Quality Gaging Tips - What’s your sine?
A few months ago this column described the use of surface plates,
observing that a flat surface is the basis for most dimensional
measurements. Many workpieces, of course,
are neither flat nor straight. In order to measure the angular accuracy
or straightness of an angled surface using a surface plate, a sine
instrument comes into play. By placing the
workpiece on the sine instrument and raising one end of the
instrument to the proper height, it is possible to orient the
workpiece parallel to the surface plate.
Straightforward measurements can then be performed with a test indicator
and height stand.
Sine bars are relatively narrow
(up to about one-inch wide) fine-ground or lapped steel bars, with
precision cylinders at each end resting against stops machined into the
bottom surface. Some sine bars are completely ambidextrous; others have
"upper" and "lower" end as well as distinct top and bottom surfaces.
Holes machined in the instrument enable the placement of stops or clamps
to hold workpieces in place. Close cousins
to sine bars include sine blocks, which are simply wider sine bars; and
sine plates (the most popular version), in which the bottom cylinder is
actually part of a hinge connected to an attached base. While most sine
instruments serve primarily as measuring instruments, some sine plates
are rugged enough to serve as fixturing
devices for machining operations. The principle of operation is
identical for all versions, so for the sake of simplicity, we'll refer
only to sine plates in the following discussion.
To set the sine plate at the proper angle, one simply selects a gage
block or gage block stack of the appropriate height and places it under
the upper cylinder. An imaginary right triangular prism is thus created,
the vertical face of which passes through the gage block and terminates
at the axis of the upper cylinder. The horizontal base of the prism is
above and parallel to the surface plate, terminating at the axis of the
lower cylinder (hinge), while the ends of the hypotenuse are defined by
the axes of the two cylinders. The top surface of the sine plate is
therefore parallel to the hypotenuse. The use of cylinders as contact
points ensures that the length of the hypotenuse remains the same
regardless of its angle. Most sine instruments set the cylinders at a
fixed distance between centers that is easy to manipulate
mathematically, 5 inch and 10 inch being the most common lengths.
To calculate the required height of gage blocks, use the following
B = b/a
B = required angle b = height of triangle a = length of hypotenuse.
For example, say we want to measure the straightness of a surface on a
workpiece that's angled 27 degrees from a
reference surface on the same workpiece.
Let's also say our sine plate is 5[inches] between cylinder centers. To
obtain the sine value, we either refer to a table of trig values, or
simply punch it up on a $10 scientific calculator.
27 [degrees] = b/[inches]" 0.453,990,499 = b/5[inches] b = 2.270[inches]
So we wring up a stack of gage blocks, place it beneath the upper
cylinder of the sine plate, and voila, we have a surface that's 27
degrees out-of-parallel with the surface plate. We stage the
workpiece on the sine plate facing the
opposite direction and, if all is well, the
workpiece surface should be parallel to the surface plate. We can
then measure it for flatness, straightness, and angular accuracy, using
conventional surface plate methods. To measure straightness, an
indicator held by a test stand is drawn across the surface, and
comparative height measurements are taken at regular intervals. By
drawing a best-fit line through the data, it is possible to break out
the flatness of the surface and to calculate the accuracy of the
Because sine values change rapidly between angular measurements of low
numerical values, and change very little between higher numerical value
angles, the accuracy that can be achieved using a sine instrument varies
considerably: precision is much better for shallow angles than for steep
ones. Therefore, where the surface of a workpiece
is angled at greater than 45 degrees, it is often advisable to use the
complement of the angle (90[degrees] -x) in the calculation.
Even so, the accuracy that can be achieved with sine instruments is
somewhat limited, because there are so many separate mechanical elements
to the setup (the surface plate, the gage block(s), the test indicator,
the test stand, and the sine instrument itself), each of which poses a
certain degree of uncertainty. We'll look at methods to perform
higher-precision angular measurements in a future column.
Article courtesy of MMS Online.
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