1. Overview
The piston rod transmits force between the piston and the crosshead/crankshaft mechanism. Rod load analysis ensures the combined gas and inertia forces do not exceed the mechanical limits of the rod, crosshead, crosshead pin, connecting rod, or crankshaft. It is one of the most critical checks in reciprocating compressor sizing.
Gas Load
Pressure x Area
Varies with crank angle per PV diagram
Inertia Load
Mass x Acceleration
Reciprocating mass at piston acceleration
Combined Load
Gas + Inertia
Must stay within frame rating at all angles
Reversal
Load Sign Change
Required for crosshead pin lubrication
Sign Convention (per GPSA Section 13 / API 618)
| Direction | Sign | When It Occurs | Critical Component |
|---|---|---|---|
| Compression (rod squeezed between piston and crosshead) | Positive (+) | HE TDC: HE just discharged, CE at suction (net gas force pushes piston toward crank) | Rod buckling, packing |
| Tension (rod stretched) | Negative (-) | CE TDC: CE just discharged, HE at suction (net gas force pulls piston toward head) | Rod threads, crosshead pin |
Critical check: The combined rod load (gas + inertia) must not exceed the frame manufacturer's allowable rod load in either tension or compression at any crank angle during operation. Additionally, the load must reverse direction to ensure crosshead pin lubrication.
2. Gas Load Calculation
Gas loads are the forces exerted by gas pressure on the piston. For a double-acting cylinder, the head-end (HE) and crank-end (CE) act simultaneously but in opposite directions.
Gas Load at Any Crank Angle
Net gas rod load (double-acting):
F_gas(theta) = P_HE(theta) * A_HE - P_CE(theta) * A_CE
Where:
P_HE(theta) = Head-end cylinder pressure at crank angle theta
P_CE(theta) = Crank-end cylinder pressure at crank angle theta
A_HE = Head-end piston area = (pi/4) * D^2
A_CE = Crank-end piston area = (pi/4) * (D^2 - d_rod^2)
Convention (GPSA ยง13 / API 618):
Positive F_gas = rod in compression (HE pressure pushes piston toward crank/crosshead, squeezing rod)
Negative F_gas = rod in tension (CE pressure pushes piston toward head, stretching rod)
Note: P_HE and P_CE are obtained from the PV diagram.
The crank-end is 180 degrees out of phase with the head-end.
When HE is at TDC (theta=0), CE is at BDC (theta=180) and vice versa.
Simplified Gas Loads (Key Crank Positions)
Maximum compression (approximate at theta = 0, HE TDC):
HE at discharge pressure, CE at suction pressure
F_compression = P_d * A_HE - P_s * A_CE
Maximum tension (approximate at theta = 180, CE TDC):
HE at suction pressure, CE at discharge pressure
F_tension = P_d * A_CE - P_s * A_HE
For simplified (rectangular PV) rod load check (GPSA ยง13):
F_max_compression = P_d * A_HE - P_s * A_CE (rod squeezed at HE TDC)
F_max_tension = P_d * A_CE - P_s * A_HE (rod stretched at CE TDC)
Note: The actual maximum combined load occurs at a
crank angle that depends on the PV shape and inertia, not
necessarily at 0 or 180 degrees.
Gas Load Components by Crank Position
| Crank Angle | HE Process | CE Process | Net Rod Load Direction |
|---|---|---|---|
| 0 deg (HE TDC) | Start of re-expansion (P_d) | Start of compression (P_s) | Compression (peak) |
| 0-90 deg | Re-expansion then suction | Compression | Compression decreasing |
| 90 deg | Suction | Compression or discharge | Near zero or slight tension |
| 90-180 deg | Suction then compression | Discharge then re-expansion | Tension increasing |
| 180 deg (CE TDC) | Start of compression (P_s) | Start of re-expansion (P_d) | Tension (peak) |
| 180-360 deg | Mirror of 0-180 | Mirror of 0-180 | Cycle repeats |
3. Inertia Forces
Inertia forces arise from accelerating and decelerating the reciprocating mass (piston, rod, crosshead, and portion of connecting rod). These forces vary sinusoidally with crank angle and can be significant at high speeds.
Reciprocating mass:
m_recip = m_piston + m_rod + m_crosshead + m_conrod_recip
Where m_conrod_recip = approximately 1/3 of connecting rod mass
(the portion that reciprocates vs. rotates)
Piston acceleration (simplified):
a(theta) = R * omega^2 * [cos(theta) + (R/L) * cos(2*theta)]
Where:
R = Crank radius = Stroke / 2 (in)
L = Connecting rod length (in)
omega = Rotational speed = 2 * pi * RPM / 60 (rad/s)
R/L = Crank ratio (typically 0.20-0.33)
Inertia force:
F_inertia(theta) = -m_recip * a(theta)
F_inertia(theta) = -m_recip * R * omega^2 * [cos(theta) + (R/L)*cos(2*theta)]
Primary inertia force (1x RPM):
F_primary = m_recip * R * omega^2 * cos(theta)
Secondary inertia force (2x RPM):
F_secondary = m_recip * R * omega^2 * (R/L) * cos(2*theta)
Inertia Force Magnitude
Maximum inertia force (at TDC, theta = 0):
F_inertia_max = m_recip * R * omega^2 * (1 + R/L)
Practical formula:
F_inertia_max = (W_recip / g) * (Stroke/2) * (2*pi*RPM/60)^2 * (1 + R/L)
Where:
W_recip = Reciprocating weight (lb)
g = 32.174 ft/s^2 = 386.1 in/s^2
Stroke in inches
RPM = compressor speed
Quick estimate:
F_inertia_max (lb) = W_recip * Stroke * RPM^2 / (2,189,000) * (1 + R/L)
Significance by speed:
300 RPM, 12" stroke: F_inertia ~ 5-10% of gas load
600 RPM, 8" stroke: F_inertia ~ 15-25% of gas load
1,000 RPM, 6" stroke: F_inertia ~ 30-50% of gas load
1,500 RPM, 4" stroke: F_inertia ~ 50-80% of gas load
High-speed compressors: At speeds above 900 RPM, inertia forces become a significant fraction of the total rod load. They cannot be neglected, and in some cases they dominate the combined load. Inertia always acts to reduce the peak gas load near TDC but can create load reversal issues.
4. Combined Rod Load Diagram
The combined rod load diagram plots the sum of gas load and inertia load versus crank angle through a full revolution. This diagram reveals the peak loads and whether load reversal occurs.
Combined rod load at each crank angle:
F_combined(theta) = F_gas(theta) + F_inertia(theta)
Construction procedure:
1. Calculate F_gas(theta) from PV diagrams for HE and CE
at 10-degree or smaller intervals (0, 10, 20, ..., 350)
2. Calculate F_inertia(theta) at each angle:
F_inertia = -(W_recip/g) * R * omega^2 * [cos(theta) + (R/L)*cos(2*theta)]
3. Sum: F_combined(theta) = F_gas(theta) + F_inertia(theta)
4. Plot F_combined vs theta (0 to 360 degrees)
5. Identify: max tension, max compression, reversal points
Sign convention for combined diagram (GPSA ยง13):
Positive (+) = Compression (rod squeezed; piston pushed toward crankcase)
Negative (-) = Tension (rod stretched; piston pulled toward head end)
Critical Points on Combined Diagram
| Point | Location | Significance | Check Against |
|---|---|---|---|
| Max compression | Near 0 deg (HE TDC) | Highest squeezing force on rod | Frame compression rating, rod buckling |
| Max tension | Near 180 deg (CE TDC) | Highest pulling force on rod | Frame tension rating, rod thread fatigue |
| Zero crossing (C to T) | 60-120 deg typically | Load reversal point | Must occur for crosshead lubrication |
| Zero crossing (T to C) | 240-300 deg typically | Second reversal point | Combined reversal > 15 deg minimum |
| Minimum compression | Near 90 deg | Lowest compression before reversal | Reversal adequacy |
5. API 618 Limits & Crosshead Reversal
API 618 establishes rod load limits and crosshead pin reversal requirements to protect the compressor mechanical components from overload and lubrication failure.
API 618 Rod Load Requirements
Maximum allowable rod load:
F_combined_max <= F_rated (manufacturer frame rating)
Check both:
|F_max_tension| <= F_rated_tension
|F_max_compression| <= F_rated_compression
Typical frame rod load ratings (examples):
Small high-speed (2-throw): 5,000-15,000 lb
Medium separable (4-throw): 15,000-40,000 lb
Large separable (6-throw): 30,000-80,000 lb
Slow-speed integral (multi-throw): 50,000-150,000 lb
Rod buckling (compression loading):
F_compression_allow = pi^2 * E * I / (K * L_rod)^2
Where:
E = Rod elastic modulus (30 x 10^6 psi for steel)
I = Rod moment of inertia = (pi/64) * d_rod^4
K = Effective length factor (1.0 for pin-pin)
L_rod = Unsupported rod length
Safety factor for buckling:
Typically 3:1 to 5:1 against Euler buckling
Crosshead Pin Reversal
The crosshead pin must experience load reversal (change from
tension to compression and back) during each revolution.
Purpose: Load reversal momentarily unloads the crosshead pin
bearing, allowing lubricating oil to enter the bearing surface.
Without reversal, the bearing runs dry and fails.
API 618 requirement:
Combined rod load must change sign (cross zero)
Minimum reversal duration: 15 degrees of crank angle
(Some operators require 30 degrees for critical service)
Reversal angle calculation:
theta_reversal = theta_zero_crossing_2 - theta_zero_crossing_1
(for the shorter of the two intervals)
Factors that reduce reversal:
- High compression ratio (large gas load amplitude)
- Low speed (small inertia force)
- Unequal pressures on single-acting configuration
- Added clearance reducing gas load range
Remedies for insufficient reversal:
1. Increase speed (larger inertia force)
2. Unload one end (reduce peak gas load)
3. Add clearance to reduce peak pressure
4. Change to single-acting operation
5. Add a tail rod (equalize piston areas)
Special Loading Conditions
| Condition | Effect on Rod Load | Check Required |
|---|---|---|
| Startup (no pressure) | Inertia only; no gas load | Reversal OK (gas load = 0) |
| Blocked discharge | Very high gas load; limited by relief valve | Rod load at relief valve set pressure |
| Single-end unloading | Asymmetric gas load | May lose reversal; verify |
| Variable speed | Inertia changes with RPM^2 | Check at minimum and maximum speed |
| Interstage pressure upset | Higher-than-design ratio on one stage | Check rod load at upset conditions |
| Liquid carryover | Hydraulic load (incompressible) | Can exceed frame rating; immediate shutdown |
Most common rod load problem: Insufficient crosshead pin reversal when operating at reduced capacity with clearance pockets open. Always verify reversal at minimum load (maximum clearance) and maximum load conditions, plus all unloading step combinations.
6. Worked Examples
Example 1: Simplified Gas Rod Load
Given:
Double-acting cylinder: Bore = 9 in, Rod = 2.75 in, Stroke = 6 in
P_suction = 300 psia, P_discharge = 900 psia
Speed = 900 RPM
Reciprocating weight = 350 lb
R/L = 0.25
Step 1: Piston areas
A_HE = (pi/4) * 9^2 = 63.62 in^2
A_CE = (pi/4) * (9^2 - 2.75^2) = 63.62 - 5.94 = 57.68 in^2
Step 2: Maximum gas loads (simplified rectangular PV, GPSA ยง13)
F_compression_gas = P_d * A_HE - P_s * A_CE
F_compression_gas = 900 * 63.62 - 300 * 57.68
F_compression_gas = 57,258 - 17,304 = 39,954 lb (compression, at HE TDC)
F_tension_gas = P_d * A_CE - P_s * A_HE
F_tension_gas = 900 * 57.68 - 300 * 63.62
F_tension_gas = 51,912 - 19,086 = 32,826 lb (tension, at CE TDC)
Step 3: Maximum inertia force
omega = 2 * pi * 900 / 60 = 94.25 rad/s
R = 6/2 = 3.0 in
F_inertia_max = (350/386.1) * 3.0 * 94.25^2 * (1 + 0.25)
F_inertia_max = 0.9065 * 3.0 * 8,883 * 1.25
F_inertia_max = 30,179 lb
Step 4: Combined loads (sign convention: + = compression, - = tension)
At theta = 0 (HE TDC):
F_combined = F_compression_gas - F_inertia (inertia opposes compression at HE TDC)
F_combined = 39,954 - 30,179 = +9,775 lb (compression)
At theta = 180 (CE TDC):
F_combined = -F_tension_gas + F_inertia = -32,826 + 30,179 = -2,647 lb (tension)
Peak compression (adjusted): ~40,000 lb at ~20-30 deg past TDC
Peak tension: ~33,000 lb at ~200-210 deg
(Exact values require full crank-angle analysis with PV data)
Reversal check:
Load changes sign from +9,775 (compression) to -2,647 (tension) -- reversal EXISTS
But need to verify at all operating conditions.
Example 2: Crosshead Reversal Check
Given: Same cylinder but with clearance pocket open
With 25% added clearance, P_discharge effectively reached
at later crank angle, reducing peak gas tension load.
Modified gas loads (approximate with clearance):
F_compression_gas_max = 32,000 lb (reduced from 39,954, at HE TDC)
F_tension_gas_max = 28,000 lb (reduced from 32,826, at CE TDC)
Combined loads with clearance (+ = compression, - = tension):
At theta = 0 (HE TDC):
F = 32,000 - 30,179 = +1,821 lb (compression โ barely positive)
At theta = 180 (CE TDC):
F = -28,000 + 30,179 = +2,179 lb (compression โ no reversal!)
Problem: Load stays in compression throughout revolution.
The crosshead pin never unloads -- lubrication failure will occur.
Solutions:
1. Reduce clearance pocket opening (less capacity reduction)
2. Increase speed to 1,000 RPM:
F_inertia_max = 30,179 * (1000/900)^2 = 37,258 lb
At theta=180: -28,000 + 37,258 = +9,258 lb compression
Still no reversal into tension direction.
3. Unload CE instead of adding HE clearance:
Single-acting HE only:
F_compression = P_d * A_HE - P_atm * A_CE (HE TDC, unchanged)
F_tension = P_atm * A_CE - P_s * A_HE (CE TDC; typically negative for positive P_s)
At theta=180 with P_s suction on HE only: -19,086 + 30,179 = +11,093 compression
Still problematic.
4. Best solution: Use combination of moderate clearance +
speed increase + verify with full crank-angle analysis.
This example illustrates why rod load/reversal checks must be
performed at ALL capacity control step combinations.
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