A Campbell Diagram (also called an interference diagram) plots natural frequencies against rotational speed to identify critical speeds and resonance conditions in rotating machinery. It overlays engine order excitation lines (diagonal lines from the origin) on top of natural frequency curves, with intersections marking critical speeds where resonance may occur. This visualization is essential for ensuring safe operating ranges in turbomachinery, automotive powertrains, and other rotating equipment.
# anyplot.ai
# campbell-basic: Campbell Diagram
# Library: makie 0.22.10 | Julia 1.11.9
# Quality: 90/100 | Created: 2026-05-28
using CairoMakie
using Colors
using Random
Random.seed!(42)
# Theme tokens
const THEME = get(ENV, "ANYPLOT_THEME", "light")
const PAGE_BG = THEME == "light" ? colorant"#FAF8F1" : colorant"#1A1A17"
const ELEVATED_BG = THEME == "light" ? colorant"#FFFDF6" : colorant"#242420"
const INK = THEME == "light" ? colorant"#1A1A17" : colorant"#F0EFE8"
const INK_SOFT = THEME == "light" ? colorant"#4A4A44" : colorant"#B8B7B0"
const INK_MUTED = THEME == "light" ? colorant"#6B6A63" : colorant"#A8A79F"
const IMPRINT_PALETTE = [
colorant"#009E73", # 1 — brand green (1st Bending)
colorant"#C475FD", # 2 — lavender (2nd Bending)
colorant"#4467A3", # 3 — blue (1st Torsional)
colorant"#BD8233", # 4 — ochre (Axial)
]
const CRITICAL_COLOR = colorant"#AE3030" # semantic: danger / resonance
# Data — turbine rotor, 0–6000 RPM operating range
speeds = collect(range(0.0, 6000.0; length = 100))
speed_eo = [0.0, 6000.0]
# Natural frequency curves (Hz) — gyroscopic variation with speed
freq_1b = @. 50.0 + 25.0 * (speeds / 6000.0) # 1st Bending: 50 → 75 Hz
freq_2b = @. 120.0 + 25.0 * (speeds / 6000.0) # 2nd Bending: 120 → 145 Hz
freq_1t = @. 200.0 - 15.0 * (speeds / 6000.0) # 1st Torsional: 200 → 185 Hz
freq_ax = @. 310.0 + 8.0 * (speeds / 6000.0) # Axial: 310 → 318 Hz
# Engine order excitation lines (Hz = n × RPM / 60)
eo_freq_1x = speed_eo ./ 60.0
eo_freq_2x = 2.0 .* speed_eo ./ 60.0
eo_freq_3x = 3.0 .* speed_eo ./ 60.0
# Critical speed intersections (mode curve ∩ engine order line, analytically solved)
# Mode 1 + 1×: 4000 RPM, 66.7 Hz | Mode 2 + 2×: 4114 RPM, 137.1 Hz
# Mode 1 + 2×: 1714 RPM, 57.1 Hz | Mode 2 + 3×: 2618 RPM, 130.9 Hz
# Mode 1 + 3×: 1091 RPM, 54.5 Hz | Mode 3 + 3×: 3810 RPM, 190.5 Hz
crit_spd = [4000.0, 1714.3, 1090.9, 4114.3, 2618.2, 3809.5]
crit_frq = [66.67, 57.14, 54.55, 137.14, 130.91, 190.48]
# Figure
fig = Figure(
size = (1600, 900),
fontsize = 14,
backgroundcolor = PAGE_BG,
)
ax = Axis(
fig[1, 1];
title = "campbell-basic · julia · makie · anyplot.ai",
titlesize = 20,
titlecolor = INK,
xlabel = "Rotational Speed (RPM)",
ylabel = "Frequency (Hz)",
xlabelcolor = INK,
ylabelcolor = INK,
xlabelsize = 14,
ylabelsize = 14,
xticklabelcolor = INK_SOFT,
yticklabelcolor = INK_SOFT,
xticklabelsize = 12,
yticklabelsize = 12,
backgroundcolor = PAGE_BG,
topspinevisible = false,
rightspinevisible = false,
leftspinecolor = INK_SOFT,
bottomspinecolor = INK_SOFT,
xtickcolor = INK_SOFT,
ytickcolor = INK_SOFT,
xgridvisible = false,
ygridcolor = RGBAf(INK.r, INK.g, INK.b, 0.12),
yminorgridvisible = false,
xminorgridvisible = false,
)
# Engine order excitation lines (dashed reference lines from origin)
l_eo = lines!(ax, speed_eo, eo_freq_1x; color = INK_MUTED, linestyle = :dash, linewidth = 1.5)
lines!(ax, speed_eo, eo_freq_2x; color = INK_MUTED, linestyle = :dash, linewidth = 1.5)
lines!(ax, speed_eo, eo_freq_3x; color = INK_MUTED, linestyle = :dash, linewidth = 1.5)
# Natural frequency curves
l_1b = lines!(ax, speeds, freq_1b; color = IMPRINT_PALETTE[1], linewidth = 2.5)
l_2b = lines!(ax, speeds, freq_2b; color = IMPRINT_PALETTE[2], linewidth = 2.5)
l_1t = lines!(ax, speeds, freq_1t; color = IMPRINT_PALETTE[3], linewidth = 2.5)
l_ax = lines!(ax, speeds, freq_ax; color = IMPRINT_PALETTE[4], linewidth = 2.5)
# Critical speed intersection markers
sc_crit = scatter!(ax, crit_spd, crit_frq;
color = CRITICAL_COLOR,
marker = :diamond,
markersize = 14,
strokewidth = 0,
)
xlims!(ax, 0.0, 6100.0)
ylims!(ax, 0.0, 360.0)
# Engine order labels (placed mid-plot to avoid overlap with mode curves)
text!(ax, 2100.0, 1.0 * 2100.0 / 60.0 + 3.0; text = "1×", color = INK_MUTED, fontsize = 11, align = (:left, :bottom))
text!(ax, 2100.0, 2.0 * 2100.0 / 60.0 + 3.0; text = "2×", color = INK_MUTED, fontsize = 11, align = (:left, :bottom))
text!(ax, 2100.0, 3.0 * 2100.0 / 60.0 + 3.0; text = "3×", color = INK_MUTED, fontsize = 11, align = (:left, :bottom))
# Legend
Legend(
fig[1, 2],
[l_1b, l_2b, l_1t, l_ax, l_eo, sc_crit],
["1st Bending", "2nd Bending", "1st Torsional", "Axial", "Engine Orders", "Critical Speed"],
backgroundcolor = ELEVATED_BG,
framecolor = INK_SOFT,
framewidth = 0.5,
labelcolor = INK,
)
colsize!(fig.layout, 1, Relative(0.82))
save("plot-$(THEME).png", fig; px_per_unit = 2)
Part of Campbell Diagram on anyplot.ai.