2.72 Team 1 Lathe Report 1
Lathe Specifications
FEATURES
 Spindle supported by precision tapered roller bearings
 Easy spindle reversal
 Backlash adjustments provided on carriage and cross
feed lead screws
 Small for portability
SPECIFICATIONS
Spindle Speeds
Spindle Speed
 11.32 V
Maximum Tool Size
Maximum Part Diameter
 Clamping (internal)
 Jamming
 Clamping (external)
Cross Slide Travel
Carriage Travel
Motor
Overall Dimensions (LxWxH)
Voltage Dependent
2080 RPM
0.25” x 0.25”
0.08” – 0.59”
0.78” – 1.89”
0.86” – 1.85”
0.63”
3.3”
24V/81% efficiency
18” x 11.5” x 12”
Design
Cross Feed Flexure
The primary design goals for the cross feed flexure were to minimize the stiffness in the direction of travel,
maximize the stiffness in all other directions, and increase the first resonant frequency to well above any
possible excitation from the cutting. Using beam bending theory, the stiffness in the direction of travel (X)
Ebh 3
was found to be proportional to
, where E is the modulus of elasticity and b, h, and L are the width,
L3
thickness, and length of the flexure blades (respectively). From the same calculation, the maximum stress

Ehx
in the beam for a given tip deflection x was found to be
. Incorporating these results into the equation
4L2
of motion for a spring-mass-damper system, the natural frequency of the flexure was found to be
proportional to


Ebh3
. From this, the thickness h was chosen as the critical dimension to vary; the
mL3
natural frequency increases with a power of 1.5 while the maximum stress at the beam root increases
linearly. A more detailed list of design considerations can be found in Appendix C.
The final design for the cross feed flexure, with all of the design considerations implemented, was analyzed
using Finite Element Analysis (FEA) methods to ensure that we achieved the desired amount of deflection
for the force we would impart. Appendix C shows a sample screen showing FEA analysis of the cross feed
flexure.
Leadscrew Flexure
The leadscrew flexure allows for compliance in the X-Y plane to adjust for inconsistencies (flexing) in the
carriage leadscrew while providing stiffness in all other degrees of freedom to ensure the cutting precision
of the lathe. The flexure’s one inch thickness provides stiffness in the Z direction and two points of
attachment to the carriage are used to minimize rotation about the X axis. A split Teflon nut interfaces the
leadscrew flexure with the leadscrew in order to eliminate backlash. Two bolts at the bottom of the flexure
tighten the Teflon nut around the lead screw.
Compliance in the X-Y plane was maximized by designing the flexure to take up as much space in inside the
structure tube as is allowed, lengthening the blades for increased deflection. Longer blades allow for an
increase in thickness without sacrificing compliance, resulting in a strong yet compliant flexure. The
flexure allows for 0.08” of compliance in both the X and Y without exceeding a fifth of the allowed stress.
A more detailed list of design considerations and pictures of the FEA for the leadscrew flexure can be found
in Appendix C.
Belt Tensioning
We opted to use a round belt and two pulleys (with 2:1 ratio) to drive the spindle with the motor. We
utilized a simple wedge to drive the driving pulley away from the spindle pulley. The wedge moves when a
¼-20 threaded rod is turned. Using a wedge that contacts both supports of the motor ensures that the
2.72 Team 1 Lathe Report 3
motor is evenly lifted, reducing excess bending of the motor shaft and pulley. The mechanism can be seen
in Appendix C.
Spindle and Housing Interface
The lathe’s spindle is supported in the housing by two tapered roller bearings and pretensioned using
several belleville spring washers and nut. Tapered roller bearings allow for thermal expansion down the
length of the shaft and also self-center the spindle in the housing. A properly applied preload centers the
spindle in the housing and eliminates chatter/spindle motion. A cross section of the housing and spindle
assembly can be seen below.
Figure 1 housing cross section
Measurements
Spindle Runout
The initial runout of the spindle, with un-greased bearings and no preload applied, was approximately 30
microns. An additional runout measurement, with proper preload and bearing grease applied resulted in a
nearly four-fold increase in error. This was attributed primarily to the inaccuracies of the chuck. A third
measurement, with proper preload, grease, and no chuck resulted in a runout measurement of 10 microns.
This measurement was taken on the spindle shaft. Spindle runout measured on a part in the chuck was
approximately 238 microns. The disparity is attributed to inaccuracies within the chuck itself. We came to
this conclusion by measuring the runout on the shaft itself (10 microns), dial indicating to a thousandth of an
inch when threading the shaft, and attempting to shim between the chuck and the shaft. Shimming did
nothing to decrease the runout, so the disparity does not lie between the shoulder and the chuck. The only
conclusion we can reach is an issue within the chuck.
Spindle Error
Displacement (microns)
150
100
50
0
0
50
100
150
200
250
300
350
400
-50
-100
-150
Radial (degrees)
Figure 2 Spindle Runout Error On Part With Chuck
Cross-slide Error
Cross-slide error measurements taken with the CMM show that the actual x position deviates from the
command x position by 2%, which could be due to inconsistencies in the driving leadscrew. Through the
maximum motion of the cross-slide, the slide deviated by 35 microns in the Z direction and approximately
157 microns in the Y direction. The lathe was shimmed and both errors were reduced. The final Z
deviation was 22 microns and the final Y deviation was 36. We suspect waterjetting to have contributed to
this error but there is no dependable machining process available to address errors in the flexure directly
without damaging them.
Carriage Error
Carriage error measurements show that the actual z position only deviates from the commanded z position
by less than 0.2%. The carriage leadscrew is both stiffer and more precisely threaded than the cross-slide
2.72 Team 1 Lathe Report 5
leadscrew, accounting for it’s significantly higher accuracy. The final Y deviation was 255 microns per inch.
The final X deviation was 223 microns per inch. We believe the rails to be the source of the error, more
specifically the holes the rails are mounted to. Since the holes for the rails were machined at a 1:1 fit, no
shimming of the rails is possible. We do not believe the set screws securing the rails are the source of the
error since they do not move the rails any appreciable amount within their holes.
Calculated Specifications
A parametric system model was made using Excel to predict the errors in the lathe. Homogeneous
transformation matrices (HTMs) between components of the lathe were constructed using free body
diagrams, beam bending theory, and bolt stiffness calculations. These HTMs were used to visualize the
propagation of errors through various coordinate systems, resulting in a total error at the point where the
tool touches the part. Errors from the structural compliance due to cutting forces, thermal expansion,
measured runout error of the spindle, carriage, and crossfeed, vibration, and backlash were considered in
the model. More detail about the error modeling is explained in Appendix B. To cut a 0.4” diameter
aluminum part extending 1.5” from the chuck, and assuming a thrust force of 60 pounds axially, a cutting
force of 90 pounds vertically and a dive force of 20 pounds radially, we expect errors of 0.0028 inches in
the radial direction (X), 0.038 inches in the vertical direction (Y), and 0.0026 inches in the axial direction
(Z). A block model for the coordinate transformations can be found in Appendix B.
Performance
The lathe does not vibrate noticeably when running and can cut metal to a beautiful shine, shown in
Appendix A. It’s important to remember not to ram the carriage into the chuck while the chuck is spinning
and also to tighten the chuck fully on the piece. The carriage lead screw is slightly more difficult to turn
than the cross feed lead screw, but neither render the lathe unusable. In general, it is very pleasant to use
and can cut metal well without feeling dangerous.
Lessons Learned
We learned how to design a complex machine! Specifically, we learned how to break the complex problem of
analyzing a complete machine into smaller, easily solvable chunks. For example, to measure the deflection between
the part and the tailpiece that occurs under cutting forces and uneven machine heating, we broke the machine into
individual pieces - the headstock, the rails, the carriage - and examined the deformations each would undergo
individually. Incorporating the stiffnesses of the bolted connections between these parts, we were able to use
homogenous transform matrices to collect the individual part contributions and estimate the deformation of the
entire machine.
We also learned the importance of good engineering communication, in a multitude of ways. Our external
communication, involving process plans and part drawings, wildly improved over the course of the semester as we
attempted to follow the plans ourselves and received feedback from Bill. This went hand-in-hand with an increased
appreciation for the pain involved in holding parts to fine tolerances.
On the other hand, our internal engineering communication enabled us to move forward quickly. Our
team adopted a strategy of total communication, where major design decisions involved the entire group.
This could potentially have bogged us down in minutiae, but ended up keeping the entire team abreast of
design changes. This prevented us from designing on different part versions and encouraged everyone to
participate in design decisions.
Overall, it was a pleasant experience and all of us have much more confidence tackling tricky design and
precision machining projects. Our modeling and machining abilities have soared and we all had a great
time.
Team one
Michael Snively
Jacklyn Holmes
Raymond Ma
Xuefeng Chen
Nick Wiltsie