Proceedings of Indian Geotechnical Conference December 13-15,2012, Delhi (Paper No.H834)
MODELLING OF IMPACT TYPE MACHINE FOUNDATIONS
Ms. M. Bharathi, M.Tech. Student (Soil Dynamics), IIT Roorkee, E-mail ID:
[email protected] Dr. Swami Saran, Professor Emeritus, IIT Roorkee, E-mail ID:
[email protected] Dr. Shyamal Mukerjee, Assistant Professor, IIT Roorkee, E-mail ID:
[email protected]
ABSTRACT: This paper describes the different types of modeling used for an impact type machine foundation. Usually, the impact type machine foundation is modeled as a two degree of freedom system. Here, an attempt has been made to reduce the transmission of vibration from the machine to its adjacent structures and hence the system is modeled as a three degree of freedom system. The design parameters are selected from the actual impact type machines that are used in the industry. Amplitude variation obtained in the different models, with varying machine and soil parameters, have been analyzed and charts prepared. The effect of different types of foundation soil ranging from soft soil to hard rock has also been studied. INTRODUCTION Impact type machines produce transient dynamic loads of short duration. These include machines like forging hammers, punch presses and stamping machines. The speed of operation usually ranges from 50 to 150 blows per minute. The horizontal imbalance is controlled by mounting the equipment parts without any eccentricity. The vertical imbalance i.e. the displacement is limited by providing suitable isolator material. MODELLING OF MACHINE FOUNDATION SYSTEM
(4) Solving the above equation we will get the three natural frequencies ωn1, ωn2 and ωn3. Amplitudes of the system shown in Fig. 1 may be obtained by following equations. z1 = A1sinωn1t+A2cosωn1t+A3sinωn2t+ A4cosωn2t+A5sinωn3t+A6cosωn3t
(5)
z2 = B1 sinωn1t+B2cosωn1t+B3sinωn2t+ B4cosωn2t+ B5sinωn3t+B6cosωn3t
(6)
z3 = C1 sinωn1t+C2cosωn1t+C3sinωn2t+ C4cosωn2t+ C5sinωn3t+C6cosωn3t
(7)
Solutions of Eqs. (5), (6) and (7) are obtained satisfying following boundary conditions: At t=0 Z1 =0, Z2=0, Z3 =0 At t=0 where Va is the velocity of anvil. The maximum displacements may be obtained using the following equations. Fig. 1 Model 3DOF system
(8) (9)
The equations of motion are m1 + K1Z1+ K2 (Z1-Z2) =0
(1)
m2 + K2 (Z2-Z1) + K3 (Z2-Z3)=0
(2)
m3 +K3 (Z3-Z2) =0 (3) Solutions of Eqs. (1), (2) and (3) may be obtained in usual way, and it will give
(10) Where, a1 = a2 = a3 =
M.Bharathi, Dr. S. Swami Saran, Dr. S. Mukerjee
b1 = b2 = b3 =
PARAMETERS SELECTION Soil The values of coefficient of elastic uniform compression are selected for different types of soils ranging from soft soil to rock i.e. from 2.5x107 to 12.5x107in steps of 2.5x107.
Fig. 2c Trough Amplitude for 80 kN tup
Tup Weight The tup for impact machines available in the market ranges from 10kN to 100kN and values for the analysis are selected in between this range (20kN, 40kN, 60kN, 80kN and 100kN). ANALYSIS OF MACHINE FOUNDATION SYSTEM The analysis of the three different models of impact machine foundation system for the above said values is been done with the help of MATLAB software and charts are been prepared showing the variation of amplitude with the tup weight for different soil and different isolator materials. Fig. 3a Foundation Amplitude for 20 kN tup
Fig. 2a Trough Amplitude for 20 kN tup Fig. 3b Foundation Amplitude for 40 kN tup
Fig. 2b Trough Amplitude for 40 kN tup Fig. 3c Foundation Amplitude for 80 kN tup
Modelling of Impact Type Machine Foundations
Fig. 4a Anvil Amplitude for 20 kN tup Fig. 5 3DOF model
Fig. 4b Anvil Amplitude for 40 kN tup
Wf = 4000 x 103 = 25 x 103 x Volume of foundation block Volume of foundation block = 160 m3 Assuming the thickness of foundation block as 2.25m Base area of foundation block, A2 = 160/2.25 = 71.11 m2 Let the base area of trough A1 = 1.25 times the base area of foundation block = 88.88 m2 K1= 4.44 x 109 N/m K2 = 1.0 x 109 N/m K3 = 0.18 x 109 N/m m1 = 203.87 x 103 kg m2 = 407.75 x 103 kg m3 = 101.94x 103 kg ωn1 =164.91 rad/sec ωn2 = 54.87 rad/sec ωn3 = 33.94 rad/sec ωna = 42.02 rad/sec VTi = 2.575 m/s = 0.184 m/s Z1m = 2.42x 10-4 m, Z2m = 1.3x10-3 m , Z3m = 3.6x10-3 m
Fig. 4c Anvil Amplitude for 80 kN tup COMPARISON OF A SYSTEM WITH DIFFERENT DEGREES OF FREEDOM Three degree freedom system: (i)
Wa = W3 = 20 x WT = 1000 kN Wf = W2 = 80 x WT = 4000 kN Wtr = W1 = 40 x WT = 2000 kN (assumed)
Two degree freedom system: Wa = 1000 kN Wf = 4000 kN Volume of foundation block = 160 m3 Assuming the thickness of foundation block as 2.25m Base area of foundation block, A1= 88.88 m2 Cu' = 5 x 107 N/m3 K1 = 4.44 x 109 N/m K2 = 0.18 x 109 N/m
M.Bharathi, Dr. S. Swami Saran, Dr. S. Mukerjee
m2 = m3
ωn2 VTi = η
= 39.74 rad/sec = 2.575 m/s = 0.184 m/s
K2 m1= m1+m2
Z1m Z2m
= 0.89x 10-3 m = 4.56 x 10-3m
Single degree freedom system:
K1
m1
Fig. 6a 2DOF system Case (i) m1 = 611.62 x 103 kg m2 = 101.94x 103 kg µm = m2/m1 = 0.167 =
ωna= 42.02 rad/sec
Fig. 7 SDOF system
= ωnl= 78.88 rad/sec
Wa = 1000 kN Wf = 4000 kN Volume of foundation block = 160m3 Assuming the thickness of foundation block as 2.25m Base area of foundation block, A1 = 88.88 m2 Cu' = 2 x 2.5 x 107 = 5 x 107 N/m3 ωnl= 78.88 rad/sec VTi = η = 2.575 m/s
ωn1 = 87.43 rad/sec ωn2 = 40.95 rad/sec VTi = η = 2.575 m/s = 0.184 m/s Z1m Z2m
K1
= 0.22x 10-3 m = 4.426 x 10-3m
= 0.0382 m/sec =
Fig.6b 2DOF system Case (ii) m1 = 203.87 x 103 kg m2 = 509.68x 103 kg µm = 2.5 = (109/509.68x103) ωna= 44.30 rad/sec ωnl= 78.88 rad/sec ωn1 = 164.52 rad/sec
0.484 mm
CONCLUSION i. Impact machine foundation systems when modeled as a single degree of freedom system give the maximum amplitude. ii. Amplitudes can be brought within the permissible limits by choosing an appropriate value for stiffness for the isolator. Thus by limiting the amplitude to its permissible value the stiffness of the isolator can be selected for a particular tup weight, knowing this stiffness value, the appropriate isolator material and its thickness can be determined. iii. The amplitudes of the impact machine foundation system can be controlled by selecting a suitable isolator location. REFERENCE [1] A. Major (1962), “Vibration Analysis and Design of foundation for machines and turbines”, Akademiai kiado, Budapest, Collet’s Holdings ltd, London. [2] Barkan D.D (1962), “Dynamics of Bases and Foundation”, McGraw hill book company, New York.
Modelling of Impact Type Machine Foundations
[3] Indrajit Chowdury, Shambu P.Dasgupta (2009), “Dynamics of Structure and Foundation – A Unified Approach”,CRC Press, Netherlands. [4] IS: 2974 (Part II)-1980, “Foundations for Impact Type Machines (Hammer Foundations)”, I.S.I. New Delhi. [5] Rudra Pratap,”Getting Started with MATLAB”, Oxford University Press, Oxford. [6] S R Otto, Denier, “An Introduction to Programming and Numerical Methods In MATLAB”, Springer. [7] Srinivasulu P, Vaidyanathan C.V (1976), “Handbook of Machine Foundation”, Tata McGraw Hill Publishing Company Ltd, New Delhi. [8] Suresh C. Arya, Michael W. O’Neil and George Pincus (1979),”Design of Structures and Foundation for Vibrating Machines”, Gulf Publishing Company, London. [9] Swami Saran (2006), “Soil Dynamics and Machine Foundation”, Galgotia Publications Pvt. Ltd.
Symbols DOF = Degree of freedom h = Drop of tup in m g = Acceleration due to gravity, m/s2 η = Efficiency of drop (0.45 to 0.80) WT = Gross weight of dropping parts, including upper half of the die in kN, p = Pneumatic (i.e. steam or air) pressure in kN/m2 Ac = Net area of cylinder in m2 Wa = Weight of anvil (plus frame if it mounted on the anvil) kN Va = Velocity of anvil after impact m/s VTa = Velocity of tup after impact m/s Wf = Weight of the foundation (plus frame if mounted on it) kN Vaf = Velocity of anvil plus foundation after impact m/s Va = Velocity of anvil after impact m/s
