Glossary

The terms that appear in Axomek’s inputs and results, each in a few sentences that say how the app uses it. Every term links to the calculations and guides that go into detail.

Application factor K_A (KA, application factor): A factor on the nominal load for the peaks from the driving and driven machines (shocks, torque fluctuation) that the nominal torque does not contain: commonly 1.0 for uniform drive and load, 1.25 to 2 or more for shocks. In Axomek it is an input to the gear ratings and the key and spline check; a gear load spectrum is rated with K_A = 1, since the spectrum is itself the load variation.Gear calculation · Bevel gear calculation · Parallel key and spline calculation · Gear rating (ISO 6336)
Ball screw critical speed and buckling load (ball screw critical speed, ball screw buckling, permissible speed, Euler buckling, end fixity): The speed at which the screw shaft whirls in resonance, and the axial force at which it buckles. Neither is part of ISO 3408: Axomek takes a beam of the root diameter d₂ with factors for the end fixity (fixed–fixed, fixed–supported, supported–supported or fixed–free) and allows 80 % of the critical speed and, when the force compresses the shaft, 50 % of the Euler buckling load.Ball screw calculation · Ball screws
Basic dynamic load rating C (C, Cr, Ca, dynamic load rating, dynamic capacity): The load a rolling bearing carries for a basic rating life of one million revolutions at 90 % reliability (ISO 281). Axomek computes it from the internal geometry, with f_c of ISO/TR 1281-1 at the bearing’s own groove radii, so it can differ from a catalogue value. Ball screws (C_a) and linear guides (per 50 or 100 km) use the catalogue value you enter.Bearing life calculation · Ball screw calculation · Linear guide life calculation · Rating life (ISO 281)
Basic rating life L₁₀ (L10, L10h, basic rating life, bearing life, nominal life): The life that 90 % of a large group of identical bearings reach or exceed before the first sign of material fatigue: L₁₀ = (C/P)^p million revolutions, with p = 3 for ball and 10/3 for roller bearings, or L_10h in hours at the bearing’s speed. Axomek takes P as the ISO/TS 16281 reference load from the solved element loads, not from X and Y factors.Bearing life calculation · Bearing load distribution · Rating life (ISO 281)
Basic static load rating C₀ (C0, C0r, static load rating, static capacity): The static load that gives the ISO 76 limit of Hertz contact stress at the centre of the most heavily loaded contact, at which the permanent deformation is about 0.0001 of the element diameter: 4 600 MPa for self-aligning ball bearings, 4 200 MPa for other ball bearings, 4 000 MPa for roller bearings. Axomek derives C₀ from Hertz contact at the actual groove radii, not from the standard’s tables.Bearing static safety and static load rating · Static load rating and static safety
Campbell diagram and gyroscopic effect (Campbell diagram, gyroscopic effect, forward whirl, backward whirl, whirl): A spinning disc that tilts produces a gyroscopic moment that stiffens forward whirl (the shaft centre orbits with the rotation) and softens backward whirl. The Campbell diagram plots each bending mode’s natural frequency over the shaft speed as a rising forward and a falling backward branch; a synchronous critical speed is where a branch crosses frequency = speed. When a part has polar inertia, Axomek checks the first forward one, since unbalance excites forward whirl.Shaft critical speed calculation · Deflection, critical speeds and whirl
Conformity (osculation) (osculation, groove conformity, groove radius, fi, fe, inner conformity, outer conformity): The groove radius of a ball bearing raceway over the ball diameter, f = r/D_w, entered as Inner conformity and Outer conformity (typically 0.52 and 0.53). Nearer 0.5 the groove hugs the ball: lower contact pressure, higher stiffness and ratings. Axomek uses the actual radii throughout, also for C, C₀ and C_u, so grooves tighter than 0.52/0.53 raise ratings that ISO 281 and ISO 76 do not credit.Bearing life calculation · Bearing load distribution · Hertzian contact stress calculator · Internal load distribution (ISO/TS 16281)
Contact angle α (contact angle, nominal contact angle, operating contact angle, free contact angle): The angle between the radial plane of a bearing and the line along which a rolling element transmits its load. The ratings use the nominal angle; in the load distribution Axomek computes each ball’s own angle, which starts from the free contact angle set by the clearance and grows under axial load or spreads under tilt. A single angular contact bearing held square needs an axial load of at least F_r·tan α.Bearing load distribution · Bearing life calculation · Internal load distribution (ISO/TS 16281)
Contamination factor e_C (eC, ec, contamination factor, cleanliness): A factor from 0 to 1 in a_ISO for the dents that particles in the lubricant leave in the raceways (ISO 281, Annex A). Axomek computes it from κ, the bearing size and the Lubrication and cleanliness choice: 14 cases of oil with on-line filter, oil without one and grease. Water and other fluids in the lubricant are not covered.Bearing life calculation · Rating life (ISO 281)
Critical speed (critical speed, whirling speed, natural frequency, first critical speed): A speed at which the shaft runs in resonance with one of its bending natural frequencies, so that a small unbalance gives a large deflection. Axomek finds the natural frequencies of the Timoshenko beam model on its supports (with the bearings’ stiffness when coupled) and checks the first against Min 1st critical speed. A common rule keeps a stiff shaft’s running speed below about 70 % of its first critical speed.Shaft critical speed calculation · Shaft deflection calculation · Deflection, critical speeds and whirl
Damage sum (Palmgren–Miner) (Miner rule, Palmgren-Miner, damage accumulation, cumulative damage, linear damage): The sum of the cycle ratios n_i/N_i of a load spectrum, each block’s cycles over the cycles to failure at its load; failure is expected at a sum of 1, or at a lower effective sum. Axomek uses it for gear load spectra (ISO 6336-6), weld fatigue (EN 1993-1-9, maximum 1 by default) and FKM shaft strength over load cases, and combines bearing load cases by 1/L = Σ t_i/L_i.Gear calculation · Weld calculation · Shaft strength to the FKM guideline · Equivalent bearing load
Detail category Δσ_C (detail category, FAT class, reference fatigue strength, delta sigma C, EN 1993-1-9): In EN 1993-1-9, the reference fatigue strength of a structural detail: the stress range it endures for 2 million cycles, which names the detail and fixes its S–N curve. Axomek’s weld groups default to Δσ_C = 36 MPa (root failure of load-carrying fillet welds) and Δτ_C = 80 MPa, with slopes 3 then 5 for normal stress, 5 for shear and a cut-off at 10⁸ cycles; each line can take its own.Weld calculation · Weld groups
DIN 743 fatigue safety (DIN 743, shaft fatigue safety, Smin, minimum fatigue safety): The fatigue safety S of a shaft section after DIN 743-1, eq. (2), from the stress amplitudes over the component’s amplitude strengths: S =1/√((σ_zda/σ_zdADK + σ_ba/σ_bADK)² + (τ_ta/τ_tADK)²). Axomek evaluates it at every shoulder and notch and the most stressed plain section; the check passes when the lowest S reaches Min fatigue safety (DIN 743 asks for at least 1.2). A static safety against yield is checked too.Shaft strength calculation · Shaft strength: DIN 743 and FKM
Dynamic factor K_v (Kv, dynamic factor, internal dynamic factor, resonance ratio): In ISO 6336, the factor for the internal dynamic loads from the mesh’s own vibration. Axomek computes it by method B from the resonance ratio N, the pinion speed over the mesh’s main resonance speed, with separate expressions below, at and above resonance; accuracy grade, pitch deviations, tip relief and mesh stiffness enter.Gear calculation · Gear rating (ISO 6336)
Embedding loss (embedding, fZ, FZ, preload loss, settling): The preload a bolted joint loses after tightening as the roughness peaks in the thread, under head and nut and at the interfaces flatten. VDI 2230 (step R4) takes the embedding f_Z from its Table 5 and the loss F_Z = f_Z/(δ_S + δ_P); Axomek adds F_Z to the minimum assembly preload and takes it from the residual clamp load.Bolted joint calculation · Bolted joints (VDI 2230)
Equivalent load P and P₀ (P, P0, Pref, dynamic equivalent load, static equivalent load, reference load, X and Y factors): The constant load of the rated kind (radial or axial) equivalent to a bearing’s real combination of loads: P = X·F_r + Y·F_a in ISO 281 for the life, P₀ = X₀·F_r + Y₀·F_a in ISO 76 for static load. Axomek instead takes the ISO/TS 16281 reference load P_ref from the solved element loads, which sees clearance, tilt and contact angle change, and judges static load by the largest contact stress.Bearing life calculation · Bearing static safety and static load rating · Equivalent bearing load
Face load factor K_Hβ and K_Fβ (KHβ, KHb, KFβ, KFb, face load factor, load distribution factor): The ISO 6336 factors for uneven load across the face width from helix deviations and shaft deflection: K_Hβ for contact and K_Fβ = K_Hβ^N_F for root stress. Axomek uses a given K_Hβ (1.15 by default) or, with Compute KHβ, ISO 6336-1 method C from the pinion shaft layout, the manufacturing misalignment and running-in. In a gearbox model, shaft and housing deflection is not fed in automatically; enter it as a mesh misalignment.Gear calculation · Gear rating (ISO 6336)
FKM degree of utilisation (FKM guideline, degree of utilisation, aBK, aSK, utilization): In the FKM guideline, the stress times its safety factor over the component strength: a_BK = σ_a·j_D/S_BK for fatigue and a_SK for static strength, each combined over the stress types. The safety factors are inside it, so a section passes when a_BK ≤ 1 and a_SK ≤ 1; Axomek also reports the safeties j_D/a_BK and j_ges/a_SK.Shaft strength to the FKM guideline · Shaft strength: DIN 743 and FKM
Flank pressure (key flank pressure, surface pressure, bearing pressure, DIN 6892): The mean pressure on the load-carrying flanks of a key or spline. For a parallel key Axomek uses p = 2·T·K_A·K_λ/(d·h′·l_tr·i·φ) as in DIN 6892, with the heights h′ the key bears in the shaft groove and in the hub from the keyway geometry (close to DIN 6892 method C’s 0.45·h for DIN 6885-1 keyways), against f_S·R_e for shaft and hub and R_e for the key. Splines are rated alike on the mean flank diameter, with 75 % of the teeth carrying.Parallel key and spline calculation · Keys and splines
Hertzian contact pressure (Hertz pressure, Hertzian stress, contact stress, p0, pmax, contact ellipse): The pressure between two curved elastic bodies pressed together, after Hertz: semi-ellipsoidal over the ellipse of a point contact, semi-elliptic across the strip of a line contact, peaking at p₀ in the centre (point contact: p₀ = 3·Q/(2·π·a·b)). In bearings it decides the static rating and safety, the fatigue load limit and the load–deflection law. Axomek solves the ellipticity numerically, not with curve fits.Hertzian contact stress calculator · Bearing static safety and static load rating · Bearing load distribution · Hertz contact and subsurface stress
Interference fit (press fit, shrink fit, interference, DIN 7190): A fit in which the shaft is always larger than the hole, so the smallest interference is at least 0. Axomek’s DIN 7190-1 press fit treats shaft and hub as thick-walled elastic cylinders: the interference, less 0.8·(Rz_A + Rz_I) for surface smoothing, gives the joint pressure. Torque and axial capacity are taken at the smallest interference, the stresses at the largest.Press fit and shrink fit calculation · ISO 286 limits and fits calculator · Fits: ISO 286 and press fits (DIN 7190)
IT grade and fundamental deviation (ISO 286) (IT grade, standard tolerance grade, fundamental deviation, tolerance class, ISO 286, H7): The two parts of an ISO 286 tolerance class such as H7 or s6. The number is the standard tolerance grade IT, which sets the width of the zone; the letter is the fundamental deviation, the limit nearest the zero line, which places it (capitals for holes, lower case for shafts; H holes start at the zero line, h shafts end at it). Axomek computes hole letters F to S and shaft letters f to s in grades 4 to 7.ISO 286 limits and fits calculator · Fits: ISO 286 and press fits (DIN 7190)
Life modification factor a_ISO (aISO, a_ISO, life modification factor): The factor in L_nm = a₁·a_ISO·L₁₀ for lubrication, contamination and the fatigue limit of the steel, a function of e_C·C_u/P and κ (ISO 281, 9.3). It is limited to 50, and κ above 4 counts as 4. Below κ = 0.1, where ISO 281 gives no value, Axomek takes a_ISO at κ = 0.1 and warns that the life is optimistic.Bearing life calculation · Rating life (ISO 281)
Load distribution (ISO/TS 16281) (ISO/TS 16281, ISO 16281, internal load distribution, element loads, load zone): The share of a bearing’s load that each rolling element carries, found after ISO/TS 16281 from the equilibrium of the inner ring, with the operating clearance, tilt, contact angle change and, for rollers, the load along the roller in slices (laminae). Axomek solves it for every bearing and takes the reference load, life, contact stresses and stiffness from the element loads.Bearing load distribution · Bearing life calculation · Bearing static safety and static load rating · Internal load distribution (ISO/TS 16281)
Load factor Φ (VDI 2230) (Φ, Phi, load factor, Φn, force ratio, joint diagram): In VDI 2230, the share of an axial working load F_A that adds to the bolt force: F_SA = Φ·F_A, while (1 − Φ)·F_A relieves the clamped parts. For a load introduced at the head and nut faces Φ = δ_P/(δ_S + δ_P) from the resiliences of plates and bolt; the load introduction factor n gives Φ_n = n·δ_P/(δ_S + δ_P), and eccentric joints use Φ_en*.Bolted joint calculation · Bolted joints (VDI 2230)
Modified rating life L_nm (Lnm, L10m, modified rating life, modified life, adjusted life): The rating life corrected for reliability, lubrication, contamination and the fatigue limit of the steel: L_nm = a₁·a_ISO·L₁₀ (ISO 281, Clause 9), with n the failure probability in %; L_10m is the modified life at 90 % reliability. Axomek computes it from the element loads (ISO/TS 16281) and checks it against Minimum life at the reliability you choose.Bearing life calculation · Bearing load distribution · Rating life (ISO 281)
Notch factor β_σ and stress concentration factor α_σ (notch effect, notch factor, fatigue notch factor, stress concentration factor, Kt, Kf, βσ, ασ, Kerbwirkungszahl, Formzahl): The stress concentration factor α_σ (K_t in the FKM guideline) is the peak elastic stress at a notch over the nominal stress, from geometry alone. The fatigue notch factor β_σ (K_f in FKM) is the plain fatigue limit over the notched one, smaller than α_σ because the material round a steep stress gradient supports the peak. DIN 743-2 gives β = α/n with the support number n for shoulders, round grooves and cross bores, and measured factors for keyways, press fits, V-notches and retaining-ring grooves.Shaft strength calculation · Shaft strength to the FKM guideline · Shaft strength: DIN 743 and FKM
Pitting safety S_H (SH, pitting safety, contact safety, flank safety, surface durability): The safety of gear flanks against pitting: in ISO 6336 the pitting stress limit over the contact stress, S_H = σ_HG/σ_H. As σ_H grows with the square root of the load, S_H = 1.2 means only 1.44 times the load to the limit. Axomek’s default minimum is 1.0 (limits.minContactSafety), also for bevel and worm gears.Gear calculation · Bevel gear calculation · Worm gear calculation · Gear rating (ISO 6336)
Preload F_M and F_V (FM, FV, FMzul, FMmax, FMmin, assembly preload, bolt preload, clamp load): In VDI 2230, F_M is the assembly preload from tightening and F_V the preload left in the joint after embedding and temperature changes. Axomek works with F_Mmin, the preload the joint needs, F_Mmax = α_A·F_Mmin, and the permissible F_Mzul, at which the von Mises stress at assembly reaches ν·R_p0.2 (ν = 0.9 by default); the check passes when F_Mmax ≤ F_Mzul.Bolted joint calculation · Bolted joints (VDI 2230)
Reliability factor a₁ (a1, reliability factor, reliability, L1, L0.05): The factor in L_nm that converts the 90 % rating life to a higher reliability, after ISO 281, Table 12: a₁ = 1 at 90 % (L_10m), 0.25 at 99 % (L_1m) and 0.077 at 99.95 % (L_0.05m). Axomek offers every level of the table under Reliability, and the life check uses that level.Bearing life calculation · Rating life (ISO 281)
Safety factor and utilisation (safety factor, utilisation, utilization, check, margin): The ratio of what a part can take to what it gets, as each standard defines it, so safeties of different modules are not comparable. Every Axomek check also reports a utilisation: value over limit for a maximum (deflection, stress, damage), limit over value for a minimum (life, safety, critical speed). A check passes up to 100 % and warns above 85 % (in the bolt, fit and key modules, when the safety is less than 15 % above its minimum).Reading checks and safeties
Scuffing (flash and integral temperature) (scuffing, scoring, flash temperature, integral temperature, SB, SintS, FZG load stage): The sudden welding and tearing of gear flanks when the lubricant film breaks down at high sliding speed and load; a single overload can cause it, so it is not a fatigue failure. Axomek rates cylindrical gear pairs by the flash temperature method of ISO/TS 6336-20 (safety S_B, default minimum 2.0) and the integral temperature method of ISO/TR 13989-2 (S_intS, default minimum 1.8), both from the oil temperature and FZG load stage.Gear calculation · Gear scuffing (flash and integral temperature)
Shrink temperature (shrink fit temperature, joining temperature, assembly temperature, hub heating): The temperature to which a hub must be heated to slide over its shaft without force. Axomek expands the hub by the largest interference of the tolerances plus an assembly clearance of 0.001·d: θ = θ_room + (Z_max + 0.001·d)/(α·d), with α the hub’s coefficient of thermal expansion.Press fit and shrink fit calculation · Fits: ISO 286 and press fits (DIN 7190)
Spring index w (spring index, w, D/d, coil ratio, stress correction factor): The mean coil diameter of a helical spring over its wire diameter, w = D/d. It sets the stress correction k = (w + 0.5)/(w − 0.75) that EN 13906-1 applies for fatigue. Axomek needs w above 2 and warns outside 4 to 20, where a spring is hard to coil and the results are less reliable.Helical spring calculation · Helical springs
Static safety factor s₀ (S0, s0, static safety, static safety factor): The safety of a rolling bearing against harmful permanent dents in the raceways, s₀ = C₀/P₀ in ISO 76. Axomek takes it from the largest contact stress of the solved load distribution, s₀ = (σ_lim/p_max)³ for balls and squared for rollers, so clearance, tilt and preload count. s₀ ≥ 1 to 2 is typical for normal service; linear guides and ball screws check their own static safety, by default against 2.Bearing static safety and static load rating · Linear guide life calculation · Ball screw calculation · Static load rating and static safety
Subsurface shear stress and case depth (subsurface stress, maximum shear stress, orthogonal shear stress, case depth, hardening depth): Below a Hertzian contact the shear stress peaks some way under the surface: below a line contact the largest shear stress reaches 0.300·p₀ at a depth of 0.786·b. Rolling contact fatigue usually starts there, so the case of a case-hardened ring must reach well below that depth. Axomek suggests 3 times the depth of the largest shear stress, a rule of thumb rather than a standard, and checks the case depth you enter against it.Hertzian contact stress calculator · Bearing load distribution · Hertz contact and subsurface stress
Throat thickness a and the directional method (throat thickness, weld throat, a-dimension, directional method, simplified method, fillet weld): The throat a of a fillet weld is the height of the largest triangle that fits in its cross-section, about 0.7 times the leg for an equal-leg fillet; the weld is rated on its throat area. The directional method of EN 1993-1-8, 4.5.3.2, splits the throat stress into σ_⊥, τ_⊥ and τ_∥ and requires √(σ_⊥² + 3·(τ_⊥² + τ_∥²)) ≤ f_u/(β_w·γ_M2) and σ_⊥ ≤ 0.9·f_u/γ_M2. The simplified method of 4.5.3.3 is more conservative.Weld calculation · Weld groups
Tightening factor α_A (αA, alphaA, tightening factor, tightening scatter): In VDI 2230, the scatter of the tightening method: α_A = F_Mmax/F_Mmin, about 1.4 to 1.6 for a torque wrench and 1 for yield- or angle-controlled tightening (Table A8). The bolt must withstand F_Mmax while the joint must still work at F_Mmin, so a lower α_A allows a smaller bolt.Bolted joint calculation · Bolted joints (VDI 2230)
Timoshenko beam (Timoshenko beam, shear deformation, rotary inertia, beam finite element): A beam theory that adds shear deformation and rotary inertia to bending, which matters for short, thick sections. Axomek models the shaft with Timoshenko finite elements, shear parameter φ = 12·E·I/(κ·G·A·l²) with the shear correction factor κ: under a central load a simply supported uniform shaft deflects F·L³/(48·E·I) in bending plus F·L/(4·κ·G·A) in shear. Shear deformation can be switched off.Shaft deflection calculation · Shaft critical speed calculation · Deflection, critical speeds and whirl
Tooth root safety S_F (SF, tooth root safety, bending safety, root strength): The safety of a gear tooth against root breakage: in ISO 6336 the tooth root stress limit over the root bending stress, S_F = σ_FG/σ_F, with the load at the outer point of single pair tooth contact (method B). σ_F is proportional to the load, and because a broken tooth usually ends a gearbox’s life, Axomek’s default minimum for cylindrical gears is 1.4 (limits.minBendingSafety), above the 1.0 for pitting.Gear calculation · Bevel gear calculation · Plastic gear calculation · Gear rating (ISO 6336)
Transverse load factor K_Hα (KHα, KHa, KFα, KFa, transverse load factor): The factors K_Hα (contact stress) and K_Fα (root stress) of ISO 6336 for the uneven sharing of the load between the tooth pairs in contact, which comes from pitch deviation. Axomek computes them by method B; the spur gear pair template has K_Hα = 1.0.Gear calculation · Gear rating (ISO 6336)
Viscosity ratio κ (κ, kappa, viscosity ratio, ν1, rated viscosity, reference viscosity): The lubricant’s kinematic viscosity at operating temperature over the reference viscosity a bearing needs for an adequate film, κ = ν/ν₁ (ISO 281); ν₁ falls with speed and pitch diameter, and a grease counts by its base oil. Axomek takes ν from the Walther (ASTM D341) curve through ν₄₀ and ν₁₀₀. κ above 4 counts as 4; below 0.1, a_ISO is taken at 0.1 with a warning.Bearing life calculation · Rating life (ISO 281)