Gradient determination for measuring rotational speeds

Abstract

An assembly has a rotating element, a sensor, and an evaluation unit; wherein the element has a number a of markings; wherein the markings pass through a region detected by the sensor in cycles when the element rotates; wherein the sensor is configured to send a signal to the evaluation unit; and wherein the evaluation unit is configured to assign a time t.sub.i for when each signal is sent, wherein the evaluation unit is configured to calculate a function m(t) over time t as a measure for a gradient of the rotational rate of the element.

Claims

1. An assembly comprising: a rotating element; a sensor; and an evaluation unit; wherein the element has a number a of markings; wherein the markings pass through a region detected by the sensor in cycles when the element rotates; wherein the sensor is configured to send a signal to the evaluation unit; and wherein the evaluation unit is configured to: assign a time t.sub.i to when each signal is sent, where i∈{0, 1, . . . } and t.sub.i<t.sub.i+1 for all i∈{0, 1, . . . }, and calculate a function n(t) over time t as a measure for a rotational rate of the element, where $n\left(t_i\right)=\frac{1}{a*\left(t_i-t_{i-1}\right)}$ for all i∈{1, 2, . . . }; calculate a function m(t) over time t as a measure for a gradient of the rotational rate of the element, where $m\left(t_j\right)=\frac{n\left(t_j\right)-n\left(t_k\right)}{t_j-t_k}$ for at least one j∈{1, 2, . . . }, wherein k∈{0, 1, . . . } is selected such that: t.sub.k≤t.sub.j−T<t.sub.k+1, when Tis a constant.

2. The assembly according to claim 1, wherein $m\left(t_{j^{\prime }}\right)=\frac{n\left(t_{j^{\prime }}\right)-n_{\min }}{t_{j^{\prime }}-t_k}$ for at least one j′∈{1, 2, . . . }; and wherein n(t.sub.k′)<n.sub.min, and k′∈{0, 1, . . . } is selected such that: t.sub.k′≤t.sub.j′−T<t.sub.k′+1.

3. The assembly according to claim 1, wherein
m(t′)=m(t.sub.j) for at least one time t′, where t.sub.j<t′<t.sub.1+1.

4. A method of measuring a rotational rate of a rotating element, the method comprising: monitoring, by a sensor, markings on the rotating element that pass through a region monitored by the sensor in cycles when the rotating element rotates, wherein the element has a number a markings; sending, by the sensor, signals to the evaluation unit, wherein each signal is assigned a time t.sub.i for when it was sent, where i∈{0, 1, . . . } and t.sub.i<t.sub.i+1 for all i∈{0, 1, . . . }; calculating, by the evaluation unit, a function n(t) over time t as a measure for a rotational rate of the element, where $n\left(t_i\right)=\frac{1}{a*\left(t_i-t_{i-1}\right)}$ for all i∈{1, 2, . . . }; and calculating a function m(t) over time t as a measure for a gradient of the rotational rate of the element, where $m\left(t_j\right)=\frac{n\left(t_j\right)-n\left(t_k\right)}{t_j-t_k}$ for at least one j∈{1, 2, . . . }, wherein k∈{0, 1, . . . } is selected such that: t.sub.k<t.sub.j−T<t.sub.k+1, when T is a constant.

Description

(1) Preferred exemplary embodiments are shown in the figures. Identical reference symbols indicate identical or functionally identical features. In detail:

(2) FIG. 1 shows a first method for determining gradients from the prior art;

(3) FIG. 2 shows a second method for determining gradients from the prior art;

(4) FIG. 3 shows a method for determining gradients with a time constant;

(5) FIG. 4 shows a rotation starting from a standstill; and

(6) FIG. 5 shows an improved method.

(7) In FIGS. 1 to 5, the curve of a rotational rate function n(t) and a rotational rate gradient m(t) is shown in relation to time t. A hypothetical curve of the rotational rate n(t), that would correspond to the calculated gradient m(t) is indicated by dotted lines.

(8) A rotating transmitter wheel is sampled by means of a sensor. The sampling takes place at discrete successive times in a temporal spacing—a sampling interval—of t.sub.s. The times t.sub.i, where i∈{0, 1, . . . }, at which a marking on the transmitter wheel is detected by the sensor, are whole number multiples of the sampling interval t.sub.s.

(9) The rotational rate function n(t) is calculated in the FIGS. 1 to 4 as follows:

(10) $n\left(t_i\right)=\frac{1}{a*\left(t_i-t_{i-1}\right)}$

(11) for all i∈{1, 2, . . . }.

(12) The rotational rate gradient m(t) is m(t)=n(t)−n(t−t.sub.s)/t.sub.s according to FIG. 1.

(13) Regardless of whether the curve of the rotational rate is continuous or not, the gradient m(t) at t.sub.3 and t.sub.4 has pulse-like peaks. This can be prevented in that the gradient m(t) is obtained as a difference quotient via the last two available rotational rate data, as follows:

(14) $m\left(t_i\right)=\frac{n\left(t_i\right)-n\left(t_{i-1}\right)}{t_i-t_{i-1}}$

(15) where i∈{1, 2, . . . }.

(16) The gradient m(t) shown in FIG. 2 is still subject to noise and has been subjected to a phase shift, which is dependent on the rotational rate, despite its smoothed curve. This problem can be solved in that the gradient m(t), as shown in FIG. 3, is obtained via a time constant T that can be parameterized. The gradient m(t) is calculated here for j∈{1, 2, . . . } as

(17) $m\left(t_j\right)=\frac{n\left(t_j\right)-n\left(t_k\right)}{t_j-t_k}$

(18) wherein k∈{0, 1, . . . } is selected such that: t.sub.k≤t.sub.j−T<t.sub.k+1, when T is a constant.

(19) FIG. 4 shows a curve of the rotational rate function n(t) with a transmitter wheel that starts to rotate from a standstill. The broken line shows the actual curve of the rotational rate. Because of the long standstill between the times t.sub.1 and t.sub.2, a rotational rate is calculated at time t.sub.3 that is much lower than the actual rotational rate. This results in a peak formed in the gradient m(t) in the region t.sub.3≤t<t.sub.4.

(20) Such peaks can be eliminated, as shown in FIG. 5, by providing a minimum rotational rate n.sub.min. If the rotational rate n(t) calculated from the sensor signals at a time t is lower than the minimum rotational rate n.sub.min, then the minimum rotational rate n.sub.min is used to determine the gradients, instead of the calculated rotational rate n(t). For t.sub.3≤t<t.sub.4, m(t) is therefore calculated as

(21) $m\left(t\right)=\frac{n\left(t_3\right)-n_{\min }}{t_3-t_2}.$

(22) In this case, T is parameterized as t.sub.s for purposes of simplicity.