NSWC-11 Coupling, Brake & Clutch Reliability Model

A coupling joins two shafts and carries torque between them while forgiving a little misalignment. A brake or clutch converts motion into heat through a friction lining, so its life is set by how fast the lining wears. All of these are built from parts that have their own chapters in the handbook: gears, seals, bearings, springs, actuators and fasteners.

This tool follows Chapters 17 and 12 of the Naval Surface Warfare Center Handbook of Reliability Prediction Procedures for Mechanical Equipment (NSWC-11). The failure rate of the assembly is the sum of the rates of its parts. For couplings you can also start from the manufacturer’s cycles to failure. For brakes and clutches the new piece is the friction material. Its base rate comes from the lining wear or from the manufacturer. It is then adjusted for brake type, dust, plate count and temperature.

The result is a failure rate per million hours with FIT and MTBF for a FMECA. Every step is under “Show detailed calculation steps”. For the component rates, run the matching calculator and enter the result with its unit.

NSWC-11 Chapters 17 & 12 Failure Rate Calculator
Coupling, Brake & Clutch Reliability (NSWC-11 Eq. 17-2 / 12-1 / 12-11)
What are you analysing?
Each is built up from its parts. Couplings can instead use the manufacturer’s endurance data.
Converts rates per million cycles to per million hours. The handbook does not say what a cycle is for a coupling. A start-stop or torque cycle is typical. Counting every revolution (60 × rpm) makes the result very large.
Coupling
The handbook’s typical value is 5.0.
Component Failure Rates (from the other chapters)
Chapter 8. Use the Gear & Spline calculator.
Chapter 3. Use the Static or Dynamic Seal calculator.
The handbook estimates 0.001 per 106 cycles.
Chapter 7. Use the Bearing calculator.
Chapter 16.
Chapter 9.
Chapter 4. Use the spring calculators.
Mission (optional)
8,760 h is one year of continuous operation. Leave blank to skip.
Failure Rate & Reliability Metrics
Predicted Failure Rate, λ (failures / 106 h) iThe sum of the failure rates of the parts: coupling λCP (Eq. 17-1 or 17-2), universal joint λUJ (Eq. 17-3), brake λBR (Eq. 12-1) or clutch λCL (Eq. 12-11).
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Failure Rate (FIT) iFailures In Time = failures per 109 hours. The same number as failures per million hours, multiplied by 1000.
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MTBF (hours) iMean time between failures = 106 / λ. It assumes a constant failure rate. Friction linings wear out, and the handbook counts a lining replaced before its service life as a failure.
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MTBF (years) iMTBF in hours divided by 24 × 365.25.
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Expected Failures over the Mission iλ × mission hours / 106. The expected count of failures for one unit, so a value above 1 means one failure is more likely than not.
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Survival Probability over the Mission iR(t) = e−λt, the chance one unit survives the mission with no failure, assuming a constant failure rate.
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Intermediates
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Multiplying Factors
SymbolMeaningValue
Show detailed calculation steps
How the Model Works

Nothing in a coupling, brake or clutch is modeled by a single factor stack. The handbook breaks the assembly into its parts and adds their failure rates, because any part failing fails the assembly.

1. The equations

\[ \lambda_{CP} = \frac{1}{N}\qquad \text{(17-1)} \] \[ \lambda_{CP} = \lambda_{CP,B}\,C_{SF} + \lambda_{GR} + \lambda_{SE} + \lambda_{H}\qquad \text{(17-2)} \] \[ \lambda_{UJ} = \lambda_{BE} + \lambda_{SE} + \lambda_{H} + \lambda_{F}\qquad \text{(17-3)} \] \[ \lambda_{BR} = \lambda_{AC} + \lambda_{SP} + \lambda_{FR} + \lambda_{BE} + \lambda_{SE} + \lambda_{HO}\qquad \text{(12-1)} \] \[ \lambda_{CL} = \lambda_{AC} + \lambda_{BE} + \lambda_{CF} + \lambda_{SE} + \lambda_{SP}\qquad \text{(12-11)} \] \[ \lambda_{FR} = \lambda_{FR,B}\,C_{BT}\,C_{RD}\,C_{T}\qquad \text{(12-6)} \] \[ \lambda_{CF} = \lambda_{CF,B}\,C_{NP}\,C_{T}\qquad \text{(12-16)} \]
SymbolMeaning
λCP,BCoupling base rate, typically 5.0 failures per million cycles
CSFCoupling service factor (Table 17-3)
λGR, λSE, λBE, λF, λAC, λSPFailure rates of gears, seals, bearings, fasteners, actuators and springs from Chapters 8, 3, 7, 16, 9 and 4
λH, λHOCoupling housing (0.001 per million cycles) and brake housing (3.0 per million hours)
λFR, λCFFriction material of the brake and of the clutch
CBT, CRD, CNP, CTBrake type, dust, plate quantity and temperature factors

2. Cycles and hours

Some of these rates are per million cycles and some per million hours. The handbook says to convert a per-cycle rate to per-hour by multiplying by the number of cycles per hour. The page does this for you: set the cycles (or applications) per hour once, and choose the unit of each component rate.

3. Friction lining life

\[ W_p = \frac{k_o\,P\,v_s\,t}{A}\ \text{(in per application)} \] \[ \text{Life} = \frac{d}{W_p} \] \[ \lambda_{FR,B} = \frac{1}{\text{Life}} = \frac{W_p}{d}\ \text{per application} \]

The lining wears in proportion to the load, the sliding distance and a wear coefficient ko. Dividing the wear per application by the lining thickness d gives the fraction of life used each time. The page multiplies by applications per hour and 106 to get a rate per million hours. Wear is sacrificial and designed in, so the handbook counts a lining as failed only if it needs replacing before its service life.

4. Step by step

  1. Pick the component and set the cycles or applications per hour.
  2. For a brake or clutch, give the lining data (or the manufacturer’s rate) and the temperature. The page finds the friction rate.
  3. Enter the rates of the other parts, with their units, from the other calculators.
  4. The page adds everything and converts to FIT, MTBF, and, with a mission time, expected failures and survival probability.
Read the result with care. The total is only as good as the component rates you enter. Misalignment, lubrication and bolt torque dominate real coupling life. The handbook says at least 75 % of gear coupling failures come from lack of lubrication. The calculator cannot see those. The handbook also warns that not every equation could be validated.
Factor Reference Guide
NSWC-11 Chapters 17 and 12: Couplings, Brakes and Clutches
T 17-3

Coupling Base Rate & Service Factor

Equations 17-1, 17-2 and Table 17-3
Eq. 17-1 \[ \lambda_{CP} = \frac{1}{N}\ \ \text{per }10^6\text{ cycles}\quad(N\text{ in millions of cycles}) \]

Coupling makers test their designs to an endurance curve (Figure 17.3). As the stress falls, the cycles to failure rise. Below some stress the curve is flat. The cycles to failure at the operating stress give a base rate of 1/N. Without that data, the rate is built from the parts. It is a base rate of about 5.0 per million cycles times a service factor. A gear coupling adds its gears, seals and housing.

The handbook says the failure rate depends more on the application than on the design. A coupling is normally chosen with a torque capacity many times what is needed.

The handbook does not define a cycle for couplings. Set cycles per hour to the cycles that matter to your coupling, such as starts and stops. Suppose every revolution were a cycle. Then 5.0 per million cycles at 1,800 rpm would mean a failure every couple of hours. That is not a credible coupling rate.
Table 17-3: Service factor, CSF
Driven machineryNormal torqueHigh or non-uniform torque
Uniform1.11.2
Light shock1.21.3
Medium shock1.31.4
Heavy shock1.41.5
Housing

The housing is very reliable. The handbook estimates its failure rate at 0.001 per million cycles. Its larger effect is on the bearings and seals through the load the lubricant puts on the shaft.

T 17-3

Universal Joint

Equation 17-3
Eq. 17-3 \[ \lambda_{UJ} = \lambda_{BE} + \lambda_{SE} + \lambda_H + \lambda_F \]

A universal joint is two hinges set 90° apart on a cross shaft. Its rate is the sum of its bearings (Chapter 7), seals (Chapter 3), housing and fasteners (Chapter 16). Its life depends on torque, speed and joint angle, and the load-speed-life relations of rolling bearings apply to the rolling elements in the joint.

FR

Brake Friction Material

Equation 12-6, brake type and dust factors
Eq. 12-6\[ \lambda_{FR} = \lambda_{FR,B}\cdot C_{BT}\cdot C_{RD}\cdot C_T \]

Disk brakes wear better than drum brakes because they shed heat faster. Slots cut in an annular disk lower its surface temperature but, per the field data, do not change the factor.

Brake typeCBT
Drum type1.25
Slotted annular disk1.25
Pad disk1.00
Annulus disk0.90
Table 12-6: Dust contamination, CRD
Binder resinCRD
Phenolic3.5
Oil-modified phenolic1.2
Rubber phenolic1.1
Cashew1.1
Oil-phenolic1.1
Table 12-8: Wear coefficients, ko (against cast iron or steel)
Lining (pad) materialko (psi−1)
Asbestos-type I composite6.46×10−11
Asbestos-type II composite8.09×10−11
Carbon-carbon composite2.24×10−11
Sintered bronze (dry)2.42×10−10
Non-asbestos composite (dry)9.90×10−10
Sintered bronze (wet)5.02×10−13
Sintered bronze composite9.31×10−11
Sintered resin composite3.03×10−11
The handbook prints the carbon-carbon value as “2..24”, a typo for 2.24. A wet sintered bronze lining wears far less than a dry one.

The brake housing adds 3.0 failures per million hours. Seals in a hydraulic brake must keep their hardness and not swell in brake fluid. Heat conducted from the friction surface can thin the bearing lubricant and shorten bearing life.

CF

Clutch Friction Material

Equation 12-16 and the plate factor
Eq. 12-16\[ \lambda_{CF} = \lambda_{CF,B}\cdot C_{NP}\cdot C_T \] \[ C_{NP} = \text{number of disks in the clutch} \]

Clutch lining wear follows the same form as brake wear (Eq. 12-12 to 12-15), with the engagement time in place of the braking time. Multiplate clutches share the load over several discs.

Direction of CNP. The handbook text says more plates raise reliability, but defines CNP only as “the number of disks”. Multiplied as printed, more plates would raise the failure rate. The page defaults to 1/N so more plates lower it, and offers the printed N as an option. Check your own data if the plate count matters.
Clutch types (section 12.4.2)
  • Plate: single plate for light and medium power, multiplate for high torque at moderate clamping pressure.
  • Cone: small, medium-power, low-speed, rough duty. Heat dissipates readily.
  • Rim, block and centrifugal: radial engagement. Centrifugal types engage automatically at a set speed.
  • Coil (wrap) spring, chain and sprag: high torque from low power, oil-filled friction rings, and one-way over-running, respectively.

Hydraulic clutch failures are almost always loss of fluid pressure, usually through internal seal leakage.

CT

Temperature Factor: CT

Equations 12-7 to 12-10 (brakes) and 12-17 to 12-20 (clutches)
CT polynomials \[ C_T = a + b\,X + c\,X^{2} \] \[ X = 590 + T\quad (T\ \text{in }^\circ\text{F}) \]
Liningabc
Sintered metallic truck linings1.42−0.001541.38×10−6
Resin-asbestos, automotive and moderate industrial2.79−0.01091.24×10−5
Carbon-carbon3.80−0.00759 (clutch: −0.00758)5.07×10−6
Resin-asbestos truck linings17.59−0.06035.34×10−5

Friction material wear depends on the temperature it works at. Each polynomial is close to 1.0 at room temperature (about 70 °F, X = 660), and moves with ambient temperature from there. The handbook prints the carbon-carbon linear coefficient as −0.00759 for brakes and −0.00758 for clutches. The page uses each as printed.

CT vs ambient temperature (brake equations)
The marker follows your temperature and lining type for brakes and clutches.
T 12-2 – 17-2

Failure Modes

Table 17-2: Failure modes of couplings (handbook reference 66)
Failure modeFailure cause
Worn flexing element or shaft bushingsExcessive shaft misalignment
Ruptured elastomeric flexing element, sheared hub pins or teethTorsional shock overload
Fatigue of flexing element, hub pins, or discsExcessive starts and stops; torsional vibration
Shaft bearing failureLubricant failure; excessive shaft misalignment; operational temperature extremes
Loose hubs on shaftTorsional shock overload; high peak-to-peak torsional overload
Worn gear teethLubrication failure; high peak-to-peak torsional overload
High pitched hammering or clacking noiseExcessive shaft misalignment; loose hubs or bolt connections; lubricant failure
Swollen, distorted, or cracked elastomeric flexing member, severe hub corrosionChemical attack; excessive heat
Table 12-4: Brake system failure modes (handbook reference 9)
Failure modeFailure causeFailure effect
Sticking pistonContaminationLow output pressure
Leaking cylinderContaminationLow output pressure
Broken/weak springFatigue activationUnable to adjust pressure
Sticking bleeder valveContaminationInadequate dissipation of air
Deteriorated liningAged/heatExposed metal-on-metal contact reduces arresting capability
Worn bearingLack of lubricationLow rotary motion
Worn sealsAgedExternal leakage
Cracked housingVibration, fatigueExternal leakage
Handbook Tables 17-2 and 12-4. The friction surface and countersurface modes (heat spotting, crazing, scoring, fade, dishing, bond failure and others) are in handbook Tables 12-2, 12-5 and 12-7.
Worked Example

Gear coupling. A gear coupling sits in a drive that starts and stops about 12 times an hour. The source is high-torque and the load is light-shock. It uses the typical base rate of 5.0 per million cycles. From the other calculators, the gears are 2 and the seals 0.5 failures per million hours. The housing is the handbook’s 0.001 per million cycles. These are the calculator’s default inputs.

  • CSF = 1.3 (light shock, high torque)
  • Coupling term = 5.0 × 1.3 = 6.5 per 106 cycles, × 12 cycles/h = 78 per 106 h
  • Housing = 0.001 × 12 = 0.012 per 106 h

λCP = 78 + 2 + 0.5 + 0.012 = 80.5 failures / 106 h, an MTBF of 12,421 h. Over a year the expected failure count is 0.71 and the survival probability is 49.4 %. The coupling term is 97 % of the total, so the base rate and the cycle count are the numbers to question.

Drum brake. Switch to brake. A drum brake has an asbestos-type I composite lining, 40 in2 in area and 0.3 in thick. It is applied 4 times an hour at 1,500 lbf. Each application slides at 600 in/s for 4 s. The binder is cashew resin, the lining is resin-asbestos (automotive), and the ambient temperature is 100 °F. The actuator is 1, the spring 0.5, the bearing 2 and the seal 0.5 failures per million hours. Set applications per hour to 4 to match (the default is 12).

  • Wp = 6.46×10−11 × 1500 × 600 × 4 / 40 = 5.81×10−6 in per application
  • λFR,B = 5.81×10−6 / 0.3 × 4 × 106 = 77.5 per 106 h
  • CBT = 1.25 (drum), CRD = 1.1 (cashew), CT = 2.79 − 0.0109(690) + 0.0000124(690)2 = 1.1726
  • λFR = 77.5 × 1.25 × 1.1 × 1.1726 = 125.0

λBR = 1 + 0.5 + 125.0 + 2 + 0.5 + 3.0 = 132.0 failures / 106 h, an MTBF of 7,576 h. The lining is 95 % of the total, as the handbook says it should be. Changing to a wet sintered bronze lining (ko = 5.02×10−13) removes almost all of the friction term.

Important Notices
  • Not an official DoD document. NSWC-11 is the product of a Naval Surface Warfare Center research program, approved for public release. The handbook cautions that limited funding prevented full validation of every prediction equation. It should not be treated as an official Department of Defense standard.
  • No Navy affiliation or endorsement. The Naval Surface Warfare Center, Carderock Division and the U.S. Navy have not participated in the development of this calculator and do not approve or endorse it.
  • Use with the full procedure. NSWC-11 warns against extracting equations without regard to application procedures and parameter limits. Results are a design screening tool, not a substitute for the manufacturer’s rating, testing, or the judgment of a qualified engineer.
  • You supply the parts. The assembly rate is the sum of the rates of its parts, and most of those come from other chapters. Use the matching calculators and enter the results with the right unit.
  • Cycles for couplings. The handbook does not say what a cycle is. The result depends directly on the cycles per hour you enter, so choose it deliberately.
  • Interpretations. The clutch plate factor CNP and the unit of the spline-style inputs are read as described in the cards. The clutch page defaults to the physically sensible direction and shows the printed one as an option.
  • Lining replacement. Friction linings are sacrificial. The handbook counts a lining as a failure only when it is replaced before its service life. So a rate here is not the same as scheduled lining changes.
  • Constant failure rate. An MTBF assumes a constant failure rate. Friction linings wear out, so treat the estimate as a rough guide over long missions.

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