Design of crankshaft

DESIGN OF CRANKSHAFT:

The crankshaft is the most complicated and strained engine part subjected to cyclic loads due to gas pressure, inertial forces and their couples. The effect of these forces and their moments cause considerable stresses of torsion, bending and tension-compression in the crankshaft material. Apart of this, periodically varying moments cause torsional vibration with the shaft with the resultant additional torsional stresses.
Therefore, for the most complicated and severe operating conditions of crankshaft, high and diverse requirements are imposed on materials utilized for fabrication of the crankshaft. The crankshaft material has to feature high strength and toughness, high resistance to wear and fatigue stresses, resistance to impact loads and hardness. Such properties are possessed by properly machined carbon and alloy steels and also high duty cast iron. Crankshafts of the soviet made automobile and tractor engines are made up of steels 40, 45, 45T2, 50, of a special cast iron, and those for augmented engines, of high alloy steels, grades 18XHBA, 40XHMA and others.
The intricate shape of the crankshaft, a variety of forces and moments loading it, changes in which are dependant on the rigidity of the crankshaft and its bearings, and some other causes do not allow the crankshaft strength to be compute precisely. In view of this various approximate methods are used which allow us to obtain conventional stresses and safety factors for individual elements of a crankshaft. The most popular design diagram of the crankshaft is a diagram of a simply supported beam with one and two spans between the supporters (FIGURE 13.1).
When designing a crankshaft, we assume that:
A crank (or two cranks) is freely supported by supporters;
The supporters and the force points are in the center planes of the crankpins and journals;
The entire span (one or two) between the supports represents an ideally rigid beam.
The crankshaft is generally designed for the nominal operation (n=nN), taking into account the action of the following forces and moments,

1) Kp,th = K + KR = K + KR c.r + KR c are the forces acting on the crankshaft throw by the crank, neglecting counterweights. where K=p cos(+) / cos is the total force directed along the crank radius; KR= - mRRω2 is the inertial force of rotating masses; KR c.r = -mc.r.cR ω2 is the inertial force of the rotating mass of the connecting rod; KRc = - mcRω2 is the inertial force of the rotating mass of the crank;

2) ZE = Kp,th +2Pcw and the total force acting on the crank plane, where
Pcw = + mcwrω2 is the centrifugal inertial force of the counterweight located on the web extension;

3) T is the tangential force acting perpendicular to the crank plane;
4) ZCE= K’p,th +2P’cw are the support reactions to the total forces acting on the crank plane,
where K’p,th = -0.5 Kp,th and Pcw = - 2P’cw ;

5) T`=-0.5T are the support reactions to the tangential plane perpendicular to the crank;

6) Mm.j.i is the accumulated (running on) torque transmitted to the design throw from the crankshaft nose;

7) Mt.c = TR is the torque produced by the tangential force;

8) Mm.j.(i+1) = Mm.j.i + Mt.c is the diminishing (running off) torque transmitted by the design throw to the next throw.

The basic relations of the crankshaft elements needed for checking are given in the table 13.1

Engines l/B dc.p/B Lc.p/B* dm.j/B lm.j/B**

Diesel engines In-line
1.25-1.30
0.64-0.75
0.7-1.0
0.70-0.90
0.45-0.60
0.75-0.85
[*B(D) is the engine cylinder bore diameter; lc.p is the full length of the crankpin including fillets.
** The data are for the intermediate and outer (or center) main journals.]

The dimensions of the crankpins and journals are chosen, bearing in mind the required shaft strength and rigidity and permissible values of unit area pressures exerted on the bearings. Reducing the length of crankpins and journals and increasing their diameter add to the crankshaft rigidity and decreases the overall dimensions and weight of the engine. Crankpin-and-journal overlapping (dm.j + dc.p > 2R) also adds to the rigidity of the crankshaft and strength of the webs.
In order to avoid heavy concentration of stresses, the crankshaft fillet radius should not be less than 2 to 3 mm. In practical design it is taken from 0.035 to 0.080 of the journal of cranking diameter, respectively. Maximum stress concentration occur when the fillet of the crankpins and journals are in one plane.

According to the statistical data, the web width of crank shaft in automobile and tractor engines varies within (1.0 to 1.25) B for carburetor engines and (1.05 to 1.30) B for diesel engines, while the web thickness, within (0.20 to 0.22) B and (0.24 to 0.27) B, respectively.

UNIT AREA PRESSURE ON CRANKPINS AND JOURNALS:
The value of unit area pressure on the working surface of a crankpin or a main journal determines the conditions under which the bearing operates and its service life in the long run. With the bearings in operations measures are taken to prevent the lubricating oil film from being squeezed out, damage to the whitemetal and premature wear of the crankshaft journals and crankpins is made on the basis of the action of average and maximum resultants of all forces loading the crankpins and journals.
The maximum (Rm.j max and Rc.p max) and mean (Rm.j.m and Rc.p.m) values of resulting forces are determined from the developed diagrams of the loads on the crankpins and journals.

The mean unit area pressure (in Mpa) is:
On the crankpin
Kc.p.m = Rc.p.m / (dc.p l’c.p)

On the main journal
Km.j.m = Rm.j.m / (dm.j l’m.j) or
Km.j.m = Rcw m.j.m / (dm.j l’m.j)

Where Rc.p.m and Rm.j.m are the resultant forces acting on the crankpin and journal, respectively, MN; Rcw m.j.m is the resultant force acting on the main journal when the use is made of counterweights, MN; dc.p and dm.j are the diameters of the crankpin and main journal, respectively, m; l’c.p and l’m.j are the working width of the crankpin and the main journal shells, respectively, m.
The value of the mean unit area pressure attains the following values:

Diesel engines………………..6-16 Mpa

The maximum pressure on the crankpins and journals is determined by the similar formulae due to the action of the maximum resultant forces Rc.p max, Rm.j max or Rcwm.j max. The values of maximum unit area pressures on crankpins and journals Kmax (in MPa) vary within the following limits:

Diesel engine………………….20-42

DESIGN OF JOURNALS AND CRANKPINS:
DESIGN OF MAIN JOURNALS:
The main bearing journals are computed only for torsion. The maximum and minimum twisting moments are determined by plotting diagrams (Fig.13.4) or compiling tables (table 13.2) of accumulated moments reaching in sequence individual journals to compile such table use is made of dynamic analysis data.



 Mm.j2 Mm.j3 Mm.j,i. Mm.j.(i+1)
0
10 ( or 30)
And so on
Table 13.2
The order of determining accumulated (running-on) moments for inline engines which shown in Fig.13.2a.
The running-on moments and torques of individual cylinder are algebraically summed up following the engine firing order starting with first cylinder.
The maximum and minimum tangential stresses (in MPa) of the journal alternating cycle are:
max = Mm.j,I max / Wm j (13.3)
min = Mm.j,I min / Wm. j (13.4)

Where Wm. j = (  / 16) x d3m.j [ 1-(m.j / dm.j ) 4 ] is the journal moment resisting to torsion, m3 ; dm.j and m.j are the journal outer and inner diameter respectively.
With max and min known, we determine the safety factor of the main bearing journal. An effective factor of stress concentration for the design is taken with allowance for an oil hole in the main journal. For rough computation we may assume K / (s ss ) = 2.5.
The safety factors of main bearing journals have the following values:
Unsupercharged diesel engine…………………...4-5
Supercharged diesel engine………………………2-4.

Design of crankpin:
Crankpins are computed to determine their bending and torsion stresses. Torsion of a crankpin occurs under the effect of a running-on moment Mc.p,i . Its bending is caused by bending moments acting in the crank plane Mz and in the perpendicular plane MT. Since the maximum values of twisting and bending moments do not coincide in time, the crankpin safety factors to meet twisting and bending stresses are determined separately and then added together to define the total safety margin.
The twisting moment acting on the ith crankpin is:
For one span crankshaft (see fig. 13.1 a and b)
Mc.p,i = Mm.j,i –T’iR

For two span crankshaft (see fig.13.1 c and d)
Mc.p,i = Mm.j,i – T’iR

To determine the most loaded crankpin, a diagram is plotted (see fig. 13.5) or a table is compiled (Table 13.3) showing accumulated moments for each crankpin.
The associated values of Mm.j,i are transferred into Table 13.3 from Table 13.2 covering accumulated moments, while values of T’i or T’i are determined against Table 9.6 or 9.15 involved in the dynamic analysis.
The values of maximum Mc.p,i max and minimum Mc.p,i min twisting moments for the most loaded crankpin are determined from data of Table 13.3. The extreme of the cycle tangential stresses (in Mpa) are:

° 1st crank-
pin 2nd crankpin ith crankpin
Mc.p1=
-T’1R Mm.j2 T’2R Mc.p2 =
= Mm.j2-T’2R Mm.j,i T’iR Mc.p,i=
=Mm.j,i- T’iR
0
30
and so
on
Table 13.3

max = Mc.p,i max / W c.p (13.5)
min = Mc.p,i min / W c.p (13.6)

Where W c.p =( /16 ) * d3c.p [1-(c.p /dc.p )4] is the moment resisting to crankpin torsion, m3; dc.p and c.p are the outer and inner diameters of the crankpin , respectively, m.
The safety factor  is determined in the same way as in the case of the main journal, bearing in the mind the presence of stress concentration due to an oil hole.
Crankpin bending moments are usually determined by a table method (Table 13.4).

° T’ MT MT sino K’p, th Z’ Z’ l/2 Mz Mz coso Mo
0
30
and so
on
Table 13.4

The bending moment (Nm) acting on the crankpin in a plane perpendicular to the crank plane
MT = T’ l/2 (13.7)

Where l=(lm.j +lc.p +2h) is the center to center distance of the main journals, m.
The bending moment (Nm) acting on the crankpin in the crank plane

Mz= Z’ l/2 +pcwa (13.8)

Where a = 0.5(lc.p +h), m; Z’ = k’p.th + p’ cw, Pa.

The values of T’ and k’p.th are determined against Table 9.6 of the dynamic analysis and entered in Table 13.4.
The total bending moment
Mb=( M2T +M2Z) (13.9)
Since the most severe stresses in a crankpin occur at the lip of oil hole, the general practice is to determine the bending moment acting in the oil hole axis plane:
Mo= MT sino - Mz coso (13.10)
Where o is the angle between the axes of the crank and oil-hole usually located in the center of the least loaded surface of the crankpin. Angle o is usually determined against wear diagrams.
Positive moment Mo generally causes compression at the lip of an oil hole. Tension is caused in this case by negative moment Mo.
The maximum and minimum values of Mo are determined against Table 13.4

DESIGN OF CRANKWEBS:

The crankshaft webs are loaded by complex alternating stresses:
Tangential due to torsion and normal due to bending and push-pull. Maximum stresses occur where the crankpin fillet joins a crankweb (section A-A, fig 13.1b).
Tangential torsion stresses are caused by twisting moment

Mt.w= T’.0.5( lm.j+h) (13.14)

The values of T’max and T’min are determined in Table 13.4. The maximum and minimum tangential stresses are determined by the formulae:

max = M t.w max / W w
min = Mt.w min / Wc w (13.15)

Where W t.w = bh2 is the moment resisting to twisting the rectangular section of the web. The value of factor  is chosen, depending on the ratio of width b of the web design section to its thickness h;

b / h 1 1.5 1.75 2.0 2.5 3.0 4.0 5.0 10.0 
 0.208 0.231 0.239 0.246 0.258 0.267 0.282 0.292 0.312 0.333

The torsion safety factor n of the web and factors k , s and ss are determined by the formulae given.
Normal bending and push-pull stresses are caused by bending moment Mb.w, Nm (neglecting the bending causing minute stresses in a plane perpendicular to the crank plane) and push or pull force pw, N:

Mbw=0.25(K+KR+2Pcw) lm.j (13.16)
pw=0.5(K+KR) (13.17)

Extreme values of K are determined from the dynamic analysis table (KR and Pcw are constant), and maximum and minimum normal stresses are determined by the equations
max = mb.w max / Ww + Pw max / Fw (13.18)

min = mb.w min / Ww + Pw min / Fw (13.19)

Where Ww = bh2 / 6 is the moment of web resistance to the bending effect; Fw= bh is the area f design section A-A of the web.

For web factor of safety is:

Automobile engines ………………………………... not less than 2.0 - 3.0