Post on 31-Jan-2022
1 Copyright © 2014 by ASME
DESIGN AND ANALYSIS OF AN EXAMPLE LATHE SPINDLE
Rupal Vyasa Department of Mechanical Engineering V. G. Engineering College, Chandkheda
Ahmadabad, Gujarat, India
Raghu Echempati Department of Mechanical Engineering
Kettering University Flint, MI, U.S.A.
ABSTRACT This paper discusses the modeling and analysis of an
example medium speed medium precision lathe spindle. This
and few other similar topics have been assigned as term
projects in an introductory senior undergraduate/graduate level
finite element analysis course taught at Kettering University.
The experiences and the general feedback from the students of
the class show satisfactory organization of the course material
that includes modeling and analysis of real life examples.
With reference to the specific topic on design of machine
tool spindles, it is not a new area, however, it is generally
taught at the graduate and research levels. Use of modern
computational tools to perform iterative design and analysis
calculations of such spindles make the senior undergraduate
and/or graduate master students aware of the implications of
modeling a real life system using the 1D and 3D finite beam
elements and to validate those results by a CAE tool. Final
course projects such as this serve as a good learning tool to the
graduating engineers. Sample results obtained from various
CAE tools such as UG-NX 7.5 are presented in the paper and
discussed.
INTRODUCTION The work presented in this paper is based on the
unpublished thesis carried out by the first author [1]. A lot of
theoretical and experimental work has been done in the
machine tool design area since last several decades which
resulted in the development of modern high speed, high
precision machine tools [2 to 4]. However, many universities in
USA have dropped teaching a course on kinematics and
dynamics of machine tools. Due to the nature of the academic
calendar at our university, many mechanical engineering
students are exposed to either design of or use of machine tools
at their work places. Applying the knowledge gained in finite
element analysis course to real life applications such as this,
helps them appreciate the subject matter better. This paper
therefore discusses some technical details about the design and
analysis of an example lathe machine spindle and the
assessment of the learning outcomes from this and the other
similar final projects of this course. Math tools such as MatLab
and a variety of CAE tools such as NX I-DEAS, UG NX 7.5,
Solid Works and Autodesk have been extensively used by the
students of this class. Finite element formulation and solution
by direct stiffness method or by energy methods for 1D beam
element modeling along with the assessment results are
presented and discussed [5 to 7]. Validation of some of the
results by simple beam theory and through a Visual Basic
Program specially developed for this purpose is presented
briefly [1]. It is hoped the outcome of this paper may be
beneficial to the academic community and industry partners to
understand medium to high-speed machine tool spindle
designs.
The main function of the machine tool spindle are to center
and hold the work piece (turning) or cutting tool (drilling,
grinding, milling and boring) under the effects of weights and
cutting forces on one hand and driving forces and torque on the
other . Therefore, it fulfills two functions, i.e. it not only locates
the work piece or the tool respectively but also drives and
guides them with the required accuracy and stiffness in their
operational movements (rotation and sometimes axial feed
movement). There are several textbooks and research papers in
the machine tool design area, however, only a few are cited in
this paper with the understanding that this list by no means is
complete.
For the purpose of the paper here, an existing lathe
machine tool spindle is considered. From earlier machining
experiences this unit is considered as critical one from the
rigidity and vibration point of view because high surface finish
is expected. Machining accuracy and surface finish depend
Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition IMECE2014
November 14-20, 2014, Montreal, Quebec, Canada
IMECE2014-39665
2 Copyright © 2014 by ASME
upon the accuracy of rotation of spindle that imparts torque to
the wheel. Therefore, the spindle should meet certain
requirement in order to produce the high surface finish.
Generally, lathe machine spindle is designed for the
requirements of (a) a high degree of accuracy (b) high rigidity
and (c) accurate guidance. Under all load and speed conditions
the lathe spindle operates smoothly and free from vibrations.
Both the end of the spindle is fitted with spindle bearings,
which ensure high radial load carrying capacity and rigidity.
Therefore, a proper selection of rolling element bearings, their
location, pre loading in the case of rolling element bearing and
lubrication method will help the spindle to run at higher speeds
with high rotational accuracy and stiffness. This paper is
concerned with the stress and vibration analysis of a medium
speed lathe machine spindle with the aid of CAD/CAE
software. As mentioned before, a lot of work has already been
carried out by number of authors in the vibration analysis of
machine tool spindles and structures [7 to 9].
ANALYSIS
Based on the background and importance of the problem, a
computer software program using Visual Basic has been
developed for the design of spindle based on strength and in
accordance with the existing standards used for machine tools
such as BIS and ASTM (including the database of different
material) [1]. Typical flow-chart of the developed VB Program
is presented in Annexure A. The bearings for the spindle have
been selected using the AFBMA and other bearing standards.
Several engineering assumptions had to be made while
developing the software for the basic design of the spindle.
As is evident from the numerous references, the turning
process on a typical lathe involves three stages, which depends
on the interference condition of the tool to the work piece, the
type of material being cut and the operational conditions of the
machine tool. In general, in the first stage, the work piece
undergoes elastic deformation due to the load from the cutting
tool. At this stage, no chips material particles are taken away
from the work piece. In the second stage the work piece is
subjected to plastic deformation following the elastic
deformation, when the cutting tool is fed against the work
piece. In the final stage the cutting tool is further fed deep
against the work piece and it produces chips from work piece.
To cut precisely with good efficiency, the cutting condition
should be of the third stage with as small a cutting force as
possible. In addition, high peripheral speed and sharp cutting
edges of the cutting tool are two important cutting conditions to
improve cutting quality and efficiency.
The mechanics of cutting in lathe operations is well-
established and available in the literature [2, 11]. It is also well-
known that the dynamics of the flexible cutting tool and the
workpiece affects the cutting process sometimes leading to
chatter (or self-induced vibrations). Therefore, while cutting,
the tool might face a hard spot on the metal surface and start to
oscillate, which then results in chatter or instability of the entire
cutting operation. The dynamic cutting force (dp) can be
expressed as follows:
dp = k1. a. ds + (2/) k2. dr + k3. d
Here, 𝑑𝑠 is the change in the chip thickness, 𝑑𝑟 is the change in the feed rate, 𝑑Ω is the incremental change in the
spindle speed, and 𝑘1, 𝑘2 and 𝑘3 are the corresponding force
coefficients. Since the intent of this paper is modeling and
analysis of lathe spindle, the cutting mechanics aspects are only
included as forces acting on the spindle. Obviously, these forces
vary as the operating parameters vary on the machine tool.
The example machine tool used for the work presented in
this paper is a Model EP-1330 Mysore Kirloskar Lathe
Machine manufactured by Kirloskar Enterprise in India [10].
The main motor power is 2.2 kW with 8 spindle speeds: 54, 90,
140, 224, 315, 550, 775, and 1200 R.P.M. Other specifications
of the machine are as follows [1, 10]:
Center height – 175 mm
Swing over Bed – 350 mm
Swing over cross Slide – 200 mm
Swing in Gap – 520 mm
Width of Gap in front of Face Plate – 130 mm
Spindle nose – 4” D1 Cam lock
Morse Taper in Spindle Sleeve – Mt 3/5
Spindle Bore – 41 mm
Longitudinal Feed Range – 0.048 to 0.716 mm/rev.
Transverse Feed Range – 0.0008 to 0.012 inch/rev.
It may be noted that this machine is no longer
manufactured as new technology and new materials are
available, which is part of the students’ exercise to understand
where the developments of the modern machine tools are taking
place. More detailed specifications of this machine can be
found in the reference. Figures B1 to B3 in Annexure B show
respectively the photograph view of the headstock drivetrain,
the blueprint drawing of the headstock drivetrain assembly and
the dimensions of the spindle. The blueprint drawings were
provided by the manufacturer but they are not very clear.
However, the students were given these figures to carefully
study and to extract the critical dimensional data from this
information only for carrying out their project work.
The design of lathe spindle is carried out step by step by
using a computer program developed specially for this case.
However, the developed program can be used for other models
and spindles. The program is based on Visual Basic 6 (VB 6)
that uses the empirical formulas and data for the beam models
used for the spindle. Three different windows are designed in
the program: the first one is for the lathe spindle input output
specifications data entry. The other windows are designed for
material code and data entries and bearing data entries. One
example window from VB 6 is shown below in Figure 1.
3 Copyright © 2014 by ASME
Fig. 1: Input-Output Data Entry Window [1]
Spindles are stepped and hollow to accommodate the work
piece. It has a Morse Taper on one side to which the heavy
head-stock and chuck assembly are fitted. Taper roller bearings
with proper orientations secure the spindle from moving axially
while the gear forces from the drive train and the cutting forces
act of the spindle. Analyzing the spindle in its present form and
as shown in the blueprint drawings of Figures B2 and B3 (of
Annexure B), is complex by solid mechanics approach.
Understanding the assumptions to simplify the model is one of
the students’ course learning objectives (CLOs). Carrying out
the stress analysis to determine the shaft dimensions by
machine design approach is possible to some extent; however,
the deflection analysis is complicated. The students of this
group carried out the mechanics approach first to verify that the
dimensions of the spindle at critical locations are close to what
the lead author obtained using the Visual Basic Program. The
VB Program is based on the traditional machine design
procedure for sizing the members.
Rigidity calculations for the spindles involve the
determination of the deflection in bending and in some cases
the twist in torsion. In working out the design diagram, the
spindle is usually replaced by beam on hinged supports. Such
an assumption is valid when there is one ball or roller bearing
at each support. In more exact calculations, several ball or
roller bearings in a single support are to be regarded as an
elastic support, while a spindle running in sleeve bearings is
regarded as a beam on an elastic foundation. This last case can
also be conditionally reduced to a beam on hinged supports to
which a reactive moment M is applied in the support [2]. The
value of this moment varies, according to experimental data,
from zero (for insignificant loads, as in finishing machines) to
0.3 – 0.35 of the external moment acting in the middle section
of the spindle on the support [3]. As lot of literature is available
on this aspect of spindle design, it is not discussed in this paper.
Several calculations were made to obtain the design
dimensions of the spindle using the developed VB 6 program.
Due to space limitations the details of this are not presented in
this paper. However, standard textbooks such as those given in
references [11] to [13] can be used to understand the details of
cutting loads, two-plane bending and torsion analysis of the
spindle model, etc., and to obtain the spindle dimensions.
However, at the time of the conference, some of the important
details of these calculations (also shown in Annexures A & B)
will be shown for easy understanding of the work presented in
this paper. Few important steps for the design of the spindle are
given below following the two-plane bending model shown in
Figure 2. SI units have been used; therefore, all loads are in
Newton and all linear dimensions are in mm.
The design steps carried out in this work involved:
a. Calculation of cutting forces acting on the Spindle
b. Force analysis of the Spindle
c. Calculation of Spindle diameters by hand
calculations
d. Selection of the front and rear bearings
e. Calculation of the total deflection of the Spindle
nose by FEA
f. Calculation of torsional twist of the Spindle
g. Calculation procedure for static stiffness of the
spindle*
h. Calculation of critical speed of the Spindle (by
hand and by FEA)
Some of these items have been explained and the data
given to the students. Figure 2 below shows the simplified
beam analysis with loads in the vertical (designated by the
letter V in front) and horizontal (H) planes. These are used to
determine the spindle diameters at critical locations and to
determine the deflections at the gear and at the free end in order
120
VF=4625
Gear
RBv RAv
40 290
D C B A
Drive end
Bearing Tool end
Bearing
VP=3783
120
HF=2157
Gear
RBh RAh
40 290
D C B A
Drive end
Bearing Tool end
Bearing
HP=1892
Fig. 2: Forces in Vertical Plane (top) and in Horizontal
Plane (bottom)
4 Copyright © 2014 by ASME
to calculate the critical speeds of the spindle. As mentioned
before, the intention of this paper is to have the students
analyze the spindle shown in Figure 2 first by verifying the
critical dimensions and to carry out analysis by FEA.
In order for the students to model the spindle using beam
elements, the conventional Euler-Bernoulli beam equation is
discussed first along with its underlying assumptions and
limitations. The out-of-plane displacement w of a beam is
governed by this theory as:
(d2/dx
2) {EI(d
2w/dx
2} = p (2)
Here, p is the distributed loading (load/unit length) acting in the
same direction as y (and w), E is the Young’s modulus and I is
the area moment of inertia of the beam’s cross section. In the
case of lathe spindle although E does not change, I changes due
to various steps in the hollow sections of the spindle. The
details of the beam equation and the theory are covered
following any mechanics of materials book (such as Beer and
Johnston). The Euler beam equation (2) arises from a
combination of four distinct subsets of beam theory: the
kinematic, constitutive, force resultant, and equilibrium
definition equations.
The outcome of each of these segments is summarized below:
Kinematics: = - = (- dw/dx) (3)
Constitutive: (x,y) = E. (x,y) (4)
Resultants: M (x) = ∫ ∫ y.(x,y). dy.dz (5)
V (x) = ∫ ∫ xy(x,y). dy.dz (6)
Equilibrium: dM/dx = V; dV/dx = - p (7)
When using the finite element analysis, the spindle is assumed
to be acted up on by cutting forces which result in reaction
forces at the bearing supports. This was shown in figure 2. The
students are asked to use the direct stiffness matrix that is based
on simple beam theory (for example, presented in Logan’s
textbook, Reference [6]). The derivation of the stiffness matrix
is shown to the students, which is based on several standard
steps followed in a typical finite element analysis course. These
steps include: choosing an element type (in this case a 1D beam
element), assuming a displacement function for the beam
deflection (a cubic polynomial), defining the constitutive
relationship, which results in equation similar to equation (4)
above, and finally, defining the stiffness matrix, k. Following
the standard notation used in finite element analysis books, the
k-matrix can be derived as [6]:
(8)
Here, k is the element stiffness matrix, E is Young’s
modulus and L is the length of each element of the spindle
(modeled as 1D beam). Since a conventional spindle has
several steps along its length, several beam element equations
need to developed and assembled following the standard
stiffness method to obtain an overall global stiffness matrix for
the entire spindle. Boundary conditions and load conditions are
imposed on the global equation of motion following the
structural analysis of beams and the equations are solved for
unknown quantities. The first quantity solved in FEA problems
is the displacement of each node, followed by reaction loads.
Stresses are computed using the constitutive equation.
DETERMINATION OF DEFLECTIONS, STRESSES AND CRITICAL SPEEDS OF THE LATHE SPINDLE
Different finite element (FE) models have been developed
to perform stress, deflection and dynamic (vibration) analyses.
These include the one-dimensional beam elements solved by
using MatLab and the full blown 3D CAE models using NX
7.5, NX I-DEAS, ANSYS and SolidWorks for deflection and
stress analysis, and Dunkerley and the Rayleigh methods to
determine the critical speeds by hand calculations [1, 13].
Students developed the MatLab program to do deflection and
vibration analyses using 1D beam elements. While performing
these calculations, the weight of the gear (= 40 N) and the
weight of the chuck (= 140 N) have been taken in to account in
the vertical plane loads. Lot of time and efforts were put in to
develope the MatLab and CAE calculations. Table 1 shows
consolidation of all the results and discussed in the next section.
RESULTS AND DISCUSSION
Table 1 shows the deflection, stress and the critical speed
results for the spindle carried by different FE models. Even
though the same dimensions, loads, and material were used in
Deflection (mm x
10-3
)
Average Stress
(MPa)
Critical Speed
(rpm x 103)
3.8 (MatLab)
5.6 (NX)
4.0 (ANSYS)
5.3 (SolidWorks)
20.34 (NX)
25.5 (SolidWorks)
21.6 (I-DEAS)
23 (ANSYS)
16.26
(Dunkerley)
20.32 (Rayleigh)
Table 1: Deflection, Stress and Critical Speeds of Spindle
5 Copyright © 2014 by ASME
all these models, the differences in the results between the 1D
FE model using MatLab with 7 nodes and 6 elements, and the
full blown 3D CAE models containing several thousand of
nodes and elements were somewhat different. This is to be
expected due to the type and order of power of the elements
used. However, the locations of the maximum stresses,
displacements and the reaction forces were relatively the same.
This indicates that all these models are responding to the
applied boundary conditions in generally the same way.
Another possible source for the differences in values can
be attributed to the dimensions of the FE model. Since the
inside diameter of the spindle has a slight taper, the one-
dimensional model, which assumed a constant diameter is
different than the three-dimensional CAE model that can more
accurately represent the steps and the taper changes in the
diameter of the spindle. Although the analysis between the
math model and the computer models also differed, the
differences were much less. This is expected since the actual
model used for both was identical and loading conditions were
held constant. The differences between Nastran solver for NX
and SolidWorks can be attributed to the differences in the
meshing the programs produced and possibly to differences in
the material properties stored within these programs.
DISCUSSION OF RESULTS AND CONCLUSIONS The results presented in Table 1 by classical design
method, software and FEA for the stress, deflection and critical
speeds show that discrepancy exists in the calculated versus
CAE results of stress. The critical speed results show that to
avoid resonance, the operational speed of the spindle should be
at least 15 - 20% away from the critical speed. Based on
Raleigh’s method a speed of around 4,000 rpm or 3,200 rpm
based on Dunkerley method, are acceptable. Usually, the
medium spindle speed such as the case in this paper is well
within the calculated values. As mentioned before, the
developed VB6 software program calculates the deflections,
stresses and the critical speeds of the spindle in a step by step
manner.
Sample CAE results from NX 7.5 are shown in Figures 3
and 4. The results shown in the above table are average values
obtained from the CAE results obtained in these figures. The
figures are self-explanatory. More results will be shown at the
time of the conference.
From this study it can be concluded that the stresses and
deflections are well within the permissible/ specified limits as
given in the various standards, i.e., the stress values are below
the permissible values of 137.5 MPa and 80 MPa in bending
and torsion respectively, and 0.0660 mm of deflection. Hence,
the design is safe from the strength and deflection point of view
for the spindle.
The student learning outcomes included study of
conventional blue-print drawings to understand the dimensions;
modeling aspects of the spindle using mechanics and machine
design approach; using simplified 1D and 3D beam models of
the real life industrial component; understanding the limitations
of modeling, and finally validation of results by CAE and other
math tools. Overall, their response was very satisfactory.
SCOPE FOR FUTURE WORK
From the earlier discussion on spindle design one can say
that the overall performance of the machine tool depends upon
the performance characteristic of the individual components.
The ability to produce a workpiece of required physical features
accurately and at minimum cost presents the performance of the
machine tool. The spindle is one of the critical components in
this consideration. In the present work manual design of the
spindle is carried out on mainly rigidity and strength
consideration. Moreover, considering the recent advancement
in computers and computer languages the software for spindle
design is developed. In addition to this the latest CAD/CAE
software are used for the spindle design based on strength and
rigidity analysis. Design the optimization is considered up to
certain extent considering ratio of length to overhang of the
spindle.
In future work one can carry out the optimum designing of
spindle unit considering space, cost and other aspects such as
vibration and chatter. Other CAD/CAE software tools with
nonlinear capabilities can be used for the analysis purpose and
compare the results with the manual design. Finally, the
database of the spindle materials can be updated by adding new
materials developed recently. Figure 3: Deflection of the Spindle by NX 7.5
Figure 4: von-Mises stress of the Spindle by NX 7.5
6 Copyright © 2014 by ASME
ACKNOWLEDGMENTS Part of this work uses Statics Online Concepts Inventory
(OLI). This is part of a collaborative grant that the second
author received from NSF under their grant number: DUE-
0918255. Their support is sincerely acknowledged. The authors
wish to acknowledge the experimental and computer laboratory
facilities provided by L. D. Engineering College and the V. G.
E. College, Ahmadabad, Gujarat (India), and the undergraduate
and graduate students at Kettering University, Flint, MI, Mr.
Adam Colvin, Mr. Kevin Lucka and Mr. Joel Laber who
performed the FE analysis of the spindle as a part of their final
project work in the finite element analysis course.
REFERENCES 1. Vyasa Rupal, “Design of Precision Lathe Spindle
(ENTERPRISE 1330) Using CAD/CAE
Technologies”, unpublished Master of Engineering
Dissertation, L. D. College of Engineering,
Ahmadabad, 2004.
2. S. A. Tobias and F. Koenigsberger, “Advances in
Machine Tool Design & Research”, Proceedings of the
7th International Machine Tool Design and Research
Conference, University of Birmingham, Sept. 1966.
3. G. C. Sen and A. Bhattacharya, “Principles of Machine
tools”, New Central Book Agency, 1967.
4. N. Acherkan, “Machine tool design”, Vol.3, Ch. 5,
University Press of Pacific, ISBN-10: 0898750482,
2007.
5. T. R. Chandraputla, “Finite Element Analysis for
Engineering and Technology”, University Press
(India), 2004.
6. D. Logan, “A First Course in Finite Element Method”,
Cengage Learning, 5th
edition, 2011.
7. S. S. Rao, “The Finite Element Method in
Engineering”, Tata McGraw-Hill Publication, 1989.
8. R. V. Reddy and A. M. Sharan, “The Finite Element
Modeled Design of Lathe Spindles: The Static and
Dynamic Analyses”, Journal of Vibration, Acoustics,
Stress, and Reliability in Design, Vol. 109, P. 407,
October 1987.
9. T. Sawamoto and K. Konishi., “Development of
machine tool spindles with higher rotational speeds”,
Tribology International, P.189, Aug.1982.
10. Kirloskar Enterprise EP-1330 Mysore Kirloskar Lathe
Machine. Information available on the internet at:
http://www.machinetools.com/en/models/kirloskar-
enterprise-1330/
11. F. Koenigsberger and J. Tlusty, “Machine Tool
Structures Volume 1”, Pergamon Press, Oxford, 1970.
12. R. G. Budynas and J. K. Nisbett, “Shigley’s
Mechanical Engineering Design”, McGraw-Hill Co.,
9th
edition, 2012.
13. F. S. Tse, I. E. Morse and Hinkle, “Mechanical
Vibrations: Theory and Applications”, Allyn and
Bacon series in mechanical engineering and applied
mechanics, 1978.
7 Copyright © 2014 by ASME
ANNEXURE A
FIG. A1: FLOW CHART OF THE SOFTWARE ARCHITECTURE FOR SPINDLE DESIGN AND ANALYSIS [1]
Input Lathe Specifications
Spindle design Calculation
Lateral & Angular Rigidity calculation
Check For bending & shear Stress
ut
ultimate
stress
y Yield
stress
Select
Standard
Bearing
form data
- base
Select Material from
database
Is it Safe?
FEA
Try
Other
Material
Selection of Bearing for
Spindle (Front & Rear)
NO
YES
8 Copyright © 2014 by ASME
ANNEXURE B
FIG. B1: PHOTOGRAPH OF THE DRIVETRAIN OF THE HEADSTOCK ASSEMBLY [1, 10]
Spindle being analyzed
9 Copyright © 2014 by ASME
ANNEXURE B
FIG. B2: BLUEPRINT OF ENTERPRISE LATHE DRIVETRAIN ASSEMBLY [1, 10]
Spindle being analyzed
10 Copyright © 2014 by ASME
ANNEXURE B
FIG. B2: BLUEPRINT OF THE LATHE SPINDLE WITH APPROXIMATE CRITICAL DIMENSIONS [1, 10]