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Criteria of design for progressive torsion-bar springs

Synthesis of torsion-bar springs having nonlinear-rate functions and development of a ramp function for multiple splines of a torsion bar, shaft or extended beam and fitted to a rigid hub or housing

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Abstract

The paper discusses the necessary conditions for attaining a design yielding a spring-rate function which is variable. The dynamic response is expressed in terms of velocity and displacement by means of a phase plot (integral curve). A method is presented which allows the generation of a ramp function of multiple shaft splines fitting into a serrated hub to yield the required spring-rate function of the torsion bar. It is shown that the engagement length of splines results in a change of the effective length of the elastic torsion spring. The ramp function can be generated directly from a known spring-rate function. In particular, the constant-frequency variable-mass system is considered.

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Abbreviations

A :

integrating constant

a :

moment arm (in.)

c :

damping constant (lb-sec/in.),C: damping parameter (1/sec)

C 1 :

integrating constant (lb-in.)

F :

force (lb)

g :

gravitational constant (386 in./sec2)

G :

shear modulus (psi)

I p,I i :

polar moment of inertia (in.4); mass moment of inertia (lb-in./sec2)

K, k :

springrate (lb/in., lb-in./rad)

L :

beam length (in.), connecting-rod length (in.)

L 0 :

initial beam length (in.)

M :

moment (lb-in.)

M i :

initial moment (lb-in.)

O :

origin, reference plane

r :

radius of gyration, moment arm (in.)

s :

displacement (in.)

T :

period (sec/cycle)

t :

time (sec)

W i :

initial load (lb)

x :

coordinate, displacement (in.)

x 1 :

distance (in.)

y :

dx/dt velocity (in./sec)

y 1 :

coordinate (in.)

α:

shape factor, average twist angle (rad)

γ:

shear angle (rad)

ϕ, ψ, θ:

twist angle (rad)

ω:

circular frequency (rad/sec)

Bibliography

  1. Polhemus, V.D., andKehoe, L.J., Jr., “Cadillac's Air Suspension for the Eldorado Brougham,”Trans. SAE,66,475 (1958).

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  2. Thomson, W. T., Vibration Theory and Application, 67, Prentice-Hall, Inc., N.J.

  3. Sachs, H. K., “Theoretical Study on Elastic Properties of Bellows Type Air Spring Suspension,”Developments in Mechanics, Vol. 1, 112–127, Plenum Press, New York, 1961).

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  4. Weigand, A., “Progressive Springs for Vehicles,” German, “Zur Theorie der Fahrzeugfederung, insbesondere der progressiven Federung,” Forsch. Ing. Wes.,11,309–323 (1940).

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  5. Roller, A. E., “Design and Calculation of Progressive Compression Springs,” Ind. Math. Jnl.,10,Part 1, Detroit, Mich. (1960).

  6. Stoker, T. J., Nonlinear Vibrations, Interscience Puboishers, Inc., Ch. IV, 81, New York.

  7. Sachs, H. K., “Vibration Isolation of a Quasi-linear System,” Ind. Math. Jnl. Vol. 14, Part 2 (1964), Detroit, Also: “Transmissibility of an Elastically Coupled System,” Proc. 9th Midwestern Conf. of Mechanics, to be published.

  8. See also, Repen, E., “Analysis of a Progressive Rate Rorsion Shaft Spring,” Master's Thesis, Approved, May 1966, Wayne State University, Detroit, Mich.

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Authors and Affiliations

  1. Engineering Mechanics Department, Wayne-State University, Detroit, Mich

    Herbert K. Sachs (Associate Professor)

Authors
  1. Herbert K. Sachs
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Sachs, H.K. Criteria of design for progressive torsion-bar springs. Experimental Mechanics 7, 105–109 (1967). https://doi.org/10.1007/BF02326376

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  • DOI: https://doi.org/10.1007/BF02326376

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