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: seaborn 0.13.2 | Python 3.13.13
Quality: 88/100 | Updated: 2026-05-28
"""
import os
import matplotlib.patches as mpatches
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns
# Theme tokens
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"
IMPRINT_PALETTE = ["#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030", "#2ABCCD", "#954477", "#99B314"]
ANYPLOT_AMBER = "#DDCC77"
# Data
np.random.seed(42)
rpm = np.linspace(0, 6000, 100)
mode_1_bending = 15 + 0.0018 * rpm + 1.2 * np.sin(rpm / 1500)
mode_2_bending = 44 - 0.0025 * rpm + 0.8 * np.cos(rpm / 2000)
mode_1_torsional = 52 + 0.0035 * rpm
mode_axial = 68 - 0.0008 * rpm + 1.0 * np.sin(rpm / 1200)
mode_3_bending = 82 + 0.0022 * rpm + 0.6 * np.sin(rpm / 1800)
modes = {
"1st Bending": mode_1_bending,
"2nd Bending": mode_2_bending,
"1st Torsional": mode_1_torsional,
"Axial": mode_axial,
"3rd Bending": mode_3_bending,
}
records = []
for mode_name, freq in modes.items():
for r, f in zip(rpm, freq, strict=False):
records.append({"RPM": r, "Frequency (Hz)": f, "Mode": mode_name})
df = pd.DataFrame(records)
engine_orders = [1, 2, 3]
critical_speeds, critical_freqs = [], []
for mode_freq in modes.values():
for order in engine_orders:
diff = mode_freq - order * rpm / 60
for idx in np.where(np.diff(np.sign(diff)))[0]:
t = abs(diff[idx]) / (abs(diff[idx]) + abs(diff[idx + 1]))
cs_rpm = rpm[idx] + t * (rpm[idx + 1] - rpm[idx])
cs_freq = order * cs_rpm / 60
if 100 < cs_rpm < 5900:
critical_speeds.append(cs_rpm)
critical_freqs.append(cs_freq)
op_low, op_high = 2800, 4200
in_operating = [op_low <= s <= op_high for s in critical_speeds]
cs_df = pd.DataFrame(
{
"RPM": critical_speeds,
"Frequency (Hz)": critical_freqs,
"Status": ["In Range" if inside else "Outside" for inside in in_operating],
}
)
# Plot setup
sns.set_theme(
style="ticks",
rc={
"figure.facecolor": PAGE_BG,
"axes.facecolor": PAGE_BG,
"axes.edgecolor": INK_SOFT,
"axes.labelcolor": INK,
"text.color": INK,
"xtick.color": INK_SOFT,
"ytick.color": INK_SOFT,
"legend.facecolor": ELEVATED_BG,
"legend.edgecolor": INK_SOFT,
},
)
fig, ax = plt.subplots(figsize=(8, 4.5), dpi=400)
fig.set_facecolor(PAGE_BG)
# Operating range highlight (amber = caution)
ax.axvspan(op_low, op_high, color=ANYPLOT_AMBER, alpha=0.10, zorder=0)
ax.axvline(op_low, color=ANYPLOT_AMBER, linewidth=0.8, linestyle="--", alpha=0.6, zorder=1)
ax.axvline(op_high, color=ANYPLOT_AMBER, linewidth=0.8, linestyle="--", alpha=0.6, zorder=1)
ax.text(
(op_low + op_high) / 2,
3,
"Operating\nRange",
fontsize=7,
color=ANYPLOT_AMBER,
ha="center",
va="bottom",
fontweight="bold",
linespacing=1.3,
)
# Natural frequency curves via seaborn lineplot with hue
mode_colors = IMPRINT_PALETTE[:5]
sns.lineplot(
data=df,
x="RPM",
y="Frequency (Hz)",
hue="Mode",
palette=dict(zip(modes.keys(), mode_colors, strict=False)),
linewidth=2.0,
ax=ax,
legend=False,
hue_order=list(modes.keys()),
)
# Engine order lines (structural reference)
eo_label_x = {1: 4600, 2: 2200, 3: 1400}
for order in engine_orders:
eo_freq = order * rpm / 60
ax.plot(rpm, eo_freq, color=INK_SOFT, linewidth=1.2, linestyle="--", alpha=0.65, zorder=2)
lx = eo_label_x[order]
ax.text(
lx,
order * lx / 60 + 1.5,
f"{order}x",
fontsize=8,
color=INK_SOFT,
fontweight="bold",
va="bottom",
ha="center",
bbox={"boxstyle": "round,pad=0.12", "fc": ELEVATED_BG, "ec": INK_SOFT, "alpha": 0.85, "linewidth": 0.5},
)
# Critical speed markers via seaborn scatterplot (split by status for independent alpha)
cs_in_df = cs_df[cs_df["Status"] == "In Range"]
cs_out_df = cs_df[cs_df["Status"] == "Outside"]
sns.scatterplot(
data=cs_in_df,
x="RPM",
y="Frequency (Hz)",
color=IMPRINT_PALETTE[4],
s=120,
ax=ax,
zorder=5,
edgecolor=PAGE_BG,
linewidth=0.8,
legend=False,
)
sns.scatterplot(
data=cs_out_df,
x="RPM",
y="Frequency (Hz)",
color=INK_MUTED,
s=30,
alpha=0.7,
ax=ax,
zorder=5,
edgecolor=PAGE_BG,
linewidth=0.8,
legend=False,
)
# Direct mode labels (right edge, increased vertical separation)
y_offsets = {"1st Bending": -2, "2nd Bending": 3, "1st Torsional": 3, "Axial": -3, "3rd Bending": 0}
for i, (name, freq) in enumerate(modes.items()):
ax.text(
6080,
freq[-1] + y_offsets[name],
name,
fontsize=8,
color=mode_colors[i],
fontweight="bold",
va="center",
ha="left",
clip_on=False,
)
# Axes limits and labels
y_max = max(m.max() for m in modes.values())
ax.set_xlim(0, 6000)
ax.set_ylim(0, y_max + 5)
title = "campbell-basic · python · seaborn · anyplot.ai"
title_fontsize = max(8, round(12 * (67 / len(title) if len(title) > 67 else 1.0)))
ax.set_xlabel("Rotational Speed (RPM)", fontsize=10, color=INK)
ax.set_ylabel("Frequency (Hz)", fontsize=10, color=INK)
ax.set_title(title, fontsize=title_fontsize, fontweight="medium", color=INK)
ax.tick_params(axis="both", labelsize=8)
ax.grid(True, axis="both", alpha=0.12, linewidth=0.5, color=INK)
ax.set_axisbelow(True)
sns.despine(ax=ax)
# Compact legend: critical speed status + operating range only
cs_in = mpatches.Patch(facecolor=IMPRINT_PALETTE[4], label="Critical (in range)")
cs_out = mpatches.Patch(facecolor=INK_MUTED, label="Critical (outside)")
op_leg = mpatches.Patch(facecolor=ANYPLOT_AMBER, alpha=0.45, label=f"Operating ({op_low}–{op_high} RPM)")
ax.legend(handles=[cs_in, cs_out, op_leg], fontsize=8, loc="lower right", frameon=True, fancybox=False, framealpha=0.9)
fig.subplots_adjust(left=0.08, right=0.80, top=0.92, bottom=0.12)
# Save
plt.savefig(f"plot-{THEME}.png", dpi=400)
Part of Campbell Diagram on anyplot.ai.