Method and system for approximating rotational speed

Abstract: A system is provided for approximating rotational speed of a oscillating rotational member such as a vehicular transmission input or output shaft (2). The system includes a rotational speed sensor (4) and a processor (6) operable to provide at an output signal (S approx. ) equal to at least one of signals (S₃, S′₃, S₅, S′₅ and S₇ S′₇) according to the number of speed measurements made by sensor (4) within a predetermined time period (T).

Description: INTRODUCTION This invention relates generally to a method and system for determining rotational speed of a rotating member such as a vehicular transmission input shaft and more particularly to a method and system for determining approximate rotational speed of a rotating member whose rotation is changing with time. US-A-3 182 503 disclose a circuitry to obtain the mean rotational speed of an anemometer. To this end the shaft of the anemometer is coupled to a device that transforms the rotation into a current being proportional to the speed. This current signal is supplied into a low pass filter in the form of an integrator. The integrator comprises a differential amplifier which is fed back to its inverted input via a parallel arrangement including a capacitor, a fixed resistor and an adjustable resistor. The time constant of this low pass filter or what is equivalent its cut off frequency depends on the value of the capacitor and the resistance of both resistors. Therefore, it is necessary to adjust the resistance for calibrating the arrangement. If the adjustment is not stable then the cut off frequency will change and as a consequence the time period which is taken into account to obtain the mean value changes also. Furthermore, this arrangement is unduly complicated if a microprocessor is used by other reasons since the mean value can be calculated by this CPU. Other examples where it is necessary to know the mean rotational speed are vehicles wherein the rotational speed, e.g. of the input shaft of the transmission is used as criteria to determine the gear shift points of an automatic or semi-automatic transmission. BACKGROUND OF THE INVENTION Automatic and semi-automatic transmissions utilizing microprocesser controllers for processing speed output signals in accordance with predetermined logic rules to issue output command signals to system activators are known in the art of which examples are disclosed in United States Patents 4,361,060; 4,595,986 and 4,648,290. Rotational speed of a rotating member however is frequently not constant and may vary with time for a variety of reasons. Such variations in rotational speed (often characterized as "loping" or "oscillations") present a real problem in determining a means or approximate speed for visual and more particularly for control purposes. Variations in speed relative time results in the problem of having to determine an approximate or mean rotational speed from a plurality of discrete rotational speed values within a predetermined time period. Although a simple arithmetic mean solution may be suitable for some purposes, a well known more accurate method for determining a mean or approximate value from an array of scattered data is the "method of least squares" which determines an estimated value of the instant value being examined according to the equation: where: The problem with this method however is that it involves complex calculations that are slow and time consuming. In many applications, a rapid and accurate approximation of a mean value must be made which is particularly true on providing approximated mean rotational speed values of a rotating shaft for controlling optimum shifting points for vehicular transmission speed change gears. In contrast to the above, the present invention establishes conditions by which the above equation is reduced to a family relatively simple linear equations for determining approximate rotational speed of a rotating member whose rotational speed may not be uniform and which can be rapidly determined by microprocessors well known to those skilled in the art. BRIEF DESCRIPTION OF THE DRAWINGS FIGURE 1 is a graph of five rotational speed measurements respectively decreasing from left to right over a predetermined time period T; FIGURE 2 is a graph of five rotational speed measurements respectively increasing from right to left over a predetermined time period T; and FIGURE 3 is a block diagram of an embodiment of the system of the invention. DESCRIPTION OF SOME PREFERRED EMBODIMENTS It is known from equation (3) on page 363 of "Computer Science; A First Course," John Wiley & Sons Inc., that: which is the equation of a line with Slope M passing through point ( x , y ) where x and y are respective mean values and x and y are actual values. It is further known from equation (4) on page 365 of the above-described reference that: which is the slope of a line passing through ( x , y ) for N number of values of x and y. Locating the origin of orthogonal axis (x, y) at ( x = o) and substituting M of equation (4) into equation (3) results in: Where N is the number of values for x and y and x = N-1 2 is the number of values on respective sides of ordinate of the orthogonal (x, y) axis resulting in: Letting N equal the number of speed measurements taken within a predetermined time period T and limiting N to odd whole integers greater than 1; and letting t n = substantially equivalent incremental time periods within time period T such that t n = t o ,t₁,t₂.....t n and (t₁-t o ) = (t₂-t₁) = (t₃-t₂)...; and substituting speed (s) for for (y) and time (t) for (x) results in the basic equation; Where N-1 2 is the even number of speed measurements on opposite sides of an orthogonal axis whose origin is located at the middle value for t n and whose ordinate is speed whose abscissa is time and for which T n has the value of zero at the origin with values of T n having opposite signs on opposite sides of the ordinate and the values of s n positive in all quadrants. This results in the equation: Application of the above equation is best illustrated by graphic examples in FIGURES 1 and 2 where, in FIGURE 1, five speed values (s o , s₁, s₂, s₃ and s₄) are respectively decreasing from left to right over time period T. Note that T₂ at the origin is assigned the value of zero and that the values for T n to the left of the ordinate (speed) are negative and to the right of the ordinate (speed) are positive and that the increments of time along the abscissa are substantially equivalent. Also note that N equals 5 which is an odd whole integer greater than 1 and that N-1 2 equals 2 which is an even integer equal to the number of speed measurements taken on opposite sides of the (speed) ordinate. FIGURE 2 is a graph of speed measurements versus time that are respectively increasing from right to left over time period T. The following pair of linear equivalents is provided by substituting the speed values s n and incremental time values t n into the basic equation with N = 5 and N-1 2 = 2 which, for FIGURE 2 results in: S (approx.) = 3s₀ +2s₁ + s₂ -s₄ 5 and, for FIGURE 1: S (approx.) = -s₀ +s₂ +2s₃ +3s₄ 5 Thus, a pair of simple linear equations are provided for approximating speed (S approx.) over a predetermined time period T. Similarly, where N = 3 and N-1 2 = 1 , it is found that the solution pairs are: S (approx.) = -s₀ + 2s₁ +5s₂ 6 and S (approx.) = 5s₀ +2s₁ - s₂ 6 Likewise, it is found when N = 7 and N-1 2 = 3, the solution pairs are: S (approx.) = -5s₀ - 2s₁ +s₂ +4s₃ +7s₄ +10s₅ +13s₆ 7 and S (approx.) = 13s₀ +10s₁ +7s₂ +4s₃ +s₄ -2s₅ -5s₆ 7 The above linear equations enable rapid calculations by a microprocessor which is extremely advantageous for control purposes such as hereinafter described with respect to FIGURE 3. In FIGURE 3, a system is provided for approximating rotational speed of a rotating shaft 2 such as an input shaft of a vehicular transmission. The system includes a speed sensor 4 and processor 6. Speed sensor 4 may be any type of sensor able to sense and transmit a signal 5 of rotational speed values (s o , s₁, s₂, s₃.....s n ) of shaft 2 within a predetermined time period T which may be in the order of micro-seconds. Hall-Effect magnetic sensors are but one way to measure rotational speed known to those skilled in the art. Signal 5 is received by processor 6 which is of the type well known to those skilled in the art operable to receive signal 5 and select certain values therefrom and perform the simple linear arithmetic calculations shown in FIGURE 3. Thus, for example, where speed measurements (s o , s₁ and s₂) are selected, they are processed according to the equation: S (approx.) = -s₀ + 2s₁ +5s₂ 6 to provide output signal s₃ therefrom. Although processor 6 is shown in FIGURE 3 as being capable of performing six calculations, such as for illustrative purposes for it may process and provide only one or any combination of output signals s₃, s₃′, s₅, s₅′, s₇ and s₇′ which may be utilized as signal for controlling shifting of vehicular transmission being driven by shaft 2. Although processor 6 is shown in FIGURE 3 as selecting certain speed values, such may be done by speed sensor 4 by selecting and transmitting only those rotational speed values for which processor 6 is adapted to make the particular linear calculations hereinbefore set forth.

Claims: A linear method for determining the approximate mean rotational speed of a rotating member, said method including the steps of: (a) determining an equation by selecting a value for the parameter N in where N is an odd whole number greater than one and equals the number of speed measurements taken within a predetermined time period T; s n are the individual speed measurements having positive sign and being taken within a time period T at equidistant times wherein s o is taken at the beginning of the time period T and s N-1 is taken at the end of time period T; (b) measuring rotational speed values s n of the rotating member as defined in step (a) and providing signals indicative thereof; and (c) determining S (approx.) by processing the speed signals of step (b) according to the equation selected at step (a). The method of claim 1 including the step of providing a signal corresponding to the value for S (approx.) determined in step (c). The method of claim 1 wherein N = 3 and N-1 2 = 1 and S (approx.) = -s₀ + 2s₁ +5s₂ 6 The method of claim 1 wherein N = 3 and N-1 2 = 1 and S (approx.) = 5s₀ +2s₁ - s₂ 6 The method of claim 1 wherein N = 5 and N-1 2 = 2 and S (approx.) = 3s₀ +2s₁ + s₂ -s₄ 5 The method of claim 1 wherein N = 5 and N-1 2 = 2 and S (approx.) = -s₀ +s₂ +2s₃ +3s₄ 5 The method of claim 1 wherein N = 7 and N-1 2 = 3 and S (approx.) = -5s₀ -2s₁ +s₂ +4s₃+7s₄ +10s₅ +13s₆ 7 The method of claim 1 wherein N = 7 and N-1 2 = 3 and S (approx.) = 13s₀ +10s₁ +7s₂ +4s₃ +s₄ -2s₅ -5s₆ 7 The method of claims 1 wherein the member is a vehicular shaft. The method of claim 1 wherein the shaft is a transmission input shaft. The method of claims 2 wherein the signal is a control signal utilized by a vehicular transmission. A system for determining approximate rotational speed of a rotating member, said system comprising; speed sensing means, said means operative to measure and provide a signal indicative of the rotational speed of the rotating member, means for selecting three values s o , s₁, s₂ of the speed signal at substantially equidistant times within a predetermined time period, and means for processing the selected speed values to determine the approximate rotational speed S (approx.) according to one of the equations: s₀ +2s₁ - 5s₂ 6 = S (approx.) and 5s₀ +2s₁ - s₂ 6 = S (approx.) A system for determining approximate rotational speed of a rotating member, said system comprising; speed sensing means, said means operative to measure and provide a signal indicative of the rotational speed of the rotating member, means for selecting five values s₀,s₁,s₂,s₃,s₄ of the speed signal at substantially equidistant times within a predetermined time period, and means for processing the selected speed values to determine approximate rotational speed S (approx.) according to one of the equations: S (approx.) = 3s₀ +2s₁ +s₂ -s₄ 5 and S (approx.) = -s₀ +s₂ +2s₃ +3s₄ 5 A system for determining approximate rotational speed of a rotating member, said system comprising: speed sensing means, said means operative to measure and provide a signal indicative of the rotational speed of the rotating member, means for selecting seven values s o , s₁, s₂, s₃, s₄, s₅, s₆ of the speed signal at subtantially equidistant times within a predetermined time period, and means for processing the selected speed values to determine the approximate rotational speed S (approx.) according to one of the equations: S (approx.) = -5s₀ -2s₁ +s₂ +4s₃ +7s₄ + 10s₅ + 13s₆ 7 S (approx.) = 13s₀ +10s₁ +7s₂ +4s₃ +s₄ -2s₅ - 5s₆ 7 The system of claims 12, 13 or 14, including means for providing a signal indicative of S (approx.) . The system of claims 12, 13 or 14 wherein the member is a vehicular shaft. The system of claim 16 wherein the shaft is a transmission input shaft. The system of claim 15 wherein the signal is a control signal utilized by a vehicular transmission.

Inventors: GOLD GARY LEE, GOLD, GARY LEE
Applicants: EATON CORP, EATON CORPORATION
Application year: 1989
Main classification: G01P11
IPC codes: G01P3, G01P11