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CHAPTER 5
STUDIES ON DYNAMIC CHARACTERISTICS OF
MINERAL CAST LATHE BED
5.1 INTRODUCTION
In the previous chapter, the characteristics for the epoxy granite
with varying resin content were studied. It was observed that the composition
with, 12% by weight of epoxy resin mixture having 1% by weight of resin
used as hardener and 88% of aggregate mixture consisting of coarse, medium
and fine particles taken in the ratio 50:25:25 gives better results.
In this study, a cast iron micro-lathe bed shown in Figure 5.1,
having a bending stiffness of 117 kN/m was selected for analysis.
An epoxy granite lathe bed having bending stiffness equal to that of
the cast iron bed was fabricated using the aforesaid composition, adopting
mineral casting techniques. The design details of the lathe bed are discussed
in section 5.3.
The dynamic characteristics of the fabricated epoxy granite lathe
bed were evaluated. The dimensional stability, surface finish and wear
resistance for the fabricated lathe bed were studied.
98
Figure 5.1 Cast iron lathe bed selected for analysis
5.2 METHODOLOGY
A cast iron micro-lathe bed was selected for analysis. An epoxy
granite lathe bed of model size 1:1was fabricated. The wall thickness of
epoxy granite structure was increased such that it has same bending stiffness
about the X-axis, as that of the cast iron lathe bed. The equal stiffness for the
beds was verified using FEM analysis.
Modal analysis was carried out to determine the dynamic
characteristics of the cast iron bed and epoxy granite bed using an
experimental setup. The properties like damping ratio, fundamental frequency
and the weight for the fabricated lathe bed were measured and compared with
cast iron lathe bed. The experimental and numerical values of natural
frequencies were compared.
Cast iron lathe bed
99
The Finite Element Method (FEM) was used to study and compare
the characteristics of the epoxy granite and cast iron lathe beds numerically.
The equal stiffness characteristics for the lathe beds were evaluated using
finite element deflection analysis.
To verify the dimensional stability of the fabricated bed, oil and
water immersion tests were conducted. The methodology followed in this
study is given in Figure 5.2.
Figure 5.2 Methodology
5.3 DESIGN DETAILS OF LATHE BEDS
The selection of geometry and dimensions of the lathe beds was
made, such that it fulfills the functional requirements and contain all the
Modal Analysis using ANSYS
CAD Modeling
Comparing naturalfrequencies of cast ironand epoxy granite lathe
beds.
Modeling of lathe bed
Analytical study
FEM analysis
Fabrication of epoxy granite bed
Modal analysis on lathe beds
Comparative study
Measurement of Cast iron lathe bed
Dimensions for epoxy granite lathe bed
Preparation of mould
100
auxilliaries like tail stock and tool carriage attached to it. From this point of
view, the epoxy granite lathe bed was designed similar to the cast iron lathe
bed selected for analysis, with slight modifications in geometry to reduce the
complication in fabrication.
The external loads acting on the lathe bed consists of the forces that
are involved in the stress state analysis and strength evaluation of lathe bed.
The major static forces acting on the lathe are the cutting forces produced
during extreme cutting operations and the gravity forces from the weight of
the bed, tail stock, head stock and the carriage. The dynamic force to the lathe
body comes from the inertial forces due to the movement of the slide over the
lathe bed.
Staneik et al, has studied the stress and displacement on a cast iron
lathe body. Assuming a lathe power of 15 kW, with a drive efficiency of 0.8
and a cutting speed of 120 m/min, for a rough cutting of shaft with diameter
65mm, the researchers determined the cutting force (Pz), feed force(Px) and
thrust force (Py) acting on a lathe body as 6000 N, 2400 N and 2400N
respectively.
Analysis of various forces acting on a centre lathe due to the cutting
force was done by the researchers Sen and Bhattacharya (1975). The
components of cutting force and its components and the effect of cutting force
on different components of lathe are given in Figure 5.3. From this Figure the
dissipation of cutting force into the lathe bed can be studied.
101
Figure 5.3 Forces acting on the lathe
Where, PZ , PY, PX are the components of the cutting force. PXH, PYH
and PZH are the forces acting on head stock and PXT, PYT and PZT are the
forces acting on tail stock due to the cutting force. ‘W’ is the weight of
workpiece. The cutting tool receives all the forces PX, PY and PZ but in
opposite direction and these forces are transmitted through the saddle to the
lathe bed.
Due to machining operations, lathe bed will be mainly subjected to
bending and compression. Assuming, the cutting force 6000 N is acting on the
fabricated epoxy granite lathe bed, then using the dimensions of the epoxy
granite lathe bed, the maximum compressive stress produced was found using
the equations derived by Sen and Bhattacharya (1975). The cutting force is
transmitted to the lathe bed through the cross slide via the tool post,
compound rest and the cross slide as shown in Figure A 4 in Appendix 4. The
X
Z
Y
PZH
Forcestransferredthrough headstock to lathebed
Tail stock
W/2
Px
PZPY
PXH
PYH
PYT
PZT
PXT
Saddle
Head stock
Lathe bed
Work piece
W/2
Forces transferred through saddle tolathe bed
Forcestransferredthroughtail stockto lathe bed
Forces inthe bearinghousings
W
102
contact area of the cross slide with the lathe bed was noted and the maximum
compressive stress corresponding to it was calculated as 150 kPa, which is
much smaller than the compressive strength (114 MPa), determined
experimentally, for the epoxy granite material.
Also, the tensile force acting on the lathe bed is too small. Hence, it
was concluded that, the dimensions selected for the bed are satisfactory from
the point of view of strength.
From the experimental studies discussed in chapter 4, it was
observed that, the elastic modulus of cast iron is about 3.8 times more than
epoxy granite material. Hence, the bending stiffness of epoxy granite will be
smaller than the cast iron by the same order. To increase the bending stiffness,
the moment of inertia was increased, by increasing the wall thickness as much
as possible, without affecting the outer dimensions of the structure.
Figure 5.4 (a) and Figure 5.4 (b), shows the changes in dimensions
and geometry, made for epoxy granite lathe bed compared to the cast iron
lathe bed. It can be observed that, the dimensions of the guide way and the
key way remains the same, to incorporate the accessories.
The trapezoidal part of cast iron bed with 25 mm depth was changed
to a cuboid of 39 mm depth for the epoxy granite bed, so that the moment of
inertia for the epoxy granite bed becomes 3.8 times that of the cast iron lathe
bed. Thus, the bending stiffness of the structures were made equal. The
column wall thickness was also increased sufficiently to support the bed.
103
(a) Cast iron lathe bed (Moment of Inertia, Izz= 156.25x10-09 m4)
(b) Epoxy Granite lathe bed (Moment of Inertia, Izz= 594.95x10-09 m4)
Figure 5.4 Design changes for the lathe beds.
The detailed drawings of the existing cast iron lathe bed and the
fabricated epoxy granite lathe bed are shown in Figure 5.5 (a) and Figure 5.5
(b) respectively.
Z
Y
Z
Y
104
105
106
5.4 NUMERICAL ANALYSIS
The lathe bed was modeled using Pro Engineer 5.0 software and the
geometry, converted into Initial Graphics Exchange Specification (IGES)
format was imported to ANSYS 14.0 software.
Modal analysis was carried out using ANSYS 14.0 software to find
the natural frequency and mode shapes of lathe bed, and the result was
compared with experimental values.
The stages of FEM analysis using ANSYS were as follows.
5.4.1 Selection of Material Properties
The model of the lathe bed created in Pro Engineer 5.0 was
converted to Initial Graphics Exchange Specification (IGES) format to allow
digital exchange of information among Computer Aided Design (CAD)
systems. The file was then imported to ANSYS.
The material selected for analysis was gray cast iron and epoxy
granite composite. The material properties for analysis are listed in Table 5.1.
The properties, except Poisson ratio, for the epoxy granite were obtained
experimentally, as discussed in the previous chapter. The Poisson ratio for
epoxy-granite was taken from literature (Rahman et al, 2001). The properties
of gray cast iron were taken from the summary of properties of cast iron
materials available in the database, www.matweb.com.
107
Table 5.1 Material properties of gray cast iron and epoxy granite
Properties Gray Castiron
Epoxy granite
Density(kg/m3) 7150 2300
Young’s modulus (GPa) 118 31
Compression strength (MPa) 950 114
Tensile strength (MPa) 243 12
Thermal Conductivity (W/mK) 50 2-3
Poisson’s ratio 0.28 0.25
5.4.2 Development of Meshed Model
The geometry was meshed using SOLID 187-Tet 10 element. This
is a tetrahedron element with ten nodes and 3 translational degrees of freedom
per node. Staneik et al (2012) reported that, this solid element selected takes
care of the complicated shape of the cast iron lathe bed. The automatically
generated meshed model, after giving the input parameters, is shown in
Figure 5.6 (a).
5.4.3 Boundary Conditions
After meshing the model, boundary conditions were applied. The
lathe bed selected for analysis was fixed to the table using nut and bolt
arrangements provided at the bottom of the column. Hence the bottom part of
the column in the tail stock end and the chuck end was constrained in all
directions, (Staneik et al, 2012).
108
The model was solved and natural frequencies and mode shapes
were extracted. The boundary conditions applied on the bottom part of the
cast iron lathe bed which are fixed are shown as the hatched area in Figure 5.6
(b) and a detailed illustration of boundary conditions and loadings are shown
in Figure A 5 in Appendix 5. A similar analysis was done for the epoxy
granite lathe bed.
a) Meshed model
(b) Boundary conditions applied on the model
Figure 5.6 Meshed Model and boundary conditions for cast iron lathebed
5.5 RESULTS AND DISCUSSIONS
The bending stiffness of the epoxy granite bed and the cast iron bed
were verified using FEM analysis. The deflection analysis was carried out for
the loads ranging from 500 to 2000N in steps of 500 N on both cast iron and
epoxy granite bed. The minimum load 500 N was selected because, the
Head stock column
Tail stock column
Bottom part of head stock column (fixed) Bottom part of tail stock column (fixed)
109
deflections obtained below it were not significant, the higher range for the
load, 2000 N was arrived at considering the load acting on the selected epoxy
granite lathe bed due to the dead weight from tail stock, tool post etc. under
static conditions. The deflections produced during extreme load conditions
were noted. The deflections produced by the beds when subjected to loads
ranging from 500-2000N were found to be same (±4%). The deflections
obtained for both the beds from FEM simulation is shown in Figure 5.7.
Figure 5.7 Deflection analysis for bed structures
It was observed that the deflections produced by both the beds were
very close to each other, indicating same stiffness for the beds. Hence, it was
concluded that, the epoxy granite bed is stable and is comparable with cast
iron bed within the range of load tested.
The natural frequencies and mode shapes of the epoxy granite and
cast iron lathe beds were determined using modal analysis. The mode shapes
obtained corresponding to the first four natural frequencies for the cast iron
bed and epoxy granite bed are shown in Figure 5.8 and Figure 5.9
respectively.
110
111
112
For a continuous beam fixed at both ends, the natural frequencies are
given by Thomson (1985) as given in Equation (5.1),
24( )n n
EIfml
(5.1)
Where, ‘m’ is the mass density defined as mass per unit length, fn is the
natural frequency corresponding to mode number ‘n’ and n is a constant which
varies with mode number. A table of natural frequencies obtained from FEM
analysis is given in Table 5.2.
Table 5.2 Natural frequencies from FEM analysis
Lathe bedMaterial
Natural Frequency, HzFirst Second Third Fourth
Cast Iron 656.2 700.52 750.82 780
Epoxy Granite 726.05 778.3 818.74 861.78
In this study, the structural rigidity, EI was made equal for both
material structures, by adding more volume of material into the fabricated epoxy
granite structure. The density of cast iron is 7150 kg/m3 and the equivalent
density of epoxy granite material is 2300 kg/m3, which is about 3 times lesser
than that of cast iron. The higher density of cast iron is balanced by the higher
material volume for the epoxy granite, resulting in similar natural frequencies for
both the lathe beds.
113
It was observed from the modal analysis that the first fundamental
frequency for the epoxy granite lathe bed is higher than that of the cast iron lathe
bed. Since the stiffness for the lathe beds were equal, the higher natural
frequency for epoxy granite lathe bed could be due to the lesser mass of the
epoxy granite lathe bed. However, the higher value of natural frequency is
advantageous for the lathe bed as it delays the resonance conditions. The
numerical values obtained were tested experimentally by conducting modal
analysis on the fabricated lathe bed as discussed in the following sections.
5.6 FABRICATION OF EPOXY GRANITE LATHE BED
The mould for the mineral casting was made as shown in Figure 5.10,
with 8mm thick wood strips which are cut into required sizes for making
different portions of the bed and strips are assembled with screws. The epoxy
concrete was manufactured using a mixture containing 88% by weight of granite
aggregate and the remaining, a mixture of resin and hardener.
Figure 5.10 Wooden mould for mineral casting
The granite aggregate consist of coarse particles of size ranging
from 1.5-2.25 mm (50% by weight), medium particles ranging
from 0.5-1.5 mm (25% by weight) and fine particles of size less
than 0.5 mm (25% by weight).
114
To facilitate the easy movement for dynamic parts like tail stock
and the tool post, a smooth surface for the lathe bed was provided
at the top. The smooth surface, 20 mm in depth was fabricated
using fine particles having size less than 0.5 mm.
The resin mixture consists of mixture of epoxy resin (LY 556)
and hardener (HY 951) which is 1% by weight of the resin used.
The granite aggregate was washed thoroughly using water to get rid of
any foreign material. It was then dried to remove the traces of water to ensure
proper binding of the granite particles with the resin material. The dried granite
particles were mixed thouroughly with the binder-hardener mixture.The mixture
was filled into the mould before it hardened and was shaken regularly to remove
air particles trapped which would improve the compactness of the bed. The
epoxy granite lathe bed was cured at room temperature for three weeks before
testing. The fabricated epoxy granite bed is shown in Figure 5.11.
Figure 5.11 Fabricated epoxy granite lathe bed
115
5.7 MODAL ANALYSIS: EXPERIMENTAL SETUP
Modal analysis was carried out using an experimental setup shown
in Figure 5.12. The experimental system consists of a miniature type
accelerometer having a sensitivity 96.72 mV/g was interfaced with a personal
computer. LabVIEW (v8.2) software was used for data acquisition, through a NI
9234 Data Acquisition (DAQ) card.
Figure 5.12 Experimental setup for modal analysis
The accelerometer was attached to the structure where maximum
deflection was expected to occur. A modally tuned impact hammer was used to
develop vibrations in the bed. The DAQ card registers the vibrating signals from
the accelerometer which was displayed as a frequency spectrum through the
PC with LabVIEWsoftware
Accelerometer
Impact hammerDAQ card
116
LabVIEW software. The frequency spectrum was used to analyse the
fundamental frequencies and to determine the damping ratio of the lathe bed.
5.8 RESULTS AND DISCUSSIONS
Modal analysis was conducted to verify the damping ratio of both bed
materials. The frequency response curves obtained using LabVIEW programme
for the cast iron bed and epoxy granite bed are shown in Figures 5.13 and Figure
5.14 respectively.
From the frequency response curves obtained, the frequency values
corresponding to peak acceleration was taken as the fundamental frequency.
The damping ratio ( ) was calculated using half power band width
method given by Rao (2009), as given by Equation (5.2).
2 1
2 n
f ff (5.2)
where, fn represents fundamental frequency at which the damping ratio is
calculated and f =f2 f1, is the bandwidth corresponding to half power points.
A brief description of half power bandwidth method used in the determination of
damping ratio is given in Appendix 3.
117
Figure 5.13 Frequency response spectrum for cast iron lathe bed
Figure 5.14 Frequency response spectrum for epoxy granite lathe bed
The fundamental frequency and damping ratios were found using
modal analysis and given in Table 5.3.
620 Hz Hz
665 Hz Hz
118
Table 5.3 Dynamic characteristics obtained from experiment
MaterialNatural
frequency (Hz)Dampingratio ( )
Weight(kg)
Cast Iron 620 0.0079 43.350
Epoxy Granite 665 0.0181 31.600
It was observed that, the damping ratio for epoxy granite bed was 2.28
times high compared to cast iron bed. The high damping ratio for the epoxy
granite bed may be due to the granular aggregate material present in the
structure. The shift in fundamental frequency towards right, for epoxy granite
structure, indicates delay in resonance conditions. The weight of the epoxy
granite bed was found to be 27.1% lesser than cast iron bed.
Comparing the values of the granite-epoxy composites developed in
this research with those found in the literature, the maximum damping factor
obtained was 1.81% and close to those presented by Orak (2000), which varied
between 1.65 and 3.10%, as a result of a processing with 20% in weight of
polyester resin and 80% in weight of quartz, with grain sizes varying between 0.5
and 8 mm. Li et al (1996), observed that the addition of acrilonitrile-butadiene
rubber with epoxy at 20% in weight and granite or limestone increases the
damping factor to values between 2.18 and 2.67%.
The composition, with 12% resin mixture and 88% aggregate mixture
used in this analysis was observed to improve the dynamic properties of the
structure fabricated. The use of an aggregate consisting of a mixture of three
different sizes of granite particles reduces porosity, while improving the
119
compactness of the structure. Epoxy binder provides a stronger bond between the
granite particles which also gives higher strength to the structure.
5.8.1 Comparison of Numerical and Experimental Study
A comparison of the numerical and experimental natural frequency
values obtained for the cast iron and epoxy granite bed are shown in
Figure 5.15.
Figure 5.15 Comparison of numerical and experimental values
It was observed that, the error value between the numerical and
experimental values for the cast iron lathe bed and epoxy granite lathe bed are
5.52% and 8.41% respectively. The error values are within acceptable limits and
indicate that, the natural frequencies obtained using FEM analysis for the lathe
beds are in acceptable range and are comparable with the experimental values.
120
5.9 COST ANALYSIS
The initial investment in the manufacture of the cast iron lathe bed
involves furnaces and primary installations. Whereas, for the epoxy granite lathe
bed fabricated using mineral casting techniques, the initial investment would be
in a stone crusher, sieves, the wooden mould preparation, the aggregate and a
resin mixer and shaker. It was observed that the initial investment for the
fabrication of epoxy granite lathe bed is less compared to that of a cast iron lathe
bed.
The cast iron lathe bed used in this analysis was a precast one and the
initial investment details were not accurately available. Hence, this cost analysis
was limited to comparison of material costs involved in the manufacture of lathe
beds. In this view, the material cost for the manufacture of cast iron lathe bed
was found to be INR 2508 and the cost for epoxy granite lathe bed containing
88% granite and 12% epoxy resin and hardener was INR 3240. The material cost
for epoxy granite was found to be 29% higher than that of cast iron.
5.10 CONCLUSIONS
In this study, an attempt was made to fabricate an epoxy granite lathe
bed having equal stiffness as that of a cast iron micro lathe bed using mineral
casting techniques. The epoxy granite lathe bed was analysed for dynamic
performances in comparison with conventional cast iron lathe bed used in a
micro lathe. The design changes required for the epoxy granite lathe bed, to have
equal stiffness as that of the cast iron micro-lathe bed was also analyzed. A cost
analysis was done for the fabricated epoxy granite lathe bed cast iron lathe bed
121
and it was observed that the material cost for epoxy granite lathe bed is 29%
more than that for the cast iron lathe bed.
Experimental modal analysis was conducted on the fabricated epoxy
granite and cast iron lathe beds to determine fundamental frequencies and
damping ratios. It was observed that the epoxy granite bed gives 2.28 times
higher damping ratio and a 27.1% reduction in weight compared to the cast iron
lathe bed, maintaining same stiffness. The fundamental natural frequency for
epoxy granite lathe bed was found to be higher.
Material costs for the epoxy granite lathe bed was found to be 29%
higher than that for the cast iron lathe bed. However, the initial investment for
the manufacture of lathe bed was not considered in the cost analysis.