Theory and Application of Alternative Scroll Geometries

This paper describes the geometric properties required to form the walls of a functional scroll compressor, and a practical design procedure that has been used at the University of Maryland to generate more general scroll geometries and model their performance. It presents several examples of this technique, showing how it can be used to meet practical design challenges, optimize operating parameters, and design scrolls of different configurations, such as sloped and tapering walls, reduced turns, fitted shapes, and through drive shafts. SCROLL GEOMETRY THEORY The walls of typical scroll compressors are formed as the involute of a circle, that is, the curve traced by a point on a taut string as it unwraps from a circle; see Figure 1. The (x,y) location vector of a wall of the fixed scroll is given by [ -re sint+(ret+s0 )cost] X (t) = f re cost+(ret+so)sint where re is the radius of the circle, s 0 is the string length when horizontal, and t is a parameter. The location vector x"' (t) of the wall of the moving scroll in centered position is given by a similar expression with a different s 0 , as are the other sides of the walls. The circle is known as the base curve or evolute. Other base curves are possible; line segments and squares have been considered [7]. Involute designs have several advantages: Figure 1. Involutes of a circle simple formulation, uniform wall thickness, minimal coupling torque, and small separation force. However, there are limitations. The circle involutes cannot extend inside the base curve, so some other method must be used to complete the design of the inner tips. The shape is fixed once the base curve is specified, so there is no provision for adjusting the profile to achieve other design goals. More general shapes than involutes are possible for a scroll, and have been mentioned under the term conjugate surface generation [2, 3, 4], in which one scroll is determined from the other. This paper discusses an alternate approach in which both scrolls are determined from the same curve, allowing a formulation that is general, simple, symmetrical, and has features convenient for design engineering. Fifteenth International Compressor Engineering Conference at Purdue University, West Lafayette, IN, USAJuly 25-28, 2000 699 The most general shape for a functional scroll must satisfy a simple geometric requirement: the scroll walls must form equidistant, or parallel, curves when the orbiting scroll is translated to the center of its orbit; see Figure 2. If ro denotes the constant distance between the curves, a displacement of the orbiting scroll by r 0 in any direction will then cause contact at all the points with normals along the direction of displacement. If the walls are formed as multi-