In the field of coal mining machinery, the rocker arm shell of a shearer serves as a critical load-bearing component within the cutting unit. These shell castings are subjected to substantial operational loads, necessitating exceptionally high quality standards. Due to their complex geometry, rocker arm shell castings are predominantly manufactured via casting processes. Cast steel, known for its high strength and favorable mechanical properties, is typically selected as the material for these shell castings to meet performance demands. However, the casting of steel presents challenges such as poor fluidity and high linear shrinkage, which can lead to defects like shrinkage porosity and cavities during solidification. Risers, as essential feeding mechanisms in casting, play a pivotal role in mitigating these defects. Their placement, dimensions, quantity, and type significantly influence the feeding efficiency and the final quality of the shell castings. In this research, we employ casting simulation software to systematically design and optimize the riser system for a shearer rocker arm shell casting, aiming to eliminate defects and ensure the integrity of the component.
The rocker arm shell casting houses internal components such as the cutting motor, spur gear transmission system, and internal spray device, while external attachments include the planetary transmission mechanism and the drum. Additionally, cooling water channels are often integrated into the surface of the shell casting to dissipate heat from the gear transmission system. The geometry of these shell castings is highly irregular, featuring numerous shaft holes and non-uniform wall thicknesses. Typical wall sections range from 60–70 mm, with local regions exceeding 200 mm, categorizing them as complex structural castings. This complexity, combined with the inherent poor fluidity of cast steel, results in multiple thermal centers during solidification, leading to numerous potential shrinkage zones. Consequently, the design of an effective riser system for such shell castings is particularly demanding.
To facilitate mold design, a parting plane is established for the casting process. For rocker arm shell castings, two primary parting plane orientations are common: a vertical pouring orientation with the parting plane through the middle of the gear cavity, or a upright pouring orientation with the parting plane defined by the axes of the planetary head mounting cylinder and the transmission gearbox shaft holes. The upright pouring method often results in relatively flat top and bottom surfaces for the shell casting, which better facilitates directional solidification from the casting towards the risers, minimizing interference from other factors. Therefore, our study bases its riser design on the upright pouring orientation.
The initial step in riser design involves identifying the thermal centers or hotspots within the casting—areas most prone to shrinkage defects. For the specific model of shearer rocker arm shell casting under investigation, regions with greater wall thickness, such as the motor cylinder and the planetary head mounting area, exhibit larger volumes of molten metal and are consequently more susceptible to significant shrinkage porosity and cavities. Gravity influences the solidification process, meaning shrinkage defects tend to migrate towards the upper sections of the casting. Given the chosen parting plane, the top of the planetary head mounting cylinder is elevated relative to other parts, making it especially vulnerable.
We utilized casting simulation software (such as Huazhu CAE) to perform solidification analysis without any risers. The simulation predicted shrinkage defects as shown in the following analysis. Large volumes of shrinkage porosity and cavities were anticipated at the tops of both the motor cylinder and the planetary head mounting cylinder. Additionally, the central section of the gearbox and the reinforcing ribs connecting the gearbox to the motor cylinder also showed smaller shrinkage zones. Interestingly, the simulation also revealed substantial shrinkage regions at the bottom of the planetary head mounting cylinder and the motor cylinder. This occurs because the central cavity of the shell casting is large, and the parting plane bisects this cavity. During solidification, the central areas near the parting plane on both sides of the shell solidify first, isolating the molten metal below and preventing feed metal from above from compensating, thus leading to shrinkage at the bottom.
Based on this analysis, we proceeded with the riser design. Top risers are generally preferred. We initially designed four top risers positioned at: above the planetary head mounting cylinder (Riser 1), the central top of the gearbox (Riser 2), the reinforcing rib connecting the gearbox and motor cylinder (Riser 3), and above the motor cylinder (Riser 4). For shell castings with thicker walls and larger metal volumes on the sides, open-top risers (Riser 1 and Riser 4) were chosen to allow for observation of mold filling, slag removal, and gas venting. The internal risers (Riser 2 and Riser 3) were designed as blind risers for better feeding efficiency and metal savings.
Regarding riser shape, the side risers (Riser 1 and Riser 4) were designed as elongated open-top risers with base dimensions adhering to standard specifications. As open risers, their height was extended to the top of the mold. The central risers (Riser 2 and Riser 3) were designed as cylindrical blind risers. For dimension calculation, we employed the modulus method, specifically the circumferential quotient method. The formula for the riser’s circumferential quotient $Q_m$ is:
$$ Q_m = \frac{\varepsilon Q_b}{(1-\varepsilon)f^3 – f^2} $$
where $\varepsilon$ is the volumetric shrinkage rate of the molten metal, $f$ is the modulus enlargement factor, and $Q_b$ is the circumferential quotient of the casting section being fed. The circumferential quotient characterizes the spatial geometry of an object and is calculated as the volume divided by the cube of its modulus ($Q = V / M^3$). For the shell casting material ZG25MnNi cast at 1560°C, the volumetric shrinkage rate $\varepsilon$ is approximately 4.5%. Given the complex shape of the shell castings, we used 3D modeling software to determine the volume and surface area of each feeding zone. Assuming standard riser geometries, the initial riser dimensions were calculated.
These initial dimensions often require adjustment based on practical casting geometry. For the open risers (Riser 1 and Riser 4), whose feeding capacity is lower than blind risers, we increased their volume to ensure effectiveness. Furthermore, since the top of the planetary head mounting cylinder (Riser 1 location) is higher than the motor cylinder top (Riser 4 location), Riser 4’s height was increased to ensure it reaches the mold top. For the blind risers (Riser 2 and Riser 3), placed near the edges due to cooling channel obstructions, we maintained their cross-sectional area but increased their height. The calculated and final adjusted dimensions are summarized in Table 1.
| Riser | Calculated Dimensions (mm) | Final Dimensions (mm) | Type |
|---|---|---|---|
| Riser 1 | 250 × 375 × 312 (Base, Height) | 280 × 420 × 350 | Open Top |
| Riser 2 | φ240 × 240 (Diameter × Height) | φ240 × 320 | Blind |
| Riser 3 | φ240 × 240 | φ240 × 320 | Blind |
| Riser 4 | 240 × 360 × 300 | 280 × 420 × 790 | Open Top |
This initial design, termed Scheme 1, was simulated. The results showed that while top shrinkage was reduced, significant shrinkage remained at the junction between the planetary head mounting cylinder and the gearbox, as well as at the bottom of the shell castings. The wall thickness variation at that junction causes uneven cooling, leading to isolated liquid pools.
To improve Scheme 1, we added two additional blind risers: Riser 5 near the gearbox close to the planetary head junction, and Riser 6 at the connection between the gearbox and motor cylinder. Both were designed as cylindrical blind risers with dimensions φ240 mm × 320 mm. This revised plan, Scheme 2, was simulated. The results indicated that top shrinkage was virtually eliminated, but bottom shrinkage persisted, concentrated at the outer motor cylinder, its junction with the gearbox, and the planetary head-gearbox junction. The large central cavity limited the effective feeding distance of the top risers for these bottom sections of the shell castings.
To address bottom shrinkage in shell castings, feeding aids known as chills or padding (often referred to as “feed aids” or “padding” in this context) can be employed. We applied vertical padding (feed metal supplements) beneath certain risers to extend their effective feeding range and promote directional solidification upwards. Padding modifies the solidification sequence, preventing isolated liquid zones at the bottom. Based on the Scheme 2 simulation, padding was added beneath Risers 1, 4, 5, and 6. The height and taper of the padding vary with local casting geometry. For instance, the motor cylinder area (Riser 4) has the greatest casting height and required the tallest padding. The cylindrical planetary head area (Riser 1) required padding that tapers outward. The padding parameters are detailed in Table 2.
| Riser | Padding Height (mm) | Padding Taper (%) |
|---|---|---|
| Riser 1 | 480 | 21 |
| Riser 4 | 600 | 12 |
| Riser 5 | 500 | 14 |
| Riser 6 | 500 | 14 |
The design with padding, Scheme 3, was simulated. Results showed shrinkage defects were largely confined to the risers themselves, with bottom shrinkage nearly eliminated. However, a significant shrinkage zone remained at the bottom junction between the motor cylinder and gearbox, an area difficult to feed via top risers due to overhead reinforcing ribs.
To feed this isolated hotspot in the shell castings, a side riser was introduced. Unlike top risers, a side riser connects to the casting’s sidewall via a neck. We placed a side riser (Riser 7) at the problematic bottom junction. It was designed as a cylindrical blind riser. Since side risers are at a lower elevation and metal can freeze more readily in the neck, their dimensions should be slightly larger than an equivalent top riser. Given the previous design margins, Riser 7 was also sized at φ240 mm × 320 mm, with a neck height of 400 mm. The comprehensive design, Scheme 4, includes six top risers (two open, four blind, four with padding) and one side riser. The final riser layout is conceptualized in the accompanying figure.
The solidification simulation for Scheme 4 confirmed that all shrinkage porosity and cavities were successfully redirected into the risers, with the shell casting itself being free of such defects. This validates the effectiveness of the designed riser system for these complex shell castings.
The modulus method, particularly the circumferential quotient approach, provides a scientific basis for riser sizing. The modulus $M$ of a casting section is defined as its volume $V$ divided by its cooling surface area $A_s$: $M = V / A_s$. For a riser to effectively feed a casting section, its modulus should be greater than that of the section. The relationship can be expressed as:
$$ M_r > k \cdot M_c $$
where $M_r$ is the riser modulus, $M_c$ is the casting section modulus, and $k$ is a safety factor (typically >1). For cylindrical risers, the modulus is $M_r = D/6$ for a diameter $D$ (assuming height-to-diameter ratio ~1). The volumetric feeding requirement dictates the riser volume $V_r$ must compensate for the shrinkage in the feeding zone volume $V_c$:
$$ V_r \geq \frac{\varepsilon V_c}{\eta} $$
where $\eta$ is the riser efficiency (typically 14-20% for blind risers). Combining modulus and volume requirements allows for optimal riser design. For shell castings with variable sections, we compute the required riser dimensions iteratively for each feeding zone.
The simulation process itself involves solving the heat transfer equation during solidification. The governing equation for transient heat conduction is:
$$ \rho c_p \frac{\partial T}{\partial t} = \nabla \cdot (k \nabla T) + Q_L $$
where $\rho$ is density, $c_p$ is specific heat, $T$ is temperature, $t$ is time, $k$ is thermal conductivity, and $Q_L$ is the latent heat release due to phase change. The simulation predicts temperature fields, solidification fronts, and ultimately identifies regions where liquid metal is isolated, leading to shrinkage defects. By iteratively modifying riser parameters and observing the simulation results, we optimized the design for these shell castings.
Further considerations in riser design for large shell castings include the use of exothermic riser sleeves to improve thermal efficiency, insulating toppings to reduce heat loss from open risers, and the strategic placement of chills to control solidification direction. The gating system design also interacts with the riser system; a well-designed gating system ensures proper mold filling and thermal distribution, supporting the riser’s feeding function. For the rocker arm shell castings, we assumed a bottom gating system to minimize turbulence and oxidation, which complements the upright pouring orientation and top riser placement.
Economic factors are crucial in production. Minimizing riser volume reduces yield loss and melting costs. The final Scheme 4, while employing multiple risers, uses calculated minimum dimensions and a mix of open and blind types to balance effectiveness and economy. The total riser volume as a percentage of casting volume (yield) can be estimated. For complex shell castings like these, achieving a yield above 50% is often challenging but targeted through optimized riser design.
Quality verification extends beyond simulation. Practical foundry trials involve non-destructive testing (NDT) such as ultrasonic testing or radiography to detect internal defects in produced shell castings. The simulation predictions should align with actual casting outcomes. Process windows for pouring temperature, mold preheat, and alloy composition also affect shrinkage behavior and must be controlled.
In conclusion, the design of an effective riser system for shearer rocker arm shell castings is a multifaceted engineering task. Through systematic analysis of casting geometry, application of modulus-based calculations, strategic use of padding and side risers, and validation via solidification simulation, we developed a riser scheme that effectively eliminates shrinkage defects. The final design features seven risers: six top risers (including two open risers for observation and four blind risers for efficiency, with four incorporating padding) and one side riser for isolated bottom feeding. This configuration ensures directional solidification towards the risers, confines all shrinkage to the riser bodies, and maintains the structural integrity of the shell castings. The methodology demonstrated here, combining theoretical calculation with advanced simulation, provides a robust framework for optimizing riser design in complex steel castings, ultimately enhancing the reliability and performance of critical mining machinery components like the rocker arm shell.
The successful design of risers for these shell castings hinges on a deep understanding of solidification principles. The Chvorinov’s rule, which states that solidification time $t_s$ is proportional to the square of the volume-to-surface area ratio $(V/A)^2$, or the modulus squared, is fundamental: $t_s = C (M)^2$, where $C$ is a mold constant. This explains why sections with larger modulus solidify slower and require feeding for a longer duration. For the rocker arm shell castings, identifying sections with large modulus (thick sections, junctions) was key to riser placement.
Furthermore, the concept of feeding distance is critical. The maximum distance over which a riser can effectively feed a section of a casting is limited. For steel castings, empirical rules suggest a feeding distance of approximately 4.5 times the section thickness for end-fed plates. For complex shell castings, this distance is reduced due to geometrical constraints. Our use of multiple risers and padding effectively managed the feeding distances for various zones of the shell castings.
To generalize the riser design process for shell castings, we can outline a step-by-step methodology:
- Geometric Analysis: Create a detailed 3D model of the shell casting. Identify and segment major sections based on wall thickness and connectivity.
- Modulus Calculation: Compute the modulus $M_i$ for each significant section $i$ of the shell casting using $M_i = V_i / A_{s,i}$, where $A_{s,i}$ is the cooling surface area (excluding contact areas with cores or other non-cooling surfaces).
- Thermal Center Identification: Sections with locally maximum modulus are thermal centers. Use casting simulation software for initial defect prediction without risers to corroborate.
- Riser Type Selection: Decide on open vs. blind risers based on placement (top/side), need for observation, and desired efficiency.
- Riser Sizing: For each feeding zone, determine the required riser modulus $M_r \geq 1.2 \times M_c$ (safety factor). Calculate riser dimensions (diameter $D$, height $H$) for standard shapes. For cylindrical risers, $M_r = D/6$ for $H/D = 1$. Adjust for different $H/D$ ratios using: $M_r = \frac{D H}{2(2D + H)}$ for a cylinder with one end active (top riser on flat surface).
- Volume Check: Ensure riser volume $V_r$ satisfies: $V_r \geq \frac{\varepsilon V_f}{\eta}$, where $V_f$ is the volume of the feeding zone (casting volume that solidifies after the riser neck seals), and $\eta$ is the expected riser efficiency (e.g., 0.15 for blind risers).
- Padding Design: For sections where the riser’s natural feeding distance is insufficient, design padding to increase the effective modulus of the casting path towards the riser. The padding dimensions can be derived to create a tapered modulus gradient.
- Side Riser Consideration: For isolated lower sections, design side risers with adequate neck dimensions to prevent premature freezing. The neck modulus $M_n$ should satisfy $M_n > M_c$ to remain open longer than the casting section.
- Simulation Iteration: Use casting simulation to test the design. Analyze shrinkage predictions. Iteratively adjust riser sizes, positions, and padding until defects are confined to risers.
- Economic Optimization: Evaluate yield (casting weight / total poured weight) and consider riser removal costs. Explore options like exothermic risers to reduce size.
Applying this methodology to the rocker arm shell castings involved several iterations. The initial modulus calculations for key sections are summarized in Table 3.
| Casting Section | Approximate Volume, $V$ (cm³) | Cooling Surface Area, $A_s$ (cm²) | Modulus, $M = V/A_s$ (cm) |
|---|---|---|---|
| Planetary Head Cylinder Top | 8500 | 1200 | 7.08 |
| Motor Cylinder Top | 9200 | 1300 | 7.08 |
| Gearbox Central Section | 6800 | 1100 | 6.18 |
| Motor Cylinder Bottom Junction | 5500 | 950 | 5.79 |
For a required riser modulus $M_r \geq 1.2 \times 7.08 \approx 8.5$ cm for the top sections, a cylindrical riser diameter $D$ can be found from $M_r = D/6 \Rightarrow D = 6 \times 8.5 = 51$ cm. This is impractically large, indicating that a single riser per large section may not be efficient. Instead, we divided the feeding zones and used padding to increase the effective modulus of the casting path, allowing for smaller risers. The final riser dimensions in Table 1 reflect this practical adjustment based on simulation feedback.
The padding design involves creating a geometrical extension that ensures the modulus decreases gradually from the riser down to the casting. The padding height $H_p$ and taper are designed so that the modulus at any horizontal section satisfies the feeding path criterion. An approximate formula for the required padding taper angle $\theta$ can be derived from Chvorinov’s rule to maintain a constant solidification time gradient. For simplicity, empirical tapers of 10-20% are often used, as reflected in Table 2.
The side riser design requires careful neck calculation. The neck must solidify after the casting hotspot but before the riser itself to allow feeding. The neck modulus $M_n$ should be between the casting modulus $M_c$ and the riser modulus $M_r$: $M_c < M_n < M_r$. For Riser 7 feeding the bottom junction with $M_c \approx 5.8$ cm, a neck with cross-sectional area equivalent to a modulus of about 6.5 cm was designed. For a cylindrical neck of diameter $d_n$ and height $h_n$, assuming $h_n \approx 2d_n$, the modulus is approximately $d_n/5$. Setting $d_n/5 = 6.5$ cm gives $d_n = 32.5$ cm. However, practical constraints led to a neck height of 400 mm with an effective diameter derived from the riser connection area.
Simulation software employs finite element or finite difference methods to solve the heat transfer equation. The latent heat release $Q_L$ is handled by methods like the enthalpy method: $H = \int \rho c_p dT + f_s L$, where $H$ is enthalpy, $f_s$ is solid fraction, and $L$ is latent heat. The simulation outputs include temperature contours, solid fraction plots, and shrinkage prediction algorithms such as the Niyama criterion. The Niyama criterion $Ny$ is given by:
$$ Ny = \frac{G}{\sqrt{\dot{T}}} $$
where $G$ is the temperature gradient and $\dot{T}$ is the cooling rate at the end of solidification. Regions with $Ny$ below a critical value (e.g., 1 °C¹/²·s¹/² for steel) are predicted to contain shrinkage porosity. Our simulation results used such criteria to identify defect zones.
In summary, the comprehensive riser design for shearer rocker arm shell castings integrates fundamental solidification science, empirical rules, and computational simulation. The iterative process ensures that the final casting is sound, meeting the rigorous demands of mining equipment. The methodologies and principles discussed here are applicable to a wide range of heavy-duty shell castings in various industries, emphasizing the importance of tailored feeding system design for achieving high-integrity cast components.