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.

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.

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

Calculate the load capacity of spur gears per ISO 6336.

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.

Calculate extend and retract forces of pneumatic cylinders per ISO 15552.

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.

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 tau and angle of twist phi 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 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.

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.

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

Look up strength and material properties of common engineering materials.

Convert hardness values between Vickers, Brinell, Rockwell C and tensile strength per ISO 18265.

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

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.

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.

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, lambda 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 eps-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.

Convert engineering units: length, area, force, pressure, torque, power, temperature and more.