ANALYSIS OF CNC LATHE SPINDLE FOR MAXIMUM CUTTING FORCE CONDITION AND BEARING LIFE

International Journal of Innovative Research in Advanced Engineering (IJIRAE) ISSN: 2349-2163
Volume 1 Issue 6 (July 2014) http://ijirae.com
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© 2014, IJIRAE- All Rights Reserved Page - 346
ANALYSIS OF CNC LATHE SPINDLE FOR MAXIMUM
CUTTING FORCE CONDITION AND BEARING LIFE
Santosh Arali1
, V.V.Kulkarni2
1
PG Student, Machine Design, Gogte Institute of Technology Belgaum
2
Asst.Professor, Department of Mechanical Engineering, Gogte Institute of Technology Belgaum
Abstract-The present CNC machine structures consist of spindle system which plays a relating to the quality of the
final product and the overall productivity and efficiency of the machine tool itself. The spindle of a CNC lathe
machine, which is rotated by the main motor, holds the cutting tool, which cuts the work piece, so that the cutting
forces are generated which effects the spindle accuracy directly. The forces which are affecting the CNC machine tool
spindle are tangential force (Ft), feed force (Fc), radial force (Fr) and will be estimated. Based on maximum cutting
force incurred the analysis will be carried out. The main objective is to find the static, fatigue analysis of spindle
structure for maximum cutting force condition and predicting life of bearings. From static analysis stress and
deformation of the spindle can be found. Stress obtained from the stress analysis is less than the yield strength of the
material and deformation of the spindle is very less which can be neglected. Equivalent alternating stress, factor of
safety and life of the spindle is found by fatigue analysis and which results are closely matches with the analytical
value.
KEY WORDS: CNC, Spindle, Bearings, Cutting Forces, Static and Fatigue analysis, Code Generation.
I. INTRODUCTION
Machine tool spindle is the most important mechanical component in removing metal during machining
operations. Spindle is a rotating axis of the machine, which frequently used has a shaft at its heart. The shaft itself is
called spindle, it is including three bearing in the front and two bearings in the rear of the spindle. Machine tool spindles
lead to unstable chatter vibrations, cutting forces and uneven tensions in the belt and pulleys. This thesis presents static
and fatigue analysis by considering cutting forces and tensions in the pulleys. CNC machining is an important technology
increasing productivity and reducing production costs. Compared to conventional machine spindles, motorized spindles
are equipped with built in motors introduces huge amount of heat into the spindle system as well as additional mass to the
spindle shaft. Depending on the machining processes, the tool is fixed in the tool post and the work piece is held on the
chuck of a typical lathe structure. The relative motion is achieved by the movements parallel to the three spatial axes.
This can be achieved by the, axial movements are along the screws, rack and pinion arrangements, linear guide ways and
bearings etc. The machine is made up of heavy steel material and iron parts. The base of the machine is rigid and usually
is of cast iron. The spindle of the machine is hollow and material is 20MnCr5.
Fig. 1 Bearing arrangement in CNC lathe
II.THEORETICAL ANALYSIS
Theoretical analysis involves the calculations of cutting forces and its effect on the CNC lathe spindle, tensions in the
belt, and deformations of the spindle by using Macaulay’s Method and equivalent alternating stress, safety of factor by
using Modified Goodman method. Following table shows the material properties of concern.
Table 1 Material properties
Physical Properties Values
Material of the Spindle 20MnCr5
Ultimate Strength ( ult) 682 MPa (N/mm2
)

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A. Total Deformation Using Macaulay’s Method of spindle
Fig 2 Loading condition of lathe spindle
EI = -654.9(x-120)+2451.2(x-156)−3511.6(x-240) +1715.3(x-356) (1)
Final equation to find deformation is obtained from the above generalized equation as follows:
EI y = 723902560−4607760x−654.9
( )
+2451.2
( )
−3511.6
( )
+1751.2
( )
Ymax=0.0066908 mm
B. Fatigue Analysis
Distortion energy theory is used when the factor of safety is to be held in close values and the cause of failure of
the component is being investigated. According to the distortion energy theory,
eq= ( + 3( ) (2)
Where,
eq= Equivalent stress (MPa) , bmax= Bending Stress(MPa) and max= Max shear stress(MPa)
In this section, Von-Mises (equivalent) stress ( ), factor of safety (fs) are calculated. Initially, maximum and
minimum bending moments at different points are also calculated as follows with respect to Fig 1.2.Maximumbending
moment (Mb)max= 198.91 × 103
N mm, maximum bending moment (M)bmin= 48.02 × 103
N mm, maximum torque
transmitted by the spindle (Mt)max= 71.6 × 103
N mm and minimum torque transmitted by the spindle (Mt)min= 17.9 ×
103
N mm
I. “Mean and Amplitude Bending Moments”
Mean bending moment [Mb]m and amplitude bending moment [Mb]a are obtained by the following equations:
(Mb) m= ½ ((Mb) max + (Mb) min) (3)
=123.46 × 103
N mm
(Mb) a = ½ ((Mb) max- ((Mb) max (4)
=75.44 ×103
N mm
II. “Mean and Amplitude Stresses”
Mean Stress [σxm] and Amplitude Stress [σxa] are obtained by the following equations:
σxm =
( )
π( )
× (5)
Where, (Mb)m = Mean stress(MPa), do = Outer diameter of spindle in mm, di = Inner diameter of the spindle in mm.
Yield Strength (Syt) 375 MPa (N/mm2
)
Young’s Modulus (E) 190×103
N/mm2
Poisson’s Ratio ( ) 0.27-0.3
Density ( ) 8030 kg/m3

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σxm = 7.046 N/mm2
σxa =
( )
π( )
× (6)
σxa = 4.28 N/mm2
III.” Mean and Amplitude Shear Stresses”
Mean shear stress [τxym] and amplitude shear stress [ τxya] are obtained by the following equations:
xym =
( )
π( )
× (7)
xya =1.021 N/mm2
From Von-Mises theorem equation we know that,
eq = ( ) + 3( ) Where, kf= Fatigue stress concentration factotr = 3 (8)
= (7.046 × 3) + 3(4.08 × 3)
= 30 N /mm2
Since m= eq = 30 N /mm2
, that is equivalent Von-Mises stress is 30 N /mm2
IV. “Alternating Stress”
Alternating Stress (σa) are obtained by the following equation:
σa = ( × ) + 3( × ) (9)
= (4.28 × 3) + 3(1.021 × 3)
σa = 14 N / mm2
tan = and also, tan = (10)
Where, Sa= Alternating strength in N/mm2
, Sm= Mean strength in N/mm2
tan = 0.4667
= 25.01 ≅ 25 degrees
V. “Endurance Strength”
Endurance Strength [Se] are obtained by the following equation:
Se =Ka× Kb ×Kc× Kd×Se’ = 0.8 ×0.75 ×0.897 ×0.4347 ×Se’ (11)
Where, Se’= Endurance limit stress of a rotating beam specimen subjected to reversed bending stress(N/mm2
), Se=
Endurance limit stress (N/mm2)
, Ka = surface finish factor, For machined or cold rolled process the value of the Ka =
0.8, Kb = size factor, diameter > 50 the value of the Kb = 0.75, Kc=reliable factor, For 90% reliability, the value of the
Kc= 0.897, Kd = modifying factor Kd = modifying factor is given by Kd= = 0.4347, Se’=0.5 Sut (for steel) = 0.5 ×
682.
Se’ = 341 N/ mm2
Se = 79.778 N / mm2
From modified Goodman method,
+ =1 where, Where, Sy = Yield tensile strength (N/mm2
), Se = Modified Endurance limit (N/mm2
), put all above
values, (12)
.
.
+ =1
Sm =115 N / mm2
Sa =55.28 N / mm2

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VI. “Factor of safety (fs)”
Factor of safety (fs) are obtained by the following equation:
fs= =
.
= 3.9 (13)
III FATIGUE AND STATIC ANALYSIS BY FEA
A. Static Analysis of the Spindle
Fig. 3 Meshed spindle component in Ansys workbench Fig. 4 Boundary conditions of spindle in Ansys workbench
Two loads for the spindle are applied on the Fz negative direction shown in fig. 4. One load is tensions in the belt and
another one is maximum cutting force during machining. One torque is applied on end of the spindle in the clockwise
direction. The meshed CNC spindle component is shown in above fig. 3.
Fig.5 Total deformation of the spindle Fig.6 Von-Mises stress on spindle
Table 2 Deformation comparison between theoretical and fem
Approach Theoretical FEM % Error
Maximum deflection of the
spindle (in mm)
0.0066908 0.0066784 0.1853
From the above table 2 it is conclude that analytical method value is very nearer to the value of FEM, in terms of
error there is only 0.1853% error between theoretical and FEM value. From the ANSYS result shown in, Fig 7 (stress)
and it is confirmed that the maximum (Von-mises) stress is 25.985 N/mm2
, which is in the limit of yield strength of
20MnCr5 steel 375 N/mm2
. Hence the design of the spindle is safe. From the ANSYS result shown in, Fig.8 (stress)

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and it is confirmed that the maximum (Von-mises) stress is 25.985 N/mm2
, which is in the limit of yield strength of
20MnCr5 steel 375 N/mm2
. Hence the design of the spindle is safe. It is clear from the fig.8 the fatigue factor of safety
calculated from theoretical is 3.9 and by FEA approach 3.3173 again these values are approximately same.
Fig.7 Equivalent alternating stress on spindle Fig.8 Factor of safety of spindle by FEA
B.Comparisons of theoretical and FEM
Table 3 Fatigue factors comparisons between theoretical and fem
Theoretical Approach FEM Approach Percentage Error
σeq = 30 N/mm2
σeq = 25.98 N/mm2
13.4%
fs = 3.9 fs = 3.3173 14.94%
Infinite life Infinite life
From above Table 3 It is clear that, the fatigue analysis of CNC lathe spindle gives close results by analytical and FEA
approach. From optimization point of view the FEA analysis is very useful tool. Also, the value of fatigue factor of
safety theoretical and FEM approach are 3.9 and 3.3173. Software used for fatigue analysis CATIA V5, ANSYS13
which gives moderate results.
IV CODE GENERATION TO CALCULATE LIFE OF THE BEARING

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Fig. 9 Layout of bearing configuration in C-programming
Comparisons of theoretical and code generation
Fig 4 Bearing life Comparisons between theoretical and code generation
Bearing type Theoretical Approach
C-Code
Approach
% Error
Front Bearing (Life in Hours) 15,586.37 15,556.92 0.1889
Rear Bearings (Life in Hours) 9198.7 9182.3 0.1782
V CONCLUSION
Usually spindles are mounted in antifriction bearings such spindles are found in several machine structures including
lathe, milling machine and all machine tools. The analysis has been carried out for CNC lathe with 7.5kW and spindle
speed of 4000 rpm. The total deformation, equivalent stress and factor of safety has been calculated. The fatigue life
prediction is performed based on finite element analysis and analytical Method. Using the modified Goodman method,
the fatigue life of the CNC lathe spindle has been predicted. This study will help to give information for the manufacturer
to improve the fatigue life of the CNC lathe shaft using FEA tools. It can help in reducing the cost, as well as
understanding better in which area stresses are more.
1. Static analysis showed that deformation is very small and approximately equal to theoretical values.
2. Von-Mises equivalent stress value by analytical approach 30 N/mm2
which are nearly same by using FEA
approach having difference of 13.4% in both results which is acceptable range.
3. The fatigue factor of safety calculated from theoretical is 3.9 and by FEA approach 3.3173 again these values
are approximately same.
4. The life of the front and rear bearings is 9198.7 and 15,586.3 hours.
ACKNOWLEDGEMENT
The author thanks Prof. Vivek V. Kulkarni, Asst. Professor, Department of Mechanical Engineering., KLS Gogte
Institute of Technology Belgaum, for his esteemed suggestions, sincere efforts and inspiration given in completing this
work. The author is also thankful to one and all to who directly or indirectly encouraged in completing this paper.
REFERENCES
[1] Osamu Maeda, Yuzhong Cao, “Expert Spindle Design”, Proc of International Journal of Machine Tool and
Manufacturer, August 24, 2007
[2] Chi-Wei Lin, Jay F Tu, Jou Kamman “An integrated thermo mechanical dynamic model to characterize motorized
machine tool spindles during very high speed rotation”, International Journal of Machine Tool and Manufacturer, 27
February 2006
[3] Dr. S. Shivakumar, Dr.Anupama N Kallol, Vishwanath Khadakbhavi, “analysis of lathe spindle using ansys”,
International Journal of Scientific & Engineering Research, Vol 4, pp 2229-5518, September-2013

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[4] Mr. Sahil, Mr. Jiten Saini “Fatigue and Modal Analysis of Connecting Rod under Different Loading Conditions”,
Proc of ISSN, pp 2277-9655
[5] Tobias Maier, Michael F. Zaeh, “Modelling of the Thermo mechanical Process Effects on Machine Tool Structures”,
Proc of CIRP Conference on Process Machine Interactions, 2012
[6] A.Erturk, H.N Ozguven, “Effect Analysis of bearing and interface dynamics on tool point FRF for chatter stability in
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Manufacturer, 27 February 2006

ANALYSIS OF CNC LATHE SPINDLE FOR MAXIMUM CUTTING FORCE CONDITION AND BEARING LIFE

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