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Basic Parameters in Gear Shaper Cutter Design
Views: 0 Author: Site Editor Publish Time: 2025-11-27 Origin: Site
A gear shaper cutter is essentially a modified gear that cuts the tooth profile of a workpiece gear through backlash-free "meshing" (i.e., generating motion). It can machine various types of cylindrical gears, including external spur and helical gears, internal gears, and double gears with narrow relief grooves. Below is a detailed overview of the basic design parameters for gear shaper cutters:
I. Classification of Gear Shaper Cutters
Based on their structure, gear shaper cutters are categorized into three types:
Disc-type: Primarily used for machining external spur and helical gears.
Cup-type: Suitable for machining tower-shaped spur or helical gears.
Taper-shank type: Designed specifically for machining internal gears.
II. Basic Design Parameters
1. Modification Coefficient (x₀)
Due to the relief angle of the gear shaper cutter, its dimension gradually decreases from the rake face to the back. Consequently, the modification coefficient varies across different cross-sections: the original cross-section has a modification coefficient of 0, with positive values increasing toward the front end and negative values becoming more pronounced toward the back end. The relationship between the modification coefficient (x₀) and the relief angle (αₑ) is expressed as:x₀ = b·tanαₑ(where b = distance from the original cross-section)
Key considerations for selection:
A larger modification coefficient is preferred for new cutters, as it increases regrinding times, extends service life, improves the top edge rake angle, and enhances the surface quality of machined gears.
Maximum modification coefficient (x₀max): Limited by tooth tip sharpening of the cutter and potential transition curve interference of the workpiece gear.
Minimum modification coefficient (x₀min): Restricted by cutter strength and risks of root cutting or tip cutting on the workpiece gear.
2. Tooth Profile Angle Correction (α₀)
The presence of rake and relief angles in the cutter causes tooth profile errors. To minimize these errors, the tooth profile angle is corrected, resulting in a value different from the pressure angle of the workpiece gear. The corrected tooth profile angle (α₀) is related to the workpiece gear's pressure angle and the cutter's rake/relief angles by the formula:tanα₀ = (tanα_w) / (1 - tanγ·tanαₑ)(where α_w = pressure angle of the workpiece gear; γ = rake angle; αₑ = relief angle)
3. Relief Angle (αₑ)
Closely associated with cutter durability, an appropriate increase in the relief angle can enhance tool life but may increase machining errors. The standard range is 4°–8°, which can be increased by 1°–2° to improve durability.
4. Rake Angle (γ)
The top edge of the cutter features a rake angle (γ), with its rake face being a concave conical surface. Standard cutters adopt a top edge rake angle of γ = 5°. For machining steel gears, increasing the rake angle improves both surface finish and cutter durability but may also amplify tooth profile errors.
5. Reference Circle Diameter (d₀)
Standard nominal reference circle diameters are preferred, including 25, 30, 38, 75, 100, 125, 160, and 200 mm. Within the capacity of gear shapers and gear grinders, larger diameters are recommended as they enhance durability and reduce the risk of transition curve interference, though they increase tool costs.
6. Number of Teeth (z₀)
Once the nominal reference circle diameter (d₀') is determined, the number of teeth is calculated based on the workpiece gear's module (m) using the formula:z₀ = d₀' / m (rounded to the nearest integer)
Considerations: Verify compatibility with the gear grinder's indexing plates. The actual reference circle diameter is then computed as d₀ = m·z₀.
7. Addendum Coefficient
Determines the root circle diameter of the workpiece gear, calculated based on the workpiece's root circle diameter and the cutter's modification amount. For standard nominal reference circle diameters, the coefficient is typically 1.25 or 1.3.
8. Base Circle Diameter of Tooth Profile (d_b₀)
Calculated as: d_b₀ = m·z₀·cosα₀
9. Base Helix Angle of Tooth Profile (β_b₀)
Expressed as: tanβ_b₀ = sinβ₀·tanαₑ (where β₀ = helix angle of the cutter)
10. Tooth Thickness at Original Cross-section (s₀)
Standard specification: s₀ = π·m/2. For thinner workpiece gears, increase the cutting depth; to maintain root radial clearance, increase the circular tooth thickness at the reference circle.
