# Finite Element Analysis Report for Drying Raw Mill new

Finite Element Analysis Report for Drying Raw Mill 1. Introduction
The main components and dimensions of the mill CBMI designed are shown in figure 1. The main shell is a cylindrical vessel with 4.6m inside diameter by 15.1 m long and divided into four chambers by three diaphragms. One manhole is in chamber I and the other manhole is in chamber Ⅳ.The two holes are 180 apart. The driving tube is a cylindrical shell with 1.8 m inside diameter by about 2.832 m long, perforated by 6 holes. The main shell and driving tube are jointed by bolts which are simulated by constraint equation, which means taking the driving tube and shell as a whole. The mill is supported by four 0.6 m wide bearing pads at each end. The shell in contact with bearing pads are thicken to 100 mm and axially driven at outlet end flange with a normal operating power of 3000 kw at 15 rpm. All other dimensions are referred to relevant engineering drawings. Figure 2 shows the local magnifying of the
manhole 1. Figure3 shows local magnifying of the hole of discharged chamber 3.

Figure1.

FE model showing main components and dimensions

1

Figure2.

local magnifying of the manhole 1

Figure3.

local magnifying of the hole of discharged chamber 3

2. Boundary conditions
3-Dstructure element and quadratic shell element are used to model the mill.

2.1 Driving torque and offset load
A driving torque T= 1910000 N.m which corresponds to about 3000 kw at 15rpm is applied by circumferential forces on end flange. A load of 200736.3 kg internal balls and material is applied as additional mass on bottom part of main shell and offset to the left as illustrated in figure 4. The angular positions of A and B are approximately -1800 and -600 respectively, found by trial and error so as to counterbalance the applied additional mass.

Figure 4.

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Figure 5 Model of 8 support pads

2.2 Liner masses
7559 kg for head liner at inlet end, 7942kg for head liner at outlet end,14782.56 kg for shell liner in chamber I, 38088 kg for shell liner in chamberⅡ ,10760 kg for shell liner in chamber Ⅲ, 22954 kg for shell liner in chamber Ⅳ are applied as additional distributed mass of corresponding components (head plates and main shell).

2.3 Diaphragm
16402 kg weight for diaphragm between chamber I and Ⅱ, 8201 kg weight for the two diaphragms respectively in discharged chamber Ⅲ , all the weights are applied as distributed mass of an annular plate using very small Young's modulus so that the diaphragm does not contribute to the stiffness of the shell.

2.4 Driving tube and shell masses
12399 kg for driving tube(See drawing NO.BMRaCD46.3.7), 122683 kg for shell (See drawing NO. BMRaCD4685/35.3.4), all of the weights will be calculated by defining dense of the material through ANSYS system, and ultimately applied to the model.

2.5 Support
The contact model is introduced to simulate the frictionless contact between shell rings and the 200 mm thick support pads. Radial reactions illustrate in figure 5. Totally, 12 models are studied, each one for every hour position in according to the position of pads, and only important and critical results are reported below.

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3. Result analysis
3.1 Results for forces and stresses on pads
As illustrated in figure 5 and through contact model simulation, F1 =551380，

F2 =592676, F3 =666763N， F4 =964697N， F5 =581772N， F6 =557564N， F7 =581077N， F8 =948661N, finally the vertical reaction totally equals to 4697300 N (about 479.36
tons). With 0.2 m thick plates for pads, the maximum Von Mises stress is 7.57MPa (figure 6). For any other thickness of pads, by function ?Vonmises = 7.57 ? (0.2 / t )2 in MPa and t in meter, based on the fact that bending stress in plates is inversely proportional to the square of its thickness ( ?Vonmises = 6M / t 2 ). Using the yield strength 185 MPa of the pads material and safety factor 2, the function gives the thickness of pads is 57 mm.

Figure 6 The maximum Von Mises stress in pads

Pads have a safety factor greater than 2 while they are stronger than 57 mm thick plate.

3.2 Maximum stress in driving tube
As illustrated in figure7, "The Von Mises stress distribution of driving tube" shows the maximum Von Mises stress is 17.6 MPa. Considering the startup torque 2.5 times greater, then the safety factor against yield is 200/17.6/2.5=4.54 . Figure8 shows satisfactory
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the maximum Von Mises stress of driving tube hole, which is 4.17 MPa, much smaller than the material breakage limit.

Figure 7 The Von Mises stress distribution of driving tube

Figure 8 The Von Mises stress distribution of driving tube hole

3.3 stress analysis of manholes
3.3.1 Von Mises stress around manhole For manhole 1, the maximum static Von Mises stress is 66.7MPa at 4h position(see Fig9); for manhole 2, the maximum static Von Mises stress is79.4MPa at 4h position(see Fig10); the safety factor with respect to yield is f＝250/79.4＝3.15
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satisfactory

Fig 9 Maximum Von Mises Stress around manhole 1

Fig 10 Maximum Von Mises Stress around manhole 2

3.3.2 Fatigue stress around manhole For manhole 1, the worst principal stress range occurs on the edge of shell between ? max at 4h= 68.4 Mpa and ? min at 7h= -12.9Mpa(Fig11-12). Thus, stress range= 68.4-(12.9)=81.3Mpa. Safety factor with respect to allowable infinite life category A stress according to AISC: f=165(Mpa)/(81.3Mpa)=2.02。
satisfactory

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Fig11

Max. principal stress on manhole 1

Fig12 Min. principal stress on manhole 1

For manhole 2, the worst principal stress range occurs on the edge of shell between ?
max at 10h=

82.1Mpa and ?

min at 2h=

-19.7Mpa (Fig13-14). Thus, stress
satisfactory

range=82.1-(19.7)=101.8Mpa. Safety factor with respect to allowable infinite life category A stress according to AISC: f=165(Mpa)/(101.8Mpa)=1.62。

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Fig13 Max. principal stress on manhole 2

Fig14 Min. principal stress on manhole 2

3.4 Fatigue stress around discharged hole
For the symmetrical characteristics of the hole in the discharged part, this report just studies one hole with the same position of manhole 1 of every hour position. For the discharged hole, the worst principal stress range occurs on the edge of inside shell between ? max at 4h= 45.5 Mpa and ? min at 10h= -14.7Mpa(Fig15-16). Thus, stress range ? ? =45.5-（-14.7）=60.2Mpa.Safety factor with respect to allowable infinite life category A stress according to AISC: f =(165Mpa)/(60.2Mpa)=2.74
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Satisfactory

Fig15

Max. principal stress on discharged hole

Fig16 Min. principal stress on discharged hole

3.5 Fatigue stress of “T” shape butt joint
For the symmetrical characteristics of slider ring, take one side of the “T” shape butt joint in the position of inlet end for example. The worst principal stress range occurs on the edge of shell between ?
max at 1h=

2.35 Mpa and ?

min at 3h=

-9.5Mpa(Fig17-18). Thus, stress range ? ? =2.35-（-9.5）=11.85Mpa. Safety factor with respect to allowable infinite life category A stress according to AISC:

f =(165Mpa)/(11.85Mpa)=13.92

Satisfactory
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Fig17 Max. principal stress of “T” shape butt joint

Fig18 Min. principal stress of “T” shape butt joint

4 General conlusions
1.The safety factor with respect to yield of manholes and main shell＝3.15 which meet the strength requirement. 2. For manhole 1, fatigue stress range =81.3Mpa, safety factor=2.02; for manhole2, fatigue stress range =101.8Mpa, safety factor=1.62; for discharged hole, fatigue stress range =60.2Mpa, safety factor=2.74. For “T” shape butt joint, fatigue
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stress range =11.85Mpa, safety factor=13.92. The fatigue strength of manholes meet design requirement. 3. The maximum stress on driving tube =17.6 Mpa, considering the startup torque 2.5 times greater, safety factor= 4.54，which are safe enough. 4. The maximum Von Mises stress of bearing pads = 7.57Mpa. The maximum Von
Mises stress of the contact surface of slider ring =10.0Mpa.

In a word , the design of mill meets static and fatigue requirement.

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