Step by Step Procedure For Designing a Vibration Isolation System For Vibratory Compactors

1. DESIGN OF VIBRATION ISOLATION SYSTEM FOR
VIBRATIORY COMPACTORS
Manohar M Hegde
F
f
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ResultantAmplitudeofMass,mm
Natural Frequency, Radians/Sec

2. DESIGN OF VIBRATION ISOLATION SYSTEM FOR
VIBRATIORY COMPACTORS
CONTENTS
1. Vibratory Compactors - Their Function, Types and Working Principle
2. Effect of Vibration on Operator (HAV and WBV)
3. Challenges in Designing a Suitable Vibration Control System
4. Vibration Mechanism and Principle of Isolation
5. Examples of Vibration Isolation Methods
6. Lumped Parameter Modeling
7. Considerations in Selecting Rubber Mounts
8. Steps in Selecting Rubber Mounts
9. Detailed Design Process Flow Chart
10.Analysis Examples of Lumped Mass Systems
11.Summary of Data Used and Results
12.Details of Typical Rubber Mounts
13.Notes

3. FUNCTION : Increasing The Density of Soil / Base Layer By Compacting
In construction industry, loose soil needs to be
densified so that it can take heavy loads without
caving-in.
Examples : Foundations of big buildings, laying of pipes
In road building industry, the newly laid
asphalt needs to be pressed down to ensure
inter-particle adhesion and also to increase
firmness of the road.
Examples : Highway construction , laying asphalt on pavement
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS

4. Types of Vibratory Compactors
Plate
Drum- Drum
Wheel- Drum
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS

5. Principle of Compaction
For Shallow DepthFor Moderate DepthFor Deeper Layers
Effect of Compaction on Soil
Normal Soil Compacted Soil
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS
Water Air

6. Importance of Vibration Control
WBV – Whole Body Vibration
Max limit 0.5 m/sec2
HAV - Hand Arm Vibration
Max limit 2.5 m/sec2
“ Magnitude of force F may vary from 9kN (Plate Compactor)
to 350kN (27 ton Drum -Wheel Compactor ) “
F
“Maximum Levels of Vibration Felt By The Operator Should
Conform to Occupational Safety Standards”
f
F
f
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS
ISO 2631,
ISO 5349,
BS 6841,
VDI 2057,
EN2002/44/EC
………..

7. Challenges Faced While Designing a Vibration Control system
2. System Analysis (Lumped Mass-Stiffness) and Math Modeling
1. Choosing a Simple and Effective System
3. Collection of Appropriate Data
5. Design Verification And Validation
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS
4. Handling Complex Calculations

8. Vibration Mechanism and Vibration Isolation
Plate Compactor Drum Compactor
F
X
Z
Vibrating
Plate
X
Y
Machine
Frame
Isolation
Mounts
Handle
Z
Y
Vibrating
Drum
Operator’s
seat
Chassis
Isolation
Mounts
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS

9. Isolation in Single Stage
Drum Compactor
X
Y
Y
Stage-1
Plate Compactor
F
X
Y
Y
Stage-1
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS

10. Isolation in Multiple Stages
Plate Compactor
F
X
Z
Y
Stage-1
Stage-2
Drum Compactor
X
Z
Y
Stage-1
Stage-3
Stage- 2
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS

11. Plate Compactor
Example of Using Vibration Isolation
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS
Rubber Mount

12. Drum-Drum Compactor
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS
Example of Using Vibration Isolation
Rubber Mount
Rubber Mount

13. Drum-Wheel Compactor
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS
Example of Using Vibration Isolation
Rubber Mount
Rubber Mount

14. Lumped Parameter Modeling
Objective Function - Value of Resultant Vibration at Operators Hand /Seat
Design Parameters Considered - Mass, Spring Stiffness, Damping
Controlling Parameter – Natural Frequency of the System
Analysis Approach - Lumped Parameters and Math Modeling
Y
X
’
Vibrating
Drum
Operator’s seat
Chassis
Isolation
Mounts
F
MP
Mc
Chassis
Drum
c K
Ground
↕X=X0 Sinωt
↕ Y(t)
K
Ms
c K
↕ Z(t)
Handle / Seat
Module
Isolation
Mounts
Ground
Reaction
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
0 20 40 60
ResultantAmplitudeofMass,mm
Natural Frequency,
Radians/Sec
Amplitude Vs Frequency
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS

15. Considerations in Selecting a Rubber Mount
Load Capacity of The Mount.
Stiffness K of The Mount.
Type, Size and Mounting Method.
Ease of Assembly and Dis-assembly.
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS

16. Steps in Selecting Rubber Mounts
1. Design a Lumped Mass - Stiffness System ; Set Isolation Targets.
2. Determine by Iteration Values of Required Stagewise Stiffnesses.
3. Select Rubber Mounts Meeting The Minimum Load Criteria and
Stiffness Values.
4. Use The Stiffness Values of The Selected Mounts To Verify
Calculations.
5. Adapt The Selected Mounts in The Compactor Design.
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS

17. Vibration Isolation System Design Process Flow Chart
Set-up Isolation
Model
Estimate Values of the
Lumped Parameters
Set a Target Value
for Isolation
Derive Math
Expression For
Isolation
Decide by Iteration
Required Stagewise
Stiffnesses
Decide the no. of
Mounts at Each
Stage
Calculate the Static
Deflection of Each
Mount
Short list Mount
Suppliers; Collect
Catalogues
Select Mounts
Meeting Deflection
and Size Criteria
Adapt The Selected
Mounts in Detail
Design
Use K Values in
Calculation ;Check if
Isolation is Achieved
Obtain Stiffness
Value K For
Identified Mounts
Iteration
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS

18. Example –1 ; Plate Compactor ; Single Stage Isolation
Total Machine Weight, MM – 96 Kgs
Weight of The Chassis Including
Handle, Mc – 40 Kgs
Stiffness of Stage -1 Isolation, K1 – 800 N/mm
F
X
Y
Y
Stage-1
Amplitude, mm – 1.7 mm
Frequency, - 75 Hz (471 rad/sec)
Centrifugal Force, F0 – 16 kN
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS

19. Mathematical model – SDOF with Forced Vibration
Plate /
Drum
MM =40
Kgs
Total Chassis
Weight Lumped
c K=800N/mm
Ground
↕X=X0 Sinωt
↕ Y0, Y(t)
↕ F(t)
Motion Transmissibility = Y0/X0
Example –1 ; Plate Compactor ; Single Stage Isolation
Resultant Vibration Level at Handle bar: 2.3 m/sec2
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS

20. Example –1 ; Plate Compactor ; 2 - Stage Isolation
Total Machine Weight, MM – 96 Kgs
Weight of The Chassis, Mc – 35 Kgs
Weight of The Handle, Ms - 5 Kgs
Stiffness of Stage-1 Isolation, K1 – 800 N/mm
Stiffness of Stage- 2 Isolation, K2 – 400 N/mm
F
X
Z
Y
’
Stage-1
Stage-2
Amplitude,mm – 1.7 mm
Frequency, - 75 Hz (471 rad/sec)
Centrifugal Force, F0 – 16 kN
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS

21. Plate /
Drum
Mc
K1
Ground
↕X=X0 Sinωt
↕ Y0, Y(t)
↕ F(t)
K2
Ms ↕ Z0, Z(t)
Chassis
Handle
Module
Motion Transmissibility = Z0/X0
Resultant Vibration Level at Handle bar: 1.3 x10-5 m/Sec2
Example –1 ; Plate Compactor ; 2 stage Isolation
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS
Mathematical model – 2 DOF with Forced Vibration

22. Example –2 ; Drum Compactor Single Stage Isolation
Total Machine Weight, MM – 20000 Kgs
Weight of The Chassis Including Operator’s
Platform, Mc – 2500 Kgs
Stiffness of Stage-1 Isolation, K1 – 12000 N/mm
Amplitude, mm – 2.1 mm
Frequency, - 28 Hz (176 rad/sec)
Centrifugal Force, F0 – 330 kN
Drum Compactor
X
Y
Y
Stage-1
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS

23. Mathematical model – SDOF with Forced Vibration
Plate /
Drum
MM =2500
Kgs
Total Chassis
Weight Lumped
c K=330kN
Ground
↕X=X0 Sinωt
↕ Y0, Y(t)
↕ F(t)
Motion Transmissibility = Y0/X0
Example –2 ; Drum Compactor ; Single Stage Isolation
Resultant Vibration Level : 0.47 m/Sec2
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS

24. Total Machine Weight, MM – 20200 Kgs
Weight of The Chassis, Mc – 2000 Kgs
Weight of The Operators Platform, Ms -500 Kgs
Stiffness Stage-1 Isolation, K1 – 12000 N/mm
Stiffness Stage- 2 Isolation, K2 – 8000 N/mm
Amplitude,mm – 2.1 mm
Frequency, - 28 Hz (176 rad/sec)
Centrifugal Force, F0 – 330 kN
Example –2 ; Drum Compactor ; 2 Stage Isolation
Drum Compactor
X
Z
Y
Stage-1
Stage-2
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS

25. Plate /
Drum
Mc
K1
Ground
↕X=X0 Sinωt
↕ Y0, Y(t)
↕ F(t)
K2
Ms ↕ Z0, Z(t)
Chassis
Seat Module
Motion Transmissibility = Z0/X0
Resultant Vibration Level : 6 x10-6 m/Sec2
Example –2 ; Drum Compactor ; 2 Stage Isolation
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS
Mathematical model – 2 DOF with Forced Vibration

26. SUMMARY OF DATA
Sl
No
Machine Data For 1-Stage
Isolation
Data For 2-Stage
Isolation
1 Plate Compactor
Mtotal=96 Kgs
CF=16 kN
X0= 1.7mm
Mc =40 Kgs
K1= 800 N/m2
Mc=35 Kgs
K1=800 N/m2
Ms=5 Kgs
K2=400 N/m2
2 Drum Compactor
Mtotal=20000 Kgs
CF=330 kN
X0=2.1 mm
Mc =2500 Kgs
K1 =12000 N/m2
Mc =2000 Kgs
K1 =12000 N/m2
Ms=500 Kgs
K2=8000 N/m2
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS

27. SUMMARY OF RESULTS
Sl
No
Machine Maximum
allowed
Vibration Level
Vibration
Level with 1-
Stage Isolation
Vibration Level
with 2- Stage
Isolation
1 Plate
Compactor
2.5 m/sec2 2.3 m/sec2 1.3 x 10-5 m/sec2
2 Drum
Compactor
0.5 m/sec2 0.47 m/sec2 6 x 10-6 m/sec2
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS

28. Some Typical Rubber Mounts
Compression-Shear
Mount
Shear Mount
Shear MountBush
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS

29. NOTES
1. Use Simplified Math Models,To Begin With.
2. Lumped Parameters With 2-Stage Reduction is Preferable.
3. Effect of Damping in Rubber Mount Can Be Ignored.
4. Collect Equipment Related Data by Benchmarking.
5. Verify Calculations Using Measured Values on
Benchmarked Equipment.
6. Use Combination of Shear and Compressive Modes, if
Necessary, While Using The Rubber Mounts.
7. Real Problem is More Complex ; Requires Much Mathematical Effort.
8. Progressively Develop More Complex Math Models and
Refine Calculations.
9. Use Simulation With Specialised Software Packages to
Account For Distributed Nature Of Mass and Stiffness.
10.Include Ground Resistance in The Form of Stiffness Value
in The Calculation, if Accurate Data is Available.
DESIGN OF VIBRATION ISOLATION SYSTEM FOR VIBRATIORY COMPACTORS