In the field of automotive drivetrain systems, hyperbolic gears, also known as hypoid gears, play a critical role in transmitting power between non-intersecting axes, particularly in drive axles. The machining of these complex gear geometries has long relied on specialized equipment, often imported at high cost. As a researcher involved in gear manufacturing technology, I have focused on developing affordable and efficient solutions for producing hyperbolic gears. This article presents my first-person perspective on the structural innovation of a four-axis CNC milling machine, specifically the YK2260X model, and its experimental application in machining hyperbolic gears. The goal is to demonstrate how domestic CNC technology can achieve high-quality gear production while reducing reliance on expensive imported machinery.
The demand for hyperbolic gears in automotive applications has driven the need for advanced machining centers. Traditionally, mechanical milling machines with complex mechanisms like rockers and eccentric drums were used, but these have limitations in precision, flexibility, and maintenance. With the advent of CNC technology, multi-axis联动 machines have emerged, offering improved accuracy and reduced dependency on operator skill. However, high-end CNC milling machines from international manufacturers often come with prohibitive costs and high tool consumption, making them inaccessible for widespread adoption. In my work, I aimed to bridge this gap by innovating a four-axis CNC milling machine that incorporates a modified-roll method for machining hyperbolic gears. This approach leverages existing research to develop driver software, enabling efficient and cost-effective production. The key innovation lies in the machine’s structural design, which enhances rigidity and allows for dry cutting, as well as the integration of software that simplifies the programming process for hyperbolic gears.
To begin, let me introduce the structural innovations of the YK2260X CNC milling machine. Unlike conventional four-axis CNC milling machines where the tool spindle is mounted on a vertical slide with linear guides, the YK2260X features a side-mounted tool box on a column with rectangular cast-iron guides. This design ensures that the main cutting force acts on the正面 of the guides, reducing the span between them and improving stiffness. The workpiece spindle is driven by a servo motor through a high-precision gear reduction mechanism with backlash elimination, which minimizes transmission error and enhances accuracy. Additionally, the machine incorporates a manual adjustment for the workpiece installation angle, displayed via a built-in rotary encoder, significantly lowering manufacturing costs compared to servo-driven B-axis systems. The tool spindle can achieve speeds up to 500 rpm, facilitated by a servo motor and a single-stage gear reduction, making it suitable for high-speed dry cutting. All guides are enclosed for protection, and the machine includes an automatic chip removal system, promoting environmentally friendly operations. These structural enhancements are summarized in the table below, highlighting the advantages over traditional designs.
| Feature | YK2260X CNC Milling Machine | Traditional Four-Axis CNC Milling Machine |
|---|---|---|
| Tool Box Mounting | Side-mounted on column with rectangular cast-iron guides | Vertical slide with linear guides |
| Workpiece Spindle Drive | Servo motor with backlash-eliminating gear reduction | Servo motor with worm gear mechanism |
| Workpiece Installation Angle | Manual adjustment with rotary encoder display | Often servo-driven, increasing cost |
| Tool Spindle Speed | Up to 500 rpm, suitable for dry cutting | Lower speeds, often requiring coolant |
| Chip Management | Automatic chip removal with enclosed guides | Limited chip removal, may use coolant |
| Cost Efficiency | Reduced manufacturing and operational costs | Higher cost due to complex mechanisms |
The machining of hyperbolic gears on the YK2260X relies on a driver software that implements the modified-roll method, specifically the HFM (Hypoid Formate Modified) method for pinion machining. This software is integrated into the Siemens 828D SL CNC system, providing a user-friendly interface for inputting machining parameters. In my research, I derived the motion expressions for each axis to simulate the virtual rocker motion, which replaces the physical rocker in traditional machines. The coordinate systems involved include the tool center position, virtual rocker, and workpiece coordinates, as shown in the mathematical model. The key parameters include radial cutter distance, angular cutter position, vertical wheel offset, and machine center distance, all essential for positioning the tool relative to the workpiece during the machining of hyperbolic gears.
The motion of the four axes—X (horizontal), Y (vertical), Z (feed), and A (workpiece rotation)—is governed by mathematical expressions derived from the modified-roll method. For the machining of hyperbolic gears, these expressions ensure precise tool-workpiece relative motion. Let $S_r$ be the virtual radial cutter distance, $q$ the virtual angular cutter position, $E_m$ the vertical wheel offset, $\Delta A$ the axial wheel offset correction, $\Delta B$ the machine center distance correction, $L$ the distance from the design crossing point to the workpiece rotation center, $\gamma$ the workpiece installation angle, $m$ the roll ratio, $q_0$ the reference point angular cutter position, $\varphi_0$ the initial workpiece rotation angle, and $c$ and $d$ the second and third-order coefficients from the machining card. The axis movements are expressed as follows:
$$ \varphi = m \left[ q – q_0 – c (q – q_0)^2 – d (q – q_0)^3 \right] + \varphi_0 $$
$$ x = S_r \cos q – (\Delta A – L) \cos \gamma $$
$$ y = E_m + S_r \sin q $$
$$ z = \Delta B – (\Delta A – L) \cos \gamma $$
Here, $L = L_0 – C – D$, where $L_0$ is the machine constant distance from the spindle end face to the workpiece rotation center, $C$ is the mounting distance of the hyperbolic gear, and $D$ is the axial thickness of the fixture. These equations define the coordinated movement required for generating the tooth surfaces of hyperbolic gears. To determine the starting and ending positions for machining, let $\theta$ be the swing angle of the virtual rocker. At the reference point, $q = q_0$. The angular cutter positions at the start and end are:
$$ q_1 = q_0 – \frac{\theta}{2} $$
$$ q_2 = q_0 + \frac{\theta}{2} $$
The corresponding workpiece rotation angles are:
$$ \varphi_1 = m \left[ -\frac{\theta}{2} – c \left( -\frac{\theta}{2} \right)^2 – d \left( -\frac{\theta}{2} \right)^3 \right] + \varphi_0 $$
$$ \varphi_2 = m \left[ \frac{\theta}{2} – c \left( \frac{\theta}{2} \right)^2 – d \left( \frac{\theta}{2} \right)^3 \right] + \varphi_0 $$
These formulas are crucial for programming the CNC system to machine hyperbolic gears accurately. The programming workflow involves inputting gear design parameters, calculating axis movements, and simulating the tool path. The table below summarizes the key steps in the programming process for the YK2260X when machining hyperbolic gears.
| Step | Description | Key Parameters |
|---|---|---|
| 1 | Input gear design data | Tooth number, module, face width, offset distance |
| 2 | Calculate machining parameters | Radial cutter distance, angular cutter position, roll ratio |
| 3 | Determine axis motion expressions | Use derived formulas for X, Y, Z, A axes |
| 4 | Set reference points | Starting and ending positions based on virtual rocker swing |
| 5 | Generate CNC code | Integrate motions into G-code for the Siemens system |
| 6 | Simulate and verify | Check tool path for errors before actual machining |
To validate the performance of the YK2260X CNC milling machine in machining hyperbolic gears, I conducted a cutting experiment on a set of hyperbolic gears used in an automotive drive axle. The gear set consisted of a pinion with 6 teeth and a gear with 41 teeth, designed for a 90-degree shaft angle. The gear was machined using the formate method, while the pinion was machined using the modified-roll method on the YK2260X. The geometric parameters of the gear blanks are provided in the table below, emphasizing the specifications for these hyperbolic gears.
| Parameter | Pinion (Hyperbolic Gear) | Gear (Hyperbolic Gear) |
|---|---|---|
| Number of Teeth | 6 | 41 |
| Module | 10.588 | 10.588 |
| Face Width (mm) | 67.2 | 62 |
| Offset Distance (mm) | 35 | 35 |
| Shaft Angle (°) | 90 | 90 |
| Outer Cone Distance (mm) | 213.192 | 220.678 |
| Addendum (mm) | 13.603 | 1.644 |
| Dedendum (mm) | 3.788 | 15.487 |
| Working Depth (mm) | 15.369 | 15.31 |
| Whole Depth (mm) | 17.39 | 17.15 |
The machining parameters for the pinion, crucial for producing hyperbolic gears, included cutter radius, tool pressure angle, and roll ratio, as detailed in the following table. These parameters were input into the driver software to generate the axis movements.
| Parameter | Concave Side (Pinion) | Convex Side (Pinion) |
|---|---|---|
| Cutter Radius (mm) | 143.345 | 159.25 |
| Tool Pressure Angle (°) | 20.0 | 24.5 |
| Workpiece Installation Angle (°) | 9.82 | 9.82 |
| Radial Cutter Distance (mm) | 176.53 | 152.9 |
| Angular Cutter Position (°) | -62.13335 | -63.0833 |
| Vertical Wheel Offset (mm) | 49.86 | 25.31 |
| Horizontal Wheel Offset (mm) | 7.43 | -6.7 |
| Machine Center Distance (mm) | -4.72 | -2.04 |
| Roll Ratio | 7.70375 | 6.377562 |
| Second-Order Coefficient | 0.209965 | -0.176999 |
| Third-Order Coefficient | 0 | 0.08 |
The cutting experiment was performed using dry cutting, with the YK2260X operating smoothly without significant vibration. The pinion was rough-machined using the generating method and finish-machined using the modified-roll method, completing each hyperbolic gear in approximately 6 minutes. The efficiency of this process highlights the machine’s capability for high-speed machining of hyperbolic gears. During the operation, the automatic chip removal system effectively managed debris, ensuring a clean working environment. To illustrate the setup, below is an image showing the machining process of hyperbolic gears on the YK2260X CNC milling machine.
After machining, the hyperbolic gears were subjected to rolling tests to evaluate the contact pattern. For the non-working side (pinion convex side and gear concave side), the contact area was centered on the tooth surface, with no edge contact or higher-order defects. For the working side (pinion concave side and gear convex side), the contact pattern was favorable, covering about one-third of the face width and half of the tooth height, with no diagonal contact. These results confirm that the hyperbolic gears machined on the YK2260X meet design requirements, demonstrating the effectiveness of the modified-roll method and the machine’s structural innovations. The successful production of hyperbolic gears with optimal contact patterns underscores the potential of domestic CNC technology in advancing gear manufacturing.
In conclusion, the YK2260X CNC milling machine represents a significant innovation in the machining of hyperbolic gears. Its structural design, featuring a side-mounted tool box and high-precision workpiece spindle drive, enhances rigidity and accuracy while reducing costs. The integration of driver software based on the modified-roll method enables efficient programming and machining of hyperbolic gears, eliminating the need for expensive servo-driven B-axis systems. The experimental results show that hyperbolic gears produced on this machine exhibit excellent contact patterns, satisfying automotive drive axle requirements. This research contributes to the development of affordable and high-performance CNC solutions for hyperbolic gears, promoting broader adoption in the industry. Future work may focus on optimizing tool paths for even faster machining speeds and exploring applications in other complex gear types, further solidifying the role of CNC technology in hyperbolic gear production.