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Thursday, March 16, 2017

TECHSHORE INSPECTION SERVICES :The working of Slider-crank mechanism

Slider-crank mechanism, mechanical parts are arranged and designed to convert straight-line motion to rotary motion, same as in a reciprocating piston engine, or to convert rotary motion to straight-line motion, as in a reciprocating piston pump. The nature of the mechanshaft, or a separate disk or arm attached to it. Attached to the end of the crank by a pivot is a rod, usually referred a connecting rod . The end of the rod attached to the crank moves in a circulatory motion, while the other end is usually constrained to move in a sliding motion.

ism and the relative motion of the parts can best be described with the aid of the accompanying diagram. The arm may be a bent portion of the

The term often refers to a human-powered crank which is used to manually turn down the axle, as in a bicycle crank set . In this case a person's arm or leg plays as the connecting rod, applying reciprocating force to the crank. There is usually a bar is attached perpendicular to the other end of the arm, often with a rotatable handle or pedal attached.

Using the right angled triangles formed at the dead centre positions:

Noting s =se-sf =stroke = the slider distance travels between dead-centres. If we let l= a2/a3 and e = c/a3 , the stroke will be given by:

If the eccentricity, c (or a1), is zero ( c = 0) then the slider crank mechanism is called an in-line slider-crank and the stroke is twice the crank length (s = 2a₂). If the eccentricity is not zero ( c ¹0), it is usually known an offset slider-crank mechanism.

The transmission angle can be determined from the equation:

a₃cosµ=a₂sinθ₁₂-c (1)

Maximum deviation of the transmission angle occurs when the derivative of m with respect to q ₁₂ is zero. Hence differentiating equation (1) with respect to q ₁₂ :

(2)

Maximum or minimum deviation occurs when q ₁₂ is 90⁰ or 270⁰ (Fig. 7.19 ) and the value of the minimum or maximum transmission angle is given by:

(3)

If c is positive as given below, transmission angle is critical when q ₁₂ =270⁰. If c is negative, then the most critical transmission angle is a

q ₁₂ =90⁰ .

If the eccentricity, c, is zero, maximum value of the transmission angle is:

(4)

In reciprocating pumps, the crank-to-connecting rod ratio is kept less than 1/4, which corresponds to 14.48⁰ maximum deviation of the transmission angle from 90⁰. Since the crank length is fixed by the required stroke (a₂ = s/2) one must increase the connecting-rod length for better transmission angles. However, the size of the mechanism will be increased.

Similar to the transmission angle problem in the four-bar mechanisms, the transmission angle problem in slider-crank mechanisms can be mentioned as follows:

"Determine the slider-crank proportions with a given stroke, s, and corresponding crank rotation between dead-centers, f, such that the maximum deviation of the transmission angle from 90⁰ is a minimum.”

The problem can again be considered in two parts. The first part is the determination of slider crank mechanisms with a given stroke and corresponding crank rotation. The second part will be the determination of one particular slider-crank mechanism with maximum transmission angle variation.

For the first part of the problem says that the stroke s is a function of the ratio of link length, i.e. if we double the length of the links, the stroke will be doubled. Therefore without loss of generality, let s=1 (the link lengths thus found should be multiplied by the stroke to give the exact values values).

Referring to the figure where the slider crank mechanism is drawn at its dead centers, the vector loop equations at the dead centers are shown below:

(5)

(6)

in complex numbers:

(7)

(8)

Subtracting eq.(8) from eq. (7) and noting s_e-s_f = s = 1 :

(9)

If we let Z =

and l = a2/a3 equation (8) can be rewrite as

(10)

For a full rotation of the crank a necessary (but not sufficient) condition is l<1. Equation 10 can be solved for Z to yield:

(11)

If l is taken as a free parameter, as it varies, the tip of Z at (7), will generate a circle which is the locus of all possible moving pivots for the crank when the crank and the coupler are at extended position (k_a circle). The locus of all possible fixed pivots is another circle (k₀ circle) which is given by Z(1+l) (the origin for both vectors is B_e with the real axis parallel to the slider axis).. Any line drawn from B_e intersects these circles at A_e and A₀Respectively, yielding the slider-crank mechanism in extended dead centre position. Below these circles are shown for f=160⁰.