Calculation tools for mechanical engineering

Size the complete drivetrain: motor, gearbox, inertias and torques in a single calculator.

Convert between torque, speed and power: P = M·ω for rotating drives.

Gear ratio i from tooth counts, diameters or a speed pair, reflecting speed, torque and inertia through the stage.

Kinematics of uniformly accelerated motion: solve the missing quantity from distance, velocity, acceleration and time.

Mass moment of inertia of homogeneous bodies: solid cylinder, tube, cuboid, sphere, cone and ring.

Slider-crank mechanism: piston displacement, velocity and acceleration from crank and rod geometry.

Required braking torque, static and dynamic, plus braking energy and deceleration time.

Pre-size a rack-and-pinion drive for linear axes: pinion torque, power, gear mesh forces (Fn, Fr, Fa) and a module estimate with traffic-light rating.

Cycle time of a positioning axis from multiple move and dwell segments: trapezoidal, triangular and S-curve profiles, segment time and peak velocity plus combined position, velocity and acceleration plots.

Size a ball screw: drive torque, speed from feed rate, critical speed with bearing factor, DN value, Euler buckling load and L10 life with traffic-light rating.

Rotary indexing table: switching torque, cycle time and acceleration profile from station count, index time and table inertia.

Inertia, static load moment and payload at the robot flange: parallel-axis contribution per mass, compared against datasheet limits with traffic-light rating.

Air consumption (standard volume) per stroke, cycle and minute plus approximate extension time of a pneumatic cylinder: piston and annulus area, compression ratio, load ratio and force balance.

Holding force of a vacuum gripper and required number of suction cups: theoretical force per cup, load cases, safety factor with traffic-light rating.

Required gripping force of a mechanical jaw gripper (friction or form fit): grip force per jaw from workpiece mass, acceleration, friction, jaw count and safety with traffic-light rating.

Size industrial shock absorbers and end-position damping: energy per stroke and per hour and effective mass from moving mass, impact velocity, drive force and stroke with traffic-light rating.

Toggle clamp force: mechanical advantage and resulting clamping force of a toggle clamp from actuation force, lever geometry and toggle angle.

Calculate the nominal L10/L10h life of profile rail guides (ball or roller type) using the manufacturer catalogue method: effective load, life in kilometres and operating hours, plus static safety factor S0 with traffic-light rating.

Design a trough screw conveyor for bulk material: volume and mass flow rate, drive power and torque, axial conveying speed, plus critical speed and incline rating with fill level and resistance factor presets.

Calculate the drive power of a belt conveyor using the simplified main resistance method of DIN 22101: main resistance, gradient resistance, driving force, pulley and motor power.

Design a trough/scraper chain conveyor for bulk material: conveyed material mass per metre, horizontal resistances of material and chain, gradient resistance, driving force, drive power and chain tension with a check against the allowable chain tension.

Design motion laws, check characteristic values and calculate cam profiles per VDI 2143.

Design spur and helical gear pairs: profile shift coefficients, operating pressure angle via the involute function, centre distance, pitch, tip, root and base circles, tip clearance plus transverse, overlap and total contact ratio.

Verify tooth root and flank stress of a spur gear pair per DIN 3990 / ISO 6336, with the safety factors SF and SH.

Estimate the bending critical speed of shafts using the Rayleigh and Dunkerley methods.

Design roller chain drives per ISO 606: chain length, ratio and power rating.

Design timing belt drives: ratio, belt length, centre distance, teeth in mesh and belt speed.

Design planetary gear sets: stationary ratio, ratio per operating mode, all shaft speeds, output torque and the planet assembly and neighbour conditions.

Calculate extend and retract forces of pneumatic and hydraulic cylinders per ISO 15552 and ISO 6020-2, including the piston rod buckling check.

Calculate a straight bevel gear online: pitch cone angles, outer and mean pitch diameters, cone distance, virtual tooth number and tangential force with a sketch and traffic-light rating.

Calculate a cylindrical worm gear per DIN 3975 online: ratio, lead angle, diameters, centre distance, driving efficiency and self-locking with a traffic-light rating.

Size a shaft coupling from nominal torque and service factor: application, starting and temperature factors determine the required coupling torque, with traffic-light rating.

Size a variable frequency drive for a three-phase induction motor: motor rated current from power, power factor and efficiency, switching-frequency and temperature derating, required drive rated current, overload reserve (VT/CT/heavy duty) and recommended drive size with a traffic-light rating.

Calculate the safety verification for shafts and axles per DIN 743.

Calculate deflection and bending stress of beams for common support and load cases.

Calculate damage sum and fatigue life of load spectra per the Palmgren-Miner rule.

Verify the buckling safety of compression members per Euler and Tetmajer.

Calculate contact pressure and deformation for point and line contact using Hertz theory.

Calculate area moment of inertia and section modulus of common cross-sections: rectangle, circle, tube, I- and U-profile.

Calculate equivalent stress online by the von Mises (distortion energy), Tresca (maximum shear) and Rankine (maximum principal stress) theories: plane stress state or combined shaft loading, principal stresses, Mohr's circle and a safety check with traffic-light rating.

Calculate torsional shear stress τ and angle of twist φ of shafts online: solid circle, circular tube, thin-walled closed Bredt sections and rectangle, with torsional section modulus and torsion constant plus shear check with traffic-light rating.

Calculate wall thickness and stresses of pressure vessels and pipes online: boiler formula for thin-walled cylinders and spheres, Lamé for thick-walled pipes, equivalent stress per von Mises and Tresca, safety against yield with traffic light. Preliminary sizing.

Flexural buckling verification of compression members to DIN EN 1993-1-1 with buckling curves.

Verify steel bolted connections to DIN EN 1993-1-8 for shear, bearing and tension.

Calculate the free and damped vibration of a single-degree-of-freedom system: natural frequency, damping ratio, decay and resonance.

Calculate belt and rope friction with the Euler-Eytelwein equation: force ratio, holding force and wrap angle.

Calculate normal stress, strain and elongation of tension and compression rods, including thermal stress with restrained expansion.

Calculate the centrifugal force of rotating masses from speed or angular velocity and radius: centrifugal force and circumferential velocity.

Design and verify bolted joints per VDI 2230.

Design and verify cylindrical interference fits per DIN 7190.

Verify parallel key joints per DIN 6892 against surface pressure.

Verify fillet welds per EN 1993-1-8: weld stresses and design resistance.

Design flange joints per EN 1092-1 and AD 2000-B7: dimensions, bolts and gasket forces.

Verify pin and bolt joints against shear, surface pressure and bending per Roloff/Matek.

Verify riveted joints online: shear τ = F/(z·n·A) and bearing pressure σ_l = F/(z·d·t) with safety factors and traffic-light rating, single and double shear.

Calculate the required thread engagement depth against stripping, with material presets for steel, cast iron, aluminum and brass.

Calculate the joining temperature for thermally assembling an interference fit: heat the outer part, cool the inner part, or combine both, with material presets and a traffic-light rating.

Verify a single-lap adhesive joint: mean shear stress τ = F/A, allowable stress and utilization, required overlap length with traffic-light rating, with adhesive presets for epoxy, polyurethane, methacrylate, cyanoacrylate and silicone.

Size a locking assembly for a friction-fit shaft-hub connection: required nominal torque, combined utilization from torque and axial force, required interface pressure and transmittable torque, with application factor presets and a traffic-light rating.

Flank pressure verification for involute splined shaft connections per DIN 5480: number of teeth, mean load-carrying diameter, flank pressure, allowable pressure and transmittable torque with a traffic-light rating.

Calculate cylindrical compression springs per DIN EN 13906-1: spring rate, forces and stresses.

Calculate the basic rating life of rolling bearings per ISO 281.

Calculate spring rate, force and shear stress of cylindrical helical extension springs online: with initial tension F0, curvature correction after Bergsträßer or Wahl, stress check with traffic-light rating and PDF report.

Calculate Belleville disc springs to DIN 2093 (Almen-Laszlo) online: spring force F(s), nonlinear characteristic, factors K1/K2/K3 and edge stress with a traffic-light rating.

Calculate cylindrical torsion (leg) springs per DIN EN 13906-3 online: spring rate, moment per degree and bending stress with curvature correction and traffic-light rating.

Calculate bearing pressure, sliding velocity and p·v value of plain bearings using the p·v rating method, with material presets for bronze, sintered bronze, PTFE and POM composite bearings, and polyamide.

Look up groove dimensions for shaft and bore retaining rings and verify the groove against bearing pressure, with material presets for the shaft/hub and a traffic-light rating.

Size gas springs for hoods and covers: required extension force, spring lengths, stroke and hand force when opening and closing, from the moment equilibrium about the hinge.

Determine limit deviations, clearance and interference for hole and shaft per ISO 286.

Calculate tolerance stackups per DIN 7186 arithmetically, statistically and via Monte Carlo simulation.

Evaluate position tolerances per ISO 1101: actual deviation, true position and bonus tolerance.

Look up limit deviations for linear and angular dimensions without individual tolerances per ISO 2768.

Calculate the flat length of sheet metal bends per DIN 6935.

Calculate the bending force for air bending in a V-die online: F = k·Rm·s²·b/V. With recommended die width, minimum bend radius and minimum flange length, live on every input.

Determine cutting speed, spindle speed and feed for turning, milling and drilling.

Determine tapping drill diameters for metric threads per DIN 13 and clearance holes per EN 20273.

Calculate the drawing force and stress in wire and tube drawing with Siebel's equation online: true strain, area reduction, ideal, friction and shear share with a drawing-limit check.

Determine cutting force, power and machining time for turning, milling and drilling with the Kienzle model.

Calculate punching and shearing force and work for shear cutting of sheet metal.

Determine heat input and specific energy of a weld from current, voltage and travel speed.

Calculate machining time for turning, milling and drilling: spindle speed, cutting speed, feed rate and total feed travel from approach, working length and overtravel.

Calculate grinding cutting data for external cylindrical grinding and surface grinding: cutting speed v_c, speed ratio q, specific material removal rate Q'w and equivalent chip thickness h_eq with a traffic-light guideline rating.

Look up strength and material properties of common engineering materials.

Convert hardness: HV to HRC, HRC to HV, Brinell and tensile strength per ISO 18265.

Calculate the weight of sheets, round bars, tubes and profiles from material density and volume.

Calculate the available NPSH and cavitation margin of centrifugal pumps and check it against the required NPSH.

Calculate system head, hydraulic power and shaft and motor power of centrifugal pumps.

Determine the specific speed n_q and impeller type from flow rate, head and rotational speed.

Convert flow rate, head and power of centrifugal pumps for a changed speed or impeller diameter.

Calculate flow rate, torque and power of positive displacement pumps from displacement volume and pressure difference.

Size a hydraulic cylinder: piston force when extending and retracting, area ratio, piston speed, stroke time, oil demand and drive power - plus the buckling verification of the piston rod per Euler and Tetmajer with the maximum permissible stroke.

Solve the ideal gas law online: from any three of pressure, volume, mass and temperature find the fourth. Mass form with R_s (gas selection) and molar form with R_m, including density.

Calculate state changes of ideal gases online: isothermal, isobaric, isochoric, adiabatic and polytropic. From an initial state and one target value get the final state, boundary work, heat, internal energy and entropy with a p-V diagram and PDF.

Calculate the thermal efficiency of the ideal Otto and Diesel cycles online: enter compression ratio and isentropic exponent to get corner states, heat, mean effective pressure and the p-V diagram, live.

Calculate heat flow, thermal resistance and temperature profile of multilayer walls and pipes online: Fourier's law, λ selection for insulation and metals, temperature profile chart, PDF report.

Calculate the convective heat transfer coefficient α for forced pipe flow online: Reynolds, Prandtl and Nusselt number, Dittus-Boelter and Gnielinski, laminar Nu = 3.66, heat flow Q = α·A·ΔT and report PDF.

Size a recuperator online: LMTD method and ε-NTU method, counterflow and parallel flow, heat duty, outlet temperatures and temperature profile as a chart, live with every input.

Calculate the heat loss of insulated pipes online: pipe wall and insulation as a series of cylindrical thermal resistances, heat flow per length and total, surface temperature with touch-protection indicator and radial temperature profile.

Calculate a reciprocating compressor online: compression power, discharge temperature, mass flow and cooling duty for isothermal, isentropic and polytropic compression. Multi-stage with intercooling, optimum intermediate pressures and savings against a single stage.

Calculate the vapour-compression cycle online: four enthalpies from the log p-h chart give mass flow, refrigerating capacity, compressor power and condenser duty. COP for refrigeration and heat pump operation, Carnot comparison and second-law efficiency.

Compare and convert the roughness parameters Ra and Rz per ISO 21920.

Measurement system analysis to AIAG MSA and VDA 5: Type 1 (Cg/Cgk), Gage R&R (%GRR, ndc) and Q_MS/Q_MP with traffic-light rating.

Calculate pressure drop in pipes per Darcy-Weisbach: friction, friction factor and minor losses.

Convert engineering units: power, rotational speed, torque, pressure, force, energy, length, mass, speed and temperature.