In my extensive experience within the gear manufacturing industry, one of the most intricate challenges involves adapting advanced calculation programs to existing machinery. This is particularly true for the complex and precise field of spiral bevel and hypoid gear cutting. The introduction of electronic computer programs from Gleason for calculating the geometry and machine settings of these gears represents a significant technological leap. These programs, once debugged and validated, are handed over for production use. However, a fundamental issue arises: the output data from these sophisticated Gleason programs is often incompatible with the parameter systems of most domestically produced gear cutting machines. Therefore, a critical process of parameter conversion is an indispensable step before these advanced calculations can be utilized on the shop floor.
Domestically manufactured machines for this purpose primarily fall into two categories. The first category comprises machines equipped with a cutter tilt and swivel mechanism. For these machines, certain Gleason programs can be used directly. The second, and more common, category consists of machines featuring a ratio change (or modified roll) mechanism. This category also includes simpler machines without this specific mechanism. For this latter group, the data output from Gleason programs cannot be applied directly and must undergo a systematic conversion.
The core of the gear cutting adjustment lies in translating key machine settings. When planning a gear cutting operation, settings from machines like the Gleason No. 116 or No. 108 must be converted for use on domestic models such as the Y2250 or Y2280. The fundamental parameters requiring conversion include the machine’s basic kinematic settings and its specialized modification mechanisms.
1. Conversion of Basic Cutting Parameters from Gleason to Domestic Machines
The foundational settings for any gear cutting operation involve the spatial relationship between the cutter head and the gear blank. The following conversions are essential.
1.1 Cutter Center Position (Machine Center)
The radial distance of the cutter center from the machine center, often termed the “cutter center distance” or “machine center,” is calculated differently. For a Gleason No. 116, it is derived from the eccentric drum diameter and angle. The conversion formula to a domestic machine setting (denoted as \( S \)) is:
$$ S = \sqrt{X^2 + Y^2} $$
Where \( X \) and \( Y \) are orthogonal components. For a Gleason No. 116:
$$ X = \frac{E}{2} \cos q $$
$$ Y = \frac{E}{2} \sin q \pm \Delta S $$
Here, \( E \) is the eccentric drum diameter (e.g., 304.8 mm), \( q \) is the eccentric angle, and \( \Delta S \) is a correction value from the calculation card. The plus sign is used for left-hand gears and the minus sign for right-hand gears in gear cutting.
For a Gleason No. 108, the calculation is:
$$ X = R_c \cos q $$
$$ Y = R_c \sin q $$
Where \( R_c \) is the computed cutter radius.
1.2 Radial (Polar) Angle
The angular orientation of the cutter center position, crucial for setting the machine, also differs. For conversion from a Gleason No. 116 setting (\( \theta_{116} \)):
$$ \theta_{Y2250/80} = \theta_{116} \mp q $$
For conversion from a Gleason No. 108 setting (\( \theta_{108} \)):
$$ \theta_{Y2250/80} = \theta_{108} – (90^\circ \mp q) $$
Again, the upper sign is for left-hand gears and the lower for right-hand gears in the gear cutting process.
1.3 Cradle Angle
The rotational position of the machine’s cradle at the start of cut is another vital parameter. The conversion is uniform for both source machines:
$$ Q_{Y2250/80} = Q_{Gleason} \mp q $$
Where \( Q_{Gleason} \) is the cradle angle from the Gleason card. The sign convention remains the same.
1.4 Index (Dividing) and Ratio
The number of teeth indexed per cycle and the basic rolling ratio between the cradle and the workpiece are fundamental to generating the correct tooth form. The index pattern is typically selected from charts. The rolling ratio conversion depends on the gear cutting operation phase (roughing or finishing) and the gear’s pitch angle.
For roughing a pinion or a gear with a pitch angle greater than 70°, a specific speed reduction ratio \( i_d \) is used. The conversion from a Gleason No. 116 ratio (\( i_{116} \)) is:
$$ i_{Y2250/80} = \frac{i_{116}}{i_d} $$
The conversion from a Gleason No. 108 ratio (\( i_{108} \)) is:
$$ i_{Y2250/80} = \frac{i_{108} \cdot \pi}{180^\circ \cdot i_d} $$
For finishing operations or for gears with smaller pitch angles, a different ratio (often 1:1) is applied, requiring a different set of conversion factors.
The following table summarizes the source and target of these primary parameter conversions for the gear cutting setup:
| Parameter | Gleason Source Machine | Domestic Target Machine | Key Conversion Element |
|---|---|---|---|
| Cutter Center (S) | No. 116 / No. 108 | Y2250 / Y2280 | Eccentric Angle (q) & Components |
| Radial Angle (θ) | No. 116 / No. 108 | Y2250 / Y2280 | Eccentric Angle (q) & 90° offset |
| Cradle Angle (Q) | No. 116 / No. 108 | Y2250 / Y2280 | Direct adjustment by ± q |
| Rolling Ratio (i) | No. 116 / No. 108 | Y2250 / Y2280 | Reduction Ratio (i_d) & π/180° factor |
2. Conversion of Modified Roll (Ratio Change) Mechanism Parameters
A critical aspect of high-quality spiral bevel and hypoid gear cutting is the modification of tooth geometry along the length of the tooth to ensure proper localization of contact. Gleason machines often use a modified roll mechanism, and their calculation cards provide specific parameters for it: the initial phase angle of the eccentric cam (\( P_0 \)), the eccentric radius of the cam (\( R_0 \)), and the change gear ratio for the mechanism (\( i_{m} \)).
For domestic machines like the Y2250/Y2280, the values of \( P_0 \) and \( R_0 \) can usually be taken directly from the Gleason calculation card. The challenge lies in determining the correct change gear ratio for the domestic machine’s own modified roll mechanism.
The core relationship for the modified roll mechanism’s gear ratio is given by:
$$ i_m = \frac{K_m}{R_0} $$
Where \( i_m \) is the change gear ratio, and \( K_m \) is a fixed transmission ratio within the modified roll mechanism of the specific machine.
The conversion process involves these steps:
1. Obtain \( R_0 \) and \( i_m^{(G)} \) from the Gleason (No. 116 or 108) calculation card.
2. Calculate the Gleason mechanism’s \( K_m^{(G)} \) value using the formula derived from the above: \( K_m^{(G)} = i_m^{(G)} \cdot R_0 \).
3. Determine the acceleration coefficient \( C \) for the Gleason setup. This is often given on the card (e.g., 0.02 or 0.04). It relates to the machine’s cradle radius \( R \): \( C = \frac{R_0}{R^2} \).
4. Calculate the required eccentric radius \( R_0^{(Y)} \) for the domestic machine using its cradle radius \( R^{(Y)} \) and the coefficient \( C \): \( R_0^{(Y)} = C \cdot (R^{(Y)})^2 \).
5. Finally, compute the change gear ratio \( i_m^{(Y)} \) for the domestic Y2250/Y2280 machine using its fixed \( K_m^{(Y)} \): \( i_m^{(Y)} = \frac{K_m^{(Y)}}{R_0^{(Y)}} \).
2.1 Calculating the Eccentric Angle and Small Cradle Angle
During the gear cutting cycle, the modified roll mechanism itself has dynamic settings. The eccentric angle \( \varepsilon \) and the small cradle angle \( \alpha \) for the domestic machine are calculated as follows:
$$ \varepsilon = \arcsin\left(\frac{e_1}{e_{max}}\right) $$
$$ \alpha = \arctan\left(\frac{X}{Y}\right) $$
Where \( e_1 \) is an intermediate calculation value, and \( e_{max} \) is the maximum eccentric radius of the mechanism’s cam (e.g., 42.5 mm).
The calculation of \( \alpha \) depends on the hand of the gear and the tooth surface being cut (concave or convex), following specific sign conventions to ensure correct tooth form generation in the gear cutting process.
3. Comprehensive Calculation Example
To solidify understanding, let’s walk through a practical example of converting gear cutting data from a Gleason No. 116 machine for use on a domestic Y2250 machine. The process involves three main stages: converting basic settings, calculating modified roll parameters, and compiling the final machine setup sheet.
3.1 Original Gleason No. 116 Data
The following table represents the initial setup data from the Gleason calculation card for finishing a gear and roughing/finishing a pinion.
| Adjustment Item | Gear Finish | Pinion Rough | Pinion Concave Finish | Pinion Convex Finish |
|---|---|---|---|---|
| Machine Root Angle (deg) | 43.000 | 20.800 | 21.000 | 21.000 |
| Gear Position Correction (mm) | 0 | -0.254 | -0.254 | -0.254 |
| Sliding Base (mm) | Retract 0.254 | Retract 0.508 | Retract 0.254 | Retract 0.254 |
| Vertical Gear Position (mm) | Down 3.048 | Up 3.048 | Up 3.048 | Up 3.048 |
| Eccentric Angle, q (deg) | 329.500 | 0 | 30.000 | 30.000 |
| Radial Angle, θ (deg) | 4.500 | 90.000 | 76.500 | 103.500 |
| Cradle Angle, Q (deg) | 24.500 | 250.000 | 22.500 | 49.500 |
| Rolling Ratio, i | 2.18750 | 1.62891 | 1.74609 | 1.74609 |
| Modified Roll Eccentric Radius, R0 (mm) | – | – | 21.500 | 21.500 |
| Modified Roll Initial Phase, P0 (deg) | – | – | 30.000 | 30.000 |
| Modified Roll Gear Ratio, i_m | – | – | 0.17000 | 0.17000 |
3.2 Step-by-Step Conversion of Basic Parameters
Using the formulas from Section 1, we convert the basic settings for pinion concave finish. Assume \( E = 304.8 \) mm and \( \Delta S = 0 \).
| Step | Calculation | Formula | Result |
|---|---|---|---|
| 1. Cutter Center (X) | \( X = (304.8/2) \cos(30^\circ) \) | \( X = \frac{E}{2} \cos q \) | 132.000 mm |
| 2. Cutter Center (Y) | \( Y = (304.8/2) \sin(30^\circ) + 0 \) | \( Y = \frac{E}{2} \sin q + \Delta S \) | 76.200 mm |
| 3. Cutter Center (S) | \( S = \sqrt{132.0^2 + 76.2^2} \) | \( S = \sqrt{X^2 + Y^2} \) | 152.400 mm |
| 4. Radial Angle (θ) | \( \theta_{Y2250} = 76.5^\circ – 30^\circ \) | \( \theta_{Y2250} = \theta_{116} – q \) (for LH pinion) | 46.500° |
| 5. Cradle Angle (Q) | \( Q_{Y2250} = 22.5^\circ – 30^\circ \) | \( Q_{Y2250} = Q_{116} – q \) (for LH pinion) | -7.500° (or 352.500°) |
| 6. Rolling Ratio (i) | \( i_{Y2250} = 1.74609 / i_d \) (using appropriate i_d) | \( i_{Y2250} = i_{116} / i_d \) | Calculated value |
3.3 Step-by-Step Conversion of Modified Roll Parameters
Continuing for the pinion concave finish, we convert the modified roll data. Assume \( K_m^{(Y)} = 3.65625 \) for the Y2250, \( R^{(Y)} = 152.4 \) mm, and the Gleason card’s \( C = 0.02 \).
| Step | Calculation | Formula | Result |
|---|---|---|---|
| 1. Calc. Gleason K_m | \( K_m^{(G)} = 0.17000 \times 21.5 \) | \( K_m^{(G)} = i_m^{(G)} \cdot R_0^{(G)} \) | 3.65500 |
| 2. Calc. Y2250 R0 | \( R_0^{(Y)} = 0.02 \times (152.4)^2 \) | \( R_0^{(Y)} = C \cdot (R^{(Y)})^2 \) | 21.500 mm |
| 3. Calc. Y2250 i_m | \( i_m^{(Y)} = 3.65625 / 21.5 \) | \( i_m^{(Y)} = K_m^{(Y)} / R_0^{(Y)} \) | 0.17006 |
3.4 Final Compiled Setup Sheet for Y2250
After performing all conversions for each operation, the final setup sheet for the domestic Y2250 gear cutting machine would be compiled as follows.
| Adjustment Item | Gear Finish | Pinion Rough | Pinion Concave Finish | Pinion Convex Finish |
|---|---|---|---|---|
| Machine Root Angle (deg) | 43.000 | 20.800 | 21.000 | 21.000 |
| Gear Position Correction (mm) | 0 | -0.254 | -0.254 | -0.254 |
| Sliding Base (mm) | Retract 0.254 | Retract 0.508 | Retract 0.254 | Retract 0.254 |
| Vertical Gear Position (mm) | Down 3.048 | Up 3.048 | Up 3.048 | Up 3.048 |
| Cutter Center, S (mm) | 152.400 | 152.400 | 152.400 | 152.400 |
| Radial Angle, θ (deg) | 35.000 | 90.000 | 46.500 | 73.500 |
| Cradle Angle, Q (deg) | 55.000 | 250.000 | 352.500 | 19.500 |
| Rolling Ratio, i | Converted Value | Converted Value | Converted Value | Converted Value |
| Change Gears (i) | Matching Gears | Matching Gears | Matching Gears | Matching Gears |
| Modified Roll Ecc. Radius, R0 (mm) | – | – | 21.500 | 21.500 |
| Modified Roll Init. Phase, P0 (deg) | – | – | 30.000 | 30.000 |
| Modified Roll Gear Ratio, i_m | – | – | 0.17006 | 0.17006 |
| Modified Roll Ecc. Angle, ε (deg) | – | – | Calculated | Calculated |
| Modified Roll Small Cradle, α (deg) | – | – | Calculated | Calculated |
| Index Pattern (Teeth) | Selected | Selected | Selected | Selected |
In conclusion, the process of parametric conversion from Gleason to domestic gear cutting machines is systematic but demands meticulous attention to detail. It involves a deep understanding of both the source and target machine kinematics. The cornerstone of successful conversion lies in accurately translating the cutter center position, its angular orientation, the cradle start position, and the fundamental rolling ratio. Furthermore, for machines equipped with a modified roll mechanism, an additional layer of calculation is required to adapt the gear ratio and dynamic settings that control the vital tooth contact localization. Mastering these conversion principles is essential for leveraging advanced computational gear cutting programs on a wider range of manufacturing equipment, thereby enhancing production flexibility and capability in the precision gear cutting industry.