How to Wind a Coil Spring on the Metal Lathe

[arvidj]

(07-03-2013, 09:33 AM)chucketn Wrote: "k = mx + b

where m = -0.0124727272727273 and b = 0.980818181818182 for music and stainless steel wire

and m = -0.0109727272727273 and b = 0.984909090909091 for phosphor bronze wire.

and x is the Spring Index."

Arvidj, are thes values for m and b constants? Or are they just for the example in the article?

Chuck

They are constants derived from the graph, not from the example.

I looked at the graph on page 20 and entered the data points into Excel ...

Music or Stainless Steel Wire

Code:

5     0.922
6     0.907
7     0.893
8     0.880
9     0.867
10    0.854
11    0.842
12    0.829
13    0.818
14    0.807
15    0.798

Phosphor Bronze Wire

Code:

5     0.933
6     0.920
7     0.908
8     0.896
9     0.884
10    0.874
11    0.863
12    0.851
13    0.842
14    0.833
15    0.823

I then ran a linest function on the data to determine the "best fit" straight line that fit the data ... i.e. a line that is defined by y = mx + b. The results are:

Music or Stainless Steel Wire

Code:

-0.0124727273          0.9808181818
0.0002209421           0.0023172607
0.9971838746           0.0023172607
3186.8803611737        9.0000000000
0.0171125818           0.0000483273

Phosphor Bronze Wire

Code:

-0.0109727273          0.9849090909
0.0001841018           0.0019308762
0.9974728525           0.0019308762
3552.3275535085        9.0000000000
0.0132440818           0.0000335545

The first row, first column is m and first row, second column is b.

The third row, first column the coefficient of determination ... a value between 0 and 1 that indicates how accurately the mx + b formula predicts the given y values for the data that was provided. A value of 1 means 'perfect fit' and 0 means 'not even close'.

In this case the values are so close to 1 that we are safe in assuming that "for any value of x [the spring index], the value of y [the elusive k] is ((-0.0124727273 * [spring index]) + 0.9808181818) for music and stainless wire and ((-0.0109727273 * [spring index]) + 0.9849090909) for phosphor bronze wire.