Prognosis Of Steerable Thruster Reliability

Published Date: 02 Nov 2017

Course: Master of Engineering in Maintenance and Asset Management

HU principle supervisor: Cyp van Rijn

HU secondary supervisor: Tim Zaal

Company supervisor: Luc Looijen

Student: Frank Velthuis

Cohort: 12

E-mail: [email protected]

Telephone: +31 (0)6 53133394

Date: xx-xx-xx

Revision: 000

Summary

Acknowledgements

Secrecy

All information, data and reporting of this thesis is considered confidential. All members of the graduation committee must adhere to this confidentiality. Wärtsilä may decide not to provide certain information to other members of the graduation committee, than herself or the student, and may force the student to alter or leave out specific data in the report, as long as the student is able to discuss and defend his work in his report and for the committee during the graduation process in a proper manner.

Version history

Version

Author*

Date

Description of changes

000

FV

20-12-2012

Outline

*Legend

FV – F.J. Velthuis

Table 0 Version history

Table of Contents

Introduction

In 2010 Wärtsilä released its condition monitoring solution for propulsion equipment. The Propulsion Condition Monitoring Service (PCMS) provides the customer with real-time advice and periodic reports about the condition of the machinery. An overview of a typical PCMS system is shown in the figure below.

PCMSOverview

Figure 1. Overview of a PCMS setup

PCMS data is analyzed in Wärtsilä CBM Centre for propulsion equipment. Data analysis consists mainly of vibration analysis for rotating equipment, oil analysis, control system- and hydraulic- performance analysis and analysis of specific manoeuvres. Data analysis is supported by an advanced automated decision support system, referred to as the PCMS central core. This decision support system assists in identifying potential failures, whereby the CBM expert can focus on resolving issues in close contact with the customer.

Traditionally thrusters are overhauled every five years, simultaneously with the obligatory internal inspection by a surveyor of a maritime class society. At that time the vessels are either removed in a dry dock or exchanged in sheltered waters. In both cases the vessel is down for a period of two to three weeks. Because PCMS is approved by the maritime class societies the requirement for internal inspection is forfeit, and the thrusters’ overhaul interval becomes dependant on the manufacturers’ recommendations.

Given that analysis of the data indicates that equipment is healthy (meaning that no potential failures are present) the optimal overhaul interval depends on the desired level of reliability and the operational history of the equipment consisting of the load distribution (or profile) and the lubrication oil contamination levels the equipment has endured.

In this graduation assignment a method will be developed for predicting the reliability of the thruster in time. This prediction needs to take into account the recorded- (with PCMS) as well as the expected mission profile of the thruster.

Company background and organization

Wärtsilä is a global leader in power solutions for the marine and energy markets. Wärtsilä consists out of three divisions, namely Power Plants, Ship Power and Services. Power Plants is a leading supplier of flexible power plants for the power generation market. Ship Power provides integrated systems to the marine industry. Amongst its products are engines, and propulsion equipment such as steerable thrusters. Wärtsilä Services supports customers throughout the lifecycle of their installations. It has a wide service network for the power plants industry and the marine markets. The figure below shows the organization structure of Wärtsilä Services. Wärtsilä Services is a matrix organization. The four areas, which together cover the world, are supported by Solutions Management and Delivery Management. The Areas are responsible for direct customer contact and sales.

Figure 2. Organization chart Wärtsilä Services

Solution management is split up into several portfolios. Each portfolio is responsible for a set of products, such as propulsion or 4-stroke engines. The portfolios are responsible for revenue and margin within their portfolio; they provide sales support to the areas, and take care of product & business development in the portfolio. Delivery Management is responsible for all delivery processes. Delivery management is split up in a number of functions. These are Wärtsilä Global Logistics Services, Field Services, Customer Assistance (Warranty), Project & Contract Management and Technical Services.

Technical Services, is the technical knowledge centre of Wärtsilä Services. Technical Services maintains, develops and makes available the needed technical knowledge to stakeholders in an efficient an effective manner. Technical Services provides technical support on propulsion matters to internal stakeholders such as the Areas and Field Service. In its role of technical knowledge centre Technical Services Propulsion is responsible for technical matters involved in product development. Technical Services also houses the CBM Centre Propulsion. This department has been established to ensure delivery in-line with contractual obligations and to facilitate further growth of the propulsion CBM business, currently driven by Propulsion Condition Monitoring Service (see also the previous paragraph) sales.

Description of the thesis problem

Traditionally thrusters are overhauled every five years, simultaneously with the obligatory visual internal inspection by the class surveyor. With the advent of class approved condition monitoring systems the requirement for internal inspection is waived. The remaining requirement from maritime class societies is that the thrusters are overhauled in accordance with the manufacturer’s recommendations.

It has been considered to carry out the overhaul solely on the bases of the equipments condition as indicated by PCMS. The P-F interval (the time between detection of a potential failure and the occurrence of an actual failure) is however too short. Vessel owners require long-term plannability of thruster maintenance. Further research and development into better condition monitoring techniques may increase the P-F interval but the desired length of one to two years can never be achieved. One to two years before occurrence of for example a bearing failure, physical phenomena of the failure, are simply not present.

Given that analysis of the data indicates that no potential failures are present, the optimal overhaul interval depends on the desired level of reliability and the operational history of the equipment consisting of the load distribution (or profile) and key service factors, such as the lubrication oil contamination levels the equipment has endured. Currently no method exists to predict the reliability of propulsion equipment as a function of the operational history of the equipment. Such a method needs to be developed. The main research question in this assignment therefore is:

How can a model be developed to predict the reliability of a steerable thruster, based upon its prior and expected use and endured operational conditions?

Since lifetime prediction and reliability models are nearly always applied at a component level the first step is to develop a generic reliability block diagram for a thruster. The first sub research question therefore is:

How is a generic reliability block diagram of a thruster composed?

Although a reliability block diagram of a steerable thruster features few redundant components not all components are equally critical. For example roller bearings and gears play a key role in the reliability and availability of a thruster, as the majority of the drive train failures can be attributed to these components. Therefore the following two sub research questions are posed:

How can a model be developed to predict the reliability of roller bearings, based upon their prior and expected use and endured operational conditions?

How can a model be developed to predict the reliability of helical gears, based upon their prior and expected use and endured operational conditions?

Fortunately there are numerous literature sources that describe how to perform design calculations and determine the lifetime of roller bearings and gears. Typically these are however not in the form required to determine the reliability of the components based upon their prior use and operational conditions endured. For most other components, such as the propeller shaft seal and the housing, less information is available in literature. For these components it will be investigated if expert judgement can be applied to predict the reliability based upon running hours and use.

How can expert judgement be applied to predict thruster component reliability based upon running hours and use?

The overall model requires a large amount of failure data to be validated. Currently however there is not sufficient data available for normal validation, e.g. by means of regression analysis. What is available is a limited set of data on the percentage of thrusters that survived until the first overhaul after five years of operation. This data set will be used for initial calibration. To ensure the model becomes more accurate over time it will be constructed such that it can be further calibrated as failure data is gathered with PCMS. Virtual failure data will be used to validate the models ability to be updated.

Once these four sub research questions are answered a model can be assembled that answers the main research question. The remaining challenges will then be to incorporate this reliability prognosis in the existing PCMS infrastructure (see also chapter 1) and in the commercial offering. Therefore the following two research questions are asked:

How can the reliability prognosis be incorporated in the existing PCMS infrastructure?

How can the reliability prognosis be incorporated in the commercial offering?

The reliability prognosis provides additional value beyond the existing offering of PCMS. Intrinsically it provides long-term predictability. However further value may be attributed to it if the maximum recommended overhaul interval is increased when the reliability prognosis is in the commercial scope of a PCMS delivery. A pricing strategy needs to be developed to incorporate the reliability prognosis in the existing commercial offering. A good pricing strategy has to consider all commercial options that exist in offering PCMS. Therefore a closer look will be taken at the possibilities for service level differentiation.

In accordance with the previously stated research questions the research model for this thesis project is defined below. The "Heinze Oost" tables that describe the reason, the related fields of knowledge, methods and desired answers are available in appendix . The figure below shows the research model for this graduation project.

Figure 3. Research model of thesis project

Model framework

Methods and techniques

Failure mode and effect analysis

Describe the technique, refer to literature.

Gebruik rapport Daniel, refer to it.

Reliability block diagram

Describe the technique, refer to literature.

Thruster FMEA

Previous studies

Give a generic FMEA for a steerable thruster.

Thruster reliability block diagram

Give a reliability block diagram of a thruster.

Describe how sub-models fit into the reliability block diagram.

Model inputs

Input parameters

Load distribution

Keep it simple, just allow load as a distribution.

PCMS data parser

Explain the 4D input.

Explain the data checks.

Scenario analysis

Roller bearing reliability predictions

This chapter describes the roller bearing reliability prediction model. It first discusses and describes the relevant methods and techniques. The second paragraph describes the structure of the reliability prediction model, referring to the actual code contained within the appendices. The third paragraph showcases preliminary results of the roller bearing reliability prediction model.

Methods and techniques

This paragraph describes all methods and techniques required to develop the reliability prediction model. Where applicable, the validity of the described methods and competing alternative methods are considered.

Lundberg-Palmgren theory

All bearing life calculations that are done today are based on the 1947 and 1952 Lundberg and Palmgren life theory [R5] [R6]. Prior to the release of this theory all bearing manufacturers used their own specific methods to calculate bearing life.

The Lundberg and Palmgren life theory is based upon a paper released by Palmgren in 1924 [R1]. This paper established functions to predict service life for bearings under purely radial load, established rules for the conversion of simultaneously effective axial and radial loads to purely radial loads and calculated the effect of different types of loads that are subject to change over time. It was however still missing a comprehensive life theory that fitted the observations made by Palmgren.

In 1939 Weibull published his theory of failure [R7] [R8]. Palmgren and Lundberg incorporated their previous work with that of Weibull (and according to Zaretsky Error: Reference source not found [R8] work of Thomas And Hoersch) to form the Lundberg-Palmgren theory. It includes the probability of survival, the internal stress created by the external load, the number of stress repetitions, the stressed volume, the contact area and the length of the raceway. It also produced the following equation which forms the basis of all standards available today:

Equation Basic rating life

L10 = Basic rating life for 90% reliability [106 revolutions]

C = Dynamic load rating [N]

Feq = Equivalent bearing load [N]

p = Exponent of lifetime formula (3 for ball bearings, 10/3 for typical roller bearings)

The equivalent dynamic load is calculated by the following equation:

Equation Equivalent bearing load

In this equation X and Y are factors calculated by Lundberg and Palmgren to determine the bearing load based upon the ratio between the radial and the axial load. Reference Error: Reference source not found sets out further how the Lundberg and Palmgren theory was constructed with respect to the equivalent load and fatigue limits, and where it deviates from preconceived notions such setting aside Hertzian equations to predict rolling bearing stresses.

Interesting is the rational for using specifically the L10 life (which calculates life for a reliability of 90%), versus lifetimes for other reliabilities, laid down by Palmgren in 1924 Error: Reference source not found. "In order to obtain a good, cost effective result, it is necessary to accept that a certain small number of bearings will have a shorter service life than longer than that stated in the formula. The calculation procedure must be considered entirely satisfactory from both an engineering and a business point of view, if we are to keep in mind that mean service life is much longer than the calculated service life and that those bearings that have a shorter life actually only require repairs by replacement of the part which is damaged first." This shows that Palmgren had already in interest in balancing engineering and business requirements, much like can be done with current day reliability prediction models.

Palmgren also recognized that the variation in both load and speed must be accounted for in order to predict bearing life. For this he developed an equation identical to the one Miner [R10] independently developed 21 years later and which become known as the linear damage rule or the Palmgren-Miner rule. The most convenient form of this equation is:

Equation Linear damage rule 1/2

And

Equation Linear damage rule 2/2

The X’s represent the fraction of total time or total revolutions (depending on the unit of L) the bearing has spent in a particular condition for which Ln was valid.

Though Palmgren-Miner's rule is a useful approximation, it has two major limitations. Firstly it fails to recognize the probabilistic nature of fatigue. The only way to relate life and reliability is by applying a distribution around the predicted life. In ISO 281 (see 5.1.4) this is handled by the reliability factor.

Secondly it does not consider the effect of the order in which different conditions occur, which may be of importance if for example heavy load cycles create residual stress. For steerable thrusters it is estimated that this is acceptable, as for a certain operational profile, the actually endured conditions will be randomly spread around this operational profile. Furthermore even at significant thruster overloads (e.g. 130% of the rated capacity) individual roller bearings will not be overloaded.

Development of an international standard

Ten years after the release of the Lundberg-Palmgren theory in 1962 ISO adopted the approach in their recommendation R281 and bearing manufacturers and users started to use it [R11]. As bearings improved engineers started to realize that many factors influenced bearing life. In 1971 ASME (the American Society of Mechanical Engineers) published a design guide on "Life Adjustment Factors". ISO took this work and launched its standard ISO 281 in 1978. This standard recognized three independent life factors:

Equation Life adjustment factors ISO 281:1978

a1 = Reliability (Converts L10 to Lna e.g. for L1, a1 = 0.21)

a2 = Bearing properties (such as special coatings, material, etc.)

a3 = Operating conditions (lubrication, contamination, temperature, etc.)

At the time it was published ISO 281 (1978) matched bearing performance reasonably. However in the 80s and the 90s the quality of bearing steel, bearing design, production methods and surface finishes went up significantly and the ISO 281 was under predicting bearing life nearly 14 times [R11]. Since then ISO has made multiple changes to the life adjustment factors, varying the types of factors, the magnitudes and the calculation methods. In the latest iteration, ISO 281:2007 [R12], the factors a2 and a3 have been replaced by aISO. This factor includes four interdependent factors: lubrication, contamination, load and the fatigue stress limit of the bearing material.

ISO 281:2007 is accepted in Europe, Japan and most other places but not in the USA. This is related to the debate [R13] on whether or not a fatigue stress limit exists for roller bearings. Nevertheless all large bearing manufacturers have adopted the ISO 281:2007 standard. Furthermore most maritime class societies (such as DNV and ABS) recognize ISO 281:2007 as a valid method to calculate bearing lifetime (see also paragraph Error: Reference source not found). Therefore ISO 281:2007 will be used as a based to develop a reliability prediction method for roller bearings.

Requirements for maritime class societies

DNV in its "Rules for Classification of Ships" (part 4, chapter 4, section 2) states the following:

702) Ball and roller bearings shall have a minimum L10a (ISO 281) life time that is suitable with regard to the specified overhaul intervals. The influence of the lubrication oil film may be taken into account for L10a, provided that the necessary conditions, in particular cleanliness, are fulfilled.

ABS in its "Rules for Building and Classing Steel Vessel Rules" (part 4, chapter 3, section 5) states:

5.3.2) the minimum L10 bearing life is not to be less than 20.000 hours for ahead drives and 5.000 hours for astern. Shorter life may be considered in conjunction with an approved bearing inspection and replacement program reflecting the actual calculated bearing life. See 5.9 for application to thrusters. Calculations are to be in accordance with an applicable standard such as ISO76:1987, ISO 281:1990 (roller bearings, for static and dynamic ratings, respectively).

And

5.9) Full bearing identification and life calculations are to be submitted. Calculations are to include all gear forces, thrust vibratory loads at maximum continuous rating, etc. The minimum L10 life is not to be less than 20.000 hours for continuous duty thrusters (propulsion and dynamic positioning) and 5.000 for intermittent duty thrusters.

Both of these requirements are applicable to the process of thruster design and preparation of design calculations. It should be noted that the stated hours should be seen in the light of a traditional maintenance scheme with a fixed five year interval for bearing replacement.

With respect to the statements two things are notable. First DNV specifically states that ISO 281 can be used and that the influence lubrication may be taken into account as long as the necessary conditions and in particular cleanliness is fulfilled. This can be translated as a permission to use aISO as described in ISO 281:2007. The statement "necessary conditions and in particular cleanliness" most likely refers to the interdependence of the four factors (lubrication, contamination, load and fatigue stress limit) making up aISO. Secondly, although ABS does not refer to the latest version of ISO281 they do not exclude it from use either. Instead they state that an applicable standard is to be used.

Further ABS states that a lifetime of less than 20.000 hours is permitted if an approved bearing inspection and replacement program, reflecting the actual calculated bearing life, is in place. By inference this could be interpreted as ‘a replacement interval of 20.000 hours may be exceeded as long as the actual calculated bearing life is sufficient and the bearing is inspected and determined to be healthy.’ Since PCMS is class approved and ABS thereby acknowledges that PCMS can replace ‘visual internal inspection’ by inference DLP in coherence with PCMS can be used to time the bearing maintenance intervals.

ISO 281:2007

In the latest iteration of ISO 281 the modified rating life is given by the following equation:

Equation Modified rating life

aISO = Life modification factor (replaces a2 and a3)

In this equation C is the basic dynamic load rating and is wholly determined by bearing specific (i.e. geometry specific) parameters. P is the dynamic equivalent load and is calculated by means of Equation .

The guideline provides a table for selecting a1, of which the following is a fragment provide for reference purposes.

Reliability %

Lnm

a1

90

L10m

1

95

L5m

0.64

96

L4m

0.55

97

L3m

0.47

98

L2m

0.37

Table 5 Life modification factor for reliability

The life modification factor can be considered as a function as follows:

Equation Life modification factor function

eC = contamination factor

Cu = fatigue load limit

P = dynamic equivalent load

κ = viscosity ratio

The following three paragraphs describe how the contamination factor, the dynamic equivalent load and the viscosity ratio can be calculated. The subsequent paragraph describes how the life modification factor itself can be calculated.

Calculation of contamination factor

The contamination factor eC is dependent on:

The type size and hardness and quantity of particles

Lubricant film thickness (interdependent with κ)

Bearing size

In appendix 5 of the ISO guideline a detailed method is described to calculate the value of the contamination factor for systems with off-line filters, such as steerable thrusters. For this the ISO guideline uses 5 different equations. Each equation is valid for a certain range of oil contamination levels as determined in accordance with ISO 4406 [R14]. ISO 4406 describes a method for coding the level of contamination by solid particles. It is based on the counting the number of particles of different size classes. The code has the format d4/d6/d14. The first scale number represents the number of particles equal to or larger than 4 μm per milliliter of fluid, the 2nd represents 6 μm and above and the 3rd 14 μm and above.

Below is depicted, one of those equations, valid for ISO 4406 codes -/13/10, -/12/10, -/11/9 and -/12/9.

Equation Contamination factor 1/3

With,

Equation Contamination factor 2/3

And the restriction,

Equation Contamination factor 3/3

Graphically this equation is displayed as follows.

Figure 5. Contamination factor for ISO 4406 codes -/13/10, -/12/10, -/11/9 and -/12/9

Calculation of the fatigue load limit

In the calculation of the fatigue load limit Cu the following influences have to be considered:

the type, size and internal geometry of the bearing;

the profile of rolling elements and raceways;

the manufacturing quality;

the fatigue limit of the raceway material.

The ISO guideline provides the following a simple and an advanced method for calculating the fatigue load limit. The advanced one is preferred by ISO as the results of the simple method can differ significantly from the results of the advanced method. Unfortunately the advanced method requires a multitude of geometric bearing parameters to function. Such is undesirable because not all parameters are easily obtainable. For DLP to be successful the required input parameters should be obtainable with relative easy.

Fortunately the large bearing manufacturers SKF and FAG state bearing fatigue load limits on their websites. Therefore it has been decided to use those fatigue load limits directly and resort to the simple method provided by ISO in case they are not available.

The simple method uses the following equations:

Equation Simple method to calculate the fatigue load limit 1/4

For,

Equation Simple method to calculate the fatigue load limit 2/4

And,

Equation Simple method to calculate the fatigue load limit 3/4

For,

Equation Simple method to calculate the fatigue load limit 4/4

Calculation of the viscosity ratio

The effectiveness of lubricant is primarily determined by the degree of surface separation between the rolling contact surfaces. If an adequate lubricant separation is to be formed, the lubricant must have a given minimum viscosity when the application has reached its operating temperature. The condition of the lubricant separation is described by the viscosity ratio:

Equation Viscosity ratio

ν = actual kinematic viscosity in mm2/s

ν1 = reference kinematic viscosity in mm2/s

The reference kinematic viscosity can be calculated by:

Equation Reference viscosity 1/4

For,

Equation Reference viscosity 2/4

And,

Equation Reference viscosity 3/4

For,

Equation Reference viscosity 4/4

Calculation of the actual kinematic viscosity is oil dependant and therefore not described in ISO 281. How the actual viscosity is calculated in DLP is described in paragraph 5.1.5.

Calculation of the life modification factor

Given a known contamination factor, fatigue load limit, dynamic equivalent load and a viscosity ratio the life modification factor aISO can be calculated.

The ISO guideline provides sets of equations for various types of bearings. As thrusters are constructed with roller bearings there are two relevant sets of equations. The first set is used for radial roller bearings and the second set for thrust roller bearings. The set used for radial roller bearings is shown below.

Equation Life modification factor 1/6

For,

Equation Life modification factor 2/6

And,

Equation Life modification factor 3/6

For,

Equation Life modification factor 4/6

And,

Equation Life modification factor 5/6

For,

Equation Life modification factor 1/6

Calculation of actual kinematic viscosity

To accurately use ISO 281 for bearing life predictions the viscosity ratio as described in 5.1.4.3 needs to be calculated. The viscosity of lubrication oil is mainly dependant on its temperature. The ASTM standard D341 describes the Walther equation which can be used for this purpose:

Equation Walther equation

ν = kinematic viscosity in cSt [mm2/s]

A, B = constants

It is noted that the logs in this paragraph are 10-based logs, and the temperatures are in degrees Kelvin.

Typically oil data sheets will state the viscosity for at least two temperatures. By plugging in these coordinates in the equation above the following equations can be derived.

Equation Constant A for calculation of actual kinematic viscosity

And,

Equation Constant B for calculation of actual kinematic viscosity

The equation for the actual kinematic viscosity based on the actual temperature of the oil then becomes:

Equation Actual kinematic viscosity

There are more accurate methods available to describe the relationship between oil temperature and oil viscosity. An example is the Vogel equation [R16] which makes use of three coordinates instead of two and is thereby slightly more accurate. However to ensure the DLP is compatible with the data sheets of both large and small oil companies the ASTM standard is followed.

Calculating reliability for a given time

The methods described in ISO 281 make it possible to calculate the bearing lifetime for a given reliability. However for the DLP it is required to calculate the bearing reliability as a function of time. This is the universal format in which the bearing-, gear- and expert judgement models output their results.

To make this possible for the bearing model a curve has been fitted to the reliability modification factor (Table 5 Life modification factor for reliability), writing a1 as a function of the reliability:

Equation Function of reliability modification factor

By analytic methods a function has then been derived for the reliability itself.

Equation Reliability as a function of time and the modified bearing lifetime (this function is to be created ask Anum)

The curve-fit procedure and the analytic derivation of the above equation can be found in appendix 15.

This paragraph needs to be updated when appendix 2 is completed.

Calculation of equivalent bearing load

The equivalent bearing load can be calculated by means of equilibriums of moments and forces. Such a calculation is straightforward but requires a multitude of parameters describing the thruster geometry. To keep the DLP model maintainable a function will be created that describes the actual equivalent bearing load as function of the actual thruster load (0 – 100% of the nominal power) and the equivalent bearing load at nominal power.

The equivalent bearing load at 100% power is calculated by design engineers at new-built and can be obtained from the technical data sheet of a thruster.

As appendix 16 proves the equivalent bearing load varies proportionally to thrust (shaft) torque (M).

M = Thruster shaft torque [kNm]

Equation Proportionality of bearing load and thruster torque

Because thruster power is a function of torque and RPM the following equation is also valid:

P = Thruster load [kW]

n = Thruster input shaft speed [RPM]

Equation Proportionality of bearing load with Power/RPM ratio

Introduce a formula describe the equivalent bearing load as a function of the:

thruster load,

the thruster input shaft speed,

the nominal thruster load,

nominal input shaft speed and the

equivalent bearing load at 100% power.

Dear Anum could you prepare this formula.

It should be noted that that proportionality between propeller thrust and propeller shaft torque does not exist. Such would only be the case when propeller efficiency is constant. Hence bearing loads originating from the propeller thrust are not completely proportional to the torque. The DLP will nevertheless pretend that this is the case; this inaccuracy will cause slightly lower lifetimes to be calculated for the thrust bearing. The alternative would be to incorporate a propeller efficiency prediction model in the DLP which is undesirable.

Model design

The previous paragraph describes all methods and techniques required to design the bearing reliability prediction model. This paragraph describes how the model has been designed. It gives the reader an overview of the functions used and how they interface with each other.

Modified bearing life function

The methods and techniques described in paragraph 5.1 can be used to form the following inner function of the bearing reliability prediction model. The inner function calculates the modified bearing lifetime in hours for 90% reliability as a function of the variables bearing load, RPM, oil temperature and oil contamination levels.

Figure 5. Modified bearing lifetime function

The actual function can be found in appendix 17.1.

Dynamic lifetime function

To calculate the lifetime for a bearing that endures constant conditions throughout its life the function described in the previous paragraph suffices. However in practice all bearings endure varying conditions throughout their life. To calculate the dynamic lifetime of a bearing, which takes into account all these conditions, the linear damage rule (see also 5.1.1) can be used.

Figure 5. Dynamic lifetime function

The actual function can be found in appendix CalcDynamicLife17.2.

Bearing reliability function

With the method described in paragraph 5.1.6 a function can be created to calculate the reliability as a function of time and modified bearing lifetime (5.2.1) or the dynamic modified bearing lifetime (5.2.2).

Figure 5. Bearing reliability function

The actual function can be found in appendix 17.3.

Actual load function

To calculate the equivalent bearing load without having to input a multitude of thruster geometrical parameters it will be calculated as a function of the bearing load at 100% power, and the power and RPM itself. This function is based on the methods and techniques described in paragraph 5.1.7.

Figure 5. Actual load function

The actual function can be found in appendix 17.4.

Approximate RPM function

When the DLP model is used on the bases of PCMS data the RPM variable is always available. However when the DLP model is used to make predictions about the feature it is practical if the RPM can be estimated, and only the load has to be input.

Figure 5. Approximate RPM function

Note that the above function can only be used for FPP thrusters as the RPM for CPP thrusters can be approximated as a constant.

The actual function can be found in appendix 17.5.

Preliminary results

This paragraph showcases preliminary results of the bearing reliability prediction model.

Make predictions for a 3510 thruster.

Helical gear reliability prediction

A gear is a wheel-like rotating machine component with a number of cut teeth that meshes with another toothed part in order to transmit torque. Two or more gears working in tandem are called a transmission and can produce a mechanical advantage through a gear ratio, see Figure 6.. Geared devices can be used to change the speed, torque, and/or direction of a power from a source. The most common situation is for a gear to mesh with another gear; however, a gear can also mesh with a non-rotating toothed part, for example a rack, thereby producing translation instead of rotation. When two gears of unequal number of teeth are combined, a mechanical advantage is produced, with both the rotational speeds and the torques of the two gears differing in a simple relationship. In two gear system the smaller gear is the pinion and larger one is the gear/wheel. In most applications the pinion is the driver, this arrangement results in reduction of the rotational speed but it increases torque.

ugu2155x_1102

Figure 6. Simple gear and pinion assemble.

There are different methods of classifying gears. The most common method of classification is based on the formation of the gear teeth. An external gear is one with the teeth formed on the outer surface of a cylinder or cone. Conversely, an internal gear is one with the teeth formed on the inner surface of a cylinder or cone. It is also possible to classify gears based on the shape of the gear tooth. Some of these are: Spur gears where each tooth is straight and aligned parallel to the axis of rotation. Helical gears where the edges of the teeth are not parallel to the axis of rotation, but are set at an angle. Bevel gear is shaped like a right circular cone with most of its tip cut off. Figure Figure 6. shows some of these types of gears.

Figure 6. Common types of gears (ref. EngineersEdge).

An example of spiral bevel gear application, common in the lower gearbox (LGB) of a propulsion system, is shown in Figure 6..

Figure 6. Gears in propulsion systems.

Gear terminologies and definitions

In this section we will discuss parameters used to describe gear geometry and some common terminologies used in modern gear designs. Some of the gear geometry parameters are shown in Figure 6.. Figure 6. shows a meshing gear teeth and corresponding geometric parameters.

Figure 6. Geometric parameters of a gear/gear tooth (source RoyMech).

Some of the common gear design and manufacturing terminologies shown in Figure 6. and their definitions is given in Table 6 .

Table 6 Gear terminologies and definitions.

Addendum

The height by which a tooth projects beyond the pitch circle

Dedendum

The depth of a tooth space below the pitch circle. It is normally greater than the addendum of the mating gear to provide clearance.

Pitch circle

Circle on which tooth profile and tooth proportions are constructed. It is an imaginary circle that rolls without slipping with a pitch circle of the mating gear.

Backlash

The amount by which the width of the tooth space exceeds the thickness of the engaging tooth on the pitch circle

Circular pitch

The distance along the pitch circle between corresponding profiles of adjacent teeth

Tooth circular thickness

The length of the arc between the two sides of a gear tooth on the pitch circle

Contact ratio

The number of angular pitches through which a tooth surface rotates from the beginning to the end of contact

Diametral pitch

The ratio of the number of teeth to the pitch diameter of the gear.

Normal plane

The plane normal to the tooth surface at a pitch point and perpendicular to pitch plane

Pressure angle

Angle at pitch point between the line of pressure which is normal to tooth surface and the plane tangent to the pitch circle

Tip relief

An arbitrary modification of tooth profile whereby a small amount of material is removed near the tip of the gear tooth

Working depth

The depth of engagement of two gears (sum of two addendums)

Figure 6. Geometric parameters of a gear mesh (source RoyMech).

The meaning of the these parameters and their notation along with the measure of units are given in Table 6 .

Table 6 Gear geometric parameters and units of measure.

a

Operating centre distance, in mm

h

Tooth depth, in mm

b

Common face width, in mm

αn

Normal pressure angle at reference cylinder, in rad

B

Total face width of double helix gears, including gap, in mm

αt

Transverse pressure angle at reference cylinder, in rad

d

Reference diameter, in mm

αtw

Transverse pressure angle at working pitch cylinder, in rad

da

Tip diameter, in mm

β

Helix angle at reference cylinder, in rad

db

Base diameter, in mm

β b

Base helix angle, in rad.

df

Root/fillet diameter, in mm

Ɛa

Transverse contact ratio

dw

Working pitch diameter, in mm

Ɛb

Overlap ratio

x

Addendum modification coefficient

Ɛg

Total contact ratio

z

Number of teeth

ρao

Tip radius of the tool,

zn

Virtual number of teeth

ρF

Tooth root radius at the critical section, in mm

n

Rotational speed, in rpm

v

Linear speed at pitch diameter, in m/s.

U

Reduction ratio

mn

Normal module, in mm

Gear failure

The gear is said to be failed when it can no longer "efficiently" perform the operation for which it was designed. The most common modes of gear failure are wear, surface fatigue, plastic flow, and tooth breakage.

shows more detailed classification of gear failure modes along with the cause and effect of the damage.

Tooth breakage and fatigue failure of gears can lead to the catastrophic failure of equipments. Because of this, effective procedures and information to evaluate the load capacity and useful life of gears are needed. In this sense, ISO 6336 has introduced useful information to consider the bending and fatigue load capacity of gears. The procedure takes into account the pitting resistance (surface fatigue failure) and bending strength capacity (volumetric fatigue failure) of helical gears.

According to ISO 6336, gear failures can be classified in two major categories. One is tooth breakage failure and other is surface failure. Each of these failure modes has a different causes and driving conditions as shown in

. In gear failures as provided in Table 1, tooth breakage failure largely occurs due to misalignment problems that results in excessive surface contact fatigue. These problems can easily be reduced or eliminated by adopting the correct gear mounting procedures during assembly. However, gear surface failures normally occur due to critical operational parameters such as external loading, lubrication and operating speed [3-5]. These operational parameters are actually stimulating the generation of a complex wear mechanism on the gear surface which ultimately leads a surface failure during gear operation.

Gear failure modes

The distinguishing characteristic of materials associate with the lost of resistance under the action of repeated or fluctuating stresses is called fatigue failure. The study of fatigue failure is not an exact and absolute science, of which precise results can be obtained. The prediction of fatigue fracture is very often approximate and relative, with many components of the statistical calculation, and there are a great many factors to be considered, even for very simple load cases. In this sense the determination of the fatigue limit for materials with industrial purposes demands a great variety of test to define the magnitude of fatigue limit reported at a specific number of cycles. This argument works equally for any other mode of gear failure, for example, gear tooth bending. For this reason, it is important to distinguish all types of failure modes in order to determine the reliability of gears. Some of the common failure modes in gears operating under any service condition is described in the next section.

Wearing is the removal of metal, worn away normally in a uniform manner from the contacting surface of the rear teeth. Specific types of gear wear include abrasive wear, corrosive wear, and scoring. Abrasive wear is caused by an accumulation of abrasive particles in the lubrication system. Corrosive wear is caused by the presence of water or chemical additives in the lubrication oil resulting in deterioration of the gear surface from chemical action. Scoring type of wear is caused by failure of the lubricant film due to overheating resulting in metal-to-metal contact and tearing of the surface metal.

Surface fatigue is the failure of gear as a result of repeated surface or even subsurface stresses that are beyond the endurance limit of the gear material. Surface fatigue generally results in the removal of metal and formation of cavities on the gear tooth surface. This pitting can be caused by the gear tooth surfaces not properly conforming to each other due to lack of proper alignment. Spalling is similar to pitting except that the pits are relatively larger, shallower, and very irregular in shape. Spalling is usually caused by excessive contact stress on the gear tooth surface.

Plastic flow is generally due to the cold working of the gear tooth surfaces, caused by heavy loads and rolling/sliding action of the gear mesh. The result of high contact stress level in the gear mesh is the yielding of the surface/subsurface material and thus gear tooth deformation.

Gear tooth breakage is a failure caused by the fracture of a whole tooth or substantial portion of the tooth. Gear overload or cyclic stress of the gear tooth beyond the endurance limit of the gear material causes bending fatigue and eventually a crack originating in the root section and then propagating and tearing away of the tooth or part of the tooth. Gear overload is generally caused by a bearing failure of any kind, system dynamic loading, or contaminants entering gear mesh area.

Table 6 Gear Failure Modes, Causes, and Effects (Ref. ISO 6336-2, [R1]).

Failure Mode

Failure Cause(s)

Failure Effect(s)

Pitting (Macro/Micro)

Cyclic contact stress transmitted through lubrication film

Local contact of asperities produced by inadequate lubrication film caused by:

Excess load/temperature, lower oil viscosity, lower operating speed, water saturation in the oil.

Tooth surface damage

Tooth root fillet cracking

Tooth bending fatigue

Surface contact fatigue

Tooth failure

Tooth shear

Fracture

Tooth failure

Scuffing

Lubrication breakdown

Wear and then eventual tooth failure

Plastic deformation

Excessive loading

Surface yielding

Surface damage resulting in:

Vibration

Noise

Tooth failure

Spalling

Fatigue

Mating surface deterioration

Welding

Galling

Tooth failure

Tooth bending fatigue

Surface contact fatigue

Tooth failure

Contact fatigue

Surface contact fatigue

Tooth failure

Thermal fatigue

Incorrect heat treatment during production

Tooth failure

Abrasive wear

Contaminants in gear mesh area and lubrication system

Tooth scoring

Gear vibration/Noise

Gear stress calculation

In reliability prediction of gears a number of parameters play significant role and the stress applied to the gear system is one of these parameters. In gear design there are a number of force components that are considered for optimal life of gear under a prescribed loading condition. The two most significant force components are bending stress and contact stress. The next two sections give a general introduction on tooth bending and contact stresses.

Gear tooth bending stress

Wilfred Lewis in 1893 provides a formula for estimating the bending stress in a gear tooth. He modeled a gear tooth taking the full load at its tip as simple cantilever beam. If we substitute a gear tooth for the rectangular beam, we can find the critical bending stress point at the root fillet of the gear tooth. This bending stress is given by the formula:

Where, is the root bending stress (N/m2), is transmitted tangential load (Newton), is face width (meters), is the module (m), is the Lewis form Factor. The Lewis form Factor is a function of number of teeth, pressure angle and depth of the gear tooth.

It is fact that, when teeth mesh, the load is delivered to the teeth with some degree of impact. Furthermore, the working condition of the gear, like wheel and pinion size, the speed of the shaft, the properties of the lubricant used, and vibrations from nearby components or machines have significant influence on the transmitted tangential load and thus the bending stress. For example, If only the effect of the impact is considered, it is necessary to introduce a velocity factor in the Lewis formula to account for the impact. Now the Lewis equation becomes,

Where, is the velocity factor. A similar change has to be made in the Lewis formula to account for all factors mentioned earlier.

Gear tooth contact stress

The contact stresses on the surface of matting gear teeth are usually determined by formula derived from Hertzian theory of non-adhesive elastic contact by H. Hertz’s in 1882. Hertz determined the width of the contact band and the stress pattern when various geometric shapes were loaded against each other. The Hertz formula for the width of the band of contact can be applied to, for example, spur gears quite easily. This can be done by considering that the contact condition of gears are equivalent to those of cylinders having the same radius of curvature at the point of contact as the gear have, see [R4].

Assuming and are the respective radius of curvature of an involute curves at the contact point, then the Hertz equation for contact stresses in the teeth becomes

where and are the pitch radius of the pinion and gear respectively, is a contact factor, and is the pressure angle. The Hertz equation for contact stress also needs to be modified depending on the contribution of the gear design, operational and environmental factors towards the tangential force.

Damage accumulation

Gears subjected to any kind of operating condition experience different types of failure mode, see section 6.1 on gear failure modes. Furthermore, each type of stresses result in different type of gear failure. In reliability analysis of gears it is then important to devise a method for combining the damage caused by different sources or failure modes. The most simple and yet practical method for accumulation of gear damages caused by different failure modes is the Palmgren-Miner rule described below.

Palmgren-Miner Rule

Suppose a body can tolerate only a certain amount of damage, D. If this body experiences damages from N sources, then we might expect that failure will occur if

There are two areas of interest in gear failure analysis where this linear damage accumulation concept can be used. The first one is for the accumulation of gear damage from different sources like surface fatigue, tooth bending stresses, scuffing damages, scoring, etc. We can also use this linear damage concept in a fatigue setting by considering the situation where the gear is subjected to cycles at alternating stress , cycles at alternating stress , … , cycles at alternating stress . Note that this is usually the case for gears under dynamic loading conditions. From the S-N curve shown in Figure 6., it is possible to calculate the number of cycles to failure for any stress level of interest.

Figure 6. An example of S-N curve, see [R2].

It is reasonable in this case to let the fractional damage at stress level simply be , so that the Palmgren-Miner rule would say that either or both gear tooth pitting and bending failures occur when

where is the number of cycles the gear is under stress level and is the total number of cycles the gear can survive before failure at stress level , or in other words is the remaining number of cycles before failure.

One of the limitations of the linear damage rule is that it does not consider the effect of sequence of multiple loading scenarios. For example, in a two-stress-level fatigue test in which a higher load is followed by a lewer load, the sum of the cycle ratios is less than 1. However, if a lower load is followed by a higher load, the summation of the cycle ratios is greater than 1.

Standards for gear life rating

There are many gear tooth and gearbox rating standards existing in the world. For a given gearbox, the rating system that is used can give very different answers in the amount of power that can be transmitted. If a user is not specific or does not have a basic understanding of the different rating system, the reliability of the gearbox can be dramatically affected. The intent of this section is to compare the recent API, AGMA, ISO, DIN, and DNV gear standards regarding gear and gearbox design and manufacturing.

Currently, ISO and AGMA standards are getting more popularity in industries. Regarding gear design, specially spur gears, DIN 3990 series and its modified release ISO 6336 series are partially equivalent to AGMA 2101-D04, according to EuroTrans, see Table 6 . Most of these standards give separate guidelines for both spur and helical gears; however ISO 6336 gives single general guidelines for both spur and helical gears only with minor changes in formulas and calculation procedures.

ISO 6336 consists of several parts dedicated to both spur and helical gears. ISO 6336-1 provide basic principles, introduction and general influence factors. ISO 6336-2 covers calculation of surface durability or pitting. ISO 6336-3 covers calculation of tooth bending strength. Part-2 and Part-3 are used to predict the two prominent failure modes in gears, according to ISO 6336. Part-5, ISO 6336-5, covers strength and quality of gear materials. The last part, ISO 6336-6, covers calculation of service life of gears under variable loading conditions. Table 6 shows equivalence of these ISO parts with the equivalent DIN and AGMA standards see [R1].

ISO 10300 on the other hand has three parts dedicated only to bevel gears. ISO 10300-1: introduction and general influence factors, ISO 10300-2: calculation of surface durability (pitting), and ISO 10300-3: calculation of tooth root strength. All the three parts of ISO 10300 use similar gear rating procedure as in the first three parts of ISO 6336, except changes in formulas to account for the conical shape of bevel gears.

Table 6 Equivalence between ISO Standards and National Standards on gear technology (ref. EuroTrans).

Gear Calculation Method

Calculation of load capacity of spur and helical gears

Equivalent National Standards

Year of Publication

Status of Equivalence

ISO 6336-1:2006

Basic principles, introduction and general influence factors

DIN 3990-1

ANSI/AGMA 2101-D04

1987

2004

P/S

P

ISO 6336-2:2006

Calculation of surface durability (pitting)

DIN 3990-3

ANSI/AGMA 2101-D04

1987

2004

P/S

P

ISO 6336-3:2006

Calculation of tooth bending strength

DIN 3990-2

ANSI/AGMA 2101-D04

1987

2004

P/S

P

ISO 6336-5:2006

Strength and quality of materials

-

-

-

ISO 6336-6:2006

Calculation of service life under variable load

DIN 3990-6

ANSI/AGMA 6032-A94

1984

1994

P/S

NO

ISO 9083

Application to marine gears

DIN 3990-31

ANSI/AGMA 6032-A94

1990

2000

P/S

NO

Status of equivalence:

S : Strictly equivalent

P : Partially equivalent

Gear life rating is, in general terms, quantification of possible gear failure modes. Both ANSI/AGMA 2101-D04 and ISO 6336 give guidelines for both pitting resistance and bending strength calculations. However, DNV CN 41.2 considers calculations for scuffing load capacity of gears as well.

Gear rating according to ANSI/AGMA 2101-D04 uses Miner’s Rule (linear damage accumulation method) to calculate gear life based on load spectrum. This rating method is based on a reliability of 99% and the lower curves for stress cycle factors, for both pitting and tooth bending resistance. Scuffing resistance is in accordance with AGMA 925–A03.

Gear rating according to ISO 6336 also uses Miner’s Rule (see ISO 6336-6) to calculate safety factors using a load spectrum. This rating method is only available for pitting and bending fatigue lives calculation. In both cases, safety factor calculations are based on a reliability of 99%. ISO 6336:1996 does not provide a rating method for scuffing.

The gear rating procedures given in DNV CN 41.2 are mainly based on the ISO6336 Part 1 to 5 for cylindrical gears, and partly on ISO 10300 Part 1 to 3 for bevel gears and ISO Technical Reports on Scuffing and Fatigue Damage Accumulation, but especially applied for marine purposes, such as marine propulsion and important auxiliaries onboard ships and mobile offshore units. The calculation procedures cover gear rating as limited by contact stresses (pitting, spalling or case crushing), tooth root stresses (fatigue breakage or overload breakage), and scuffing resistance.

Gear life calculations

Tooth breakage and fatigue failure of gears can lead to the catastrophic failure of equipments. Because of this, effective procedures and information to evaluate the load capacity and useful life of gears are needed. In this sense, ISO 6336 has introduced useful information to consider the bending and fatigue load capacity of gears. In this section, the procedure and formulas to estimate a value of gear life expectancy is given. The procedure takes into account the pitting resistance (surface fatigue failure) and bending strength capacity (volumetric fatigue failure) of helical gears.

The distinguishing characteristic of materials associate with the lost of resistance under the action of repeated or fluctuating stresses is called fatigue failure. The study of fatigue failure is not an exact and absolute science, of which precise results can be obtained. The prediction of fatigue fracture is very often approximate and relative, with many components of the statistical calculation, and there are a great many factors to be considered, even for very simple load cases. In this sense the determination of the fatigue limit for materials with industrial purposes demands a great variety of test to define the magnitude of fatigue limit reported at a specific number of cycles.

In practice, gears are mostly operated under variable loads. Even in a continuous process the load acting on gear teeth is fluctuating due to the tooth contact process and operational conditions under which the gears shall perform. Under these variable loads a tooth breakage, which most often results in a total gear failure, must be take into account during the stages of gear design or load capacity calculation. This fact has demanded that new fatigue tests for gear materials be carried out and the fatigue resistance behavior with a high number of load cycles be analyzed.

As discussed earlier in this chapter ISO 6336 only considers two groups of gear failure modes; these are pitting and tooth breakage. The next two sections discuss useful lifetime estimation of gears based on these two failure modes.

Geometrical definitions

In the calculation of surface durability, is the common face width on the pitch diameter. In tooth strength calculations, ,  are the face widths at the respective tooth roots of the pinion and the gear. In any case, and  are not to be taken as greater than by more than one module () on either side of the contact region between mating teeth. For internal gears, , , ,  ,  ,  and  are to be taken negative. From the geometry of a gear we have the following relations.

The gear ration is the ratio between the number of teeth on the gear and on the pinion and is given by

where is the number of teeth on the gear (wheel, the larger of the two meshing gears) and is the number of teeth on the pinion. For external gears both and are positive whereas for internal gears has a negative sign.

The transverse pressure angle, the normal pressure angles and the helix angle at the reference cylinder are related according to the following relation:

The relation between the normal module , the helix angle, the reference diameter , and the number of teeth, for both pinion and gear is given by:

The transverse pressure angle is proportional to the ratio of base diameter and the reference diameter following the relation:

whereas the pressure angle at the pitch cylinder is a function of the centre distance of the pinion and the gear

with and are the base diameters for the pinion and gear, respectively.

The transverse contact ratio between the meshing pinion and gear, for external/internal gears, is given by:

where is the tip diameter of a gear.

The overlap ration and then the total contact ration are given by the following equations:

and

Force, power, and torque

In gear design calculations force, torque or power can be used to describe the loading condition on the gear tooth and thus it is important to formulate the relationship between these three variables. The nominal tangential load, on which all ISO 6336 are based, is determined in the transverse plane at the reference cylinder. It is usually derived from either the nominal torque or from the power transmitted by the gear pair.

The load capacity rating of gears, according to ISO 6336-1, is mostly based on the input torque to the driven machine. However, in some applications, the nominal torque of the prime mover is used as a basis. The nominal tangential load, , is need to be defined for each mesh under consideration. The nominal tangential load is given by:

where is the nominal torque in the pinion/gear, is the nominal power, and is the tangential speed at the reference cylinder given by the formula:

where is the angular speed of the pinion/gear.

In practice the transmitted load is never uniform in which case all intermediate loads and their number of cycles need to be describe or measured. This type of loads is classified as a duty cycle and is generally represented by a load spectrum. In such cases, the cumulative fatigue effect of the duty cycle is considered in rating and life prediction of the gears. If the duty cycle is, for example, measured in units of torque, then the equivalent tangential load must be calculated from the equivalent torque. The equivalent torque is given by:

where and are the number of cycles and corresponding torque for bin, respectively, and is the slope of the Woehler-damage line (S-N curve), see Figure 6 below. Then, the corresponding equivalent power and the equivalent tangential force can be obtained from the equivalent torque using the relations given earlier in this section.

Figure 6 The Woehler-damage line (S-N curve).

The magnitudes of the maximum tangential load and the corresponding maximum power and maximum torque are limited by appropriate safety factor. Or in other words, , , and are required to determine the safety factor to minimize pitting damage and/or sudden tooth breakage due to loading close to static stress limit. The general equation for safety factor is

where is the safety factor for pinion and gear, respectively, is the contact stress at a given loading condition, and is the pitting or tooth bending stress limit.

General influence factors

In this section formulas for major factors, which are presently known to affect the design of gears for surface fatigue and tooth bending, are derived. General gear design assumptions and corresponding factors are also discussed in detail.

Application factor

The application factor  accounts for dynamic overloads from sources external to the gearing. The additional forces from external sources are largely dependent on the characteristics of the driving/drives m