Shanghai Yue Shi Welding Technology Co., Ltd.

In multi-pulse arc-welding, establish the peak current (Ip)、Baseline CurrentIbColumn diameter (Ds)、Material ThicknessTbThe mathematical relationship model requires the integration of welding physical mechanisms, experimental data fitting, and numerical simulation. Here is the step-by-step modeling approach:

Physical Mechanism Analysis (Theoretical Constraints)

Peak Current Constraint Conditions

• Energy Density Threshold：
  Peak current must meet the energy density required for droplet detachment.Ed）：
  $E_d\propto \frac{I_p^2\cdot t_p}{D_s}$
  AmongsttpFor pulse time, experiments show that the stripping threshold is approximately107J/mm3。

• Molten Pool Depth-to-Width Ratio：
  Melt DeepHNo Chinese content provided.WNo Chinese content provided.
  $\frac{H}{W}\ge \frac{T_b}{D_s}$
  Through the arc pressure formula$P_a=k\cdot I_p^2/D_s$（kThe correlation between the associated current and the melt pool size remains constant.

2. Base Current Constraint Conditions

• Arc Stability：
  The base current must be maintained to stabilize the arc's combustion and prevent "arc quenching."
  $I_b\ge \frac{V_{arc}}{R_{gap}}$
  AmongstVarcFor arc voltage (typically 10-15V),RgapFor arc gap resistance (with)DsNo Chinese content provided.

• Hot Input Control：
  Total Heat InputQAvoid material burn-through.
  $Q=\eta \cdot \left(I_p^2\cdot t_p+I_b^2\cdot t_b\right)\le Q_{max}(T_b)$
  ηFor thermal efficiency,tbAs a baseline for time.QmaxMaterial melting point determines.

Two: Data-Driven Model (Empirical Formula)

Through experimental design (DOE), we have obtained differentDsNo Chinese content provided for translation.TbOptimized current parameters, fitted with the Response Surface Method (RSM) model:

Peak Current Model

• Quadratic polynomial fitting：
  $I_p=a_1\cdot D_s+a_2\cdot T_b+a_3\cdot D_s^2+a_4\cdot D_s\cdot T_b+a_5\cdot T_b^2+ϵ$
  Determined coefficients via the least squares method$a_1-a_5$，ϵFor error terms.

2. Base Current Model

• Linear Regression Model：
  $I_b=b_1\cdot D_s^{-1}+b_2\cdot T_b^{-0.5}$
  The base current reflects an inverse proportionality to the bolt diameter and a negative square root relationship with the thickness of the base material.

Section III: Numerical Simulation Optimization (Finite Element Assistance)

Utilizing ANSYS or SIMULIA for multiphysics field coupling simulation:

1. Electromagnetic-Thermal CouplingCalculate temperature field distribution under different current conditions.

2. Melting Drop Transition SimulationTracing the droplet shedding process using the VOF method.

Model Validation and Deployment

1. Experimental Validation：
   The model's prediction accuracy is evaluated through confusion matrix, with the requirement for error rate to be less than 5%.

2. Online Deployment：
   The model has been integrated into the welding equipment control system, enabling adaptive parameter adjustment.

Section 5: Example of Typical Material Parameters

Six: Dynamic Compensation Mechanism

In practical welding, the following dynamic compensations need to be considered:

• Welding Speed Impact：$I_p\propto v^{-0.3}$

• Surface ConditionWhen an oxide film is present.IpIncrease by 10-15%

• Protective GasIn an Ar+CO₂ mixed gas.IbReduce by 5-8%.

The model ensures theoretical feasibility through physical constraints, guarantees engineering practicality with experimental data, enhances accuracy through simulation optimization, forming a "theoretical-experimental-simulation" closed loop, which can significantly improve the efficiency of welding parameter adjustment (shortening the experimental cycle by over 60%).