appendix J
• Figure 2-1 Solid Kinematic model Table of Figures
• Figure 2-2 Container is 300mm away and 1.4m below from the trailer deck - path 1........................................
• Figure 2-3 Container is 300mm away and 1.4m above the trailer deck - path
• Figure 2-4 Container is 500mm away and 1.4m below from the trailer deck - path 2........................................
• Figure 2-5 Container is 500mm away and 1.4m above the trailer deck - path
• Figure 2-6 Container is 1m away and 1.4m below from the trailer deck - path
• Figure 2-7 Container is 1m away and 1.4m above the trailer deck - path 6........................................................
• Figure 2-8 free body diagram of abc and cd rods
• Figure 2-9 free body diagram of abc rod
• Figure 2-10 free body diagram of abc and cd rods
• Figure 2-11 free body diagram of cd rod
• Figure 2-12 free body diagram of whole system
• Figure 2-13 forces at a
• Figure 2-14 cd forces (up), cd rod tangential forces (down)
• Figure 2-15 abc forces (up), abx rod tangential force (down)
• Figure 2-16 pin locations....................................................................................................................................
• Figure 2-17 double shear pin force
• Figure 2-18 shear force in the pin
• Figure 2-19 force on one side arm plate
• Figure 2-20 force at middle a rm
• Figure 2-21 force at pin from the middle arm
• Figure 2-22 tearing from the edge
• Figure 3-1 path
• Figure 3-2 position 1.3
• Figure 3-3 position 1.2
• Figure 3-4 position 1.1
• Figure 3-5 position 1.6
• Figure 3-6 position 1.5
• Figure 3-7 position 1.4
• Figure 3-8 position 1.9
• Figure 3-9 position 1.8
• Figure 3-10 position 1.7
• Figure 3-11 position 1.10
• Figure 3-12 path
• Figure 3-13 position 2.3
• Figure 3-14 position 2.2
• Figure 3-15 position 2.1
• Figure 3-16 position 2.6
• Figure 3-17 position 2.5
• Figure 3-18 position 2.4
• Figure 3-19 position 2.8
• Figure 3-20 position 2.9
• Figure 3-21 position 2.7
• Figure 3-22 position 2.10
• Figure 3-23 path
• Figure 3-24 position 3.1
• Figure 3-25 position 3.3
• Figure 3-26 position 3.2
• Figure 3-27 position 3.6
• Figure 3-28 position 3.5
• Figure 3-29 position 3.4
• Figure 3-30 position 3.9
• Figure 3-31 position 3.8
• Figure 3-32 position 3.7
• Figure 3-33 position 3.10
• Figure 3-34 r1 vs position at path 1,2,3
• Figure 3-35 r2 vs position at path 1,2,3
• Figure 3-36 r3 vs position at path 1,2,3
• Figure 3-37 position 4.1
• Figure 3-38 Position 4.3
• Figure 3-39 Position 4.2
• Figure 3-40 Position 4.4
• Figure 3-41 Position 4.6
• Figure 3-42 Position 4.5
• Figure 3-43 Position 4.7
• Figure 3-44 Position 4.8
• Figure 3-45 r1 vs position at path 4,5,6
• Figure 3-46 r2 vs position path 4,5,6
• Figure 3-47 r3 vs position at path 4,5,6
• figure 3-48 r1 vs position (path 1,2,3,4,5,6 superimposed)
  • vs position (path 1,2,3,4,5,6 superimposed)...............................................................................
• Figure 3-50 maximum bending moment vs position at upper deck paths
• Figure 3-51 maximum bending moment vs position at lower deck paths
• Figure 3-52 maximum bending moment vs position at lower deck paths
• Figure 3-53 maximum bending moment vs position at upper deck paths
• Figure 5-1 arm 1 (v rod)
• Figure 5-2 arm 2 (boom)
• Figure 5-3 stabilizer arm
• Figure 5-4 base mount
• Figure 5-5 assembly
• Figure 5-6 assembled to trailer
• Figure 5-7 at stowed position
• Figure 5-8 stabilizer arm expanded
• Figure 5-9 500mm at lower deck
• Table 1 inputs for path List of Tables
• Table 2 resultant forces for path
• Table 3 inputs for path
• Table 4 resultant forces for path
• Table 5 inputs for path
• Table 6 resultant forces for path
• Table 7 inputs for path
• Table 8 resultant forces for path
• Table 9 maximum cylinder forces
• Table 10 2-way welded hydraulic cylinder data
• Table 11 maximum bending moment at lower deck paths for boom
• Table 12 maximum bending moment at upper deck paths for boom
• Table 13 minimum section modulus for boom
• Table 14 maximum bending moment at lower deck paths forv rod
• Table 15 maximum bending moments for upper deck path for v rod
• Table 16 minimum section modules for v rod
• Table 17 inputs for pin calculations
• Table 18 initial pin dimensions
• Table 19 failure modes for pin
• Table 20 stabilizer area of contact
• Table 21 fea iterations for v rod
• Table 22 fea iterations for boom
• Table 23 fea iterations for stabilizer arm
• Table 24 fea iterations for base

1.0 ABSTRACT

Initial design procedure was carried using hand calculation and kinematic solid model. Results were validated,

and design was optimized using SolidWorks and Ansys Simulations. After studying and observing the various

side loaders and their mechanisms a kinematic diagram was drawn to minimize the overall system weight and

minimize the hydraulic cylinder forces. Kinematic model was dimensioned considering the height, width,

horizontal distance of the container and strokes length of the hydraulic cylinders. According to the kinematic

diagram, various loading and unloading scenarios of the container were considered and the traveling paths of

the container were identified. According to the identified paths some positions were taken into consideration

and that positions were used to locate the angles of the kinematic solid model. R 1

and R 2

were calculated using

hand calculations and MS. Excel work sheets. After first iteration results hydraulic cylinders were searched and

found that the column load of the cylinder is depend on the bore size, stroke length and the working pressure

of the cylinder. So, for higher column loads working pressure or bore size must be increased and working

pressure is limited due to the power requirements of the hydraulic pump. Increasing the bore size will increase

the hydraulic cylinder size and weight. Increase of the stroke length will reduce the column load. In order to

minimize the R 1

and R 2

, minimize the total weight of the system, minimize the stroke lengths, and minimize

the stowed lengths of the arms kinematic model dimensions were changed and again angles were located and

calculated the R 1

and R 2

. About 14 iterations were done to finalize the dimensions of the modal.

During the calculations found out that R 1

and R 2

will be higher when increasing the distance from the trailer

deck to loading platform and height difference between the trailer deck and loading plat form. These results

were obtained during the finalization of kinematic modal dimensions.

A shear force and bending moments analysis of the side loader arms was carried out to find the paths and

points that are experiencing maximum shear force and maximum bending moments by the side loader arms.

Then design was improved to minimize the bending moments in arms.

According to the final results two arms, stabilizer arm and base were initial simulations were done using the

SolidWorks and final simulation was done by Ansys. According to analysis results models were improved

iterative manner while checking the key requirements had been satisfied. Reduction in weight and reducing

the stress concentration were achieved.

2.0 KINEMATIC ANALYSIS AND CALCULATIONS

2. 1 Container loading and unloading paths

Required clearances and distances were checked from initial sketches for kinematic model. After that 6 paths

were defined to load (unload) the container from 1.4 m lower from the trailer deck and 1.4 m higher from the

trailer deck at 300 mm, 500 mm, and 1m clearance distances. Further design calculations were based on

positions which are situated in those paths. Solid model was helped to measure distances and angles for the

appropriate position.

Trailer Deck

Dimensions are in millimeters

FIGURE 2 - 1 SOLID KINEMATIC MODEL

2. 2 Calculations

Initially cylinder forces and reaction forces were found. Then Bending moments for the boom and V rod was

calculated. Pins at linkages also calculated with their failure scenarios. Following assumptions were made while

calculating the forces.

 All hinges are smooth. (No Friction force)

 Weights of the rods were not included.

 At each position system was in static equilibrium.

2. 2 .1 Cylinder Force Calculation

Direction of forces were taken as arbitrary

directions except for the load (W). Angles of

R1 and R2 taken from the kinematic model

since they are cylinder forces. Negative

forces may indicate at results if the taken

force direction opposite to actual one.

Angles α, δ, ϒ and β were obtained through

the kinematic model for each position.

1

sin

𝛿 + 𝛾 − 180

2

cos

𝛿 + 𝛾 − 180

− 𝑙

3

sin(𝛾 − 90 )

Consider ABC,

𝐶

𝑅

1

sin(𝛼) 𝑙

2

sin(𝛿 + 𝛾 − 180 ) − 𝑅

1

cos(𝛼) 𝑙

2

cos(𝛿 + 𝛾 − 180 ) + 𝑊[𝑙

2

cos(𝛿 + 𝛾 − 180 ) + 𝑙

1

sin(𝛿 + 𝛾 − 120 )] = 0

𝑅

1

=

𝑊[−𝑙

2

cos(𝛿 + 𝛾) + 𝑙

1

(sin(𝛿 + 𝛾)cos( 120 ) − cos(𝛿 + 𝛾)sin( 120 ))]

− cos

( 𝛼

) 𝑙

2

𝑐𝑜𝑠

( 𝛿 + 𝛾

)

• sin

( 𝛼

) 𝑙

2

𝑠𝑖𝑛

( 𝛿 + 𝛾

)

𝑅

1

= −

𝑊 [𝑙

2

𝑙

1

2

⁄ (tan(𝛿 + 𝛾) + √

3 )]

𝑙

2

cos

( 𝛼

)[ tan

( 𝛼

) tan

( 𝛿 + 𝛾

) − 1

]

FIGURE 2 - 8 FREE BODY DIAGRAM OF ABC AND CD RODS

Consider the whole system,

𝐷

𝑊𝑥 = −𝑅

2

[𝑙

3

cos(𝛽) cos(𝛾 − 90 ) + 𝑙

3

sin(𝛽) sin(𝛾 − 90 )]

𝑅

2

=

𝑊𝑥

𝑙

3

(𝑙

3

cos

( 𝛽

) cos

( 𝛾 − 90

)

• 𝑙

3

sin

( 𝛽

) sin

( 𝛾 − 90

) )

2. 2 .2 Reaction Forces at Joints Calculation

Considering ABC rod,

4

1

. Sin( 𝛿 + 𝛾 − 120 )

5

2

6

3

𝑥

1

1

𝑦

1

1

1

1

Considering ABC and CD rod,

𝑦

2

2

2

2

𝑥

2

2

FIGURE 2 - 9 FREE BODY DIAGRAM OF ABC ROD

FIGURE 2 - 10 FREE BODY DIAGRAM OF ABC AND CD RODS

For point A,

By Sin rule

1

3

𝑆𝑖𝑛( 90 + ε)

4

3

1

. 𝑆𝑖𝑛( 90 + ε)

4

1

8

9

𝑇𝑎𝑛ε =

9

FIGURE 2 - 13 FORCES AT A

2. 2 .4 Bending moment calculation

2.3.4.1 Boom Bending Moment calculation

FIGURE 2 - 14 CD FORCES (UP), CD ROD TANGENTIAL FORCES (DOWN)

0 < x < l 10

𝑦

2

2

2

2

𝐷

α

α

D

D

E

E

C

C

y

y

x

x

y

y

x

x

R

R

x2.Cos(ϒ-90) –

y1.Cos(180-ϒ)

x2.Cos(ϒ-90) –

y1.Cos(180-ϒ)

R1.Sin(α+ϒ-90)

R1.Sin(α+ϒ-90)

y3.Sin(ϒ-90) –

x3.Sin(180-ϒ)

y3.Sin(ϒ-90) –

x3.Sin(180-ϒ)

D

D

V

M

x

x

x2.Cos(ϒ-90) –

y1.Cos(180-ϒ)

x2.Cos(ϒ-90) –

y1.Cos(180-ϒ)

0 < x < l 1

𝑦

𝐴

l 1

< x < l 1

+l 2

𝑦

1

1

𝐴

1

1

A

A

V

M

W.Sin(270-δ-ϒ)

W.Sin(270-δ-ϒ)

x

x

A

A

V

W.Sin(270-δ-ϒ)

W.Sin(270-δ-ϒ)

R1.Sin(270-α-δ-ϒ)

R1.Sin(270-α-δ-ϒ)

M

x

x

2. 2 .5 Pin Calculation

All the pins are subjected to double shear. Pin locations are shown in following figure.

Pin diameter, thickness of one plate of a side arm and thickness of middle arm

are calculated following manner. Minimum pin diameter is calculated

considering the pin shear strength (to avoid shearing of the pin). Then

according to that diameter thickness of side arm and middle arm were

calculated (to avoid crushing of the plates). Then again pins were analyzed

according to following failure modes.

 Shearing of the pin

 Crushing of the plates

 Tearing of the plate at an edge

 Crushing of the pin

For pin (Shearing of the pin-failure mode 1)

𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒

2

𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒

𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒

FIGURE 2 - 16 PIN LOCATIONS

FIGURE 2 - 17 DOUBLE SHEAR PIN

FORCE

FIGURE 2 - 18 SHEAR

FORCE IN THE PIN

FIGURE 3 - 2 POSITION 1.

FIGURE 3 - 6 POSITION 1.5 FIGURE 3 - 5 POSITION 1.

FIGURE 3 - 10 POSITION 1.7 FIGURE 3 - 9 POSITION 1.

FIGURE 3 - 8 POSITION 1.

FIGURE 3 - 11 POSITION 1.

3.0 CALCULATION RESULTS AND DISCUSSION

3.1 Static Force Analysis

3.1.1 Path 1

Path is created to lift the container at lower deck at 300mm distance.

Along the path 1, 10 position were selected and according to the selected

positions angles were measured and calculated the R 1

, R

2

and R 3

FIGURE 3 - 1 PATH 1

FIGURE 3 - 4 POSITION 1. 1 FIGURE 3 - 3 POSITION 1. 2

FIGURE 3 - 7 POSITION 1.

TABLE 1 INPUTS FOR PATH 1

TABLE 2 RESULTANT FORCES FOR PATH 1

W (half mass of the container) 176.58 KN

l2 (length of arm2) 0.9 m

l1 (length of arm 1) 1.1 m

l3 (length of arm 3) 3 m

Angle between arm 1 and arm 2 150 degrees

Position R 1

(KN) R

2

(KN) R

3

(KN)