Archard Wear
Calculate the volume of material removed by wear using Archard's law, V = k·F·s ÷ H, from the dimensionless wear coefficient k, the normal force F, the sliding distance s and the hardness of the softer material H. The result is the worn volume, proportional to load and distance and inversely proportional to hardness. It is the fundamental model of adhesive and abrasive wear, used to predict the life of sliding-contact surfaces — gears, guides, bushings, tools. Harder materials and lower loads reduce wear. Enter the wear coefficient, the force, the distance and the hardness.
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Archard wear
The Archard law is the basic model for predicting how much material is lost to wear when two surfaces slide against each other under load. It states that the worn volume is V = k·F·s ÷ H, where F is the normal force pressing the surfaces together, s is the total sliding distance, H is the hardness of the softer material (which resists indentation) and k is the wear coefficient, a dimensionless number that characterizes the severity of the contact (mild lubricated wear has k ~10⁻⁸; severe metal-on-metal adhesive wear, ~10⁻³). The physical reasoning is elegant: wear happens at the microscopic peaks (asperities) that actually touch; the real area of contact is proportional to the load divided by the hardness, and the volume removed is proportional to that area times the distance slid. The practical consequences follow immediately: to cut wear, lower the load, raise the hardness of the surfaces (quenching, nitriding, hard coatings) or reduce k (lubrication, a better surface finish, compatible material pairs). Archard's law is used to estimate the service life of gears, linear guides, bushings, cutting tools and even joint prostheses. It is a simplified model — k is not constant across every condition — but it captures the essence of the phenomenon. Enter the wear coefficient, the force, the sliding distance and the hardness.
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Calculate the corrosion rate by the mass-loss method, CR = 87.6 × W ÷ (D × A × t), from the mass loss W (mg), the material density D (g/cm³), the exposed area A (cm²) and the exposure time t (hours). The result, in mm/year, is the average speed at which the metal is consumed by corrosion — the key parameter to predict the service life of structures, piping and equipment and to set the corrosion allowance in design. Rates below 0.1 mm/year are usually acceptable. Enter the mass loss, density, area and time.
Thickness with Corrosion Allowance
Calculate the total thickness to specify for a pressure-vessel component including the corrosion allowance, t_total = t_calculated + CA, from the minimum pressure-calculated thickness t_calculated (mm) and the corrosion allowance CA (mm). The thickness from the ASME formulas is the MINIMUM needed to resist pressure — but the vessel will operate for DECADES, and corrosion (and erosion) will consume wall material over time. If the vessel were made exactly at the minimum thickness, the first corrosion would already leave it below safe. So a CORROSION ALLOWANCE (CA) is added — a 'sacrificial' over-thickness, typically 1.5 to 6 mm, sized for the expected corrosion rate times the design life (e.g., 0.1 mm/year × 25 years = 2.5 mm). Thus the thickness specified for fabrication is the structural minimum plus the corrosion allowance. Over life, inspection (by ultrasound) measures the REMAINING thickness; when corrosion consumes the whole allowance and the thickness approaches the structural minimum, the vessel must be repaired or retired. The corrosion allowance is like a 'life reserve' built into the wall. Enter the calculated thickness and the corrosion allowance.
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Estimate a reservoir's useful life from sedimentation, Vu = V ÷ V_s, from the reservoir's useful (or total) volume V (m³) and the sediment volume deposited per year V_s (m³/year). Every reservoir, by impounding a river, slows the flow and makes water lose its sediment-carrying capacity — sand, silt and clay from the watershed settle on the bottom, gradually reducing storage. The useful life is the number of years until sedimentation impairs the reservoir's function (power, supply, regulation). It is a crucial design parameter in hydrology and watershed management: reservoirs in basins with erodible soils, deforestation or intensive agriculture silt up fast (decades), while well-conserved basins last centuries. The sediment inflow V_s comes from the basin's sediment yield and the reservoir's trap efficiency (Brune curve). The simple constant-rate model gives the order of magnitude. Conserving the basin and flushing through bottom outlets extend the life. Enter the reservoir volume and the annual sediment inflow.
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Calculate a cutting tool's life by Taylor's equation, T = (C ÷ Vc)^(1/n), from the constant C (the cutting speed giving 1 minute of life, characteristic of the tool-material pair), the cutting speed Vc (m/min) and the exponent n (depending on tool material). Formulated by F. W. Taylor in 1907 from thousands of tests, this is machining's most famous relation and describes a fundamental trade-off: the HIGHER the cutting speed, the SHORTER the tool life — and steeply, since it is a power law. The exponent n quantifies the sensitivity: for HSS n ≈ 0.1 (life drops very fast with speed), for carbide n ≈ 0.2-0.3, for ceramic n ≈ 0.4-0.6 (less sensitive, allowing much higher speeds). Taylor's equation is the basis of economic OPTIMIZATION of machining: there is an optimal cutting speed minimizing total cost per part, balancing cutting time (falling with speed) against tool and change-downtime cost (rising with speed). Speeds above optimum 'burn' costly tools too fast; below, waste machine time. Enter the constant C, the cutting speed and the exponent n.
Bearing Life L10
Compute nominal bearing life L10 in million revs: L10 = (C/P)^p with p=3 (ball) or p=10/3 (roller).
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Calculate the life of a sacrificial anode, life = (mass × capacity) ÷ (current × 8760), from the anode mass (kg), the material's current capacity (A·h/kg), the protection current drained (A) and the 8760 hours in a year. The result, in years, shows how long the anode (zinc, aluminium or magnesium) will provide protection before being consumed and needing replacement — essential in designing galvanic cathodic protection of tanks, pipelines and marine structures. Enter the mass, the material capacity and the current.
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