I don't really understand what you're asking, but I copied and pasted your post straight into ChatGPT and it gave this, which may well be nonsense:
Overview
What you’re trying to accomplish is to generate a set of incremental data points defining how much the rack translates relative to the pinion rotation, at small angle increments (e.g. every 1°). This data can then be used to drive a macro or script that emulates the cutting process of a variable rack or other complex gear surface. Since off-the-shelf software for this can be prohibitively expensive, the idea is to approximate the motion using Excel or a similar tool.
In simpler terms:
- You have a graph or known relationship between pinion angle and rack translation (rack gain).
- You need to discretize that relationship at fixed angle increments (for example, every 1°).
- For each 1° increment, you need to find the corresponding rack translation increment.
- You then sum these increments to find the total rack travel.
- In more complex cases, the relationship isn’t linear but follows a spline (smooth, gradually changing curve). In that case, you need to fit or interpolate the data to a spline first, then sample that spline at the desired increments.
Key Steps
- Defining the Input Data:
Typically, you start with either:
- A set of known data points (pinion angle vs. rack position) derived from measurements, another software’s output, or by reading off a graph.
- Or a known mathematical relationship (like a polynomial or piecewise function) that represents the rack gain as a function of pinion angle.
- Interpolation Using a Spline (if the relationship isn’t linear):
If you have discrete data points (e.g., at 0°, 5°, 10°, etc.) and need values at every 1°, you can use spline interpolation. Tools that can do this:
- Excel with Add-Ons: By default, Excel doesn't have a native spline function, but you can:
- Use Excel’s built-in FORECAST() or polynomial trendlines for a rough approximation.
- Use third-party Excel add-ins (e.g., XLSTAT) that can perform spline interpolation.
- Python (Recommended if Possible): Python’s scipy.interpolate module can easily fit a cubic spline to your known data and then sample at any resolution you desire.
- Mathematica or MATLAB: If you have access, these have built-in spline functions.
- Generating the Data Points in Excel: Let’s assume you have a starting angle of 0° and go up to some final angle (e.g., 800° total rotation in increments of 1°). You have two main approaches:
A. If the data is approximately linear or piecewise linear:
Suppose you know that from 0° to 100°, the rack translation increases linearly from 0.16 mm at 0° to 0.19 mm at 100°, and then stays constant at 0.19 mm beyond that. You can do:
- In one column, list angles: 0, 1, 2, …, 100, 101, etc.
- In the next column, for each angle, compute the translation:
- For angle ≤ 100°, use a formula that linearly interpolates between 0.16 and 0.19 mm.
- For angle > 100°, just set the value to 0.19 mm.
For example:
- A2: angle = 0
- B2: translation = 0.16 mm
- A3: angle = 1
- B3: translation = 0.16 + (0.00025 * angle) until it hits 0.19 mm
You can write a formula like:
=MIN(0.16 + 0.00025 * A2, 0.19)
This increments by 0.00025 mm per degree until it reaches 0.19 mm. Copy down for all rows.
Once you have all these increments, you can sum them (using =SUM(B2:B802) if you have 800 rows) to find the total rack travel.
B. If the relationship is more complex (Spline Interpolation):
If you have a set of key points, say (Angle, Rack_Translation):
(0°, 0.16 mm)
(10°, 0.1605 mm)
(20°, 0.162 mm)
(30°, 0.165 mm)
...
(N°, ...)
You need to fit a spline. Without an expensive CAD/CAM add-in, do the following:
- In Python (if possible):
import numpy as np
from scipy.interpolate import CubicSpline
# Known data arrays
angles = np.array([0, 10, 20, 30, ...]) # degrees
translations = np.array([0.16, 0.1605, 0.162, 0.165, ...])
# Fit a cubic spline to these points
cs = CubicSpline(angles, translations)
# Now sample every 1 degree
new_angles = np.arange(0, max(angles), 1) # from 0 to final angle by 1°
new_translations = cs(new_angles) # spline evaluated at each integer degree
# Save to a CSV for Excel
data_out = np.column_stack((new_angles, new_translations))
np.savetxt('output.csv', data_out, delimiter=',', header='Angle,Translation', comments='')
Once you have output.csv, open it in Excel, and you have a translation at every 1°. You can then:
- Sum the translations for total travel: =SUM(B2:B802) if you have 800 increments.
If using only Excel and without Python, consider:
- Creating a polynomial trendline from your known data points in a chart.
- Extracting that polynomial equation and applying it to each angle.
- This is less accurate than a proper spline but still better than manual steps.
- Note:
The spline or polynomial gives you the position of the rack at each angle. If what you really need is the incremental movement at each step, you can calculate the difference between successive points. For example, if at 0° your rack is at 0.16 mm, and at 1° it’s at 0.16025 mm, the incremental move from 0° to 1° is 0.16025 - 0.16 = 0.00025 mm. By doing this for each step (taking the difference between consecutive translation values), you can see how much it moves per 1° increment and integrate that into your macro.
- Summation of Rack Travel:
Once you have a column of translations corresponding to each angle, you can sum them if you’re looking at absolute increments. Typically, you might want the final rack position at each angle, not just increments. The total travel at any angle step is just the difference from the initial position to that current position. If you do need cumulative increments, just ensure you’re adding the differences, not the absolute positions.
Practical Tips:
- Read Data from a Graph: If your data is currently only in a graphical form (like a PDF or an image), you can:
- Digitize it using a tool such as WebPlotDigitizer (free online tool) to get a set of (Angle, Rack) numeric pairs.
- Once you have the numeric data, apply the spline/polynomial fitting.
- Fine-Tuning Steps: If you need smaller increments (like 0.5° or 0.1°), just adjust your array and formulas accordingly.
- Verification: Start with a smaller range and manually check a few points to ensure the interpolation and increments match your expectations from the reference graph.
Conclusion:
You don’t need a $100k software package to generate these increments. With some basic interpolation techniques, Excel or Python, and a bit of time setting up formulas or scripts, you can produce a full table of angle vs. rack translation data points. Then, summing up these increments or positions will give you the total travel needed to replicate the complex shaping of a variable rack or spiral bevel gear tooth surface.
I've been hesitant to use ai due to pride but now I really couldn't care lol.
