LifeTrac IV/Research Development/Carrying capacity - Revision history

Stavros Kalognomos: Calculator_for_Stress_Analysis_of_each_module_v0_1.xlsx added

2013-10-02T18:10:57Z

Calculator_for_Stress_Analysis_of_each_module_v0_1.xlsx added

← Older revision		Revision as of 18:10, 2 October 2013
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	The conclusion is that you should be careful when tightening the bolt because additional permanent stresses are applied to it that might become really great in value. Over-tightening must be avoided.		The conclusion is that you should be careful when tightening the bolt because additional permanent stresses are applied to it that might become really great in value. Over-tightening must be avoided.

			==Calculator for Stress Analysis of each module==

			[[file:Calculator_for_Stress_Analysis_of_each_module_v0_1.xlsx]]

			A few sets of calculations are written in the above excel workbook that concern some modules which can be used frequently in OSE machine designs. The idea is that since the machinery design is simple and uses standard parts (like beams and bolts), then analytical equations can be used to solve the stresses applied on each part. The goal is to avoid extreme oversizing of the components of the machines and therefore to reduce material and energy waste. The excel application is chosen for the calculations, since it can be found in almost every PC. The equations are also written as a text in the workbook, because it helps to an easier understanding and validation of the calculations and an easy copy/paste to other applications like [https://en.wikipedia.org/wiki/Scilab scilab]. <br />

			The V0.1 version of this excel workbook calculates:

			* The stresses on the pin of a joint
			* The forces on the mounting base of the hydraulic cylinder that is on lifetrac IV, as it is illustrated above
			* The forces on the mounting base of the hydraulic cylinder that is on the [[backhoe]]
			* The stresses on a bolt

	=See also=		=See also=

Stavros Kalognomos: Calculations of the forces on the bolts that mount the base of the hydraulic cylinders to the frame

2013-04-10T20:53:14Z

Calculations of the forces on the bolts that mount the base of the hydraulic cylinders to the frame

@@ Line 2: / Line 2: @@
 This page provides information for the approximate carrying capacity before vehicle tipping. Additional information is desired to determine structural strength when loaded. Operating load is defined as 50% of the tipping load.
-==C of G Analysis==
+=C of G Analysis=
 [[Image:lifetracCOG.jpg|600px]]
 * Mass is approximate to +/- 200lbs
@@ Line 8: / Line 8: @@
-==Force Distribution Analysis==
+=Force Distribution Analysis=
 {{Wanted| Formulas for calculating the force distribution as a function of arm angle}}
 [[file:Sideview2.PNG|thumb]]
@@ Line 21: / Line 21: @@
-===Tipping load calculations===
+==Tipping load calculations==
 [[file:Lifetrac_IV_tipping_load.bmp]]
@@ Line 68: / Line 68: @@
-===Calculations of the static force on the joint of the arm===
+==Calculations of the static force on the joint of the arm==
 '''Warning:''' This is a rough static load calculation that needs verification. Additional dynamic calculations should be considered.
-====Case 1: tractor is used for lifting objects====
+===Case 1: tractor is used for lifting objects===
 [[file:Lifetrac_IV_static_forces_on_the_joint.bmp]]
@@ Line 149: / Line 149: @@
 σ_total = ( σ_bending^2 + 4 * τ_shear^2 )^0.5
-====Case 2: tractor is used for pushing objects====
+===Case 2: tractor is used for pushing objects===
 [[file:lifetrac_IV_static_forces_on_the_joint_case_2.bmp]]
@@ Line 183: / Line 183: @@
 This force is distributed equivalently to the two joints between the arm and the frame of the vehicle. Thus, 0.5*R_JA is applied to each joint.
-====Case 3: impact====
+===Case 3: impact===
 Force F could also be considered as an impact force of several [http://en.wikipedia.org/wiki/G-force g] (x in number). In this case F = x*g*(WV/g + WA/g).
@@ Line 191: / Line 253: @@
 *[[LifeTrac IV Loader Lift Capacity]]
 *http://www.nstmop.psu.edu/tasksheets/4.12%20Tractor%20Stability.pdf

Stavros Kalognomos: minor edit

2013-04-03T18:43:56Z

minor edit

← Older revision		Revision as of 18:43, 3 April 2013
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	==C of G Analysis==		==C of G Analysis==
	[[Image:lifetracCOG.jpg\|600px]]		[[Image:lifetracCOG.jpg\|600px]]
	* ~~Weight~~ is approximate to +/- 200lbs		* Mass is approximate to +/- 200lbs
	* Tipping load is calculated by summing the moments around the front axle		* Tipping load is calculated by summing the moments around the front axle

Line 25:		Line 25:
	[[file:Lifetrac_IV_tipping_load.bmp]]		[[file:Lifetrac_IV_tipping_load.bmp]]

	WL: Weight of load (pallet) <br />		WL: [http://en.wikipedia.org/wiki/Weight Weight] of load (pallet). All the weights are forces i.e. W=m*g. <br />
	WA: Weight of arm <br />		WA: Weight of arm <br />
	WV: Weight of vehicle (without the weight of arm) <br />		WV: Weight of vehicle (without the weight of arm) <br />
Line 35:		Line 35:
	L_JA_WL: The distance between the joint of the arm and the c of g of the pallet <br />		L_JA_WL: The distance between the joint of the arm and the c of g of the pallet <br />
	θ: The angle between the L_JA_WL and the horizontal <br />		θ: The angle between the L_JA_WL and the horizontal <br />
	g: The gravity of Earth ( g = 9.81 m/(sec^2) )		g: The [http://en.wikipedia.org/wiki/Earth%27s_gravity gravity of Earth] ( g = 9.81 m/(sec^2) )

			'''Important:''' All the weights are forces. You can calculate them by multiplying the mass of each part by the gravity of Earth.

			'''W = m*g''' , where if m is in [Kg] and g is in [m/(sec^2)], then W is in [N] (i.e. Newton). (1 lbs = 0.45359237 Kg) <br /><br />

	RFW is the summation of the reaction forces applied to the two front wheels. I do not include the weight of the arm in the weight of the vehicle, because the position of the center of gravity of the arm changes while the arm rises. The same might be considered for the hydraulic cylinders, in more detailed calculations.		RFW is the summation of the reaction forces applied to the two front wheels. I do not include the weight of the arm in the weight of the vehicle, because the position of the center of gravity of the arm changes while the arm rises. The same might be considered for the hydraulic cylinders, in more detailed calculations.

	Balance of moments: <br />		Balance of moments: <br />
	L_WVWVg – L_RRWRRW – L_WLWLg – L_WAWA*g = 0		L_WVWV – L_RRWRRW – L_WLWL – L_WAWA = 0

	where, <br />		where, <br />
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	The vehicle is tipping when RRW=0. Thus the '''tipping load''' is: <br />		The vehicle is tipping when RRW=0. Thus the '''tipping load''' is: <br />
	WL_tipping = (L_WVWV – L_WAWA)/L_WL		WL_tipping = (L_WVWV – L_WAWA)/L_WL <br />

			and the mass of the tipping load is: WL_tipping/g

	For any WL, the reaction force on each wheel of the rear axis is the half of RRW, where: <br />		For any WL, the reaction force on each wheel of the rear axis is the half of RRW, where: <br />
	RRW = (L_WVWVg – L_WLWLg – L_WAWAg)/L_RRW		RRW = (L_WVWV – L_WLWL – L_WA*WA)/L_RRW

	The balance of forces implies that: <br />		The balance of forces implies that: <br />
	– RRW – RFW + WVg + WLg + WA*g = 0		– RRW – RFW + WV + WL + WA = 0

	Therefore, the reaction force on each wheel of the front axis is 0.5*RFW, where: <br />		Therefore, the reaction force on each wheel of the front axis is 0.5*RFW, where: <br />
	RFW = WVg + WLg + WAg – RRWg		RFW = WV + WL + WA – RRW

	'''Warning:''' Tipping load calculations, for the case that the vehicle is decelerating or climbing down a slope, might be also necessary.		'''Warning:''' Tipping load calculations, for the case that the vehicle is decelerating or climbing down a slope, might be also necessary.
Line 93:		Line 99:

	Balance of the moments applied at the arm (calculated at the position of JA): <br />		Balance of the moments applied at the arm (calculated at the position of JA): <br />
	L_JA_JHV* sin(90deg – ω – α)R_JHA – (L_JA + L_WL)WLg – (L_JA + L_WA)WA*g = 0 => <br />		L_JA_JHV* sin(90deg – ω – α)R_JHA – (L_JA + L_WL)WL – (L_JA + L_WA)*WA = 0 => <br />
	L_JA_JHVcos(ω+α)R_JHA – (L_JA + L_WL)WLg – (L_JA + L_WA)WAg = 0		L_JA_JHVcos(ω+α)R_JHA – (L_JA + L_WL)WL – (L_JA + L_WA)WA = 0

	Thus, the force applied from the hydraulic cylinders to the arm is: <br />		Thus, the force applied from the hydraulic cylinders to the arm is: <br />
	R_JHA = ( (L_JA + L_WL)WLg + (L_JA + L_WA)WAg )/( L_JA_JHV*cos(ω+α) )		R_JHA = ( (L_JA + L_WL)WL + (L_JA + L_WA)WA )/( L_JA_JHV*cos(ω+α) )

	The vehicle is symmetric, so '''each of the two cylinders applies a force''' to the arm that equals to 0.5*R_JHA.		The vehicle is symmetric, so '''each of the two cylinders applies a force''' to the arm that equals to 0.5*R_JHA.
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	The balance of forces at the vertical direction gives:		The balance of forces at the vertical direction gives:

	R_JAy = R_JHAsin(ω) – WLg – WA*g		R_JAy = R_JHA*sin(ω) – WL – WA

	The balance of forces at the horizontal direction gives:		The balance of forces at the horizontal direction gives:
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	where, M=F*L <br />		where, M=F*L <br />

	is the applied moment at the pin, F is the force applied at the end of the pin and L is its length (distance from the start of the pin to the point that F is applied). <br />		is the applied moment at the pin, F is the force applied at the end of the pin and L is its length (distance from the start point of the pin to the point that F is applied). <br />

	I = (pi/4)*r^4 <br />		I = (pi/4)*r^4 <br />
Line 153:		Line 159:

	If each wheel has a driving motor then: <br />		If each wheel has a driving motor then: <br />
	F = 4* T_max* r_wheel <br />		F = 4* T_max/r_wheel <br />

	Balance of the moments applied at the arm (calculated at the position of JA): <br />		Balance of the moments applied at the arm (calculated at the position of JA): <br />
	L_JA_JHVcos(ω+α)R_JHA – (L_ JA + L_ WL)WLg – (L_ JA + L_ WA)WAg – L_JA_WLsin(θ)F= 0 <br />		L_JA_JHVcos(ω+α)R_JHA – (L_ JA + L_ WL)WL – (L_ JA + L_ WA)WA – L_JA_WLsin(θ)F= 0 <br />

	Thus, the force applied from the hydraulic cylinders to the arm is: <br />		Thus, the force applied from the hydraulic cylinders to the arm is: <br />
	R_JHA = ( (L_ JA + L_ WL)WLg + (L_ JA + L_ WA)WAg + L_JA_WLsin(θ)F )/( L_JA_JHV*cos(ω+α) ) <br />		R_JHA = ( (L_ JA + L_ WL)WL + (L_ JA + L_ WA)WA + L_JA_WLsin(θ)F )/( L_JA_JHV*cos(ω+α) ) <br />

	The vehicle is symmetric, so '''each of the two cylinders applies a force''' to the arm that equals to 0.5*R_JHA. <br />		The vehicle is symmetric, so '''each of the two cylinders applies a force''' to the arm that equals to 0.5*R_JHA. <br />
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	The balance of forces at the vertical direction gives: <br />		The balance of forces at the vertical direction gives: <br />

	R_JAy = R_JHAsin(ω) – WLg – WA*g <br />		R_JAy = R_JHA*sin(ω) – WL – WA <br />

	The balance of forces at the horizontal direction gives: <br />		The balance of forces at the horizontal direction gives: <br />
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	====Case 3: impact====		====Case 3: impact====

	Force F could also be considered as an impact force of several g (x in number). In this case F = xg(WV + WA).		Force F could also be considered as an impact force of several [http://en.wikipedia.org/wiki/G-force g] (x in number). In this case F = xg(WV/g + WA/g).

Stavros Kalognomos: Case 2: tractor is used for pushing objects

2013-04-03T17:11:27Z

Case 2: tractor is used for pushing objects

Show changes

Stavros Kalognomos: Tipping load calculations & Calculations of the static force on the joint of the arm added

2013-03-20T21:17:31Z

Tipping load calculations & Calculations of the static force on the joint of the arm added

← Older revision		Revision as of 21:17, 20 March 2013
Line 19:		Line 19:
	* Please provide definitions of variables used, easily understood diagram and formulas		* Please provide definitions of variables used, easily understood diagram and formulas
	* If uploading to wiki is a problem, please email data to [[Mike Apostol]] directly		* If uploading to wiki is a problem, please email data to [[Mike Apostol]] directly


			===Tipping load calculations===

			[[file:Lifetrac_IV_tipping_load.bmp]]

			WL: Weight of load (pallet) <br />
			WA: Weight of arm <br />
			WV: Weight of vehicle (without the weight of arm) <br />
			RFW: Reaction force at the front wheels <br />
			RRW: Reaction force at the rear wheels <br />
			L_WL: The distance between the c of g of the pallet (where WL is applied) and the vector y <br />
			y: The vertical vector that passes through the axis of the front wheels <br />
			JA: The position of the joints that support the arm on the frame of the vehicle <br />
			L_JA_WL: The distance between the joint of the arm and the c of g of the pallet <br />
			θ: The angle between the L_JA_WL and the horizontal <br />

			RFW is the summation of the reaction forces applied to the two front wheels. I do not include the weight of the arm in the weight of the vehicle, because the position of the center of gravity of the arm changes while the arm rises. The same might be considered for the hydraulic cylinders, in more detailed calculations.

			Balance of momentums: <br />
			L_WVWV – L_RRWRRW – L_WLWL – L_WAWA = 0

			where, <br />
			L_WL = L_JA_WL*cos(θ) – L_JA

			Similar equation can be found for L_WA. Negative value of the L_WA implies that the c of g of the arm lies on the left side of the vector y.

			The vehicle is tipping when RRW=0. Thus the '''tipping load''' is: <br />
			WL_tipping = (L_WVWV – L_WAWA)/L_WL

			For any WL, the reaction force on each wheel of the rear axis is the half of RRW, where: <br />
			RRW = (L_WVWV – L_WLWL – L_WA*WA)/L_RRW

			The balance of forces implies that: <br />
			– RRW – RFW + WV + WL + WA = 0

			Therefore, the reaction force on each wheel of the front axis is 0.5*RFW, where: <br />
			RFW = WV + WL + WA – RRW


			===Calculations of the static force on the joint of the arm===

			[[file:Lifetrac_IV_static_forces_on_the_joint.bmp]]

			JA: The joint between the arm and the frame of the vehicle <br />
			JHV: The joint between the hydraulic cylinder and the frame of the vehicle <br />
			JHA: The joint between the hydraulic cylinder and the arm <br />
			R_JAy: The force applied from the vehicle to the arm, at vertical direction <br />
			R_JAx: The force applied from the vehicle to the arm, at horizontal direction <br />
			R_JHA: The force applied from the hydraulic cylinders to the arm <br />
			R_JHAy: The vertical component of the force applied from the hydraulic cylinders to the arm <br />
			R_JHAx: The horizontal component of the force applied from the hydraulic cylinders to the arm <br />
			ω: The angle between the direction of the hydraulic cylinder and the horizontal <br />
			L_JA_JHV: The distance between the positions of the joint JA and the joint JHV <br />
			L_JA_JHA: The distance between the positions of the joint JA and the joint JHA <br />
			L_JHV_JHA: The current length of the hydraulic cylinder (from joint JHV to joint JHA) <br />

			The force R_JHA is always in the direction of the axis of the hydraulic cylinder. That is because the joints of the cylinder cannot transmit momentums at the direction of z.

			(90deg – ω – α) is the angle between the L_JA_JHV and the L_JHV_JHA (i.e. the angle that has as a tip the joint JHV and as ends the joints JHA and JA).

			sin(90deg – ω – α)/L_JA_JHA = sin(φ)/L_JHV_JHA => <br />
			cos(ω+α)/L_JA_JHA = sin(φ)/L_JHV_JHA => <br />
			cos(ω+α) = sin(φ)*L_JA_JHA/L_JHV_JHA => <br />
			ω = arccos(sin(φ)*L_JA_JHA/L_JHV_JHA) – α

			Balance of the momentums applied at the arm (calculated at the position of JA): <br />
			L_JA_JHV* sin(90deg – ω – α)R_JHA – (L_JA + L_WL)WL – (L_JA + L_WA)*WA = 0 => <br />
			L_JA_JHVcos(ω+α)R_JHA – (L_JA + L_WL)WL – (L_JA + L_WA)WA = 0

			Thus, the force applied from the hydraulic cylinders to the arm is: <br />
			R_JHA = ( (L_JA + L_WL)WL + (L_JA + L_WA)WA )/( L_JA_JHV*cos(ω+α))

			The vehicle is symmetric, so each of the two cylinders applies a force to the arm that equals to 0.5*R_JHA.

			The balance of forces at the vertical direction gives:

			R_JAy = R_JHA*sin(ω) – WL – WA

			The balance of forces at the horizontal direction gives:

			R_JAx = R_JHA*cos(ω)

			The total force R_JA is:

			R_JA = ( (R_JAx)^2 + (R_JAy)^2 )^0.5

			This force is distributed equivalently to the two joints between the arm and the frame of the vehicle. Thus, 0.5*R_JA is applied to each joint. If there is no bending on this cylindrical joint, the maximum shear stress is:

			τ_shear = (4/3)*F/A

			where F = 0.5R_JA is the applied force and A = pir^2 is the cross-sectional area of the pin (that has radius r) of the joint. pi is 3.14.

			The equivalent tensile stress is: <br />
			σ_total = 2*τ_shear

			This equivalent stress must be less than (<) the tensile strength of the material of the pin divided by a safety factor.

			In reality the problem has three dimensions. Depending on the suspensions of the vehicle and other structural features, '''additional momentums''' at the direction of x might be applied to the joints.

			This is a rough static load calculation that needs verification. Additional dynamic calculations should be considered. Load calculations, for the case that the vehicle is decelerating or climbing down a slope, might also be necessary.


			==See also==
			*[[LifeTrac IV Loader Lift Capacity]]
			*http://www.nstmop.psu.edu/tasksheets/4.12%20Tractor%20Stability.pdf

MikeA at 04:19, 27 January 2012

2012-01-27T04:19:40Z

← Older revision		Revision as of 04:19, 27 January 2012
Line 6:		Line 6:
	* Weight is approximate to +/- 200lbs		* Weight is approximate to +/- 200lbs
	* Tipping load is calculated by summing the moments around the front axle		* Tipping load is calculated by summing the moments around the front axle


	==Force Distribution Analysis==		==Force Distribution Analysis==

MikeA: /* C of G Analysis */

2012-01-27T04:19:26Z

C of G Analysis

← Older revision		Revision as of 04:19, 27 January 2012
Line 3:		Line 3:

	==C of G Analysis==		==C of G Analysis==
	[[Image:lifetracCOG.jpg\|~~800px~~]]		[[Image:lifetracCOG.jpg\|600px]]
			* Weight is approximate to +/- 200lbs
			* Tipping load is calculated by summing the moments around the front axle

	==Force Distribution Analysis==		==Force Distribution Analysis==

MikeA: /* Analysis */

2012-01-27T04:16:43Z

Analysis

← Older revision		Revision as of 04:16, 27 January 2012
Line 2:		Line 2:
	This page provides information for the approximate carrying capacity before vehicle tipping. Additional information is desired to determine structural strength when loaded. Operating load is defined as 50% of the tipping load.		This page provides information for the approximate carrying capacity before vehicle tipping. Additional information is desired to determine structural strength when loaded. Operating load is defined as 50% of the tipping load.

	=Analysis=		==C of G Analysis==
	{{Wanted\| Formulas for calculating the ~~tipping loads and~~ force distribution}}		[[Image:lifetracCOG.jpg\|800px]]

			==Force Distribution Analysis==
			{{Wanted\| Formulas for calculating the force distribution as a function of arm angle}}
	[[file:Sideview2.PNG\|thumb]]		[[file:Sideview2.PNG\|thumb]]
	* Assume symmetric ~~weight~~		* Assume symmetric along center plane
	* [[:File:LifeTrac_sideview.doc \|LifeTrac image in MS Word file]]		* [[:File:LifeTrac_sideview.doc \|LifeTrac image in MS Word file]]
	* Basically what we need is an understanding between carried load CofG, vehicle CofG, arm pivot location, hydraulic cylinder mounted location and the front wheel which acts as the point to tip around.		* Basically what we need is an understanding between carried load CofG, vehicle CofG, arm pivot location, hydraulic cylinder mounted location and the front wheel which acts as the point to tip around.

MikeA: /* Overview */

2012-01-27T04:12:57Z

Overview

← Older revision		Revision as of 04:12, 27 January 2012
Line 1:		Line 1:
	=Overview=		=Overview=
	This page ~~attempts to determine~~ the ~~max~~ carrying capacity before vehicle tipping. ~~Formulas should be provided with variables instead~~ of ~~actual values so that different values can be input to optimize~~ the ~~design~~.		This page provides information for the approximate carrying capacity before vehicle tipping. Additional information is desired to determine structural strength when loaded. Operating load is defined as 50% of the tipping load.

	=Analysis=		=Analysis=

MikeA: moved LifeTrac IV Design Analysis/Carrying capacity to LifeTrac IV/Research Development/Carrying capacity: Wiki Reorganization for Tractor

2012-01-27T04:02:32Z

moved LifeTrac IV Design Analysis/Carrying capacity to LifeTrac IV/Research Development/Carrying capacity: Wiki Reorganization for Tractor

← Older revision	Revision as of 04:02, 27 January 2012
(No difference)