In recent years, the process of design analysis has evolved significantly through the use of advanced modeling software and programs. A common misstep, however, is to place too much emphasis on the results from this software, rather than conducting a thorough analysis. Some of the pitfalls of over reliance on modeling software can be averted by following a thorough process for design analysis. The process can be demonstrated with wear bands, devices for protecting shafts and providing a proper surface for radial lip seals in rotating equipment.
Shafts in rotating equipment tend to become grooved over time from the friction of rotational seals. Wear bands are devices that attach to a shaft to protect it from wear due to contact with these seals. All such components are subject to failure, so it is important to understand the conditions under which this can occur and design for them.
Design analysis has been inadequately defined as software for simulating physical behavior on a computer, yet simulations are no substitute for actual analysis and testing. Finite element analysis (FEA) is a helpful tool, but if you do not understand the principles of designing for failure, it is not only useless, but potentially dangerous. Therefore start with calculations of basic mechanics/physics, and then enhance your findings with FEA.
A more comprehensive definition of design analysis involves three activities. The first is an understanding of the factors that will affect the design under consideration, e.g., forces, torque, impact, etc. The next is application of mathematical models, and often direct testing, to determine the conditions under which failure will occur. And finally an appropriate safety factor must be used, based on specific operating parameters and associated risk, including any nationally established standards.
Consistent with this broader definition, a seven-step process for design analysis is proposed including:
- Definition of stresses induced by external factors
- Determination of the modes of failure based on these factors
- Determination of an acceptable factor of safety
- Researching the methods typically used for analysis and determining the best mathematical models to apply
- Application of the mathematical models to the various failure modes and comparison of the results to the factor of safety in Step 3.
- Application as needed of additional modeling techniques such as FEA
Determination if functional or physical tests are warranted to confirm analysis. (It may be necessary for these to occur earlier in process.)
Garlock Sealing Technologies has been manufacturing radial shaft seals since the1930s. These seals have stringent shaft requirements, including minimum surface hardness of 30 Rockwell C to prevent grooving; surface finish between 10 and 20 µin (0.25 to 0.50 µm) to retain lubricant; and no machining lead. However general materials may not have the necessary properties to meet these requirements. In addition many designers do not understand these requirements, resulting in equipment being built without the correct parameters for adequate sealing. Even if all the parameters are initially correct, after some time in service the shaft may no longer meet them due to wear.
Repair sleeves can be used to address these issues, but they are limited to shafts up to 12″ in diameter. Garlock recently developed a new product called the GSS Wear Band to provide a correct sealing surface for shafts 30″ to 60″ in diameter. These wear bands provide a surface hardness of 40 to 44 Rockwell C and a surface finish of 12 to 20 µin (0.30 to 0.50 µm) with no lead. Their 301 stainless steel construction protects against environmental corrosion. Made from strip, rings are formed using a flat-butt welding process with no filler materials.
Using induction heating coils or an oven, the bands are heated to 300^{o}F to 400^{o}F (149^{o}C to 204^{o}C), then slid over the shaft. Upon cooling they are held in place by interference or shrink fit (see simulation at Video Link 1. Concern over whether this interference would cause welded joints to fail due to stress called for analysis to determine if such failure would occur.
Wear Band Design Analysis
The first step of this analysis was examining the interferences in the design specifications. A wear band I.D. smaller than the shaft O.D. would induce circumferential or “hoop” stress. Researching the mathematical models referenced above would correlate operating torque and fit pressure to this stress.
The second step involved examining failure modes. These included complete brittle failure, a function of ultimate strength and the most dangerous for both personnel and equipment. Material stretching and setting, a function of yield strength, could cause component failure and the potential for severe equipment damage. Insufficient interference fit could cause the ring to slip or spin on the shaft, resulting in poor performance and moderate equipment damage. Because of the welded joints in the wear bands, the standard ultimate tensile and yield strengths for 301 SS could not be assumed. This required tensile testing of the actual welded samples and microstructural analysis of the welded areas.
The third step focused on the factor of safety, since there are no nationally recognized standards for this type of component. Total failure (induced stress > S_{UT}) has the most potential for injury, therefore a minimum 3:1 factor of safety would be required using ultimate tensile strength. Component failure (induced stress > S_{Y}) is less serious and therefore required a minimum 2:1 factor of safety using yield strength. Slippage, while undesirable, is a less serious issue, and would be acceptable at or even slightly below a 2:1 factor of safety.
Step 4 involved researching mathematical models. Interference fits are typically analyzed as pressurized vessels without a longitudinal stress component. The application can be treated either as a thick- or thin-walled cylinder. The latter is one where the ratio of the wall thickness to the I.D. is less than 1:20. The wear bands qualified as thin-walled, averaging a ratio of about 1/640. However nearly all interference or shrink fit applications utilize the thick-walled cylinder method^{1}.
Step 5 involved applying the mathematical models, based on the following assumptions:
Shaft
Representative size: 44.875″
Material: 1020 carbon steel
Configuration: solid (versus hollow)
Poisson ratio: 0.303
Modulus of elasticity: 29.50 X 10^{6} psi
Coefficient of thermal expansion: 7.00 x 10^{-6} in/in/^{o}F
Wear Band
Material: 301stainless steel
Configuration: ring
Poisson ratio: 0.305
Modulus of elasticity: 28.00 x 10^{6} psi
Coefficient of thermal expansion: 9.90 x 10^{-6} in/in/^{o}F
Next we needed to determine the basic factors related to interference:
Shaft diameter (D): 44.875″
Radius at interference (R = D/2): 22.4375″
Outer hub radius (r_{o}) from design: 22.465″
Band thickness (t) from design: 0.0625″
d_{r} = Interference
R = Shaft/2
E_{O} = Modulus of elasticity (wear band)
E_{i }= Modulus of elasticity (shaft)
r_{O} = Radius at seal engagement (shaft diameter/2) + 0.0625
r_{i }= Inside diameter of shaft (assumed to be zero)
n_{O} = Poisson ratio (wear band)
n_{i }= Poisson ratio (shaft)
p = 18.64 psi
Thin-walled cylinder stress was calculated as follows:
p = Pressure
D = O.D. of wear band in free state
t = Thickness of cylinder (band)
σ_{C} = 5,377 psi
Thick-walled cylinder stress was calculated as follows:
p = Pressure
r_{O }= Outer radius of wear band in free state
R = Shaft/2
σ_{C} = 28,491 psi
The thick-walled cylinder stress was higher, and therefore a more conservative approach is to use this value to determine factor of safety. Tensile testing of welded samples at room temperature yielded an ultimate strength of 88,387 psi and yield strength of 66,700 psi. Using these values, factors of safety was calculated as follows:
FS = S_{UT1 / }σ_{C} = 3.1
Equation 4: Factor of safety based on ultimate tensile strength
FS = S_{Y / }σ_{C }= 2.41
Equation 5: Factor of safety based on yield strength
Next we needed to determine at what interference slippage could incur. First, however, the amount of drag induced by a radial shaft seal had to be established. This depends upon seal design and material, and requires direct testing of radial load.
In this example we used a Garlock Klozure Model 64 in Mill-Right V material, operating on a 44.875″ shaft at 180 rpm with a torque loss of 14,940 in-lbf.
Fit pressure required based on torque was calculated as follows:
T = Torque
f = Coefficient of friction between band and shaft
W = Width of wear band
rO = Radius at seal engagement
p = 8.38 psi
Minimum required interference to avoid slippage was calculated as follows:
R = Shaft/2
Eo = Modulus of elasticity (wear band)
Ei = Modulus of elasticity (shaft)
r_{O} = Radius at seal engagement (shaft diameter/2) + 0.0625
r_{i} = Inside diameter of shaft (assumed to be zero)
n_{O} = Poisson ratio (wear band)
n _{I }= Poisson ratio (shaft)
d_{r} = 0.0222″
Factor of safety against slippage was calculated as follows:
FS = d_{r-design} / d_{r-required }= 2.25:1
Equation 8: Factor of safety against slippage
So therefore, based on the mathematical model, the various factors of safety can be compared to our stated requirement from Step 3:
Safety Factor Type |
Required FS |
Calculated FS |
Total failure (based on S_{UT}): |
3 |
3.1 |
Yield failure (based on S_{Y}): |
2 |
2.41 |
Slippage of shaft (based on d_{r}): |
1.5 – 2 |
2.25 |
Editor’s Note: We will run Part 2 of Design Analysis to Prevent Failure of Wear Bands in Rotating Equipment at a later time.
Filed Under: Rapid prototyping