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
SpecificationsSpindle Speeds / Voltage Dependent
Spindle Speed
· 11.32 V / 2080 RPM
Maximum Tool Size / 0.25” x 0.25”
Maximum Part Diameter
· Clamping (internal) / 0.08” – 0.59”
· Jamming / 0.78” – 1.89”
· Clamping (external) / 0.86” – 1.85”
Cross Slide Travel / 0.63”
Carriage Travel / 3.3”
Motor / 24V/81% efficiency
Overall Dimensions (LxWxH) / 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) was found to be proportional to , where E is the modulus of elasticity and b, h, and L are the width, thickness, and length of the flexure blades (respectively). From the same calculation, the maximum stress in the beam for a given tip deflection x was found to be . Incorporating these results into the equation of motion for a spring-mass-damper system, the natural frequency of the flexure was found to be proportional to . From this, the thickness h was chosen as the critical dimension to vary; the 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 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.
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 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 Xuefeng Chen
Jacklyn Holmes Nick Wiltsie
Raymond Ma