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: plotly 6.7.0 | Python 3.13.13
Quality: 91/100 | Updated: 2026-05-28
"""
import os
import numpy as np
import plotly.graph_objects as go
# Theme
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"
GRID = "rgba(26,26,23,0.15)" if THEME == "light" else "rgba(240,239,232,0.15)"
IMPRINT_PALETTE = ["#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030", "#2ABCCD", "#954477", "#99B314"]
CRITICAL_COLOR = "#AE3030"
# Data
np.random.seed(42)
speed_rpm = np.linspace(0, 6000, 80)
speed_hz = speed_rpm / 60
# Natural frequency modes (Hz) with realistic gyroscopic effects
mode_1_bending = 22 + 0.004 * speed_rpm + np.sin(speed_rpm / 1200) * 1.2
mode_2_bending = 48 - 0.003 * speed_rpm + np.cos(speed_rpm / 1800) * 1.4
mode_1_torsional = 55 + 0.0004 * speed_rpm
mode_axial = 75 - 0.004 * speed_rpm + np.sin(speed_rpm / 1000) * 2.0
orders = [1, 2, 3]
order_freq = {order: order * speed_hz for order in orders}
modes = {
"1st Bending": mode_1_bending,
"2nd Bending": mode_2_bending,
"1st Torsional": mode_1_torsional,
"Axial": mode_axial,
}
# Find critical speed intersections
critical_speeds = []
critical_freqs = []
critical_labels = []
for order in orders:
eo_freq = order_freq[order]
for mode_name, mode_freq in modes.items():
diff = mode_freq - eo_freq
sign_changes = np.where(np.diff(np.sign(diff)))[0]
for idx in sign_changes:
frac = abs(diff[idx]) / (abs(diff[idx]) + abs(diff[idx + 1]))
crit_rpm = speed_rpm[idx] + frac * (speed_rpm[idx + 1] - speed_rpm[idx])
crit_freq = order * (crit_rpm / 60)
critical_speeds.append(crit_rpm)
critical_freqs.append(crit_freq)
critical_labels.append(f"{mode_name} × {order}x")
fig = go.Figure()
# Shade only the 3 most significant critical speed zones (highest frequency) — reduces clutter
y_max = 110
if critical_freqs:
top_indices = sorted(range(len(critical_freqs)), key=lambda i: critical_freqs[i], reverse=True)[:3]
for i in top_indices:
fig.add_vrect(
x0=critical_speeds[i] - 60,
x1=critical_speeds[i] + 60,
fillcolor="rgba(174,48,48,0.08)",
line_width=0,
layer="below",
)
# Natural frequency curves
line_dashes = ["solid", "dash", "dot", "dashdot"]
n_mode_traces = len(modes)
for i, (mode_name, mode_freq) in enumerate(modes.items()):
fig.add_trace(
go.Scatter(
x=speed_rpm,
y=mode_freq,
mode="lines",
name=mode_name,
line={"color": IMPRINT_PALETTE[i], "width": 3.5, "dash": line_dashes[i]},
hovertemplate=f"<b>{mode_name}</b><br>Speed: %{{x:.0f}} RPM<br>Freq: %{{y:.1f}} Hz<extra></extra>",
)
)
# Engine order lines
n_eo_traces = len(orders)
for order in orders:
label = f"{order}x"
eo_y = order_freq[order]
mask = eo_y <= y_max
fig.add_trace(
go.Scatter(
x=speed_rpm[mask],
y=eo_y[mask],
mode="lines",
name=f"EO {label}",
line={"color": INK_SOFT, "width": 2, "dash": "dash"},
hovertemplate=f"<b>EO {label}</b><br>Speed: %{{x:.0f}} RPM<br>Freq: %{{y:.1f}} Hz<extra></extra>",
)
)
# Engine order labels at 75% along visible segment
for order in orders:
eo_y = order_freq[order]
visible_indices = np.where(eo_y <= y_max)[0]
if len(visible_indices) > 0:
label_idx = visible_indices[int(len(visible_indices) * 0.75)]
fig.add_annotation(
x=speed_rpm[label_idx],
y=eo_y[label_idx],
text=f"<b>{order}x</b>",
showarrow=False,
xanchor="left",
yanchor="bottom",
xshift=8,
yshift=4,
font={"size": 11, "color": INK_SOFT},
bgcolor=ELEVATED_BG,
borderpad=2,
)
# Critical speed markers
fig.add_trace(
go.Scatter(
x=critical_speeds,
y=critical_freqs,
mode="markers",
name="Critical Speed",
marker={"size": 14, "color": CRITICAL_COLOR, "symbol": "diamond", "line": {"width": 2, "color": PAGE_BG}},
customdata=critical_labels,
hovertemplate="<b>Critical Speed</b><br>%{customdata}<br>Speed: %{x:.0f} RPM<br>Freq: %{y:.1f} Hz<extra></extra>",
)
)
# Annotate highest-frequency and first (lowest-RPM) critical intersections
if critical_speeds:
max_idx = int(np.argmax(critical_freqs))
fig.add_annotation(
x=critical_speeds[max_idx],
y=critical_freqs[max_idx],
text=f"<b>{critical_freqs[max_idx]:.0f} Hz</b><br>{critical_labels[max_idx]}",
showarrow=True,
arrowhead=2,
arrowsize=1.2,
arrowcolor=CRITICAL_COLOR,
arrowwidth=2,
ax=50,
ay=-45,
font={"size": 10, "color": CRITICAL_COLOR},
bgcolor=ELEVATED_BG,
bordercolor=CRITICAL_COLOR,
borderwidth=1.5,
borderpad=4,
)
min_rpm_idx = int(np.argmin(critical_speeds))
if min_rpm_idx != max_idx:
fig.add_annotation(
x=critical_speeds[min_rpm_idx],
y=critical_freqs[min_rpm_idx],
text=f"<b>1st critical</b><br>{critical_speeds[min_rpm_idx]:.0f} RPM",
showarrow=True,
arrowhead=2,
arrowsize=1.2,
arrowcolor=CRITICAL_COLOR,
arrowwidth=2,
ax=-55,
ay=40,
font={"size": 10, "color": CRITICAL_COLOR},
bgcolor=ELEVATED_BG,
bordercolor=CRITICAL_COLOR,
borderwidth=1.5,
borderpad=4,
)
# Toggle visibility arrays (simplified: modes + criticals vs all)
total_traces = n_mode_traces + n_eo_traces + 1
all_visible = [True] * total_traces
modes_only = [True] * n_mode_traces + [False] * n_eo_traces + [True]
title = "campbell-basic · python · plotly · anyplot.ai"
fig.update_layout(
autosize=False,
paper_bgcolor=PAGE_BG,
plot_bgcolor=PAGE_BG,
font={"color": INK},
title={"text": title, "font": {"size": 16, "color": INK}, "x": 0.5, "xanchor": "center", "y": 0.97},
xaxis={
"title": {"text": "Rotational Speed (RPM)", "font": {"size": 12, "color": INK}, "standoff": 10},
"tickfont": {"size": 10, "color": INK_SOFT},
"showgrid": True,
"gridcolor": GRID,
"gridwidth": 1,
"zeroline": False,
"range": [0, 6100],
"dtick": 1000,
"showline": True,
"linecolor": INK_SOFT,
"linewidth": 1,
"mirror": False,
},
yaxis={
"title": {"text": "Frequency (Hz)", "font": {"size": 12, "color": INK}, "standoff": 10},
"tickfont": {"size": 10, "color": INK_SOFT},
"showgrid": True,
"gridcolor": GRID,
"gridwidth": 1,
"zeroline": False,
"range": [0, y_max],
"dtick": 10,
"showline": True,
"linecolor": INK_SOFT,
"linewidth": 1,
"mirror": False,
},
legend={
"font": {"size": 10, "color": INK_SOFT},
"bgcolor": ELEVATED_BG,
"bordercolor": INK_SOFT,
"borderwidth": 1,
"x": 0.01,
"y": 0.99,
"xanchor": "left",
"yanchor": "top",
"tracegroupgap": 0,
"itemsizing": "constant",
"orientation": "v",
},
margin={"l": 80, "r": 40, "t": 80, "b": 60},
hovermode="closest",
updatemenus=[
{
"type": "buttons",
"direction": "left",
"x": 1.0,
"y": 1.05,
"xanchor": "right",
"yanchor": "top",
"buttons": [
{"label": "All Modes", "method": "update", "args": [{"visible": all_visible}]},
{"label": "Modes Only", "method": "update", "args": [{"visible": modes_only}]},
],
"font": {"size": 10, "color": INK},
"bgcolor": ELEVATED_BG,
"bordercolor": INK_SOFT,
}
],
)
# Save
fig.write_image(f"plot-{THEME}.png", width=800, height=450, scale=4)
fig.write_html(f"plot-{THEME}.html", include_plotlyjs="cdn")
Part of Campbell Diagram on anyplot.ai.