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Homework11bsol.fall11

# Homework11bsol.fall11 - ME 352 Machine Design I Fall...

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ME 352 - Machine Design I Name of Student_______________________________ Fall Semester 2011 Lab Section Number____________________________ Homework No. 11 (60 points). Due at the beginning of lab on Monday, December 5th, or Tuesday, December 6th. The student can work on this homework in lab the weeks of November 21st and 28th. Consider the five-cylinder in-line engine shown in Figures 1a and 1b. Figure 1a is a side view of the engine and Figure 1b is a front view of the engine. The properties of the engine and the geometry of the engine layout are included in the table on page 2. A discussion of balancing multi-cylinder engines is presented in Chapter 17, see Sections 17.10 and 17.11, pages 802-812. Figure 1a. Side view of the five-cylinder in-line engine.

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2 Figure 1b. Front view of the five-cylinder in-line engine. The geometry of the engine layout and the mass properties of the engine are presented in the table below where the angle i ψ is the angle between the X-axis and the line of sliding of piston i , and the angle i φ is the angle from the reference line attached to crank 1 to crank i (by definition 1 0). = Piston i crank length, R i con rod length, L i effective mass, m i angle φ i angle ψ i 1 4 cm 10 cm 3 kg 90° 2 5 cm 12 cm 4 kg 120° 90° 3 6 cm 12 cm 5 kg 240° 90° 4 5 cm 12 cm 4 kg 120° 90° 5 4 cm 10 cm 3 kg 90°
3 If the crankshaft is rotating counterclockwise with a constant angular velocity ωθ 300 rad/s, == ± and correcting mass(es) must be added in the planes of the bearings at A and B at a radius of 10 cm to balance the primary shaking forces and a radius of 5 cm to balance the secondary shaking forces, then determine numerical values for (i) The shaking moments about the correcting plane A (at bearing A) caused by the primary and the secondary shaking forces. (ii) The shaking moments about the correcting plane B (at bearing B) caused by the primary and the secondary shaking forces. (iii) The magnitude and location of the correcting mass(es) in each correcting plane in order to balance the shaking moment due to the primary shaking forces. (iv) The magnitude and location of the correcting mass(es) in each correcting plane in order to balance the shaking moment due to the secondary shaking forces. Show all your correcting masses clearly on figures of the engine.

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4 Solution. The X and Y components of the resultant of the primary shaking forces (or the first harmonic forces) for a multi-cylinder reciprocating engine (see page 806) can be written in the form Acos Bsin = + PX S θ (1a) and Ccos Dsin = + PY S (1b) where 1 Ac o s ( ) c o s = =− n ii i P ψ φψ (2a) 1 Bs i n ( ) c o s = n i i i P (2b) 1 Cc o s ( ) s i n = n i P (2c) and 1 Ds i n ( ) s i n = n i P (2d) Equations (1) are zero if the coefficients A0 , = B0 , = C0 , = and D0 . = However, if the coefficients A, B, C, and D are not all zero then the primary shaking force must be balanced by a pair of rotating masses, or in some special cases a single mass, as shown in Figure 17.28, page 807. The correcting mass m 1 creates a correcting (or inertial) force F 1 at a location angle of 1 () γ + from the X-axis, and the correcting mass m 2 creates a correcting (or inertial) force F 2
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Homework11bsol.fall11 - ME 352 Machine Design I Fall...

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