Lathe V Ways Calculation for fitting Tailstock and Carriage _/\_

While rebuilding the Chipmaster, the problem of aligning the carriage bed ways ( bottom slide ) and top slide arise, from what information I can find these have to be at right angles. The bottom slide is worn bananas, so a simple spotting technique, on the bed might cause a lot of headache later to align the cross slide. So I decided to align the tail stock base first, and then use it on the lathe to check which original sufaces on the crosslide are closest to allignment, to be used on the mill setup.  I will then cleanup the V groves at the bottom, and do the final spot checking on the lathe beds. So the approach requires three steps.
1) Align the tail-stock on the mill, and touch-up the V slot, and flat surface. Machine one outside surface parallel to the V-Groves. Final fit on the lathe with transfer spotting.

2) Find the best reference surface on the carriage with the fitted tail-stock base as guide. Or bolt an adjustable bar to the back, where the taper attachment usually attaches.

3) Machine the cross-slide base V and flat ways, aligned to identified surface. Fit with transfer bluing.

The calculation for the depth of the V slots require similar math to that used for dovetail calculations. I used two 14 mm end mills as gauge pins, the bottom circle is used for measuring the depth, when the base is upside down on the mill, since I want to do the machining in one setup.

Height with14mm gauge pin in V slot, should be z higher than flat surface          
              
On the drawing, the top two 14mm gauge pins are used to  measure the_ /\_ ways, the
bottom gauge pin is used to measure height over the flat surface, for a level tail stock base.          
              
map the flat surface to find low points, add z, mill out v until this height is reached          
mill down flat surface         

                 measured    38,515    across pins
c1,c2,c3    r    7   
                 a    24,515    measured-2r
                 b    4,949747468   
                 c    2,050252532    r-b
                2d    14,61550506   
                d    7,307752532   
                h    9,358005063    c+d
               w    18,71601013    2*height
               e    9,899494937   
              c3    center    0,541489873    e-h
              z    7,541489873    r+c3 center

Measurement techniques for precision bearing balls

While rebuilding the Eagle surface grinder, I have to refurbish the spindle bearings. One of the challenges is to select matching bearing balls as accurately as possible.

Googling around, I could not find any information on how to do this with simple tools in the home shop. Some commercial methods which come to mind are using an optical comparator or 3d laser scanner. While taking myself and the dogs for a walk this morning at 5:30, I realised, like many times before; the old school machinists did not have all the fancy measuring equipment we have noways, yet managed to build very accurate and precise machines.  The idea of tolerance measurement similar to how snap gauges work came to mind.

To do this one has to measure the ball diameter. There are a few methods I can come up with to do
this. The intention is to measure diameter as accurately as possible, not just variations in the Lot or precision.

Tool	Method	Accuracy	Repetability	Issues
Micrometer	place the ball between the anvil and measure	Good	Fair	Measuring Force
Dial indicator	Capture ball on stand, compare height of balls.	Relative	Good	Allignment
Slip Gauge	Build gate on surface plate with high and then low tolerance, roll balls through the gate	Best	Best	Cleanliness

In a previous post I have described the calculations and selection of ball diameter. For reference, I am working with Grade 10 Balls, 13/32" or 10.31875mm

Grade	Sphericity [mm]	Lot diameter variation [mm]	Nominal ball diameter tolerance [mm] +/-	Maximum surface roughness (Ra) [µm]
10	0.00025	0.00025	0.0013	0.025

My method will firstly select balls which roll under the gauge block stack bridge setup for the high tolerance level of 10.32005mm, and then from this selection set, select the balls which do not pass under the low tolerance stack of 10.31745 mm. This is the simplest, and most accurate and precise method I could think of  for the home shop machinist.

Great resource with lots of useful information:
http://www.precisionballs.com/Ball_diameter_Calibration.php
http://www.precisionballs.com/Ball_Diameter_Errors.php