Vibration and Harmonics Dashboard
| ▼ Vibration and Harmonics | ||||
| ☰ | \( X_{\text{forcing, frequency}} \) | Forcing Frequency (Hz) | 0.8 |
View Help GuidePurpose: Excitation Frequency.
Logic: Calculates the primary vibration pulse generated by the gear-mesh cycle. This is the exact "beat" or rhythm the stand must ignore.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{forcing, frequency}} = n_{\text{rpm}} / 60$$ Python Logic:
v["Internal Gear RPM"] / 60Live Evaluation: [ROUTE: STATIC/GLOBAL] 48.0000 / 60 = 0.8000
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| ☰ | \( X_{\text{frequency}} \) | Enabler Frequency (Hz) | 0.297448 |
View Help GuidePurpose: Kinetic Circuit Cadence.
Logic: Measures the low-frequency "thump" as the heavy enabler train completes a full circuit around the track.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{frequency}} = ( v / ( 2 \times \pi \times R_{\text{inner, curved}} ) )$$ Python Logic:
( v["Operational Velocity (m/s)"] / ( 2 * PI() * v["Inner curved side wall outside radius (m)"] ) )Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 9.2800 / ( 2 * PI() * 4.9654 ) ) = 0.2974
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| ☰ | \( M_{\text{stand}} \) | Mass of Stand (kg) | 93,022.359095 |
View Help GuidePurpose: Inertial Dampening Mass.
Logic: Establishes the total dead-weight of the stationary carbon fiber structure used to absorb and dissipate operational kinetic energy.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$M_{\text{stand}} = \Sigma M_{\text{stand}}$$ Python Logic:
v["Total stand weight (kg)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 93,022.3591 = 93,022.3591
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| ☰ | \( I_{\text{combined, inertia}} \) | Combined Inertia (I walls) | 3.027968 |
View Help GuidePurpose: Global Stiffness Score.
Logic: The cumulative structural resistance of all vertical support boxes acting together as a single, rigid, monolithic body.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$I_{\text{combined, inertia}} = I_{\text{int, spine}} + I_{\text{deck, req}} + I_{\text{outer, shell}} + I_{\text{rear, gearbox}} + I_{\text{front, stabiliser}} + I_{\text{side, req}} + I_{\text{pillars, req}}$$ Python Logic:
v["Internal Spine Wall Required Inertia (I)"] + v["Deck Wall Required Inertia (I)"] + v["Outer Shell Walls Required Inertia (I)"] + v["Rear Gear-Box Core Required Inertia (I)"] + v["Front Stabiliser Wall Required Inertia (I)"] + v["Side Wall Required Inertia (I)"] + v["Pillars Required Inertia (I)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] 0.1591 + 0.0994 + 0.0331 + 2.3703 + 0.2789 + 0.0697 + 0.0174 = 3.0280
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| ☰ | \( X_{\text{lateral, stiffness}} \) | Lateral Stiffness (k) | 2,089,298,017.842 |
View Help GuidePurpose: Sway Resistance.
Logic: Determines the resistance to side-sway in Newtons per meter. High stiffness prevents sympathetic movement when the heavy weights swing.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{lateral, stiffness}} = (3 \times (\text{Fossil Carbon Fibre Modulus (GPa)} \times 10^9) \times I_{\text{combined, inertia}}) / (\Sigma H_{\text{arc}}^3)$$ Python Logic:
(3 * (v["Fossil Carbon Fibre Modulus (GPa)"] * 10^9) * v["Combined Inertia (I_walls)"]) / (v["Arc Total Wall Height (m)"]^3)Live Evaluation: [ROUTE: STATIC/GLOBAL] (3 * (230.0000 * 10**9) * 3.0280) / (10.0000**3) = 2,089,298,017.8420
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| ☰ | \( X_{\text{natural, frequency}} \) | Natural Frequency (Hz) | 23.852102 |
View Help GuidePurpose: Structural Signature.
Logic: Establishes the natural vibration frequency of the stand. This must stay far away from the machine's forcing frequency to prevent destructive resonance.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{natural, frequency}} = ( 1 / ( 2 \times \pi ) ) \times \sqrt{ X_{\text{lateral, stiffness}} / M_{\text{stand}} )$$ Python Logic:
( 1 / ( 2 * PI() ) ) * SQRT( v["Lateral Stiffness (k)"] / v["Mass of Stand (kg)"] )Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 1 / ( 2 * PI() ) ) * SQRT( 2,089,298,017.8420 / 93,022.3591 ) = 23.8521
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| ☰ | \( \eta_{\text{target, resonance}} \) | Target Resonance Ratio (%) |
View Help GuidePurpose: Isolation Threshold.
Logic: Defines the required separation gap between the machine's operational pulse and the stand's natural frequency to prevent structural humming.
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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| ☰ | \( \eta_{\text{resonance, ratio}} \) | Resonance Ratio | 0.03354 |
View Help GuidePurpose: Structural Isolation Proof.
Logic: The Final Victory. Proves total harmonic isolation, ensuring the stand remains a motionless, silent anchor during even the most violent operational pulses.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\eta_{\text{resonance, ratio}} = ( X_{\text{forcing, frequency}} / X_{\text{natural, frequency}} )$$ Python Logic:
( v["Forcing Frequency (Hz)"] / v["Natural Frequency (Hz)"] )Live Evaluation: [ROUTE: STATIC/GLOBAL] ( 0.8000 / 23.8521 ) = 0.0335
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| ☰ | \( \Sigma M_{\text{stand}} \) | Total Stand Mass (Tonnes) | 93.022359 |
View Help GuidePurpose: Global Logistics Weight.
Logic: Translates the total structural mass of the carbon fiber modular assembly into metric tonnes for shipping and crane specifications.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma M_{\text{stand}} = (M_{\text{stand}} / 1000)$$ Python Logic:
(v["Mass of Stand (kg)"] / 1000)Live Evaluation: [ROUTE: STATIC/GLOBAL] (93,022.3591 / 1000) = 93.0224
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| ☰ | \( \Sigma X_{\text{stand, cost}} \) | Total Stand Cost (£) | 1,488,357.745523 |
View Help GuidePurpose: Real-Time Budgeting.
Logic: Tracks manufacturing cost based on the target rate per kilogram, allowing for instant financial impact analysis whenever dimensions change.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\Sigma X_{\text{stand, cost}} = (M_{\text{stand}} \times \text{Fossil Carbon Fibre Cost per kg (£)})$$ Python Logic:
(v["Mass of Stand (kg)"] * v["Fossil Carbon Fibre Cost per kg (£)"])Live Evaluation: [ROUTE: STATIC/GLOBAL] (93,022.3591 * 16.0000) = 1,488,357.7455
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| ☰ | \( X_{\text{stability, rating}} \) | Stability Rating | ULTRA-STABLE (TIER 1) |
View Help GuidePurpose: Harmonic Safety Rating.
Logic: 1 if v["Resonance Ratio"] < 0.1 else (2 if v["Resonance Ratio"] < 0.7 else (4 if v["Resonance Ratio"] <= 1.3 else 3))
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{stability, rating}} = IF(\eta_{\text{resonance, ratio}} < 0.1, 1, IF(\eta_{\text{resonance, ratio}} < 0.7, 2, IF(\eta_{\text{resonance, ratio}} <= 1.3, 4, 3)))$$ Python Logic:
1 if v["Resonance Ratio"] < 0.1 else (2 if v["Resonance Ratio"] < 0.7 else (4 if v["Resonance Ratio"] <= 1.3 else 3))Live Evaluation: [ROUTE: STATIC/GLOBAL] 1 if 0.0335 < 0.1 else (2 if 0.0335 < 0.7 else (4 if 0.0335 <= 1.3 else 3)) = 1.0000
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| ☰ | \( X_{\text{precision, gap}} \) | Precision Gap Health | OPTIMAL |
View Help GuidePurpose: Magnetic Clearance Guarantee.
Logic: 1 if v["Plus (+) Skeleton Predicted Deflection (mm)"] < 0.1 else 0
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$X_{\text{precision, gap}} = IF(\Delta_{\text{plus, skeleton}} < 0.1, 1, 0)$$ Python Logic:
1 if v["Plus (+) Skeleton Predicted Deflection (mm)"] < 0.1 else 0Live Evaluation: [ROUTE: STATIC/GLOBAL] 1 if 0.0282 < 0.1 else 0 = 1.0000
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| ☰ | \( \eta_{\text{footprint}} \) | Footprint Efficiency | 52.267206 |
View Help GuidePurpose: Facility Space Management.
Logic: Measures the total square meters of floor space occupied by the machine to assist in factory floor planning and safety zoning.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
$$\eta_{\text{footprint}} = (R_{\text{outer, curved}} \times 2) \times L_{\text{plus, skeleton}}$$ Python Logic:
(v["Outer curved side wall outside radius (m)"] * 2) * v["Plus (+) Skeleton Span Distance (m)"]Live Evaluation: [ROUTE: STATIC/GLOBAL] (5.6154 * 2) * 4.6539 = 52.2672
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| ☰ | \( X_{\text{gasket, compression}} \) | Gasket Compression (mm) |
View Help GuidePurpose: Harmonic Dampening Buffer.
Logic: Defines the exact compression thickness of the recycled rubber shims between modules, acting as mechanical filters to shatter high-frequency vibrations before they hit the floor.
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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