97

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.