Design and Analysis of an Example Lathe Spindle

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unpublished thesis carried out by the first author [1].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


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.


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)


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


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


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.

http://www.machinetools.com/en/models/kirloskar-enterprise-1330/

http://www.machinetools.com/en/models/kirloskar-enterprise-1330/


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


ANNEXURE B

FIG. B1: PHOTOGRAPH OF THE DRIVETRAIN OF THE HEADSTOCK ASSEMBLY [1, 10]

Spindle being analyzed


ANNEXURE B

FIG. B2: BLUEPRINT OF ENTERPRISE LATHE DRIVETRAIN ASSEMBLY [1, 10]

Spindle being analyzed


ANNEXURE B

FIG. B2: BLUEPRINT OF THE LATHE SPINDLE WITH APPROXIMATE CRITICAL DIMENSIONS [1, 10]

Design and Analysis of an Example Lathe Spindle

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