Florian Ion PETRESCU, Relly Victoria PETRESCU, THE CAM DESIGN FOR A BETTER EFFICIENCY

Page 1

Florian PETRESCU, Relly PETRESCU

THE CAM DESIGN FOR A BETTER EFFICIENCY

Abstract: The paper presents an original method to determine the efficiency of a mechanism with cam and follower. The originality of this method consists in eliminate of the friction modulus. In this paper on analyze three types of cam mechanisms: 1.The mechanism with rotary cam and plate translated follower; 2.The mechanism with rotary cam and translated follower with roll; 3.The mechanism with rotary cam and rocking-follower with roll. In every kind of cam and follower mechanism on utilize a different method for the best efficiency design. Key Words: efficiency, power, cam, follower, roll, force, speed. 1. INTRODUCTION In this paper the authors present an original method to calculate the efficiency of the cam mechanisms. The originality consists in the eliminating of friction forces and friction coefficients. On determine just the mechanical efficiency of cam mechanism. In every kind of cam and follower mechanism on are utilizing a different method for the design with maximal efficiency. In this paper on analyze three kinds of cam and follower mechanisms. 2. DETERMINING THE MOMENTARY MECHANICAL EFFICIENCY OF THE ROTARY CAM AND PLATE TRANSLATED FOLLOWER The consumed motor force, Fc, perpendicular in A on the vector rA, is dividing in two components, [1]: 1. Fm, which represents the useful force, or the motor force reduced to the follower; 2. Fψ, which is the sliding force between the two profiles of cam and follower, (see the picture 1). Pc is the consumed power and Pu represents the useful power. The written relations are the next: Fm = Fc ⋅ sin τ (2.1)

v2 = v1 ⋅ sin τ

(2.2)

Pu = Fm ⋅ v 2 = Fc ⋅ v1 ⋅ sin 2 τ

(2.3)

Pc = Fc ⋅ v1

(2.4)

ηi =

2

Pu Fc ⋅ v1 ⋅ sin τ = = Pc Fc ⋅ v1 2

(2.5)

2

= sin τ = cos δ

sin 2 τ =

s ’2 s ’2 = 2 rA ( r0 + s ) 2 + s ’2

Fψ = Fc ⋅ cos τ v12 = v1 ⋅ cos τ 2

Pψ = Fψ ⋅ v12 = Fc ⋅ v1 ⋅ cos τ

(2.6)

F

& Fc

A rA

δ

v&2

δ

τ

s’

δ

C

v&1

v&12

D

& Fψ

B

& Fm E

s

τ

r0

O

ω

Fig. 1 Forces and speeds to the cam with plate translated follower. Determining the efficiency.

ψi =

Pψ Pc

=

Fc ⋅ v1 ⋅ cos 2 τ = Fc ⋅ v1

2

(2.10)

2

= cos τ = sin δ In the relation number (2.11) on determine the mechanical efficiency:

η = 0.5 ⋅ {1 −

(r0 + sτ M ) ⋅ s ’τ M

} τ M ⋅ [(r0 + sτ M ) 2 + s ’2τ M ]

(2.11)

3. DETERMINING THE MOMENTARY MECHANICAL EFFICIENCY OF THE ROTARY CAM AND TRANSLATED FOLLOWER WITH ROLL The written relations are the next: rB2 = e 2 + (s 0 + s) 2

(3.1)

(2.7)

rB = rB2

(3.2)

(2.8)

e cos α B ≡ sin τ = rB

(3.3)

(2.9)

sin α B ≡ cos τ =

s0 + s rB

(3.4)

DECEMBER 2006  VOLUME 1  NUMBER 2 JIDEG 33


Turn static files into dynamic content formats.

Create a flipbook
Issuu converts static files into: digital portfolios, online yearbooks, online catalogs, digital photo albums and more. Sign up and create your flipbook.