Pillars Dashboard
| ▼ Pillars | ||||
| ☰ | \( X_{\text{pillars}} \) | Number of Pillars |
View Help GuidePurpose: Perimeter Support Count.
Logic: Defines the exact total quantity of corner vertical supports used to stabilize the outer boundary of the Top Base.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input Python Logic:
N/ALive Evaluation: N/A (Input Variable)
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| ☰ | \( F_{\text{pillars, vertical}} \) | Pillars Vertical Load (N) | 9,371.854749 |
View Help GuidePurpose: Distributed Axial Load.
Logic: Determines the specific compressive dead-weight acting on each individual corner pillar from its assigned share of the load.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$F_{\text{pillars, vertical}} = ( ( M_{\text{top, base}} \times N) \times X_{\text{corner, pillar}} ) / X_{\text{pillars}}$$ Python Logic:
( ( v["Top Base Static Mass (kg)"] * v["Gravitational Field Strength (N/kg)"]) * v["Corner Pillar Gravity Share (%)"] ) / v["Number of Pillars"]Live Evaluation: [ROUTE: STATIC/GLOBAL] ( ( 47,783.1612 * 9.8066) * 0.0800 ) / 4.0000 = 9,371.8547
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| ☰ | \( \tau_{\text{pillars}} \) | Pillars Torque (Nm) | 9,019.50293 |
View Help GuidePurpose: Torsional Isolation.
Logic: Mathematically confirms that these outer supports are isolated from the machine's rotational forces, keeping them dedicated purely to vertical precision.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\tau_{\text{pillars}} = ( \tau_{\text{reaction}} \times \tau_{\text{corner, pillar}} ) / X_{\text{pillars}}$$ Python Logic:
( v["Reaction Torque (Nm)"] * v["Corner Pillar Torque Share (%)"] ) / v["Number of Pillars"]Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 1,443,120.4688 * 0.0250 ) / 4.0000 = 9,019.5029
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| ☰ | \( H_{\text{pillars, pillar}} \) | Pillars Pillar Height (m) | 10 |
View Help GuidePurpose: Structural Alignment.
Logic: Establishes the consistent vertical run from the floor to the Top Base, matching the rest of the facility footprint.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$H_{\text{pillars, pillar}} = \Sigma H_{\text{arc}}$$ Python Logic:
v["Arc Total Wall Height (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 10.0000 = 10.0000
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| ☰ | \( A_{\text{pillars, avail}} \) | Pillars Available Footprint Width (m) |
View Help GuidePurpose: Minimal Space Constraint.
Logic: Defines the slim lateral footprint allowed for the corner supports to maximize open floor space around the machine.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input Python Logic:
N/ALive Evaluation: N/A (Input Variable)
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| ☰ | \( L_{\text{pillars, benefit}} \) | Pillars Length Benefit (%) |
View Help GuidePurpose: Structural Reach Factor.
Logic: Applies a longitudinal efficiency factor, taking advantage of the pillar's reach along the gantry axis.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input Python Logic:
N/ALive Evaluation: N/A (Input Variable)
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| ☰ | \( L_{\text{pillars, pillar}} \) | Pillars Length (m) |
View Help GuidePurpose: Longitudinal Distribution.
Logic: Matches the front-to-back depth of the primary core to maintain a unified, symmetric structural envelope.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input Python Logic:
N/ALive Evaluation: N/A (Input Variable)
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| ☰ | \( I_{\text{pillars, req}} \) | Pillars Required Inertia (I) | 0.017429 |
View Help GuidePurpose: Stiffness Calculation.
Logic: Because these pillars don't fight torque, this math proves the required geometric inertia for twisting is effectively zero—confirming they are "zero-sway" columns.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$I_{\text{pillars, req}} = ( \tau_{\text{pillars}} \times H_{\text{pillars, pillar}}^2) / (3 \times ( \text{Fossil Carbon Fibre Modulus (GPa)} \times 10^9 ) \times (\Delta_{\text{max, allowable}}))$$ Python Logic:
( v["Pillars Torque (Nm)"] * v["Pillars Pillar Height (m)"]^2) / (3 * ( v["Fossil Carbon Fibre Modulus (GPa)"] * 10^9 ) * (v["Max Allowable Deflection (m)"]))Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 9,019.5029 * 10.0000**2) / (3 * ( 230.0000 * 10**9 ) * (0.0001)) = 0.0174
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| ☰ | \( W_{\text{pillars, req}} \) | Pillars Required Border Thickness (m) | 0.017429 |
View Help GuidePurpose: Minimum Shell Thickness.
Logic: Since the twist inertia is zero, this sets a hard baseline limit (e.g., 5mm) to ensure the wall is still thick enough to safely carry the vertical weight.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$W_{\text{pillars, req}} = MAX ( I_{\text{pillars, req}}, 0.005 )$$ Python Logic:
MAX ( v["Pillars Required Inertia (I)"], 0.005 )Live Evaluation: [ROUTE: STATIC/GLOBAL] MAX ( 0.0174, 0.005 ) = 0.0174
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| ☰ | \( X_{\text{pillars, sps}} \) | Pillars SPS Block Selection (m) | 0.1 |
View Help GuidePurpose: Modular Standardization.
Logic: Aligns the ultra-thin requirement with a standard, manufacturable carbon fiber block size for production efficiency.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{pillars, sps}} = ROUNDUP(W_{\text{pillars, req}} , 1 )$$ Python Logic:
ROUNDUP(v["Pillars Required Border Thickness (m)"] , 1 )Live Evaluation: [ROUTE: STATIC/GLOBAL] ROUNDUP(0.0174 , 1 ) = 0.1000
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| ☰ | \( X_{\text{pillars, final}} \) | Pillars Final Module Skin (m) | 0.017429 |
View Help GuidePurpose: Solid Material Spec.
Logic: The exact thickness of solid carbon fiber actually required inside the block to maintain basic vertical integrity.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{pillars, final}} = W_{\text{pillars, req}}$$ Python Logic:
v["Pillars Required Border Thickness (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.0174 = 0.0174
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| ☰ | \( X_{\text{pillars, solidity}} \) | Pillars Module Solidity (%) | 0.34858 |
View Help GuidePurpose: Internal Density Calibration.
Logic: Determines the volumetric ratio of solid material to void space, optimizing the pillar for required vertical stiffness without wasting material.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{pillars, solidity}} = (X_{\text{pillars, final}} \times 2) / X_{\text{pillars, sps}}$$ Python Logic:
(v["Pillars Final Module Skin (m)"] * 2) / v["Pillars SPS Block Selection (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] (0.0174 * 2) / 0.1000 = 0.3486
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| ☰ | \( A_{\text{pillars, footprint}} \) | Pillars Footprint Area (m2) | 0.1 |
View Help GuidePurpose: Floor Contact Area.
Logic: The total square meters of ground space physically occupied by a single corner pillar base.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$A_{\text{pillars, footprint}} = L_{\text{pillars, pillar}} \times A_{\text{pillars, avail}}$$ Python Logic:
v["Pillars Length (m)"] * v["Pillars Available Footprint Width (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.5000 * 0.2000 = 0.1000
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| ☰ | \( L_{\text{pillars, int}} \) | Pillars Internal Void Length (m) | 0.3 |
View Help GuidePurpose: Weight Reduction.
Logic: Maximizes the internal hollow space to eliminate unneeded mass while keeping a tough structural outer shell.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$L_{\text{pillars, int}} = L_{\text{pillars, pillar}} - (X_{\text{pillars, sps}} \times 2)$$ Python Logic:
v["Pillars Length (m)"] - (v["Pillars SPS Block Selection (m)"] * 2)Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.5000 - (0.1000 * 2) = 0.3000
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| ☰ | \( W_{\text{pillars, int}} \) | Pillars Internal Void Width (m) | 0 |
View Help GuidePurpose: Solid Profile Confirmation.
Logic: Calculates the width of the internal void based on the block selection. If the block is small enough, this may result in a completely solid vertical rib.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$W_{\text{pillars, int}} = A_{\text{pillars, avail}} - (X_{\text{pillars, sps}} \times 2)$$ Python Logic:
v["Pillars Available Footprint Width (m)"] - (v["Pillars SPS Block Selection (m)"] * 2)Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.2000 - (0.1000 * 2) = 0.0000
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| ☰ | \( A_{\text{pillars, void}} \) | Pillars Void Area (m2) | 0 |
View Help GuidePurpose: Mass Saving Check.
Logic: Calculates the total square area of the hollow center to verify our massive material and weight reduction.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$A_{\text{pillars, void}} = L_{\text{pillars, int}} \times W_{\text{pillars, int}}$$ Python Logic:
v["Pillars Internal Void Length (m)"] * v["Pillars Internal Void Width (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.3000 * 0.0000 = 0.0000
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| ☰ | \( X_{\text{pillars, fill}} \) | Pillars Fill Factor (%) | 1 |
View Help GuidePurpose: Sectional Density.
Logic: Measures what percentage of the footprint is utilized as a solid structural member versus hollow, empty air.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{pillars, fill}} = ( A_{\text{pillars, footprint}} - A_{\text{pillars, void}} ) / A_{\text{pillars, footprint}}$$ Python Logic:
( v["Pillars Footprint Area (m2)"] - v["Pillars Void Area (m2)"] ) / v["Pillars Footprint Area (m2)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 0.1000 - 0.0000 ) / 0.1000 = 1.0000
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| ☰ | \( \Sigma M_{\text{pillars}} \) | Pillars Total Mass (kg) | 627.443683 |
View Help GuidePurpose: Logistics Planning.
Logic: The definitive final weight of a single corner pillar, heavily relied upon for robotic assembly and transport logistics.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma M_{\text{pillars}} = (A_{\text{pillars, footprint}} \times H_{\text{pillars, pillar}} \times \text{Fossil Carbon Fibre Density (kg.m3)} ) \times X_{\text{pillars, fill}} \times X_{\text{pillars, solidity}}$$ Python Logic:
(v["Pillars Footprint Area (m2)"] * v["Pillars Pillar Height (m)"] * v["Fossil Carbon Fibre Density (kg.m3)"] ) * v["Pillars Fill Factor (%)"] * v["Pillars Module Solidity (%)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] (0.1000 * 10.0000 * 1,800.0000 ) * 1.0000 * 0.3486 = 627.4437
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| ☰ | \( \Sigma V_{\text{pillars}} \) | Pillars Total Volume (m3) | 0.34858 |
View Help GuidePurpose: Calculates the combined physical material volume of all vertical support pillars in the structural assembly.
Logic: Aggregates the volumetric displacement of the vertical support structures to determine the total material required for vertical load-bearing and spacing.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma V_{\text{pillars}} = \Sigma M_{\text{pillars}} / D_{\text{FCF}}$$ Python Logic:
v["Pillars Total Mass (kg)"] / v["Fossil Carbon Fibre Density (kg.m3)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 627.4437 / 1,800.0000 = 0.3486
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| ▼ Pillars Safety Audit | ||||
| ☰ | \( F_{\text{pillars, effective}} \) | Pillars Effective Load Area (m2) | 0.034858 |
View Help GuidePurpose: Net Stress Plane.
Logic: The actual square meters of solid carbon fiber effectively carrying the downward gravitational crush.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$F_{\text{pillars, effective}} = A_{\text{pillars, footprint}} \times X_{\text{pillars, fill}} \times X_{\text{pillars, solidity}}$$ Python Logic:
v["Pillars Footprint Area (m2)"] * v["Pillars Fill Factor (%)"] * v["Pillars Module Solidity (%)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.1000 * 1.0000 * 0.3486 = 0.0349
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| ☰ | \( \sigma_{\text{pillars, applied}} \) | Pillars Applied Axial Stress (MPa) | 0.268858 |
View Help GuidePurpose: Compressive Pressure.
Logic: Measures the physical downward pressure on the material to mathematically ensure it remains well within a safe elastic range.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\sigma_{\text{pillars, applied}} = (F_{\text{pillars, vertical}} / F_{\text{pillars, effective}}) / 10^6$$ Python Logic:
(v["Pillars Vertical Load (N)"] / v["Pillars Effective Load Area (m2)"]) / 10^6Live Evaluation: [ROUTE: STATIC/GLOBAL] (9,371.8547 / 0.0349) / 10**6 = 0.2689
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| ☰ | \( \sigma_{\text{pillars, applied}} \) | Pillars Applied Shear Stress (MPa) | 2.5875 |
View Help GuidePurpose: Torsional Check.
Logic: Validates that twisting stresses are virtually non-existent in the outer perimeter legs.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\sigma_{\text{pillars, applied}} = (\tau_{\text{pillars}} / (2 \times A_{\text{pillars, footprint}} \times W_{\text{pillars, req}})) / 10^6$$ Python Logic:
(v["Pillars Torque (Nm)"] / (2 * v["Pillars Footprint Area (m2)"]* v["Pillars Required Border Thickness (m)"])) / 10^6Live Evaluation: [ROUTE: STATIC/GLOBAL] (9,019.5029 / (2 * 0.1000* 0.0174)) / 10**6 = 2.5875
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| ☰ | \( \sigma_{\text{pillars, combined}} \) | Pillars Combined Von Mises Stress (MPa) | 4.489739 |
View Help GuidePurpose: Global Safety Limit.
Logic: The ultimate combined stress value used for the final safety check against the material's failure point.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\sigma_{\text{pillars, combined}} = \sqrt{\sigma_{\text{pillars, applied}}^2 + 3 \times \sigma_{\text{pillars, applied}}^2)$$ Python Logic:
SQRT(v["Pillars Applied Axial Stress (MPa)"]^2 + 3 * v["Pillars Applied Shear Stress (MPa)"]^2)Live Evaluation: [ROUTE: STATIC/GLOBAL] SQRT(0.2689**2 + 3 * 2.5875**2) = 4.4897
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| ☰ | \( SF_{\text{pillars, structural}} \) | Pillars Structural Safety Factor | 133.192607 |
View Help GuidePurpose: Global Reliability Proof.
Logic: Comparing the incredible material capacity against the minimal operational loads to demonstrate extreme, foolproof safety margins.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$SF_{\text{pillars, structural}} = \sigma_{\text{material, yield}} / \sigma_{\text{pillars, combined}}$$ Python Logic:
v["Fossil Carbon Fibre Material Yield Strength (MPa)"] / v["Pillars Combined Von Mises Stress (MPa)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 598.0000 / 4.4897 = 133.1926
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| ☰ | \( X_{\text{pillars, individual}} \) | Pillars Individual Pillar Safety Blueprint Validation | ULTRA-SAFE |
View Help GuidePurpose: Technical Validation.
Logic: 1 if v["Pillars Structural Safety Factor"] > v["Safety Factor Slider"] else 0
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{pillars, individual}} = IF(SF_{\text{pillars, structural}} > SF_{\text{safety, factor}}, 1, 0)$$ Python Logic:
1 if v["Pillars Structural Safety Factor"] > v["Safety Factor Slider"] else 0Live Evaluation: [ROUTE: STATIC/GLOBAL] 1 if 133.1926 > 2.5000 else 0 = 1.0000
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