Linear force-excited model — one degree of freedom
Rotating-Unbalance SDOF Force-Transmission Check
Calculate peak 1× excitation force,steady-state displacement and transmitted support force for one documented equivalent mass–spring–damper mode.
Peak-amplitude SDOF result
Implemented steady-state model
ω=2πn/60 ; F₀=Uω²
ωₙ=√(K/m) ; r=ω/ωₙ ; ζ=c/(2mωₙ)
D=√[(1−r²)²+(2ζr)²]
X=(F₀/K)/D
TF=√[1+(2ζr)²]/D ; FT=F₀TF
m is the combined participating mass in kg,K is the equivalent stiffness in N/m,U is converted from g·mm to kg·m by 10⁻⁶,n is rpm,ω and ωₙ are rad/s,X is the peak displacement amplitude in metres,and F₀ and FT are peak force amplitudes in newtons. Force reduction is (1−TF)×100%; a negative value explicitly means amplification.
Source and dimensional check
MIT OpenCourseWare,Rotating Imbalance derives the harmonic force components with amplitude meω². MIT OpenCourseWare,Vibration Isolation derives the force-excited SDOF response and transmitted-force ratio. Units check:F₀=(kg·m)/s²=N;F₀/K=N/(N/m)=m.
Interpretation limits
The result is not a balance tolerance,a vibration-severity value,a foundation design or a safe/unsafe verdict. Enter only equivalent mass,stiffness,damping and unbalance supported by project data. Total phase-coherent U means the vector-equivalent unbalance producing the modeled 1× force component; unrelated rotors or phases cannot simply be added as scalars. Peak amplitudes must not be compared directly with RMS or peak-to-peak limits.
Ideal undamped resonance
When ζ=0 and r=1,the steady-state transfer denominator is zero. The ideal linear model has no finite harmonic steady-state response. The calculator reports that singularity explicitly; real systems require measured/modelled damping and transient analysis near resonance.
Nikolai Shelkovenko
Nikolai Shelkovenko is a vibration analysis engineer and the founder and CEO of Vibromera. For more than 15 years he has balanced rotating equipment in the field rather than on a test bench: mulchers, industrial fans, crushers, centrifuges, shafts and spindles. That work is what the Balanset instruments grew out of — they were designed as a tool a specialist can carry to the machine and use alone, on site, not as laboratory equipment. Vibromera was founded in 2017 and has been based in Porto, Portugal, since 2023. Development, assembly and support of the Balanset line all happen here. The flagship instrument is the Balanset-1A, a portable analyser for single- and two-plane balancing and for vibration diagnostics. Nikolai is personally involved in customer support, in working through difficult balancing cases and in the development of the software. He works with customers worldwide, in any language.
