Miner’s Rule

When, in addition. Act varies during the lifetime of a component, the approach adopted is to sum the damage according to Miner s Rule of cumulative damage ... 

Here is the number of cycles to fracture under the stress cycle in region i, and Nj/Nf is the fraction of the lifetime used up after N, cycles in that region. Failure occurs when the sum of the fractions is unity (eqn. (15.4)). This rule, too, is an empirical one. It is widely used in design against fatigue failure but if the component is a critical one. Miner s Rule should be checked by tests simulating service conditions. 

In some simple cases an additive approach can be successful. The service life is divided into stages, for example moderate exposure for one year, severe exposure for one month and low exposure for five years. The predicted degradation effects for the three periods can be summed and the condition of the product at the end, and hence residual lifetime, estimated. If it is assumed that degradation is proportional to the time of exposure and that the damage from different exposure conditions can be cumulatively added then the so called Miner s rule could be used ... 

Normally, alteration at this distance (approximately 900 feet) is not expected with a dike of this size. The miner s rule is that one foot of coal will be coked on each side of a dike for each foot of thickness of the dike rock. The coal beyond these limits rarely appears to be altered at all. Clegg (2) reports a very narrow zone of visible alteration in his work. 

A similar way of modifying P lmgren-Miner s rule is by adding empirical constants, e.g. rewriting PMmgren-Miner s rule as was proposed by Owen and Howe [7] ... 

Finally, the mode of application of different forms of Palmgren-Miner s rule modifications or residual strength approaches is linked also to the counting algorithm involved, see also the next chapter. 

If one plots a variable such as stress range or strain range versus number of cycles, the resulting curve will approach a limit known as the endurance limit. Below this limit, the number of cycles that a material can withstand is theoretically infinite. Above this limit, the number of cycles that a material can withstand under a variable load can be calculated from Miner s rule ... 

EN 13760 Plastic pipes for the conveyance of fluids under pressure - miner s rule -calculation method for cumulative damage. 

Calculate the cumulative usage factor U by means of a linear damage relationship known as Miner s rule. It is assumed that if i cycles would produce failure at a stress level Si then cycles at the same stress level would use up the fraction of the total life. Failure... 

The linear damage rule is used for the design of pressure vessels for fatigue evaluation. This rule was first proposed by Palmgren and further developed by Miner, and is popularly known as Miner s rule. 

The S-N diagram plots the life time of a material at constant stress amplitude and R ratio. It is, however, not possible to assert the life time, using the diagram, if the load amplitude changes. The most obvious way to determine the life time in this case is to simulate the service load history in the laboratory. Unfortunately, this is a rather involved procedure that is not feasible in most cases. It would be helpful if it were possible to estimate the life time directly from the S-N curves. One way to do this is to use Miner s rule (also known as Palmgren-Miner rule) [99] that will be explained now. The rule is rather simple and thus easy to employ, but it has some disadvantages, discussed at the end of this section. 

To use Miner s rule, a partial damage of the component is calculated for each loading step. Assume that the component is loaded with k different stress amplitudes aa,j j = 1, , A and that the number of cycles for amplitude j is rij. We can then use the S-N curve to determine the number of cycles to failure for each of the stress amplitudes, Miner s rule now assumes that... 

To summarise, it can be stated that Miner s rule is useful to provide a first approximation of the life time, but it has to be used with great care, for the calculated life time may not be a conservative estimate. 

The life time of the fixing screw of an industrial robot is to be calculated for the expected load history. In each week, the screw is loaded 10 000 times with CTa = 60 MPa, 5000 times with 100 MPa, 2000 times with 150 MPa, and 200 times with 200 MPa, always at an R ratio of 0.3. Miner s rule is to be used for the design. The S-N curve of the material is shown in figure 12.6. 

Miner s rule states that the sum of the ratios of the actual number of cycles to fail of a given fatigue loading condition to the number of cycles to fail if only that fatigue loading condition occurs is equal to 1. Equation 59.16 contains a general expression of Miner s rule. ... 

Miner s rule can be expanded and rearranged for power cycle and minicycle considerations. Equation 59.17 contains that expression. 

Solution The process for solving this problem is as follows. The experimentally obtained qualification data (presented in Table 59.4) must be mapped into number of power cycles to failure and number of minicycles to failure. These estimates assume that only power cycles occur and that only minicycles occur (that is the underlying assumption when mapping the experimental data to the end-use power cycle and minicycle conditions). After mapping the experimental data into field conditions. Miner s rule is employed to assess the number of cycles to fail based on the simultaneous occurrence of both power cycles and minicycles throughout the package lifetime. 

Miner s rule (Eq. 59.17) can now be apphed to determine the actual number of cycles to fail. It is important to note that at this stage the number of minicycles to fail if only minicycles cx ur and the actual number of power cycles to fail if only power cycles cxx ur is known. The actual number of minicycles and power cycles to fail remains unknown thus Eq. 59.17 is only one equation, whereas two unknowns still exist Npa cmctaai and N i uctmi-... 

The present design procedure (4] for fixed offshore structures of the jacket type is based upon Miner s Rule, as represented by the relationship... 

A less common use of accelerated tests is to estimate remaining lifetime. Heat ageing of two compounds and applying the time temperature superposition principle and models based on Miner s rule of cumulative material damage is described by Gillen and Cehna (41). However, Sun and co-workers (50) found that Miner s rule did not apply for fatigue of black filled NR and SBR. 

A better approach is to consider the individual time-temperature intervals of the given time-temperature profiles separately, and to use a weighted evaluation of these intervals regarding their contribution to the aging process in the component [104]. This procedure is analogous to the degradation accumulation hypothesis by Miner s rule, Eq. 1.7. 

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