Abstract: Flowmeter with a pair of helical gears using an oval pitch curve as a reference rack tooth profile. The tooth height ratio of the reference rack tooth profile is ?/4. The reference rack tooth profile is an oval pitch curve of two or less leaves. The moving radius of the oval pitch curve is expressed by ?=a/(1?b cos n?), where ? is a moving radius which is a distance between the center of rotation and the oval pitch curve, “a” is a similarity factor, “b” is a degree of flatness, n (n?2) is the number of leaves, and ? is an argument. The tooth height ratio is h=a/(1?b)?g0, where g0 is a distance between poles of the oval pitch curve and pitch line, wherein g0=a cos ?0/(1?b cos n?0). Values for the similarity factor “a”, degree of flatness “b”, and distance g0 are determined so that the tooth height ratio may be ?m/4.

Abstract: A position displacement flowmeter having a pair of non-circular gears in a rolling contact on a pitch line without slippage. The positive displacement flowmeter comprises a casing and a pair of rotors provided in the casing and rotatable around its center axes. The pair of rotors, have a tooth profile curve which is an oval pitch curve itself having a trajectory of contact points on the pitch line, and they satisfy a condition of r1+r2=K=const r1 d?1=r2 d?2, and a moving radius of the oval pitch curve is given by ri=a/(1?b cos n?i) (i=1, 2), where “ri (i=1, 2)” is the moving radius that is a distance from a center of rotation to the oval pitch curve, “a” is a homothetic coefficient, “b” is a flattening, “n” is a number of lobes, and “?i (i=1, 2) is a moving angle.

Abstract: An ideal positive displacement flowmeter which has a pair of helical gears given by using oval pitch curve as reference rack tooth profile, with the tooth height ratio of the reference rack tooth profile even with a small number of teeth being set to ? m/4 which is a logical limit for the tooth height ratio of a one-point continuous contact tooth profile and which has no confinement phenomenon between tooth profiles. The positive displacement flowmeter has a pair of helical gears (1, 2) in a casing (3). The reference rack tooth profile of the pair of helical gears (1, 2) is an oval pitch curve of two or less leaves. The moving radius of the oval pitch curve is expressed by ?=a/(1?b cos n?), where ? is a moving radius which is a distance between the center of rotation and the oval pitch curve, “a” is a similarity factor, “b” is a degree of flatness, n (n?2) is the number of leaves, and ? is an argument.

Abstract: A position displacement flowmeter having a pair of non-circular gears in a rolling contact on a pitch line without slippage. The positive displacement flowmeter comprises a casing and a pair of rotors provided in the casing and rotatable around its center axes. The pair of rotors have a tooth profile curve which is an oval pitch curve itself having a trajectory of contact points on the pitch line, and they satisfy a condition of r1+r2=K=const r1 d?1=r2 d?2, and a moving radius of the oval pitch curve is given by ri=a/(1?bcosn?i) (i=1, 2), where “ri(i=1, 2)” is the moving radius that is a distance from a center of rotation to the oval pitch curve, “a” is a homothetic coefficient, “b” is a flattening, “n” is a number of lobes, and “?i(i=1, 2) is a moving angle.

Abstract: Each of two flow tubes assumes an arcuate shape consisting of a central arcuate segment and two linear segments located on opposite sides of the central arcuate segment. The inside diameter of the flow tubes and the linear distance between end points of each of the flow tubes are determined on the basis of a target pressure loss arising from passage of a fluid to be measured through a manifold and the flow tube at the maximum flow rate, a target time phase difference between sine wave outputs from vibration sensors at the maximum flow rate, and a target natural frequency of the flow tubes. The length of the linear segments is selected so as to reduce thermal stress induced from an abrupt change in the temperature of the fluid to be measured, and the shape of the flow tubes is determined so as to reduce the vertical height of the flow tubes, so long as the thermal stress is substantially constant even when the length of the linear segments is varied.

Abstract: Each of two flow tubes assumes an arcuate shape consisting of a central arcuate segment and two linear segments located on opposite sides of the central arcuate segment. The inside diameter of the flow tubes and the linear distance between end points of each of the flow tubes are determined on the basis of a target pressure loss arising from passage of a fluid to be measured through a manifold and the flow tube at the maximum flow rate, a target time phase difference between sine wave outputs from vibration sensors at the maximum flow rate, and a target natural frequency of the flow tubes. The length of the linear segments is selected so as to reduce thermal stress induced from an abrupt change in the temperature of the fluid to be measured, and the shape of the flow tubes is determined so as to reduce the vertical height of the flow tubes, so long as the thermal stress is substantially constant even when the length of the linear segments is varied.