Quality model and establishing method for pressing cylindrical electrode block for VAR furnace titanium ingot

Abstract

This application discloses a mass model of a pressed cylindrical electrode block for VAR furnace titanium ingot casting. This mass model is based on the geometric characteristics of the cylindrical electrode block's cross-section, which consists of an arc-shaped region and a rectangular region. First, the calculation model for the arc area, S1=1 / 2R, is derived. 2 (θ-sinθ) and the rectangular area calculation model S2=2aRsin(θ / 2), finally introducing the density of titanium raw material to obtain the mass model m=(1 / 2R 2 (θ-sinθ)+2aRsin(θ / 2))ρh; Through verification with multiple sets of samples and correction of density parameters, the model deviation is ensured to be ≤±0.5%. This invention achieves accurate quantitative prediction of electrode block quality, which can be directly used for process parameter preset and raw material usage back-calculation, significantly improving production efficiency, product consistency and reducing raw material waste, and providing technical support for high-quality production of VAR furnace titanium ingots.

Description

Technical Field

[0001] This invention relates to the field of titanium alloy preparation technology, specifically to a quality model and method for pressing cylindrical electrode blocks for VAR furnace titanium ingots. Background Technology

[0002] The VAR furnace vacuum arc remelting technology is a core process for preparing high-quality titanium ingots. Its principle is to melt the electrode material by generating arc heat between the electrode and the ingot. The molten metal then solidifies in a water-cooled copper crucible to form a titanium ingot. This technology directly determines the key indicators of titanium ingots, such as compositional uniformity, density, and mechanical properties, and is the core support for the industrial application of titanium alloys.

[0003] In the VAR furnace titanium ingot production process, cylindrical electrode blocks, as the core raw material for the remelting process, are crucial for determining the final ingot quality. Deviations in electrode block quality not only lead to arc instability during remelting and cause ingot composition to deviate from design requirements, but can also result in fatal defects such as shrinkage cavities, cracks, and inclusions, potentially causing the entire furnace of ingots to be scrapped. Furthermore, the consistency of electrode block quality directly affects the performance stability of ingots across multiple furnaces, which is critical to the reliability of downstream product mass production. Figure 1 , Figure 2 The cross-section of the cylindrical electrode block used for VAR furnace titanium ingot casting consists of an arc-shaped region and a rectangular region.

[0004] Currently, the pressing process for cylindrical electrode blocks used in VAR furnace titanium ingot casting generally relies on experience-based operation, lacking precise scientific mathematical guidance. Operators estimate the amount of raw materials based on past production experience, put the sponge titanium and alloy raw materials into the mold, and then press them. After pressing, the electrode blocks are weighed. If the quality does not meet the target value, the amount of raw materials or pressing parameters are adjusted, and pressing is repeated, forming a cyclical process of calculation, pressing, weighing, and adjustment. This model has disadvantages such as low production efficiency, poor product quality consistency, serious raw material waste, and blind quality control.

[0005] Therefore, it is urgent to establish a quality mathematical model based on the geometric features and physical properties of electrode blocks to achieve accurate prediction of electrode block quality and scientific pre-setting of process parameters, fundamentally solve the problem of blindness in existing technologies, and improve the production efficiency and product quality of VAR furnace titanium ingots. Summary of the Invention

[0006] This invention aims to provide a quality model and method for pressing cylindrical electrode blocks for VAR furnace titanium ingots. By constructing a quantitative correlation model between geometric features and quality, the quality of the electrode blocks can be accurately predicted, providing a scientific basis for optimizing pressing process parameters.

[0007] To achieve the above objectives, the first aspect of the present invention provides a modeling method for a cylindrical electrode block pressing quality model for VAR furnace titanium ingot casting, comprising the following steps: S1. Define core parameters: R is the radius of the electrode block cross section, θ is the central angle corresponding to the arc-shaped region, a is the width of the rectangular region, h is the height of the electrode block, and ρ is the density of the titanium raw material used for pressing. S2. Establish the area calculation model for the arc-shaped region: S1 = 1 / 2R 2 (θ-sinθ), where S1 is the area of ​​the arc-shaped region; establish a rectangular area calculation model: S2=2aRsin(θ / 2), where S2 is the area of ​​the rectangular region; S3. Establish the electrode block volume calculation model: V=S1+S2=(1 / 2R) 2 (θ-sinθ)+2aRsin(θ / 2))h, where V is the volume of the electrode block; S4. Establish the electrode block mass model: m = (1 / 2R) 2 (θ-sinθ)+2aRsin(θ / 2))ρh, where m is the mass of the electrode block.

[0008] Furthermore, it also includes step S5, model verification and correction: selecting electrode blocks with different parameter specifications to press the sample, and correcting the model parameters by measuring the deviation between the actual mass and the mass calculated by the model.

[0009] The optimized method calibrates the material by correcting the actual value of the titanium raw material density ρ when the deviation exceeds ±0.5%. The corrected ρ reflects the actual compaction state of the raw material during the pressing process.

[0010] Better still, the central angle θ in step S1 is in the range of (0,π], and the parameters R, a, and h are determined according to the production process requirements of VAR furnace titanium ingots and the design specifications of the electrode blocks.

[0011] A second aspect of the present invention provides a quality model obtained by the modeling method described in the first aspect of the present invention.

[0012] Furthermore, the quality model is used to preset the electrode block pressing process parameters. By inputting the target electrode block mass, the required raw material amount and at least one of the corresponding process parameters R, θ, a, and h can be deduced.

[0013] Working principle and beneficial effects of the present invention: Compared with the prior art, the present invention has the following beneficial effects: 1. Achieve accurate quality prediction: By constructing a quantitative model of geometric parameters and mass, the target mass can be calculated directly based on the design parameters of the electrode block, replacing traditional experience estimation. The prediction error is controlled within ±0.5%, improving the accuracy of quality control. 2. Optimize production efficiency: Based on the model, the amount of raw materials and pressing process parameters can be preset in advance, avoiding the cycle of "estimation-pressing-adjustment", shortening the production cycle and improving production efficiency; 3. Improve product consistency: The model provides unified mathematical guidance for pressing different batches of electrode blocks, reducing quality differences caused by fluctuations in empirical parameters and ensuring the stability of electrode block quality; 4. Reduced production costs: Accurate raw material usage forecasting reduces waste of titanium raw materials, while also reducing the generation of defective products and lowering production costs; 5. High versatility: The geometric parameters (R, θ, a, h) in the model can be flexibly adjusted according to the design requirements of different specifications of electrode blocks, making it suitable for pressing quality control of electrode blocks for titanium ingots in various VAR furnaces. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the cylindrical electrode block pressing process in this application; Figure 2 for Figure 1 A schematic diagram of the structure of the cylindrical electrode block. Detailed Implementation

[0015] The following detailed description illustrates the specific implementation method: like Figure 2 As shown, the mold width is D, the mold opening thickness is d1, and R is the radius of the electrode block cross-section. The calculated width of the electrode block is d2, where d2 = D - 2d1. Therefore, θ = accos((2R) 2 - d2 2 ) / 2R 2 ), thus calculating θ.

[0016] Example 1: Refer to Figure 1 and Figure 2 As shown, the modeling method for the mass model of the cylindrical electrode block in this invention includes the following steps: S1. Define core parameters: R is the radius of the electrode block cross section, θ is the central angle corresponding to the arc-shaped region, a is the width of the rectangular region, h is the height of the electrode block, and ρ is the density of the titanium raw material used for pressing. S2. Establish the area calculation model for the arc-shaped region: S1 = 1 / 2R 2 (θ-sinθ), where S1 is the area of ​​the arc-shaped region; establish a rectangular area calculation model: S2=2aRsin(θ / 2), where S2 is the area of ​​the rectangular region; S3. Establish the electrode block volume calculation model: V=S1+S2=(1 / 2R) 2 (θ-sinθ)+2aRsin(θ / 2))h, where V is the volume of the electrode block; S4. Establish the electrode block mass model: m = (1 / 2R) 2 (θ-sinθ)+2aRsin(θ / 2))ρh, where m is the mass of the electrode block.

[0017] Based on the above electrode block quality model, the following example illustrates the core parameters and values ​​of the electrode block in this embodiment: The electrode block cross-sectional radius R = 0.1m (100mm); the central angle θ corresponding to the arc-shaped region is π / 2rad (90°), which is within a reasonable range of (0,π] and is suitable for the arc-shaped structure design of the mold; the width of the rectangular region a = 0.05m (50mm) matches the chord length of the arc-shaped region, ensuring the integrity of the cross-sectional structure; the electrode block height h = 0.3m (300mm) meets the axial length requirement of the electrode during VAR furnace remelting; the theoretical density of titanium raw material ρ = 4500kg / m³ 3 These are the standard physical parameters for industrially pure titanium.

[0018] (1) Calculation of the area of ​​the arc-shaped region: Substitute the above parameters into the arc-shaped area model S1=1 / 2R 2 (θ-sinθ), the specific calculation process is as follows: S=1 / 2×(0.1) 2 ×(π / 2-sin(π / 2))=0.5×0.01×(1.5708-1)=0.5×0.01×0.5708=0.002854m 2 That is, the area of ​​the arc-shaped region in the cross-section of the electrode block is 0.002854 m². 2 .

[0019] (2) Calculation of the area of ​​the rectangular region: According to the rectangular area model S2=2aRsin(θ / 2), first calculate sin(θ / 2): θ / 2=π / 4rad (45°), sin(π / 4≈0.7071, then substitute the parameters to calculate the rectangular area: S=2×0.05×0.1×0.7071=0.007071m 2 That is, the area of ​​the rectangular region in the cross-section of the electrode block is 0.007071m². 2 .

[0020] (3) Electrode block volume calculation: Based on the volume model V=(1 / 2R) 2 Substituting the area of ​​the arc, the area of ​​the rectangle, and the height parameters into the equation: V = (0.002854 + 0.007071) × 0.3 = 0.009925 × 0.3 = 0.0029775m 3 That is, the theoretical volume of this electrode block is 0.0029775m³. 3 .

[0021] (4) Electrode block mass calculation: According to the mass model m=(1 / 2R) 2 Substituting the volume and density parameters into (θ-sinθ)+2aRsin(θ / 2))ρh: m=0.0029775×4500=13.39875kg, after taking an approximation, the theoretical mass of this specification of electrode block is about 13.40kg.

[0022] (5) Model Verification: An electrode block pressing experiment was conducted according to the above parameters, and three parallel samples were prepared to ensure that the process parameters such as pressure and holding time were consistent during the pressing process. The actual mass of the three samples was measured using an electronic weighing instrument with an accuracy of 0.01 kg. The measurement results are as follows: Actual mass of sample 1: 13.38 kg; Actual mass of sample 2: 13.41 kg; Actual mass of sample 3: 13.39 kg. The average actual mass was calculated as: (13.38 + 13.41 + 13.39) / 3 = 13.39 kg. The relative deviation between the theoretical mass and the actual average mass was calculated as: |13.40 - 13.39| / 13.39 × 100% ≈ 0.075%. This deviation is within the allowable range of ±0.5%, indicating that the mass model established in this invention meets the process requirements and the model is qualified.

[0023] In practical applications, the quality of the electrode block is changed by altering the value of 'a'.

[0024] Example 2: Process Application Case Based on the above-mentioned qualified quality model, if the target mass of this type of electrode block is to be 15.00 kg, the key process parameters are deduced by working backward from the model. The specific process is as follows: From the mass model m=Vρ, the required raw material volume V=m / ρ=15.00 / 4500≈0.003333m³ 3 ; Given that the total cross-sectional area of ​​the electrode block (area of ​​the arc + area of ​​the rectangle) = 0.002854 + 0.007071 = 0.009925 m² 2 ; Based on the volume model V = total cross-sectional area × height h, the electrode block height h = V / total cross-sectional area = 0.003333 / 0.009925 ≈ 0.3358m (335.8mm).

[0025] In other words, by adjusting the height of the electrode block to 335.8mm while keeping the other parameters (R, θ, a, ρ) unchanged, an electrode block with a target mass of 15.00kg can be pressed without repeated trial and error adjustments.

[0026] Example 3: Referring to the new Example 3, it is explained how to correct the actual value of the titanium raw material density ρ. Key parameters: Electrode block cross-sectional radius R = 0.12m (120mm); Central angle θ corresponding to the arc-shaped region = π / 3rad (60 degrees, within the reasonable range of (0,π); Rectangular region width a = 0.06m (60mm), matching the arc chord length; Electrode block height h = 0.25m (250mm), suitable for small and medium-sized VAR furnace body specifications; Theoretical density of titanium raw material ρtheoretical = 4480kg / m2 3 .

[0027] Based on the above calculation model, we obtain: m 理 =V×ρ 理 =0.002126×4480≈9.524kg Three parallel samples were pressed according to the new parameters mentioned above, and the actual mass was measured using an electronic weighing instrument with an accuracy of 0.01 kg. The results are as follows (the simulated porosity caused the actual mass to be lower than expected): Actual mass of sample 1: 9.40 kg, actual mass of sample 2: 9.38 kg, actual mass of sample 3: 9.42 kg.

[0028] Actual average mass calculation: m 实 =(9.40+9.38+9.42) / 3=9.40kg Initial relative deviation calculation: Relative deviation = |m 理 -m 实 | / m 实 ×10%=|9.524-9.40| / 9.40×100%≈1.32%.

[0029] Substitute the known data (V=0.002126m) 3 m 实 =9.40kg); ρ 实 =9.40 / 0.002126≈4421.45kg / m 3 The corrected actual density of the titanium raw material is 4421.45 kg / m³. 3 (approximately 4.42 g / cm³) 3 The density is 58.55 kg / m³ lower than the theoretical density. 3 This corresponds to the density loss caused by porosity.

[0030] If the target quality m needs to be produced subsequently 目 =11.00kg of the same specification electrode block (R, θ, a unchanged), using the corrected density ρ 实 =4421.45kg / m 3 Back-engineering key process parameters: Target volume calculated by reverse calculation: V_eye = m_eye / ρ 实=11.00 / 4421.45≈0.002488m 3 The height of the reverse electrode block is calculated as follows: h_mesh = V_mesh / (S1 + S2) = 0.002488 / 0.008505 ≈ 0.2925 m (292.5 mm). In other words, by adjusting the height of the electrode block to 292.5mm, the electrode block of the target quality can be accurately pressed without repeated trial and error.

[0031] It should be noted that those skilled in the art can make various modifications and improvements without departing from the technical solution of this invention. These modifications and improvements should also be considered within the scope of protection of this invention, and will not affect the effectiveness of the invention or the practicality of the patent. The scope of protection claimed in this application shall be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.

Claims

1. A modeling method for a cylindrical electrode block pressing quality model for VAR furnace titanium ingot casting, characterized in that, Includes the following steps: S1. Define core parameters: R is the radius of the electrode block cross section, θ is the central angle corresponding to the arc-shaped region, a is the width of the rectangular region, h is the height of the electrode block, and ρ is the density of the titanium raw material used for pressing. S2. Establish the area calculation model for the arc-shaped region: S1 = 1 / 2R 2 (θ-sinθ), where S1 is the area of ​​the arc-shaped region; establish a rectangular area calculation model: S2=2aRsin(θ / 2), where S2 is the area of ​​the rectangular region; S3. Establish the electrode block volume calculation model: V=S1+S2=(1 / 2R) 2 (θ-sinθ)+2aRsin(θ / 2))h, where V is the volume of the electrode block; S4. Establish the electrode block mass model: m = (1 / 2R) 2 (θ-sinθ)+2aRsin(θ / 2))ρh, where m is the mass of the electrode block.

2. The modeling method according to claim 1, characterized in that, It also includes step S5, model verification and correction: selecting electrode blocks with different parameter specifications to press the sample, and correcting the model parameters by measuring the deviation between the actual mass and the mass calculated by the model.

3. The modeling method according to claim 2, characterized in that, When the deviation exceeds ±0.5%, calibration is performed by correcting the actual value of the titanium raw material density ρ.

4. The modeling method according to claim 3, characterized in that, The central angle θ mentioned in step S1 has a range of (0,π], and the parameters R, a, and h are determined according to the production process requirements of VAR furnace titanium ingots and the design specifications of the electrode blocks.

5. The quality model obtained by the modeling method according to any one of claims 1 to 4.

6. The quality model according to claim 5, characterized in that, The quality model is used to preset the electrode block pressing process parameters. By inputting the target electrode block mass, the required raw material amount and at least one of the corresponding process parameters R, θ, a, and h are calculated.

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