Spiral bevel gears are used in vehicle, armored, and aircraft drivetrains to transfer motion between intersecting shafts with compact packaging and low noise. Their running quality depends not only on tooth geometry but also on how the gear pair is positioned inside the housing. A small axial displacement of the pinion or the gear, a radial offset, or a shaft-angle error changes the contact pattern on the tooth flank, concentrates load, and alters vibration and service life. Because the contact pattern becomes visible after a marking-compound run, it provides a direct, shop-floor-readable indicator of the assembly state.
Contact Pattern as an Assembly Diagnostic
In a marking-compound test, the wiped area on the gear flank shows where the teeth actually carried load. For a spiral bevel gear pair, this area is sensitive to the relative position of the two members. Four rigid-body installation deviations are commonly distinguished: radial offset ΔV, pinion axial displacement ΔH, gear axial displacement ΔJ, and shaft-angle error ΔE. Positive axial directions are defined by increasing the mounting position.
Tooth contact analysis (TCA) predicts pattern movement from a mathematical gear model, while image processing can extract pattern features from photographs. Both are useful, but TCA requires a calibrated model and conventional image processing relies on handcrafted geometric rules. Those workflows are difficult to apply rapidly when several deviation classes must be separated at the assembly stage. A learned image classifier offers an alternative when the pattern classes are visually separable.
The classification task is not a continuous measurement of deviation. It maps a flattened contact-pattern image to one of a small set of assembly states. This distinction matters for application: a classifier can screen for known pattern classes, but it does not replace TCA or final contact inspection unless it is trained and validated for the full deviation range of interest.
Test Rig, Imaging, and Dataset
A back-to-back gearbox test rig provided the loaded mesh. A servo motor and planetary reducer drove the input; a diaphragm coupling compensated misalignment; a torque and speed sensor measured load and speed; and an asynchronous AC motor with braking resistors applied load. The gearbox had separate adjusters: ball screws for axial positioning of the pinion and gear, and shim packs for radial positioning. Power was fed through the large gear and taken out through the pinion to raise the transmitted torque.
Contact patterns were produced with red lead marking compound on the convex flank of the large gear. The pair ran at 20 r/min under a load torque of 1,500 N·m for a fixed number of revolutions. The wiped region was then photographed with an industrial camera and a ring light. A laser displacement sensor and the ring illumination supported repeatable positioning and reduced the influence of ambient light on the contact-pattern image.
Because the tooth surface is curved, direct two-dimensional classification would mix pattern geometry with perspective distortion. The surface was therefore flattened before classification. A flexible checkerboard target partitioned the tooth surface into small patches; corner points were detected as control points; each patch was rectified by a perspective transform; and the rectified patches were stitched into a planar image. The resulting image preserves the position and shape of the contact pattern relative to the tooth surface.
The dataset contained 432 flattened contact-pattern images in three classes. The classes covered a no-deviation condition, a gear axial deviation of ΔJ = -1.0 mm, and a pinion axial deviation of ΔH = -1.0 mm. The images were divided into training and test sets, with the test set held out for final evaluation.
| Class | Assembly condition | Training images | Test images |
|---|---|---|---|
| No deviation | ΔJ = 0 mm, ΔH = 0 mm | 206 | 29 |
| Gear axial deviation | ΔJ = -1.0 mm | 81 | 17 |
| Pinion axial deviation | ΔH = -1.0 mm | 83 | 16 |
| Total | — | 370 | 62 |
The dataset does not include radial offset ΔV, shaft-angle error ΔE, positive axial deviations, or intermediate axial magnitudes. The learned classes therefore represent a narrow slice of the assembly-deviation space, and the reported performance should be interpreted within that scope.
Network Design
ResNet-18 was selected as a lightweight residual backbone. A residual block learns a residual function and adds the identity mapping, so the target mapping is formed by the residual plus the input. This structure allows gradients to pass through many layers and reduces the degradation problem that appears when plain convolutional networks are made deeper.
The standard 7×7 stem convolution was replaced by three 3×3 convolutions, with the first at stride 2 and the next two at stride 1. This preserves the downsampling ratio of the original stem while increasing nonlinearity at the input stage. The remainder of the residual backbone was kept unchanged.
Channel and spatial attention modules were inserted after the first convolutional layer and after the last convolutional layer. The channel module applies global average pooling and global maximum pooling, passes both descriptors through a shared two-layer perceptron, and combines them with a sigmoid gate. The spatial module applies channel-wise average pooling and maximum pooling, concatenates the two maps, processes them with a 7×7 convolution, and applies a sigmoid gate. These modules allow the network to emphasize contact-pattern edges and locations while suppressing irrelevant tooth-surface texture.
The model was built and trained in PyTorch 2.0 under Windows 11 64-bit, using an Intel Core i7-10700K processor, 32 GB of memory, an NVIDIA GTX 1660 graphics card, and CUDA 11.8. Classification performance was evaluated with accuracy and softmax cross-entropy loss.
Classification Performance
The improved network reached 93.55% test accuracy, compared with 90.32% for the original ResNet-18, an increase of 3.23 percentage points. Training accuracy rose from 93.78% to 97.84%, and the loss value decreased from 0.19 to 0.15, a reduction of 0.04.
| Model | Training accuracy (%) | Test accuracy (%) | Cross-entropy loss |
|---|---|---|---|
| Improved ResNet-18 | 97.84 | 93.55 | 0.15 |
| Original ResNet-18 | 93.78 | 90.32 | 0.19 |
On a 62-image test set, the 3.23-point accuracy gain corresponds to two additional correctly classified images. That difference is consistent with a useful design direction, but it is not a high-precision estimate of field performance. The lower cross-entropy loss supports the accuracy result, although it does not by itself show how errors are distributed across classes.
The class distribution is imbalanced: the no-deviation class contains 206 training images and 29 test images, while the two deviation classes contain 81/17 and 83/16 images. Overall accuracy can therefore be dominated by the majority class. A confusion matrix and per-class recall would be needed to show whether the model detects the two axial deviation classes with comparable reliability.
Both models also show a training-to-test accuracy gap, so overfitting cannot be excluded. A single train-test split does not provide variance across training runs, and no confidence interval is given for the accuracy difference. The result should be read as an initial demonstration that flattened contact patterns carry separable information about assembly state under the tested conditions.
Engineering Use and Limits
For assembly work, the practical value of the approach is a repeatable image-based screen. After a marking-compound run, a fixed camera station could classify the contact pattern and flag whether it is consistent with the no-deviation condition or with one of the trained axial deviations. Within that class set, the output could help direct an operator toward the pinion or gear axial adjustment and reduce reliance on subjective visual judgment.
Deployment would require controlled illumination, a fixed camera-to-gear pose, the same marking compound and run-in procedure, and stable flattening of the tooth surface. The classifier is also tied to the gear family and tooth geometry used for training. A change in gear size, spiral angle, housing access, or image acquisition geometry changes the input domain and requires retraining or recalibration.
The present three-class formulation is a coarse representation of assembly state. Combined deviations, unknown deviation magnitudes, and patterns outside the training set may be forced into one of the learned classes. An open-set rejection threshold or a continuous deviation estimator would be more appropriate for production diagnosis. Expanding the dataset to radial offset ΔV, shaft-angle error ΔE, positive and negative axial deviations, multiple magnitudes, and additional gear sizes would provide a more realistic basis for that step.
Within its tested scope, the improved ResNet-18 shows that a lightweight residual network with channel and spatial attention can map flattened contact patterns of a spiral bevel gear to assembly-deviation classes. The result supports further development of contact-pattern-based vision for assembly adjustment, while keeping TCA and final contact inspection as the verification layer.