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# Spot welding basic parameters setting - basic calculations / equations

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Basic mathematical equations used to approximate the optimum spot welding parameters setting for AC & DC welding through Lobe Curve

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• @Thang Tran Can U email me the picture of terminal A &amp; E of ur spot welding machine? What brand of sot welding U use? Email me at aadc_cd@hotmail.com

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• Hi, I have a big trouble with spot welding: We use spot welding to connect terminal A vs terminal E. Both of terminal make from copper, thickness of terminal A is 0.5mm, terminal E is 1mm (terminal E is coated by Si, and Ni 4-8 micron). But the quality of spot welding isn't good, some time they are self-detached. So we received so many complain. Please leave your comment or contact with me via skype: tranthang2210

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• @Sg0614 Basically, to get Jv value..need to multiply - specific heat x density x melting point. Using standard values of each parameters...the end result, Jv is obtained but the value not sufficient to simulate the actual spot weld diameter. So, the Jv that I used is basically after tuning to get the best actual result of spot weld nugget diameter....sorry for late reply

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• Hiya, just a quick question? Where did you get the values of melting energies for Low Carbon Steel and Al? Can you link me the references if that's not to much to ask for. Cheers!!

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### Spot welding basic parameters setting - basic calculations / equations

1. 1. Spot Welding Parameters Basic Calculation 𝐸 = 0.241𝑃𝑡w .........................(1) where E : Energy (J) *Calculation for AC spot welding P : Power (W) tw : Weld time (sec) = 0.241𝐼2 𝑅𝑡w .........................(2) where I : Welding Current (A) R : Panel Contact Resistance (Ω) = JvSL .........................(3) where Jv : Melting energy (J/mm3 ) S : Surface contact (mm2 ) L : Total plate thickness combination (mm) = Jv[π 𝑑2 4 ]L ........................(4) where d : Required nugget diameter (mm) Since 𝑑 = 4 𝑡min for general spot point = 5 𝑡min for important spot point Where 𝑡min : Min thickness of panel combinations So, 0.241𝐼2 𝑅𝑡 = Jv[π (4 𝑡min)2 4 ]L .......(5) Combination eqn (2) & eqn (4) = Jv[π4𝑡min]]L .............(6) Final equation; 𝐼 = Jv[π4𝑡min]]L 0.241𝑅𝑡w 2 ..............(7) *Used for minimum nugget diameter requirement (general) = Jv[π 𝑑2 4 ]L 0.241𝑅𝑡w 2 ....................(8) *Used for specific required nugget diameter Note : Steel type Melting Energy Contact Resistance Low Carbon Steel 9.7 J/mm3 100 μΩ Aluminum 2.9 J/mm3 75 μΩ  Replace 𝐸 = 0.241𝑃𝑡w to 𝐸 = 0.37𝑃𝑡w for MFDC / DC spot welding calculation 𝐹w = 250𝑡min .............................(9) where 𝐹w = Welding Force (kg) - target *Go to Quadratic approximation for best data fitting (refer reference) – No 11 𝑡w = 10𝑡min .............................(10) where 𝑡w = Weld time (cycle) – 50 hz 𝑡hold = 3 ~ 5 𝑐𝑦𝑐𝑙𝑒𝑠.................... where 𝑡hold = Hold time (cycle) – 50 hz *𝑡squeeze - Pneumatic Gun : Min 17 cycle – Min time require for applied force to stable at 80% - Servo Gun (robot) : 0 cycles – Using integrated robot function (robot will send signal once applied force is stable to welding controller) Servo Gun : 4 cycle – Min time require for applied force to stable
2. 2. References 1. Spot Welding Process Sequence 2. Relationship between welding force & resistance 𝐹w = 𝑃w 𝐴 .............(1) where Fw : Weld Force Pw : Weld Pressure A : Contact Area R = 𝜌𝐿 𝐴 ........(2) where R : Resistance, Ω So, A = 𝜌𝐿 𝑅 ........(3) ρ : Resistivity , Ω/mm L : Total plate thickness combination (mm) A : Contact Area, mm2 Combine eq (1) & (3)............ 𝐹w = 𝑃w 𝜌𝐿 𝑅 ........................(4) 𝐹w α 1 𝑅 .... Force ↑ Resistance ↓
3. 3. 3. Relationship between welding force & welding current 𝑃p = 𝑉𝐼 = 𝐼2 𝑅 .................................................(5) where Pp : Weld Power Combine eq (4) & (5)............ 𝐹w = 𝑃w 𝜌𝐿𝐼2 𝑃p ............................(6) 𝐹w α 𝐼2 .... Force ↑ Current ↑ *Lobe curve sample from Lobe Curve Generator – Welding Force vs Weld Current
4. 4. 4. Welding Condition Graph (Base on formulas) Using derived formulas as above, the new plot (yellow & blue colours) are published against original welding chart to confirm the accuracy of the formulas. Also, the Lobe Curve estimator was programmed to view weldability region as following sample;
5. 5. 5. Lobe Curve Generator (from equations) – Weld Time vs Weld Current *Improved Lobe Curve Generator
6. 6. 6. AC vs DC Spot Welding Comparison
7. 7. 7. Lobe Curve Sample (Experimental Data) 8. Welding Stepper Program Sample 3 SPCC (1.2) x SPCD-SD (1.4) x SPRC 40 (2.0) 5.5mm 250kgf Graph Part Combination Nugget Diameter (Standard) Welding Pressure Graph 3 6 8 10 12 14 16 18 20 6000 7000 8000 9000 10000 11000 12000 13000 14000 Weld Time (cycle) WeldCurrent(A) Weld Current versus Weld Time Graph weld_current_total vs. weld_time_total fit 1 weld_current_total_NF vs. weld_time_total_NF fit 2 weld_current_total_SP vs. weld_time_total_SP fit 3 Required Nugget Diameter : 5.5mm Spatter Region No Fusion Region Small Nugget Region Applicable Region 0 420 840 1260 1680 2100 2520 2940 3360 3780 4200 9500 9700 9900 10100 10300 10500 10700 10900 11100 11300 Weld Count (no) WeldingCurrent(A) Welding Current Setting versus Welding Current Actual Welding Current Setting Welding Current (Actual) WAS IS STEPPER 0 STEPPER 1 STEPPER 2 STEPPER 3 STEPPER 4 STEPPER 5 STEPPER 6 STEPPER 7 STEPPER 8 STEPPER 9 CURRENT (kA) 11.3 9.5 9.7 9.9 10.1 10.3 10.5 10.7 10.9 11.1 11.3 WTM 7 3 3 3 4 4 5 5 5 6 6 WELD COUNT 1~420 1~420 421~840 841~1260 1261~1680 1681~2100 2101~2520 2521~2940 2941~3360 3361~3780 3781~4200 WELD TIME (cycle) 13 13 PRESSURE (kgf) 250 250 UNDERBODY ROBOTUB053 / 054 (WELDING PARAMETER SETTING)
8. 8. 9. Stepper versus Typical Welding Comparison (Sample) 10. Weld Force Quadratic Approximation
9. 9. 11. Electrode Force Effect on Lobe Curve Range (Sample from experiments) 6 8 10 12 14 16 18 20 22 6500 7000 7500 8000 8500 9000 9500 10000 10500 11000 11500 Weld Time (cycle) WeldCurrent(A) Electrode Pressure Effect on Applicable Region (Between Standard Nugget & Spatter Region) Press_160_current_std vs. Press_160_weld_time_std fit 1 Press_160_current_spatter vs. Press_160_weld_time_spatter fit 2 Press_200_current_std vs. Press_200_weld_time_std fit 3 Press_200_current_spatter vs. Press_200_weld_time_spatter fit 4 160 kgf 200 kgf Spatter Region Small Nugget Region
10. 10. 12. Shear Load versus Weld Nugget diameter 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9 4.1 1000 2000 3000 4000 5000 6000 7000 8000 Nugget Diameter, d [mm] ShearLoad,F[N] Shear Load Graph (Ordinary Weld) SPCE Shear vs. Nugget Diameter fit [<390 MPa] SPFC490 Shear vs. Nugget Diameter fit [390MPa<TS<490MPa] SPFC580 Shear vs. Nugget Diameter fit [490MPa<TS<580MPa] SPFC780 Shear vs. Nugget Diameter fit [580MPa<TS<780MPa] SPFC980 Shear vs. Nugget Diameter fit [780MPa<TS<980MPa] SPFC >980 Shear vs. Nugget Diameter fit [TS>980] 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 Nugget Diameter, d [mm] ShearLoad,F[N] Shear Load Graph [Critical Weld] <390 MPa fit [<390MPa] 390MPa < TS<490MPa fit [390<TS<490] 490MPa<TS<580 fit [490<TS<580] 580<TS<780MPa fit [580<TS<780 780<TS<980MPa fit [780<TS<980] TS>980 fit [TS>980]
11. 11. 13. Temperature Distribution During Spot Welding 14. Dynamic Resistance Measurement (IJAME)
12. 12. 15. Welding Heat Distribution (SAE)