Constant-tooth-depth spiral bevel gears are widely used in construction machinery, heavy equipment, and precision drives. Klingelnberg HPG hard skiving and Gleason-type equal-height tooth grinding have raised manufacturing accuracy, but small-ratio pairs still present a geometric conflict: the rotating cutter head can interfere with the bearing journal seat of the pinion. The risk is highest when the pinion has a small pitch cone angle and a large bearing seat diameter, because the shoulder is close to the swept volume of the cutter.
Where the Interference Comes From
The cutter head is not a simple slotting tool. It generates the flank through a rolling motion, and its outer edge sweeps through a volume larger than the final tooth space. In a small-ratio pair, the pinion pitch cone angle is small, so the tooth root lies close to the shaft axis. A large bearing seat then pushes the shoulder outward into the cutter envelope. During generating motion, the cutter can nick the shoulder, leave a poor seating surface, or remove material from a region that must remain strong and square.
The usual workaround is to add a process shoulder, increasing the axial distance between the tooth root and the bearing seat. This changes the blank geometry, lengthens the shaft, and can reduce support stiffness and machining accuracy. Severe interference therefore affects not only the appearance of the part but also the load path between the bearing and the gear body.
Pitch-Cone Offset as a Geometric Remedy
Klingelnberg AMK and C-series cutting machines provide a tailstock tilting mechanism. Instead of translating the gear, the workpiece is rotated slightly about the midpoint of the face width, so the generating pitch cone is changed without altering the nominal shaft angle. For interference at the pinion bearing seat, the pinion generating pitch cone angle is reduced by a small angle μk, while the mating wheel is increased by the same amount:
$$
\delta_{E1}=\delta_1-\mu_k,\qquad
\delta_{E2}=\delta_2+\mu_k,\qquad
\delta_{E1}+\delta_{E2}=\delta_1+\delta_2 .
$$
Here δ1 and δ2 are the nominal pitch cone angles of the pinion and wheel, and δE1 and δE2 are the actual generating angles used after offset. The correction is applied to both members so that the mesh geometry remains matched. If the interference occurs at the opposite bearing seat, the sign of the offset is reversed.
| Interference location | Pinion generating angle | Wheel generating angle | Effect |
|---|---|---|---|
| Right-hand bearing seat | δ1 − μk | δ2 + μk | Shoulder moves out of the cutter sweep |
| Left-hand bearing seat | δ1 + μk | δ2 − μk | Opposite correction, same shaft angle |
The offset can be introduced by mechanical shims or directly through the KIMOS setting for the machine. Because the correction is applied to the generating cone of an equal-height pair, the direction of the spiral angle does not reverse the setting in the way it does for a hypoid offset. The method is also distinct from cutter tilt: Klingelnberg AMK and C machines use cutter eccentricity, not the cutter-tilt axis found on Oerlikon-type machines. A recommendation to increase the cutter plane inclination therefore does not describe the available Klingelnberg correction.
Geometric and Load Effects
The offset changes the mid-cone and inner-cone distances but leaves the outer cone distance and face width unchanged. With outer cone distance Re, face width b, and offset angle μk, the corrected distances are
$$
R_m=R_e-0.5b\cos\mu_k,
\qquad
R_i=R_e-b\cos\mu_k,
$$
where Rm is the mid-cone distance and Ri is the inner-cone distance. These corrections must be used when the machine setting and the cutter-clearance check are prepared.
A pitch-cone offset also changes the axial and radial forces. For a small offset applied to both members, the mesh quality is usually preserved, but bearing life and shaft strength should be recalculated when the design margin is small or when the offset is larger than the normal process window. With tangential force Ft, normal pressure angle αn, mean spiral angle βm, and actual generating angle δE, the force components are:
Convex flank in contact:
$$
F_x=\frac{F_t}{\cos\beta_m}
\left(\tan\alpha_n\sin\delta_E-\sin\beta_m\cos\delta_E\right),
$$
$$
F_r=\frac{F_t}{\cos\beta_m}
\left(\tan\alpha_n\cos\delta_E+\sin\beta_m\sin\delta_E\right).
$$
Concave flank in contact:
$$
F_x=\frac{F_t}{\cos\beta_m}
\left(\tan\alpha_n\sin\delta_E+\sin\beta_m\cos\delta_E\right),
$$
$$
F_r=\frac{F_t}{\cos\beta_m}
\left(\tan\alpha_n\cos\delta_E-\sin\beta_m\sin\delta_E\right).
$$
Here Fx is the axial force and Fr is the radial force. The sign difference between the convex and concave cases matters for bearing arrangement and for the direction of the resultant load.
Cutter-Head Clearance Check
The secondary-cutting check follows the KN3029 procedure and must use the actual generating pitch angle δE, not the nominal angle. The two extreme points of the cutter envelope, A at the outer cone and I at the inner cone, must remain inside the cutter tip circle. The non-interference conditions are
$$
M_A<r+h_{a0}\tan\alpha_n, $$="" <p="" \qquad="" m_iwhere r is the cutter-head radius and ha0 is the cutter addendum. The distances are
$$
M_A=\sqrt{(X_m-X_A)^2+(Y_m-Y_A)^2},
\qquad
M_I=\sqrt{(X_m-X_I)^2+(Y_m-Y_I)^2}.
$$
The cutter position and the extreme-point coordinates are obtained from
$$
X_m=M_d\sin(\psi_e-\lambda),
\qquad
Y_m=M_d\cos(\psi_e-\lambda),
$$
$$
X_A=\sqrt{2h\left(R_e\tan\delta_E+h_a\right)
-\left(\frac{h}{\cos\delta_E}\right)^2},
\qquad
Y_A=R_e-h\tan\delta_E,
$$
$$
X_I=\sqrt{2h\left(R_i\tan\delta_E+h_a\right)
-\left(\frac{h}{\cos\delta_E}\right)^2},
\qquad
Y_I=R_i-h\tan\delta_E.
$$
In these expressions, Md, ψe, λ, h, and ha are the cutter-head and tooth-geometry quantities defined in the KN3029 setting procedure. If either condition is violated, the cutter will recut the shoulder even though the nominal design appears to clear it.
Tailstock Setting on AMK and C Machines
The tailstock setting converts the pitch-cone correction into a spindle displacement. For small angles, the vertical offset follows the mid-cone relation; for the wheel it is
$$
h_{v2}=R_{m2}\tan\mu_{k2}.
$$
The pinion value is obtained from the same mid-cone geometry and entered as the corresponding tailstock setting dimension. On AMK machines, the workpiece spindle is raised or lowered by a manual valve-controlled hydraulic cylinder; the actual offset is set from the spindle height and the Kb distance on the setting card. On C-series machines, KIMOS controls the rotary slide, so the same correction is programmed rather than shimmed. In both cases the workpiece spindle must be repositioned relative to the centerline by the design offset angle before cutting.
Contact Pattern and Process Window
Production experience with these gear pairs shows that a pitch-cone offset of about 2° can remove a severe shoulder interference while leaving the contact pattern almost unchanged. The contact pattern becomes more sensitive when the offset is large or when the original pattern is already at an extreme toe/heel or top/root position. For a small offset, the contact quality can usually be restored by adjusting the cutter position Ex in the conventional way. If the offset is large and the contact pattern is extreme, Ex alone may not be sufficient; blade shims must also be added or removed on the cutter head.
Practical Rules and Limits
- Check with the actual generating angle. The cutter-clearance calculation must use δE, because the offset changes the cone that the machine actually generates.
- Offset both members. Reduce the pinion angle and increase the wheel angle, or reverse the signs for the opposite bearing seat, so that the shaft angle and mesh relation remain unchanged.
- Keep the offset small. An offset of about 2° is often enough to clear the shoulder. Larger offsets require renewed bearing-load, shaft-strength, and cutter-clearance checks.
- Use tailstock offset, not cutter tilt. Klingelnberg AMK and C machines provide a workpiece-axis correction through the tailstock; cutter eccentricity is not the same as a cutter-tilt mechanism.
- Recheck the contact pattern. Adjust Ex first for small offsets; add blade shims when the offset is large and the contact pattern is extreme.
- Treat a process shoulder as a fallback. It can increase clearance, but it also changes the blank, adds overhang, and may reduce shaft stiffness and machining accuracy.
Tailstock offset with a small pitch-cone correction is therefore a low-cost geometric compensation for cutter interference in Klingelnberg spiral bevel gears. It can eliminate or reduce shoulder interference, improve the bearing seating surface, and preserve shaft strength without adding a process shoulder. Its limits are the bearing load rating and the contact-pattern window: once the offset becomes large, the correction must be treated as a design change rather than a minor process adjustment.