Method of making and using a dynamically balanced walk behind trowel
View Patent ↗A method is provided of making and using a walk behind rotary trowel that is “dynamically balanced” so as to minimize the forces/torque that the operator must endure to control and guide the trowel. Characteristics that are accounted for by this method include, but are not limited to, friction, engine torque, machine center of gravity, and guide handle position. As a result, dynamic balancing and consequent force/torque reduction were found to result when the machine's center of gravity was shifted substantially relative to a typical machine's center of gravity. Dynamic balancing can be achieved most practically by reversing the orientation of the engine relative to the guide handle assembly when compared to traditional walk behind rotary trowels and shifting the engine as far as practical to the right. This shifting has been found to reduce the operational forces and torque the operator must endure by at least 50% when compared to traditional machines.
1. A method of building a concrete finishing trowel, comprising:
(A) providing a frame;
(B) providing a rotor that is mountable on said frame, said rotor including a plurality of blades which are rotatable about a rotational axis;
(C) providing a motor that is mountable on said frame;
(D) providing a guide handle that is configured to extend rearwardly from said frame;
(E) determining an offset between the rotational axis of the rotor and a center of gravity of the trowel that results in a desired dynamic balance during trowel operation; and
(F) assembling the trowel so as to achieve said offset.
2. The method as recited in claim 1 , wherein the determining step includes determining a desired lateral offset.
3. The method as recited in claim 2 , wherein the desired lateral offset is determined taking the following equation into account,
c
=
ha
μ
b
where:
c=the lateral offset;
h=the height of the guide handle;
a=the length of a horizontal line connecting the rotational axis of the rotor to the centroid of the forces acting on one of the trowel blades, “a” being assumed to be the same for each trowel blade;
μ=the dynamic coefficient of friction of the finished surface; and
b=the longitudinal distance between the rotational axis of the trowel and the guide handle.
4. The method as recited in claim 1 , wherein the determining step includes determining a desired longitudinal offset.
5. The method as recited in claim 4 , wherein the desired longitudinal offset is determined taking the following equation into account,
d
=
a
2
b
Where:
d=the longitudinal offset;
a=the length of a horizontal line connecting the rotational axis of the rotor to the centroid of the forces acting on one of the trowel blades, “a” being assumed to be the same for each trowel blade; and
b=the longitudinal distance between the rotational axis of the trowel and the guide handle.
6. The method as recited in claim 1 , wherein the determining step comprises determining desired longitudinal and lateral offsets in dependence on one another.
7. The method as recited in claim 6 , wherein the longitudinal and lateral offsets are determined based at least in part on at least one of the following equations:
F
23
=
dF
w
-
a
2
b
(
F
w
-
F
45
)
-
bF
45
(
h
-
ea
b
μ
)
where:
F 23 =the combined longitudinal forces imposed on the guide handle;
d=the longitudinal offset;
F w =the gravitational force through the center of gravity of the trowel;
a=the length of a horizontal line connecting the rotational axis of the rotor to the centroid of the forces acting on one of the trowel blades, “a” being assumed to be the same for each trowel blade;
b=the longitudinal distance between the rotational axis of the trowel and the guide handle;
F 45 =the combined vertical forces imposed on the guide handle;
h=the height of the guide handle;
e=½ the lateral length of the guide handle; and
μ=the dynamic coefficient of friction of the finished surface; and
F
45
=
F
w
(
μ
b
2
hc
-
ceab
-
h
2
a
μ
2
b
+
hea
2
μ
+
ehb
μ
d
-
eh
μ
a
2
+
ab
2
d
-
a
3
b
)
(
-
h
2
a
μ
2
+
hea
2
μ
-
eh
μ
a
2
+
ehb
2
μ
-
a
3
b
+
ab
3
)
where:
c=the lateral offset.
8. The method as recited in claim 1 , wherein the offset is determined taking guide handle length and position, machine center of gravity, and engine torque into account.
9. The method as recited in claim 8 , wherein the offset is determined taking finished surface coefficient of friction into account.
10. The method as recited in claim 1 , wherein the assembling step comprises mounting the engine on the frame such that an output shaft of the engine faces to the right of the trowel and a muffler of the engine faces forwardly of the trowel.
11. The method as recited in claim 1 , wherein
said handle extends at least generally along a line that bisects said frame;
said rotational axis of said rotor is at least approximately centered on said frame; and
said trowel has a center of gravity that is offset longitudinally behind the rotational axis of said rotor and laterally to the right side of said line when viewed from behind said trowel.
12. A method of building a concrete finishing trowel, comprising:
(A) providing a frame;
(B) providing a rotor that is mountable on said frame, said rotor including a plurality of blades which are rotatable about a rotational axis;
(C) providing a motor that is mountable on said frame;
(D) providing a guide handle that is configured to extend rearwardly from said frame;
(E) determining a desired lateral offset between the rotational axis of the rotor and a center of gravity of the trowel that results in a desired dynamic balance during trowel operation, wherein the desired lateral offset is determined taking the following equation into account:
c
=
ha
μ
b
where:
c=the lateral offset;
h=the height of the guide handle;
a=the length of a horizontal line connecting the rotational axis of the rotor to the centroid of the forces acting on one of the trowel blades, “a” being assumed to be the same for each trowel blade;
μ=the dynamic coefficient of friction of the finished surface; and
b=the longitudinal distance between the rotational axis of the trowel and the guide handle; and
(F) assembling the trowel so as to achieve said offset.
13. A method of building a concrete finishing trowel, comprising:
(A) providing a frame;
(B) providing a rotor that is mountable on said frame, said rotor including a plurality of blades which are rotatable about a rotational axis;
(C) providing a motor that is mountable on said frame;
(D) providing a guide handle that is configured to extend rearwardly from said frame;
(E) determining longitudinal and lateral offsets between the rotational axis of the rotor and a center of gravity of the trowel that results in a desired dynamic balance during trowel operation, wherein the longitudinal and lateral offsets are determined based at least in part on at least one of the following equations:
F
23
=
dF
w
-
a
2
b
(
F
w
-
F
45
)
-
bF
45
(
h
-
ea
b
μ
)
where:
F 23 =the combined longitudinal forces imposed on the guide handle;
d=the longitudinal offset;
F w =the gravitational force through the center of gravity of the trowel;
a=the length of a horizontal line connecting the rotational axis of the rotor to the centroid of the forces acting on one of the trowel blades, “a” being assumed to be the same for each trowel blade;
b=the longitudinal distance between the rotational axis of the trowel and the guide handle;
F 45 =the combined vertical forces imposed on the guide handle;
h=the height of the guide handle;
e=½ the lateral length of the guide handle; and
μ=the dynamic coefficient of friction of the finished surface; and
F
45
=
F
w
(
μ
b
2
hc
-
ceab
-
h
2
a
μ
2
b
+
hea
2
μ
+
ehb
μ
d
-
eh
μ
a
2
+
ab
2
d
-
a
3
b
)
(
-
h
2
a
μ
2
+
hea
2
μ
-
eh
μ
a
2
+
ehb
2
μ
-
a
3
b
+
ab
3
)
where:
c=the lateral offset; and
(F) assembling the trowel so as to achieve said offset.