In this work, I studied a new method for internal gear cutting based on electrochemical dissolution. The method is intended for internal gears used in transmission shafts, reducers, internal gear pumps, electric vehicles, aircraft engines, and other compact transmission systems. In my view, internal gear cutting remains a difficult operation because the tooth space is inside a small bore, often in a blind-hole configuration, and the workpiece material is usually a high-strength, high-hardness alloy. Conventional mechanical gear cutting is productive for external gears, but internal gear cutting by shaping, broaching, or milling often suffers from low efficiency, expensive tooling, and rapid tool wear. Plastic forming can produce internal teeth in one stroke, but the filling of tooth corners is incomplete and the process window is narrow. Electrical discharge machining can cut internal profiles, but it is mainly suitable for through holes and suffers from electrode wear. Therefore, I focused on electrochemical gear cutting, which removes material by anodic dissolution, has no tool wear, produces no residual stress, and can machine hard materials with complex internal shapes.
My research objective was to develop a stable electrochemical internal gear cutting process for blind-hole transmission shafts. I proposed two liquid-supply strategies: a flat-jet method and a flat-jet plus suction method. I designed the cathode, simulated the electrolyte flow field, carried out single-factor process experiments, compared the two supply methods, and finally introduced a secondary finishing pass by retracting the tool while the power remained on. The final goal was to achieve high-efficiency gear cutting with good tooth profile accuracy and a low surface roughness.
Background and Motivation
Internal gear transmission has several advantages over external gear transmission. The contact stress on the tooth surface is lower, the center distance is smaller, the structure is more compact, the sliding velocity is lower, the transmission efficiency is higher, and the end-face overlap ratio is larger. Because the teeth are inside the gear body, the meshing pair is also better protected. For these reasons, internal gear cutting is important in many machines. However, the same internal geometry that gives these advantages also makes gear cutting difficult. The tool must enter a confined space, the chip or sludge removal path is long, and the flow field in electrochemical gear cutting is difficult to control.
In the case of a transmission shaft, the internal gear is often located at the end of a hollow shaft or inside a blind cavity. The bore is small, and the tooth depth is limited. The material may be 20Cr, 40Cr, stainless steel, or another high-strength alloy. Mechanical gear cutting by shaping is a tooth-by-tooth process. It is flexible but slow, and the cutter wears quickly. Broaching is fast once a broach is made, but the broach is expensive and is not suitable for blind holes. Plastic forming can reduce material waste, but the die load is high, the corner filling is often incomplete, and die life is limited. Electrochemical gear cutting is attractive because it is a non-contact process, the cathode does not wear, and the machined surface has no residual stress and no recast layer. The main challenge is to keep the electrolyte flow uniform and to remove the solid electrochemical products from the narrow gap.
Fundamentals of Electrochemical Gear Cutting
Electrochemical gear cutting is based on anodic dissolution. The workpiece is connected to the positive terminal of a power supply, and the shaped cathode is connected to the negative terminal. An electrolyte flows through the small gap between the cathode and the workpiece. At the anode-electrolyte interface, metal atoms lose electrons and become metal ions. At the cathode-electrolyte interface, reduction reactions occur. The cathode shape is gradually copied into the workpiece. The material removal rate is governed by Faraday’s law. The theoretical dissolved volume is
$$V = \frac{M}{\rho} = \omega I t$$
where \(V\) is the dissolved volume, \(M\) is the dissolved mass, \(\rho\) is the density, \(\omega\) is the volumetric electrochemical equivalent, \(I\) is the current, and \(t\) is the time. For an alloy, the equivalent electrochemical dissolution is more complex because several elements dissolve simultaneously. I used the following form to estimate the alloy volumetric electrochemical equivalent:
$$\omega = \frac{1}{\rho F}\left(\frac{n_1 a_1}{A_1} + \frac{n_2 a_2}{A_2} + \cdots + \frac{n_j a_j}{A_j}\right)^{-1}$$
Here \(n_i\) is the valence, \(a_i\) is the mass fraction, \(A_i\) is the relative atomic mass, and \(F\) is the Faraday constant. In real electrochemical gear cutting, the actual dissolved volume is not exactly equal to the theoretical value. I therefore used the current efficiency
$$\eta = \frac{V_{\text{actual}}}{V_{\text{theory}}}$$
The current density in the gap is
$$i = \kappa \frac{U – \delta E}{\Delta_b}$$
where \(\kappa\) is the electrolyte conductivity, \(U\) is the applied voltage, \(\delta E\) is the total electrode potential, and \(\Delta_b\) is the machining gap. The anodic dissolution velocity is
$$v_a = \eta \omega i$$
For a stable frontal gap in electrochemical gear cutting, I used
$$\Delta_{bx} = \frac{\eta \omega \sigma U}{v_{cx}}$$
where \(\sigma\) is the electrolyte conductivity in the gap model and \(v_{cx}\) is the cathode feed rate. The side gap for a thin tooth cathode can be approximated as
$$\Delta_{sy} = \Delta_{sz} = \sqrt{\frac{2\eta \omega \sigma U d}{v_{cx}} + \left(\frac{\eta \omega \sigma U}{v_{cx}}\right)^2}$$
These equations show that the gap size depends on voltage, electrolyte conductivity, cathode feed rate, current efficiency, and the distance traveled by the cathode. In my process experiments, I used these relationships to interpret changes in slot width and slot depth during internal gear cutting.
Comparison of Internal Gear Cutting Methods
I reviewed the main methods for internal gear cutting and summarized their characteristics. The comparison helped me define the process requirements for electrochemical gear cutting.
| Method | Typical Tools | Advantages | Limitations for Internal Gear Cutting |
|---|---|---|---|
| Mechanical gear cutting by shaping | Pinion cutter | Flexible, suitable for internal and external gears | Tooth-by-tooth, low efficiency, tool wear, difficult for small blind holes |
| Mechanical gear cutting by broaching | Internal broach | High efficiency for through holes | Expensive tool, poor blind-hole capability, tool wear |
| Mechanical gear cutting by milling | Disc cutter, finger cutter | Simple motion | Intermittent cutting, low productivity, difficult chip removal |
| Plastic forming | Die and punch | Good material utilization, one-step forming | High forming force, incomplete corner filling, die life issues |
| Electrical discharge machining | Wire or shaped electrode | Can machine hard conductive materials | Electrode wear, mainly through holes, blind-hole difficulties |
| Electrochemical gear cutting | Shaped cathode | No tool wear, no residual stress, hard materials, complex shapes | Flow field control, gap control, electrolyte treatment |
The table shows that electrochemical gear cutting has a distinct advantage for blind-hole internal gears. The tool does not wear, and the process is not limited by material hardness. However, the flow field and the removal of solid products must be carefully designed. This is the main reason I developed the flat-jet plus suction method.
Cathode Structure and Tool Design
I designed the cathode around a thin tooth-shaped cutting edge. The tooth cathode must conduct current, resist bending under high electrolyte pressure, and keep the side gap small. I considered two configurations: a separated tooth cathode and an integrated tooth cathode. The separated design uses a tooth-shaped support and a separate thin tooth plate. The integrated design combines the support and the tooth plate into one body. I compared them as follows.
| Feature | Separated Tooth Cathode | Integrated Tooth Cathode |
|---|---|---|
| Material use | Good; only the thin plate is replaced after damage | Less favorable; the whole tooth body is replaced |
| Manufacturing process | Complex; requires wire EDM and alignment pins | Simpler; CNC milling can produce the profile |
| Surface quality | Poor; wire EDM leaves marks | Better; finish milling and polishing are possible |
| Production time | Long | Short |
| Use in my work | Used in preliminary trials | Used in single-factor and final experiments |
The cathode rod was made from a hollow copper tube. It had threaded ends, a tapered transition, and eighteen circumferential outlet slots. The tooth cathode was clamped against the rod so that its cutting face was aligned with the center plane of the outlet slots. A nozzle ring and lock nuts fixed the tooth cathode. I used POM for the insulating adapter because it is electrically insulating, corrosion resistant, and lightweight. The lower deflector and the upper deflector were added to guide the electrolyte. For the flat-jet plus suction cathode, I added a suction tube that extended into the blind-hole region. The suction tube was connected to a pump, so the electrolyte and solid products could be extracted from the bottom of the cavity.
| Cathode Component | Function | Material or Feature |
|---|---|---|
| Cathode rod | Supplies electrolyte and conducts current | Hollow copper tube, 18 outlet slots |
| Tooth cathode | Defines the internal gear tooth profile | Brass, thickness 0.3–0.6 mm |
| Nozzle ring | Forms the outlet slot and guides the jet | Diameter up to 33.5 mm in optimized design |
| Lower deflector | Improves circumferential flow uniformity | Conical or hollow conical insert |
| Upper deflector | Reduces flow loss at the inlet | Used in flat-jet plus suction cathode |
| Suction tube | Removes accumulated electrolyte and sludge | Extension length greater than 20 mm |
| Insulating adapter | Insulates the cathode from the machine | POM |
I paid special attention to the tooth thickness. A thicker cathode removes material for a longer time on the side walls and increases stray corrosion. A thinner cathode reduces the side gap but may bend under pressure. From my design review and experiments, a thickness of 0.5 mm gave a good balance between stiffness, conductivity, and side gap control in electrochemical gear cutting.
Flow Field Simulation and Optimization
Because electrochemical gear cutting is difficult to observe directly, I used COMSOL Multiphysics 5.6 to simulate the electrolyte flow field and the transport of solid products. I assumed that the electrolyte was incompressible and continuous, that the flow was turbulent, and that temperature-induced conductivity changes could be neglected in the flow model. The continuity equation was
$$\frac{\partial v_i}{\partial x_i} = 0$$
The momentum equation was
$$\rho \frac{\partial v_i}{\partial t} = \rho f_i – \frac{\partial P}{\partial x_i} + \mu \left(\frac{\partial^2 v_i}{\partial x_i^2} + \frac{\partial^2 v_i}{\partial y^2} + \frac{\partial^2 v_i}{\partial z^2}\right)$$
I also used the standard \(k\)-\(\varepsilon\) turbulence model:
$$\frac{\partial(\rho k)}{\partial t} + \frac{\partial(\rho k v_i)}{\partial x_i} = \frac{\partial}{\partial x_j}\left[\left(\mu + \frac{\mu_t}{\sigma_k}\right)\frac{\partial k}{\partial x_j}\right] + G_k – \rho \varepsilon$$
$$\frac{\partial(\rho \varepsilon)}{\partial t} + \frac{\partial(\rho \varepsilon v_i)}{\partial x_i} = \frac{\partial}{\partial x_j}\left[\left(\mu + \frac{\mu_t}{\sigma_\varepsilon}\right)\frac{\partial \varepsilon}{\partial x_j}\right] + C_{1\varepsilon}G_k\frac{\varepsilon}{k} – C_{2\varepsilon}\rho\frac{\varepsilon^2}{k}$$
where \(k\) is the turbulent kinetic energy, \(\varepsilon\) is the dissipation rate, \(\mu_t\) is the turbulent viscosity, and \(G_k\) is the production of turbulent kinetic energy due to the mean velocity gradient. I used these equations to evaluate the flow velocity in the machining gap and the uniformity among the eighteen tooth positions.
Flat-Jet Simulation
For the flat-jet method, the electrolyte entered the cathode rod from the top, passed through the internal passage, and exited through the outlet slots. It then split into an upper flow and a lower flow. Because the workpiece had a blind-hole structure, the lower flow could not escape freely. I studied the effect of outlet slot depth, lower deflector, and machining depth. The simulation parameters are listed below.
| Parameter | Values | Unit |
|---|---|---|
| Outlet slot depth | 0.2, 0.4, 0.6, 0.8 | mm |
| Lower deflector | with, without | — |
| Machining depth | 15, 30, 45, 60 | mm |
The outlet slot depth had a clear effect on the gap velocity. When the slot was too shallow, wall friction reduced the flow. When the slot was too deep, part of the electrolyte entered the blind-hole region and the velocity in the machining gap decreased. I found that 0.4 mm was the best outlet slot depth for the flat-jet method.
| Outlet Slot Depth (mm) | Maximum Gap Velocity (m/s) | Observation |
|---|---|---|
| 0.2 | 10.918 | High friction, lower flow |
| 0.4 | 11.637 | Best overall flow velocity |
| 0.6 | 11.561 | Slight decrease |
| 0.8 | 11.575 | More bypass flow into blind cavity |
I also compared a cathode with a lower deflector and one without it. The lower deflector improved the circumferential uniformity among different teeth. Without the deflector, the velocities at different outlet positions were more different. With the deflector, the flow distribution became more even. This is important for internal gear cutting because all teeth must be machined to the same depth and width.
When I increased the machining depth from 15 mm to 60 mm, the gap velocity did not change significantly. However, the transport distance for solid products became longer. In a blind hole, solid products can remain in the cavity and cause stray corrosion. This observation motivated the particle-tracking study and the flat-jet plus suction design.
Flat-Jet Plus Suction Simulation
For the flat-jet plus suction method, the electrolyte entered from both sides of the cathode rod. The upper deflector guided the flow around the suction tube. The lower deflector guided the flow toward the outlet slots. The suction tube extended into the blind-hole region and removed the accumulated electrolyte. I studied the nozzle ring diameter, suction tube extension, upper deflector, and machining depth. The simulation parameters are shown below.
| Parameter | Values | Unit |
|---|---|---|
| Nozzle ring diameter | 31, 31.5, 32, 32.5, 33, 33.5 | mm |
| Suction tube extension | 15, 20, 25, 30 | mm |
| Upper deflector | with, without | — |
| Machining depth | 15, 30, 45, 60 | mm |
The nozzle ring diameter controlled the bypass channel into the blind cavity. As the nozzle ring diameter increased, the bypass channel became narrower, and the gap velocity increased. The highest gap velocity occurred at a nozzle ring diameter of 33.5 mm. I selected this value for the optimized cathode.
| Nozzle Ring Diameter (mm) | Approximate Gap Velocity (m/s) | Effect |
|---|---|---|
| 31.0 | about 11.0 | Large bypass, lower gap velocity |
| 31.5 | about 11.0 | Similar to 31.0 |
| 32.0 | about 11.3 | Moderate improvement |
| 32.5 | about 11.5 | Higher velocity |
| 33.0 | about 12.4 | High velocity |
| 33.5 | about 13.0 | Best gap velocity |
The suction tube extension had little effect on the gap flow once it exceeded 20 mm. When the extension was only 15 mm, the simulation did not converge, which I interpreted as an unstable flow condition. Therefore, the suction tube should extend more than 20 mm into the cavity. The upper deflector reduced the flow loss caused by the two inlet jets impinging on the suction tube. With the upper deflector, the internal cathode flow velocity reached about 3.4 m/s, while without it the maximum was about 2.7 m/s. The upper deflector also improved the uniformity of the gap flow among different outlet positions.
As in the flat-jet case, the machining depth did not strongly change the gap velocity in the flat-jet plus suction method. However, the particle-tracking simulation showed a major difference. In the flat-jet method, solid products that entered the blind cavity had no direct outlet. They could remain there or re-enter the machining gap, which reduced stability. In the flat-jet plus suction method, many of the solid particles were drawn into the suction tube and removed from the cavity. The area near the tooth cathode also had a lower particle concentration. I therefore concluded that flat-jet plus suction is superior for blind-hole internal gear cutting.
| Comparison Item | Flat-Jet | Flat-Jet Plus Suction |
|---|---|---|
| Gap velocity | Good but lower near outlet entrance | Higher at initial gap region |
| Flow uniformity | Good with lower deflector | Good with upper and lower deflectors |
| Solid product removal | Limited in blind cavity | Enhanced by suction tube |
| Suitability for blind holes | Moderate | High |
| Stability at high feed | Lower | Higher |
Experimental System and Methodology
I carried out the electrochemical gear cutting experiments on a specially developed machine. The system included a machine platform, a control system, a DC pulse power supply, and an environmentally friendly electrolyte circulation system. The machine had a vertical Z-axis feed, an insulated tool holder, a conductive block, and a working table with drainage holes. The control system used a PLC and a human-machine interface. The power supply could deliver up to 30 V and 1000 A and had short-circuit protection. The electrolyte circulation system included ceramic membrane filtration, pressure filtration, cleaning, and temperature control. I controlled the electrolyte temperature between 24 °C and 28 °C because temperature affects conductivity and therefore the gear cutting accuracy.
The workpieces were 20Cr tubes. The outer diameter was 50 mm, the pre-machined bore was 34.25 mm, and the length was 60 mm or 80 mm. For the flat-jet experiments, the cutting depth was 20 mm. For the flat-jet plus suction experiments, the cutting depth was 10 mm. I used a fixture to close the through bore so that the internal cavity simulated a blind-hole internal gear. The measured responses were the slot width, slot depth, profile consistency, and surface roughness. I used a laser confocal microscope to obtain three-dimensional profiles of the internal gear teeth.
| Experimental Component | Description |
|---|---|
| Machine platform | C-frame, Z-axis feed, insulated fixture |
| Control system | PLC, touch screen, servo motor, linear guide, encoder |
| Power supply | DC pulse, 0–30 V, up to 1000 A, short-circuit protection |
| Electrolyte system | Ceramic membrane filtration, pressure filtration, temperature control |
| Workpiece material | 20Cr, outer diameter 50 mm, pre-bore 34.25 mm |
| Measurement | Laser confocal three-dimensional profilometry |
Single-Factor Experiments for Flat-Jet Gear Cutting
I first studied the flat-jet method. The factors were electrolyte pressure, voltage, and cathode tooth thickness. I kept the other factors fixed and measured the resulting slot width and slot depth. The experimental parameters are listed below.
| Parameter | Values | Unit |
|---|---|---|
| Electrolyte pressure | 0.2, 0.3, 0.4, 0.5 | MPa |
| Voltage | 14, 16, 18, 20 | V |
| Cathode tooth thickness | 0.3, 0.4, 0.5, 0.6 | mm |
When the electrolyte pressure increased from 0.2 MPa to 0.5 MPa, the slot width decreased from about 4087 μm to 3757 μm, and the slot depth decreased from about 2495 μm to 2297 μm. At low pressure, the electrolyte accumulated in the blind cavity, the flow was poor, and solid products were not removed effectively. This caused secondary corrosion and a larger slot. At higher pressure, the accumulated electrolyte and sludge were flushed away more effectively, so the slot size became smaller and the surface became smoother. However, a pressure above 0.5 MPa caused a risk of the inlet tube being pushed out of the quick connector in my preliminary trials. Therefore, I selected 0.5 MPa as the optimized pressure for flat-jet gear cutting.
When the voltage increased from 14 V to 20 V, the slot width increased from about 3671 μm to 4285 μm, and the slot depth increased from about 2407 μm to 2597 μm. Higher voltage increases the current density and the material removal rate, which can support a higher feed rate. However, it also increases stray corrosion and makes the slot larger. A voltage that is too low reduces the removal rate, and the cathode feed may exceed the dissolution rate, causing a short circuit. For the feed-rate experiments, I selected 18 V as the initial voltage for flat-jet gear cutting.
When the cathode tooth thickness increased, the side wall was exposed to electrochemical action for a longer time, so stray corrosion became more serious. The change was small from 0.3 mm to 0.5 mm, but from 0.5 mm to 0.6 mm the slot width increased from about 3810 μm to 3941 μm, and the slot depth increased from about 2453 μm to 2604 μm. A 0.5 mm tooth cathode provided enough stiffness and good conductivity. Therefore, I selected 0.5 mm as the optimized tooth thickness for flat-jet gear cutting.
| Factor | Value Range | Observed Effect on Slot Size | Optimized Value |
|---|---|---|---|
| Electrolyte pressure | 0.2–0.5 MPa | Slot width 4087→3757 μm; depth 2495→2297 μm | 0.5 MPa |
| Voltage | 14–20 V | Slot width 3671→4285 μm; depth 2407→2597 μm | 18 V for feed tests |
| Tooth thickness | 0.3–0.6 mm | Slot width 3810→3941 μm; depth 2453→2604 μm at higher end | 0.5 mm |
Single-Factor Experiments for Flat-Jet Plus Suction Gear Cutting
I then studied the flat-jet plus suction method. The parameters were electrolyte pressure, voltage, and cathode tooth thickness. Because the electrolyte had two inlet channels and one suction outlet, the pressure could be raised to 0.7 MPa without the tube ejecting from the connector. The parameters are shown below.
| Parameter | Values | Unit |
|---|---|---|
| Electrolyte pressure | 0.4, 0.5, 0.6, 0.7 | MPa |
| Voltage | 14, 16, 18, 20 | V |
| Cathode tooth thickness | 0.3, 0.4, 0.5, 0.6 | mm |
For the flat-jet plus suction method, the slot width decreased from about 4230 μm to 4130 μm and the slot depth decreased from about 2462 μm to 2354 μm when the pressure increased from 0.4 MPa to 0.6 MPa. This trend is similar to the flat-jet case. At low pressure, the flow was insufficient, solid products remained longer in the gap, and secondary corrosion increased the slot size. At 0.6 MPa, the suction helped remove the electrolyte and solid products, and the slot size became smaller. At 0.7 MPa, the conductivity effect and the higher flow velocity caused the slot size to increase again. Therefore, I selected 0.6 MPa as the optimized pressure for flat-jet plus suction gear cutting.
When the voltage increased from 14 V to 20 V, the slot width increased from about 3953 μm to 4230 μm, and the slot depth increased from about 2349 μm to 2411 μm. The trend is consistent with the flat-jet method. Higher voltage increases the dissolution rate but reduces dimensional accuracy. Lower voltage improves accuracy but may not support a high feed rate. I selected 18 V as the initial voltage for the feed-rate experiments.
When the cathode tooth thickness increased from 0.3 mm to 0.5 mm, the change in slot size was moderate. When the thickness increased from 0.5 mm to 0.6 mm, the slot width increased from about 4130 μm to 4242 μm, and the slot depth increased from about 2354 μm to 2398 μm. I again selected 0.5 mm as the optimized tooth thickness because it provided a good balance between stiffness and side gap control.
| Factor | Value Range | Observed Effect on Slot Size | Optimized Value |
|---|---|---|---|
| Electrolyte pressure | 0.4–0.7 MPa | Slot width 4230→4130 μm; depth 2462→2354 μm up to 0.6 MPa | 0.6 MPa |
| Voltage | 14–20 V | Slot width 3953→4230 μm; depth 2349→2411 μm | 18 V for feed tests |
| Tooth thickness | 0.3–0.6 mm | Slot width 4130→4242 μm; depth 2354→2398 μm at higher end | 0.5 mm |
Influence of Feed Rate and Limit Speed
After optimizing the single factors, I studied the effect of feed rate on process stability. In electrochemical gear cutting, the feed rate must match the dissolution rate. If the feed rate is too low, the side walls are exposed for a long time and the slot becomes wider and deeper. If the feed rate is too high, the gap becomes too small, the current fluctuates, and sparks or short circuits may occur. I recorded the current during each test and compared the minimum and maximum values after the cathode entered the workpiece by 10 mm. I also measured the tooth profile after each test.
| Supply Method | Voltage (V) | Maximum Feed Rate (mm/min) | Current Fluctuation (A) | Stability Observation |
|---|---|---|---|---|
| Flat-jet | 18 | 3.9 | about 11 | Stable but sensitive to sludge accumulation |
| Flat-jet plus suction | 18 | 4.5 | — | Better removal of solid products |
| Flat-jet plus suction | 20 | 4.8 | — | Stable under moderate fluctuation |
| Flat-jet plus suction | 22 | 5.1 | about 18 | Higher fluctuation, occasional sparking |
| Flat-jet plus suction | 18 | 4.2 | about 8 | Good balance for final gear cutting |
For the flat-jet method, the highest stable feed rate was 3.9 mm/min at 18 V. The current ranged from about 297 A to 308 A, giving a fluctuation of about 11 A. When I tried to increase the voltage and feed rate further, short circuits occurred. The solid products generated at the higher removal rate entered the gap and caused unstable current. For the flat-jet plus suction method, the highest feed rate was 5.1 mm/min at 22 V. However, at 5.1 mm/min the current fluctuation reached about 18 A, and repeated tests showed a high probability of sparking or short circuits. At 4.2 mm/min and 18 V, the current ranged from about 312 A to 320 A, with a fluctuation of only about 8 A. I therefore selected 4.2 mm/min as the preferred feed rate for final internal gear cutting with the flat-jet plus suction method.
The feed rate also affected the tooth profile. At a higher feed rate, the side wall exposure time was shorter, so the slot width and slot depth were smaller and closer to the cathode dimensions. For example, in the flat-jet method at 3.9 mm/min, the slot depth was about 2315 μm and the slot width was about 3786 μm. In the flat-jet plus suction method at 5.1 mm/min, the slot depth was about 2290 μm and the slot width was about 3650 μm. However, a higher feed rate produced more solid products, and the surface quality decreased. This trade-off led me to develop the secondary finishing method.
| Method | Feed Rate (mm/min) | Slot Width (μm) | Slot Depth (μm) | Surface Quality Trend |
|---|---|---|---|---|
| Flat-jet | 2.7 | Higher than at 3.9 | Higher than at 3.9 | Better than at 3.9 |
| Flat-jet | 3.9 | 3786 | 2315 | More product-induced marks |
| Flat-jet plus suction | 2.7 | Higher than at 5.1 | Higher than at 5.1 | Better than at 5.1 |
| Flat-jet plus suction | 5.1 | 3650 | 2290 | More product-induced marks |
Comparison of Flat-Jet and Flat-Jet Plus Suction
The experiments confirmed the simulation results. The flat-jet plus suction method improved both productivity and accuracy. The maximum feed rate increased from 3.9 mm/min to 5.1 mm/min, and the current fluctuation at a comparable stable condition was lower. The suction tube removed part of the solid products from the blind cavity, so the tooth surface was exposed to less stray corrosion. This improved the profile accuracy. The comparison is summarized below.
| Comparison Item | Flat-Jet | Flat-Jet Plus Suction |
|---|---|---|
| Maximum feed rate | 3.9 mm/min at 18 V | 5.1 mm/min at 22 V |
| Preferred stable feed rate | 3.9 mm/min | 4.2 mm/min |
| Current fluctuation | About 11 A at 3.9 mm/min | About 8 A at 4.2 mm/min |
| Blind-cavity product removal | Limited | Enhanced by suction |
| Profile accuracy | Good but with more stray corrosion | Better and closer to cathode shape |
| Surface quality | Marks and pits remain | Improved, but finishing is still needed |
Even with the flat-jet plus suction method, the internal gear surface still had some defects. I observed two main types. The first was micro-pitting caused by stray corrosion and solid products in the electrolyte. The second was linear marking caused by the surface quality of the tooth cathode. The cathode rod side wall and the accumulated electrolyte in the upper part of the cavity could also form a conductive path, which caused darkening and minor corrosion on the tooth surface. These observations led me to introduce a secondary finishing pass.
Secondary Finishing by Retraction
I proposed a secondary finishing method that uses the retraction motion of the machine. After the first electrochemical gear cutting pass reaches the target depth, the power remains on, and the cathode retracts at a controlled speed. During retraction, the cathode again passes over the machined tooth surface, removing a small amount of material and smoothing the surface. This method does not require a separate setup, and the relative position between the cathode and workpiece remains fixed. Therefore, the two passes are well aligned, and the finishing time is short.
| Secondary Finishing Parameter | Values | Unit |
|---|---|---|
| Voltage | 16, 18, 20, 22 | V |
| Retraction speed | 0.10, 0.15, 0.20, 0.25 | mm/s |
I studied the effect of voltage and retraction speed on the finishing result. Higher voltage increased the slot width and slot depth, which reduced dimensional accuracy. Lower voltage did not remove the small pits left by stray corrosion. I found that 18 V gave a good combination of surface improvement and dimensional control. For the retraction speed, a slower speed increased the exposure time and enlarged the slot. A faster speed reduced the finishing effect and could decrease stability. The best result was obtained at 0.20 mm/s.
| Secondary Finishing Factor | Trend | Optimized Value |
|---|---|---|
| Voltage | Higher voltage enlarges slot; lower voltage leaves pits | 18 V |
| Retraction speed | Slower speed enlarges slot; faster speed reduces smoothing | 0.20 mm/s |
Optimized Final Gear Cutting Process
Based on all experiments, I selected the final parameters for electrochemical internal gear cutting. The first pass used a feed rate of 4.2 mm/min, a voltage of 18 V, an electrolyte pressure of 0.6 MPa, and a cathode tooth thickness of 0.5 mm. The secondary finishing pass used a retraction speed of 0.2 mm/s and a voltage of 18 V. The final parameter set is shown below.
| Parameter | Value | Unit |
|---|---|---|
| First-pass feed rate | 4.2 | mm/min |
| First-pass voltage | 18 | V |
| Electrolyte pressure | 0.6 | MPa |
| Cathode tooth thickness | 0.5 | mm |
| Retraction speed | 0.2 | mm/s |
| Retraction voltage | 18 | V |
With these parameters, I successfully produced internal gears with depths of 30 mm and 60 mm. The tooth profiles were consistent, and the dimensional scatter was small. The standard deviation of the slot width for three sampled teeth was about 10.814 μm, and the standard deviation of the slot depth was about 11.921 μm. The surface roughness values measured on three sections were about 2.896 μm, 2.326 μm, and 1.323 μm. These results show that the combination of flat-jet plus suction and retraction finishing can improve both efficiency and surface quality in internal gear cutting.
| Final Result | Value |
|---|---|
| Machined depth | 30 mm and 60 mm |
| Number of teeth | 18 |
| Slot width standard deviation | 10.814 μm |
| Slot depth standard deviation | 11.921 μm |
| Surface roughness Ra | 2.896, 2.326, 1.323 μm |
| Main advantage | Stable gear cutting, good profile consistency, reduced pits and marks |
Discussion
The results show that the electrolyte flow field is the key factor in electrochemical internal gear cutting. In a blind-hole workpiece, the lower part of the cavity acts as a dead volume. Without suction, the electrolyte and solid products accumulate, which changes the local conductivity and causes secondary corrosion. The suction tube changes the flow path and removes a large fraction of the solid products. This is why the flat-jet plus suction method can support a higher feed rate and produce a better tooth profile. The upper deflector also matters because it reduces the flow loss when two inlet jets meet inside the cathode rod. The lower deflector improves the circumferential uniformity, which is essential for multi-tooth gear cutting.
The tooth cathode thickness is another important factor. A thin cathode reduces the side exposure time, but it can bend or vibrate under high pressure. A thick cathode is stiffer, but it increases stray corrosion. In my experiments, 0.5 mm was the best compromise. The outlet slot depth also affects the flow. A depth of 0.4 mm provided the highest gap velocity and the best balance between flow supply and bypass loss. The nozzle ring diameter controls the bypass flow into the blind cavity. A larger ring diameter increases the gap velocity, and 33.5 mm gave the best result in my simulations.
Voltage and feed rate must be matched. If the voltage is too low, the dissolution rate cannot keep up with the feed, and the gap becomes too small. If the voltage is too high, the gap becomes larger, stray corrosion increases, and the tooth profile becomes less accurate. The feed rate has a similar effect. A higher feed rate reduces side corrosion and improves dimensional accuracy, but it produces more solid products and can destabilize the process. The flat-jet plus suction method extends the stable feed window by removing solid products more effectively.
The secondary finishing pass is a practical addition. It uses the retraction motion of the machine and does not require a second setup. Because the cathode remains aligned with the workpiece, the finishing pass corrects small surface defects without changing the overall tooth position. The optimized voltage and retraction speed remove the pits and linear marks while keeping the slot dimensions within tolerance. This is important for internal gear cutting because the internal tooth surface cannot be easily finished by conventional grinding after electrochemical machining.
Conclusions
I developed and tested a new electrochemical internal gear cutting process for blind-hole transmission shafts. The main conclusions are as follows.
First, I designed two cathode systems: a flat-jet cathode and a flat-jet plus suction cathode. The tooth cathode was integrated with a support body, and the cathode rod had eighteen outlet slots. The optimized outlet slot depth was 0.4 mm, the optimized nozzle ring diameter was 33.5 mm, and the optimized tooth thickness was 0.5 mm. The lower deflector improved flow uniformity, and the upper deflector reduced inlet flow loss. The suction tube improved solid product removal from the blind cavity.
Second, I used COMSOL Multiphysics 5.6 to simulate the flow field and particle transport. The simulation showed that the gap velocity was relatively insensitive to machining depth, but the solid product removal was strongly affected by the supply method. The flat-jet plus suction method removed particles from the blind cavity and reduced the particle concentration near the tooth cathode. This improved the stability of gear cutting.
Third, I carried out single-factor experiments for both supply methods. For the flat-jet method, the optimized electrolyte pressure was 0.5 MPa, the voltage for feed tests was 18 V, and the tooth thickness was 0.5 mm. For the flat-jet plus suction method, the optimized electrolyte pressure was 0.6 MPa, the voltage for feed tests was 18 V, and the tooth thickness was 0.5 mm. The flat-jet method reached a maximum stable feed rate of 3.9 mm/min, while the flat-jet plus suction method reached 5.1 mm/min. At a stable feed rate of 4.2 mm/min, the flat-jet plus suction method had a current fluctuation of about 8 A, which was lower than the flat-jet method at 3.9 mm/min.
Fourth, I proposed a secondary finishing method based on retraction. The optimized finishing voltage was 18 V, and the optimized retraction speed was 0.2 mm/s. With these parameters, I produced internal gears with good tooth consistency, a slot width standard deviation of about 10.814 μm, a slot depth standard deviation of about 11.921 μm, and a minimum surface roughness Ra of about 1.323 μm. The final process solved several problems in internal gear cutting, including blind-cavity accumulation, poor solid product removal, large dimensional scatter, and surface pits and marks.
Future Work
Although the proposed method is effective, further work is needed. The alignment of the eighteen teeth with the eighteen outlet slots is time-consuming, so the cathode structure can be improved for faster assembly. The upper part of the cavity still accumulates some electrolyte, which can affect stability and surface quality. Future work can focus on optimizing the upper flow path or adding a second suction path. A gap model that predicts the tooth profile from the cathode dimensions would also be useful for cathode design. Finally, the process can be integrated with automated clamping, real-time gap monitoring, and closed-loop control to make electrochemical gear cutting more suitable for production.
In summary, my work shows that flat-jet plus suction electrochemical machining is a promising method for internal gear cutting. It combines the advantages of electrochemical machining, such as no tool wear and no residual stress, with a flow field that is suitable for blind holes. The secondary finishing pass further improves the surface quality. With continued development, this method can be used for high-efficiency and high-accuracy internal gear cutting in transmission shafts and other compact transmission components.