IRJET- Design, Static, and Modal Analysis of High Speed Motorized Milling Spindle

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 05 Issue: 08 | Aug 2018 www.irjet.net p-ISSN: 2395-0072
© 2018, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 787
DESIGN, STATIC, AND MODAL ANALYSIS OF HIGH SPEED MOTORIZED
MILLING SPINDLE
BASAVARAJ1, Dr. S. SUBRAHMANYA SWAMY2
1Assistant professor at Central University of Karnataka, Kalaburgi.
2Professor at BIET, Davangere, Karnataka
Mechanical Engineering, Departmen
----------------------------------------------------------------------***---------------------------------------------------------------------
ABSTRACT - The increasing demands for higher
productivity and lower production costs, high speed
machining tools have been widely utilized in the modern
production industries. High speed motorized spindle
systems are subjected to several effects during high speed
rotations that can cause substantial changes in their
dynamic and thermal behaviors, leading to chatter,
bearing seizure or premature spindle bearing failures.
Compared with conventional spindles, motorized spindles
are equipped with a built-in-motor, so that power
transmission devices such as gears and belts are
eliminated. This design also reduces vibrations and
achieves high rotational balance, and enables precise
control of rotational accelerations and decelerations. The
objective of this work is to optimize the parameters
influencing the high frequency or high speed milling
spindle running at 14000 rpm with power rating 15 kW.
The static deflection analysis is carried out to check the
spindle stiffness, and the dynamic behavior of spindle is
determined by characterizing its properties under
different modes of vibration. Modal analysis is carried out
using ANSYS work bench software. The modal parameters
obtained from the modal analysis can be used to analyze
the system behavior. In dynamic analysis every moment
spindle shaft changes its behavior so that it is difficult to
compare theoretically, but static analysis results can
compare with theoretical results.
Keyword: Milling, Static, modal, ANSYS, Spindle,
Assembly.
1. INTRODUCTION
Modern technology to a great extent relies on the use of
high frequency motorized spindle which is a competent
technology for significantly ever-increasing productivity
and plummeting production costs. On one hand, high
precision is essential for the ongoing trend of
manufacturing activity which is found especially in
electronic industry, automobile industry and machine
tool industry. On the other hand, high precision is
essential for leading edge research. With the help of CNC
technology, machine tools today are not limited to
human capabilities and are able to make ultra-precision
products down to nanoscales in a much faster manner.
The traditional design philosophy of machine tools is
multi-functionality and highest precision possible. For
example, a shank with spindle together with tailstock
can be included onto a standard three axis vertical
milling machine to wind up a multifunctional boring-
milling-turning machine, which means the machine
apparatus is intended to be utilized for different rather
than single purposes. However, with the dramatic
increase of industry varieties and the growing demand of
miniature products, these broadly useful machine
instruments are not effective, either in terms of machine
time or cost or in manufacturing products with special
sizes and precision requirements. In this quick changing
corporate world all business are driven by profitability,
proficiency and low cost. In assembling businesses there
is a developing interest for machine that production
completed items at energetic pace with a more elevated
amount of consistency. In this respects even machine
machines have experienced a transformation and CNC
(Computer Numerical Control) machine machines are
high sought after on account of their higher level of
automation and accuracy. The machine spindle system is
one of the most essential parts of a machine tool since its
dynamic properties directly influences the cutting ability
of the machine tool. The dimensions of the spindle shaft,
location, stiffness of the bearings and bearing preload
affect the vibration free operation of the spindle. The
bearing stiffness is dependent on the preload and is also
influenced by the deformation of the spindle shaft with
the housing during machining. Angular contact metal
ball bearings are most regularly utilized as a part of the
CNC machine spindle due to their low-friction properties
and ability to withstand external loads in both axial and
radial direction. To achieve high speed rotation,
motorized spindles have been developed. This type of
spindle is equipped with a built in motor as an
integrating part of the spindle shaft, eliminating the need
for conventional power transmission devices such as
gears and belts. This design reduces vibrations,
decelerations. However, the high speed rotation and
built in motor also introduce a large amounts of heat and
rotating mass in to the system, requires precisely
regulated cooling and lubrication.

1.1 End Milling and Face Milling
The following diagram illustrates face milling and end
milling operations. Milling cutting tools are known as
multi point cutting tools. In Face milling operation
cutters will make the flat surface finish on surface of the
object, in this number of inserts are used at the cutter
(carbide inserts), the cutting edges are located along its
sides. End mills are the tools which have cutting teeth at
one end as well as on the sides. These are generally used
to refer flat bottom cutters (creating pockets) and
rounded cutters. These are made of HSS or cemented
carbides.
Fig.1.2 Face milling and End milling operations
2. OBJECTIVES
This project work focuses on the development of low
cost CNC milling spindle. The following are the
objectives of this work:
To design the BT-40 milling spindle for a speed of 14000
rpm, by making use of precision bearings and different
bearing arrangements. Analytical calculations shall be
done for different bearing arrangements by considering
the bearing manufacturers data and using suitable
equations. Static analysis of spindle assembly for
different bearing arrangement will be carried out by
using ANSYS Work Bench and the results are compared
with the theoretical results. Dynamic Modal analysis of
different spindle arrangement would be carried out by
using ANSYS Work Bench to determine behaviour of the
spindle assembly and to find out natural frequencies and
mode shapes. Finally assemble the model using optimum
bearing arrangement.
2.1 METHODOLOGY
First, develop the parts or subcomponents according to
dimensions given by the data using suitable software.
Keeping the requirements in mind, assemblies with
bearing arrangement will be modelled using SOLID
EDGE modelling software. Theoretical deflection of the
spindle shaft assemblies will be estimated by
considering the appropriate radial cutting force at the
nose end of the spindle, material properties of the
spindle and radial stiffness of the angular contact ball
bearings. Static deflection analysis of the spindle
assembly will be carried out in ANSYS by considering the
appropriate radial cutting force at the nose end of the
spindle assembly, material properties of the spindle and
radial stiffness of the angular contact ball bearings.
Compare static analysis results with theoretical values,
from that we can take optimum bearing arrangement for
dynamic analysis. Dynamic Modal analysis of different
spindle assemblies will be carried out using ANSYS Work
Bench software to obtain the natural frequencies and
different mode shape at different speed of the milling
spindle and frequency response function. Finally, the
optimum design of the spindle would be selected on the
results of analysis and basis on the results fabrication
will be done.
3. COMPONENTS OF THE SPINDLE
3.1 Parts and materials of the spindle assembly
Milling spindles usually rotate at high speeds. In
integrated motor spindle design, selection of motor
becomes the main factor. The motor for the spindle can
be selected on the basis of torque and speed
requirements, type of cooling arrangement, dimensions
of the motor, etc. Angular contact ball bearings are
generally preferred for milling spindles. The bearings
are preloaded by means of an adjustable locknut. An
encoder is required for sensing the spindle speed and
spindle position. An integrated motor spindle assembly
is shown in the fig. 3.1.
Fig. 3.1 Integrated motor spindle assembly
Material selection is a matter of quality and cost. The
properties of the material must be adequate to meet the
design requirements and service conditions. The list of
the major parts and its materials of the spindle assembly
is listed in the table 3.1.

Table 3.1 List of parts of spindle assembly
3.1.1. Spindle main housing: As the name indicates it is
the outer most cover, or it is casing surrounded to the all
parts of the assembly. It is made up of Spheroidal
Graphite Iron to obtain better strength and toughness
for good pressure tightness and can be welded.
Applications of SG: Three jaw and four jaws chucks, gear
vices, cutter body and handles etc. through the holes
coolant will be enters into the cooling jacket and helps
the stator and rotor for cooling.
Fig. 3.2 Spindle Housing
3.1.2 Spindle shaft: This is the rotating part of the
assembly, to which cutting tool is directly attached. The
rotor is integrated part of the shaft and angular contact
ball bearings are used to support the spindle shaft. It is
made of En-24 Steel to get a high wear resistance and
strength, its composition are Steel, 0.4% Carbon and .6%
Manganese. Applications En-24: heavy duty axels, shafts,
heavy duty gears, and connecting rods, etc.
Fig. 3.3 Spindle Shaft and Bearing Housing
3.1.3 Bearing housing: As the name indicates it covers
the bearings and holds the bearings. It is made of En-8
medium carbon Steel with hardness range 180-207 HB,
to get better wear resistance and good tensile strength.
Applications of En8: housing, keys, shafts, and gears, etc.
3.2 Angular contact bearing features: Angular contact
bearings are most commonly used today in very high
speed spindle designs since they provides, High
precision, Increases capacity of load carrying, Easily
metal cutting spindle can achieve required speed. The
contact angles are 00, 150, 250, 600, the lower the contact
angle, the larger the radial load carrying capacity, the
higher the contact angle the higher the axial loading
capacity figure shows the bearing contact angles.
Fig. 3.4 Ball Bearings with Contact Angles
150- used when loading is primarily radial; for very high
speed applications. 25º - used when loading is primarily
axial. 60º - highest axial stiffness; used in ball screw
support bearings.
3.3 Bearing Preload
In a few applications, the bearings are given an initial
burden or load; this implies that the bearings internal
clearance is negative before operation. This is called
"preload" and is regularly connected to angular contact
ball bearings and tapered roller bearings. There are 3
types preloaded occurs they are - Light preloaded
bearing: These are designed to allow maximum speed
and lower stiffness.
Heavy preload bearing: This provides high stiffness at
low speed, angular contact bearings used.
Medium preload: This gives medium stiffness at
medium speed.
3.3.1 Purpose of preload
Rigidity of the bearing increases, The bearing frequency
increases and becomes suitable for high-speed rotation.
Shaft run out is suppressed; rotation and position
precision is enhanced. Vibration and noise are
controlled. Fretting produced by external vibration is
prevented. For this project we have selected NSK
bearings, with back to back arrangement, Mounting two
bearings back-to-back provides a moderately stiff
bearing configuration, which can also accommodate
tilting moments, when the bearing configuration is back-
to-back, than the loading projection lines diverge
Part
number
Part name Material
1 Spindle main housing SGIron 500/7
2 Spindle shaft En-24
3 Bearing housing En-8
4 Front cover En-8
5 Front labyrinth En-8
6 Bearing spacers En-24
7 Spring housing En-8
8 Rear labyrinth En-8
9 Spring loaded spacer En-8
10
Encoder mounting
plate
C45
11 Drawbar En-24

towards the bearing axis. Axial loads in both directions
can be accommodated, but only by one bearing in each
direction.
3.4 Selection of Bearing Arrangements
For this project we have selected three different bearing
arrangements with different bearing stiffness, they are
as shown below. Depending on the shaft length and
bearing spread distance, two single row tapers or two
couple of angular contact ball bearings mounted face-to-
face or back-to-back can be used.
Bearing arrangement 1
Fig. 3.5 Bearing Arrangement1 with Span Length 293.5 mm.
Fig. 3.5 shows the bearing arrangement 1, having its
span length 293.5mm and overhanging length 50mm. In
this arrangement there are two sets of bearings are
arranged as quadruplet back-to-back (DBTT) at the front
separated by a spacer and the rear end of the spindle is
provided with one set of bearings as back-to-back (DB)
mounting arrangement. With this arrangement the
bearings will be able to take loads from both directions
axial and radial with high stiffness and high speed.
Fig. 3.6 Bearing Arrangement 2 with Span Length 295 mm
Fig. 3.6 shows the bearing arrangement 2, having span
length 295 mm and overhanging length 68.5mm. In this
arrangement one set of bearings are used at the front
and rear end of the spindle with back to back arrange.
The rear end of the spindle is supported by one set of
bearings arranged in back-to-back (DB) fashion.
Fig. 3.7 Bearing Arrangement 3 with Span Length 331 mm
Fig. 3.7 shows bearing arrangement 3, with span length
331 mm and having span length 331 mm and
overhanging length 57 mm. span length is distance
between front and rear bearing, overhanging length is
front and nose. In this arrangement one set of bearings is
arranged at the front and rear in back-to-back (DB)
fashion, on bearing medium preload is applied. The
bearings are separated by a spacer. The bearings will be
able to carry loads from both the directions. The
dimensions of the bearings used for arrangement one,
two and three are tabulated in the table 3.10, previous
chapter.
4. THEORETICAL CALCULATIONS OF CUTTING
FORCES AND DEFLECTIONS
4.1 THEORETICAL CUTTING FORCES CALCULATIONS
To calculate the theoretical cutting forces acting on the
spindle nose for different machining process, CMTI
machine tool design data hand book is referred. Forces
mainly depend on speed and feed factors. While
analyzing cutting tool spindle mainly concentrate on the
nose of the spindle assembly.
4.1.1 Face Milling
Diameter of the work piece, b = 60 mm
No. of teeth, Z = 6, Diameter of the cutter, D = 80 mm
Depth of cut, t = 2 mm, Cutting speed, v = 80 m/min
(Table 276, page 655 CMTI hand book), Revolutions per
minute, n = = 318.3 rpm, Feed per
tooth, Sz = 0.1 mm, Feed per minute, Sm= Sz × z × n = 0.1
× 6 × 318.3 = 191 mm/min, Metal removal rate, Q
= = 22.9 cm3/min
Approach angle, x = 30˚, Average chip thickness, as
=
–
= 0.045 mm
Work material considered is steel having hardness of
100 HB and average chip thickness of 0.045 mm. Unit
power, U = 0.065 kW/cm3/min (Table 269, page 649
CMTI hand book).Considering flank wear = 0.2 mm.
Flank wear Correction factor, Kh = 1.1 for flank wear 0.2
mm (Table 270, page 650 CMTI hand book). Radial rake
angle, ɣ = -5˚; Radial rake angle Correction factor, Kɣ =
1.21 (Table 271, page 650 CMTI hand book). Power at

the spindle, N = U × Kh × Kɣ × Q = 0.065 × 1.1 × 1.21 ×
22.9 = 1.98 kW. Tangential cutting force, Pz = =
151.47kgf = 1485.9 N, Radial cutting force, Py = 0.35 × Pz
= 520 N, Axial cutting force, Px = 0.55 × Pz = 817.3 N
Torque at the spindle, Ts = = 6.06kgf-m =59.5 N-m.
4.1.2 End milling
Diameter of the cutter, D =20 mm, No. of teeth, Z =4
Width of cut, b =23 mm, Depth of cut, t =3 mm
Cutting speed, v =80 m/min (Table 276, page 655 CMTI
hand book), Revolutions per minute, n =
= 1274 rpm, Feed per tooth, Sz 0.1 mm
Feed per minute, Sm= Sz × z × n = 0.1 × 6 × 1274 = 509.6
mm/min, Metal removal rate, =
= 35.162 cm3/min, Average chip thickness,
as = = 0.038 mm.
Work material considered is steel having hardness of
100 HB. Therefore for hardness value of 100 HB and
average chip thickness of 0.045 mm. Unit power,
0.063 kW/cm3/min (Table 269, page 649 CMTI hand
book). Considering flank wear = 0.2 mm. Flank wear
Correction factor, Kh = 1.1 for flank wear 0.2 mm (Table
270, page 650 CMTI hand book). Radial rake angle, ɣ = -
5˚. Radial rake angle Correction factor, Kɣ= 1.21 (Table
271, page 650 CMTI hand book). Power at the spindle,
= U × Kh × Kɣ × Q = 0.063 × 1.1 × 1.21 × 35.162 = 2.95 kW
Tangential cutting force, Pz = = 225.675 kgf =
2213.87 N. Radial cutting force, Py = 0.55 × Pz = 1218 N.
Axial cutting force,Px= 0.25 × Pz = 553.5 N. Torque at the
spindle, Ts = = 2.25 kgf.m = 22.15 N
4.2 THEORETICAL CALCULATION OF SPINDLE
DEFLECTION
The total deflection of the spindle is due to the elastic
deformation of the spindle and the elastic deformation of
the bearings and neglecting the effects of housing
deformation on the spindle. The t0tal deflection of the
bearing system can be calculated by using below given
formula. Equation 4.1 indicates deflection formula, for
finding nose deflection of the spindle assembly.
[ ( ) ( ) ( )]
……..4.1
 Bearing Arrangement-1
Fig. 4.1 Bearing Arrangement1 with Radial Load 1218 N
Where,
a = Length of overhang in mm = 50 mm, L = Bearing span
in mm = 293.5 mm, E =Young's modulus of Spindle
material in N/mm2 = 210000 N/mm2, P = Radial force in
N = 1218 N for End Milling, SA = Stiffness of the front
bearing N/mm = 1248000 N/mm, SB = Stiffness of the
rear bearing in N/mm = 540000 N/mm, IL = Second
moment of area of the shaft at the span in mm4 =
605113.53 mm4, Ia = Second moment of area of the shaft
at the overhang in mm4 = 780010.53 mm4
By substituting all above data in the given 4.1 equation,
then the deflection (δ) of the spindle nose is given as
below
For end milling Radial load P=1218 N
δ = 4.10×10-3 mm or 4.10μm. For Face Milling
tangential force, P = 1486 N and Nose deflection is δ
= 4.96×10-3 mm or 4.96μm.
Similarly, calculations for bearing arrangement two and
three are as below
 Bearing arrangement -2
Bearing arrangement 2 is shown in fig. 4.2.
Fig. 4.2.Bearing Arrangement 2 with Radial Load 1218 N
Where, a = 68.5 mm, L = 295 mm, E= 210000 N/mm2, P =
1218 N, SA = 955400 N/mm, SB = 612000 N/mm, IL =
600195.7 mm4, Ia= 774803.56 mm4
By substituting the above values in spindle deflection
equation, the magnitude of deflection δ = 7.21 × 10-3
mm or δ = 7.21 µm for end milling, For Face Milling, P
= 1480 N. Deflection δ = 8.90 × 10-3 mm or δ = 8.90
µm.

 Bearing arrangement -3
Bearing arrangement 3 is shown in fig. 4.3
Fig. 4.3 Bearing Arrangement 3 with Radial Load 1218,
Where, a = 57 mm, L = 331 mm, E= 210000 N/mm2, P =
1218 N, SA= 702500 N/mm, SB= 540000 N/mm, IL=
598991.8 mm4 Ia= 1183653.15 mm4. By substituting the
above values in spindle deflection equation 4.1,the
magnitude of deflection, for end milling, δ = 6.12 × 10-3
mm or δ = 6.12 µm. For Face Milling P = 1480 N,
Deformation δ = 7.50 × 10-3 mm or δ = 7.50 µm.
From the NSK bearing catalog, we have taken stiffness
values for different bearing arrangements. The table 4.1
shows front and rear bearings stiffness values for
different bearing arrangements.
Table 4.1 Front and Rear Bearing Stiffness values
All the calculated theoretical values are tabulated in
table 4.2; the table shows tangential load, radial load,
axial load, torque and deflections for different operations
and bearing arrangements respectively.
Table 4.2 Theoretical Results summary
5. STATIC ANALYSIS OF SPINDLE ASSEMBLY
5.1 Introduction Static deflection analysis determines
the impacts of steady state loading conditions on body or
structure while neglecting inertia and damping effects,
such as those caused by transient or time-varying loads.
Static analysis calculates the displacements, stresses,
strains, and forces in structures or components caused
by loads that do not include inertia and damping effects.
An assembly of motorized spindle is consists of a more
numbers of different parts and subassemblies, lots of
which are complex. The spindle can be modeled as a
shaft, supported at each end by bearing sets. This
representation can be seen in the fig. 5.1. Instead of
bearing we have taken spring element while analyzing,
stiffness of the spring is as same as the bearing stiffness.
Fig. 5.1 Equivalent Model of Spindle Assembly
5.1.1 Bearing arrangement models
The figure show different bearing arrangement 3-d
models which is made through Solid Edge /Solid works
modeling software, it consists of couple of NSK bearing
sets with back to back arrangement as shown and front
bearing separated by spacer for arrangement 1&3. With
this arrangement the bearings will be able to take loads
from both directions, by using high stiffness bearings at
the front better rigidity is provided with the proper
preloading. We have taken medium bearing preload for
analysis purpose.
Fig. 5.2 Bearing Arrangement 3-D Model 1
Bearing
arrangements
Front bearing
stiffness
(N/mm)
Rear bearing
stiffness
(N/mm)
1 1248000 540000
2 9554000 612000
3 702500 540000
Oper
ation
Tange
ntial
Load
(N)
Radial
Load
(N)
Axial
Load
(N)
Torq
ue
(Nm)
Deflection (µm)
1 2 3
Face
Milli
ng
1486 520 817 59.5 4.9 8.9 7.5
End
milli
ng
2214 1218 553 22.2 4.1 7.2 6.2

5.2 Introduction to finite element analysis
5.2.1 Mesh Elements and Constrained model
The dividing the given model into number of finite
elements is known as meshing, as shown in diagram. For
this four/ten nodes tetrahedron elements are used
because it has aerodynamic shape or structure. For high
accuracy, elements should be very fine or smaller and
smaller. A tetrahedron has four vertices, six edges, and is
bounded by four triangular faces; it is a 3-d mesh
element. For this project 5 mm element size given to the
model. Any analysis system should need boundary
conditions for analysis purpose, boundary conditions
involves Load, material properties, displacement,
gravitational load, thermal or fluid load, etc.
Fig. 5.5 4 node and 10 node tetrahedron
The fig. 5.6 shows meshed and constrained model.
Fig. 5.6 Meshed and constrained 3-D Model
While applying constraints, take a spring element whose
stiffness is same as that of bearings used and add body to
ground option. In ANSYS APDL give the degrees of
freedom as UX, UY, UZ=0 and ROTX, ROTY, ROTZ=1 and
for different bearing arrangements real constants are
given as spring constant values they are mentioned in
table 4.1, for front and rear springs respectively. Along
with following material properties also applied to the
model to accomplish analysis. After meshed the
following mesh statistics are obtained as shown in the
table 5.1.
Table 5.1 Material Properties and Mesh Statistics
5.2.2 Loads applied
For this project, calculated load values i.e. radial load is
1218 N for end milling and tangential load 1486 N for
face milling applied to different bearing arrangements.
The load is applied at nose of the spindle assembly as
shown in the fig. 5.7 respectively, instead of bearings,
spring elements are used for supporting the spindle
while analyzing.
Fig. 5.7 Radial and Tangential Load Applied Model
5.3 Results
The static stress and nose deflection analysis results of
end milling and face milling operations of the spindle
assembly are as shown in the following figures. For this
analysis radial and tangential load is applied to the end
and face milling respectively.
5.3.1 End milling results:
Fig. 5.8 Deflection at the Nose for Bearing Arrangement 1
Fig. 5.9 Deflection at the Nose for Bearing Arrangement 2
Arrangements 1 2 3
Nodes 122670 112387 117792
Elements 80109 73025 76335
Material
properties
Young’s
modulus
(MPa)
Density
(kg/mm3 )
Poison’s
ratio
210×103 7.82×10-6 0.3

Fig.5.10 Deflection at Nose for Bearing Arrangement 3
The all above diagrams shows end milling spindle nose
deflection analysis results done in the ANSYS work
bench 14.5 version of radial load carried 1218 N along
the y-direction. The red color indicates maximum
deformation and blue color shows least deformations on
the spindle. The red color is appearing at the spindle
nose i.e. the maximum deformation is available at the
nose tip as shown in the figure, here instead of bearing
spring is taken for analysis purpose having same
stiffness as bearing material. In the above diagram
bearing arrangement 1 is more stiffer than the other two
bearing arrangement because its deflection is smaller
than the other two arrangements. The below table
indicates analysis results for end milling operation.
Table 5.2 ANSYS Results for End Milling.
Bearing
Arrangements
End milling
deformations (µm)
1 5.84
2 8.48
3 7.60
5.3.2 Face milling results: For this analysis we need to
take tangential load as per the analytical calculations
P=1486 N. and apply at the nose of the spindle
assembly.
Fig. 5.11 Nose Deflection for Bearing Arrangement 1
Fig. 5.12 Nose Deflection for Bearing Arrangement 2
Fig. 5.13 Nose Deflection for Bearing Arrangement3
Similar to end milling, face milling analysis also carried
out in ANSYS work bench, here tangential force is
applied to the spindle assembly. The spring is used for
analysis purpose instead of bearing with same stiffness.
Here four springs is attached to the spindle for each
bearing component and bearing stiffness is equally
divided into four springs. In these bearing arrangements
red colour shows maximum deformation of the spindle
nose, blue colour shows minimum deformation. The
arrangement 1 is having least deformation/deflection so
that it high stiffer than the other bearing arrangements.
The table indicates analysis results for face milling
spindle.
Table 5.3 ANSYS Result of Face Milling.
Bearing
Arrangements
Face milling
deformations (µm)
1 05.80
2 10.65
3 09.53
5.4 Comparison of Analytical and Numerical Spindle
Deflection and spindle stiffness
The spindle nose deflection/deformation is mainly
depends on the stiffness of the bearing used. If the
stiffness is high deflection is less and vice versa. Here we
have analysed three different bearing arrangements with
different stiffness and span length as discussed in the
previous pages. The comparison of analytical/theoretical
and numerical/ANSYS results for end milling and face
milling is as shown in the table. Comparison results are
obtained as below.

Table 5.4 Spindle Nose Deflection Comparison Results.
Operations
Bearing
arrangements
Theoretical ANSYS
End
milling
1 4.10 5.84
2 7.21 8.48
3 6.12 7.50
Face
milling
1 4.96 5.80
2 8.90 10.65
3 7.50 9.53
Rigidity of the spindle is mainly depends on stiffness of
the spindle, Spindle stiffness results for end milling and
face milling, based on deflection and load can be
calculated as follows. The spindle stiffness can be
calculated by using following equation 5.3(a).
That is (N/μm)……… 5.3(a)
Table 5.5 Spindle Stiffness Results
Operations
Bearing
Arrangeme
nts
Theoreti
cal
ANSYS
End milling
stiffness
(N/μm)
1 297.07 210.05
2 168.93 143.63
3 199.01 160.26
Face milling
stiffness
( N/μm)
1 299.60 256.20
2 165.85 139.53
3 198.13 155.92
6. MODAL ANALYSIS OF SPINDLE ASSEMBLY
6.1 Introduction
Modal analysis is the process of determining all the
modal parameters, which are then sufficient for
formulating a mathematical dynamic model. Most
practical noise and vibration issues are related to
resonance phenomena, where the operational strengths
energize one or more vibration modes. The vibration
modes represent the inherent dynamic properties of a
free structure (means, there are no forces acting on any
structure or component). Modes are associated with
structural resonance, resonance is defined as when the
external force acting on a body then, external excitation
frequency is equal to natural frequency of the system or
model is known as resonance. Resonant vibration is
caused by collaboration between the inertial and flexible
or elastic properties of the materials inside a structure. A
typical and valuable method for doing this is to define its
modes of vibration. Every mode is characterized by a
modal frequency, modal damping, and a mode shapes.
Whenever a system is subjected to an external force and
then set it to free, it undergoes natural vibrations or free
vibrations. The frequency of these free vibrations is
called as “natural frequency”. At resonant conditions
there is a maximum energy transfer between the system
and the surrounding. Modes shapes are inherent
properties of the material or structure. Modes are mainly
depends on material properties such as density,
stiffness, damping constants, inertia effect and
gyroscopic effect, etc. mode shapes are unique.
6.2 Finite Element Model
Finite Element Method is a numerical technique for
finding approximate solutions to constrained model. The
model which is creates in modeling software for analysis
along with given constraints to check the behavior of the
object is known as finite element model. The model
divided into number of equal parts or finite elements is
called meshing (descritization). For this analysis we have
taken four/ten nodes tetrahedron mesh elements of
element size 5 mm and fixed-fixed constrained as shown
in fig. 6.1. Body to ground i.e. fixed-fixed spring elements
are used for analysis purpose and no loads are applied.
The shape of the tetrahedron mesh elements are shown
previous chapter fig. 5.5.
Fig. 6.1 Finite Element Model for Modal Analysis

6.3 Modal Analysis Results
 Bearing arrangement 1
Fig. 6.2 Mode Shape 1 at Natural Frequency 1043.7Hz
Fig. 6.3 Mode Shape 2 at Natural Frequency 1830.8 Hz
The above diagrams shows different mode shapes at
different natural frequencies of spindle shaft for bearing
arrangement 1, mode shapes mainly defends on density
of the material, boundary conditions, stiffness of the
shaft etc. the following table shows natural frequencies
and mode shapes of the spindle.
Table 6.1 Bearing Arrangement-1 Mode Shapes and
Natural Frequencies
Number of
Modes
Natural
Frequency (Hz)
Mode Shapes
1 1043.7 Bending
2 1830.8 Bending
3 2657.8 Bending
4 3279.2 Torsion
5 3484.8 Buckling
6 5337.4 Elongation

Fig. 6.11Mode Shape 4 at Natural Frequency 3575.4 Hz
Similarly, bearing arrangement 2 was carried out, and
we have got six natural frequencies and its shapes are
listed in table 6.2.
Natural Frequencies
Mode No.
Natural frequency
(Hz)
Mode Shapes
1 1122.4 Bending
2 1359.8 Bending
3 2006.4 Bending
4 3575.4 Torsion
5 4252.9 Buckling
6 6047.9 Compression

Similarly, for bearing arrangement 3, six numbers of
mode shapes and natural frequencies are taken and
values are tabulated in the table.
Natural Frequencies
Mode no.
Natural frequency
(Hz)
Mode Shapes
1 858.76 Bending
2 1512.9 Bending
3 1872.2 Bending
4 3224.2 Torsion
5 3375.6 Buckling
6 5488.9 Elongation
From the above modal analysis results, no one frequency
is near to the natural frequency of the system so that
resonance will not be occurs. The consolidate frequency
table 6.4 is given below.
Table 6.4 Results Summary of Natural Frequencies
Mode
No.
1 2 3 4 5 6
Bearing
arrange
ment-1
(Hz)
1043 1830 2657 3279 3484 5337
Bearing
arrange
ment-2
(Hz)
1122 1360 2006 3575 4253 6048
Bearing
arrange
ment-3
(Hz)
858 1513 1872 3224 3375 5489
6.4 Final Assembled Milling Spindle
After completion of spindle nose deflection and dynamic
modal analysis, we known that bearing arrangement-1 is
least deflection and high stiffness spindle, so that CNC
milling spindle assembly is completed/prepared using
bearing arrangement-1, as shown in the fig.6.20
Fig. 6.20 Assembled View of BT – 40 Spindle
Fig. 6.21 Cross Sectional View of Assembled BT – 40
Spindle

7. CONCLUSION
7.1 Conclusions:
The below conclusions can be taken from this project
work: The BT-40 CNC Milling spindle has been designed
to satisfy the required specifications. The design is
optimized by proper selection of spindle components
and simplifying the design of the spindle parts from the
machining and analysis point of view. The spindle
deflection is calculated theoretically for three different
bearing arrangements with different bearing stiffness
and span length. The static stiffness analysis of spindle
assembly is carried out using ANSYS work bench 14.5 to
find out the spindle nose deflection using spring
element. There is a good correlation between the
theoretical and ANSYS spindle deflection results. The
deflection values obtained for bearing arrangement 1
with NSK bearing configuration is lower compared to
that of other bearing arrangements. The bearings with
higher stiffness should be located at the front to
minimize the deflection, hence bearing arrangement1 is
optimized. The deflection and stiffness values obtained
for this configuration is given in the following Table 7.1.
Table 7.1 Deflection and Stiffness Values for Optimized
Configuration
Theoretical ANSYS
Deflection
(μm)
Stiffness
(N/μm)
Deflection
(μm)
Stiffness
(N/μm)
4.10 297.07 5.84 210.05
The modal analysis is carried out using ANSYS work
bench-14.5 software to obtain the natural frequencies
and the mode shapes for the optimized design, these are
the frequency values which should be avoided during
operation which will cause resonance.
Table 7.2 Modal Analysis Results for Optimized
Configuration
Mode 01 02 03 04 05 06
Frequ
ency
(Hz)
1040 1831 2658 3279 3484 5337
REFERENCES
[1] Deping Liu and Hang Zhang, “Finite Element Analysis
of High-Speed M0torized Spindle Based on ANSYS”,
Journals of theoretical and applied mechanics, 2011.
[2] Tony L. Schmitz, Nagaraj Arakere, Chi-Hungcheng,
“Response Rotor Dynamics of High-Speed Machine Tool
Spindle”, Journals papers on Machinetool applications,
2011.
[3] Syath Abuthakeer.S, “Dynamic characteristics analysis
of high speed motorized spindle”, Journal papers on
Machine tool applications, 2011.
[4] Jun Wang, Cheog Yao, “Modeling and Modal Analysis
of Tool Holder-Spindle Assembly on CNC Milling Machine
Using FEA”, Journal papers on Machine tool applications,
2012.
[5] Yuzhongcao,Y, “Altintas modeling of spindle-bearing
and machine tool systems for virtual simulation of milling
operations”, Journal papers on Machine tool applications,
2010
[6] Se0n M. Han, Haym Benaroya and Timothy Wei,
“Dynamics of transversely vibrating beams using four
engineering theories”, journal papers on modal analysis,
1999.
[7] Momir Šarenac , Mechanical Faculty University of
Srpsko Sarajevo, “Stiffness 0f Machine Tooll Spindle as a
Main Factor for Treatment Accuracy “Mechanical
Engineering Vol.1, No 6, 1999 pp. 665 – 674.
[8] Mohanram P.V, “Dynamic and thermal analysis of high
speed motorized spindle”, Journal papers on Machine tool
applications, 2011.
[9] Harry peck, “Designing for manufacturing”, pitman
Publishing Corporation, 1973.
[10] CMTI Machine tool design handbook, Tata McGraw-
Hill, 1982.
[11] NSK Super Precision Bearing catalogue, NSK make.
BIOGRAPHIES
Author name: BASAVARAJ
M. Tech, Machine Design.
Working at Central University of
Karnataka as assistant Professor,
Engineering Department.

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