A/T - Math Formulas Part I
1982 Volvo 240 L4-2127cc 2.1L SOHC B21F Copyright ? 2013, ALLDATA 10.52SS Page 63
TSB: 89-23 (Aug)
SUBJECT:
TRANSMISSION MATH FORMULAS (Your most valuable tool)
Transmission math formulas are not reserved exclusively for engineers. Understanding some basic mathematical formulas can be one of your most
valuable tools.
The following information contained in this bulletin will discuss various basic formulas dealing with:
1. Shift Speed
2. Pressure
3. Speedometer ratios
Take the time, now, to understand these relatively simple concepts.
You will be saving yourself many problems, and considerable frustration, and also dollars, in the future.
Shift Speed and Pressure
SHIFT SPEED AND PRESSURE
To figure the area of a circle (valve or servo):
Radius (which is 1/2 the diameter) x Radius x 3.14159 = Area
EXAMPLE: A 1" diameter circle has a radius of 0.5"
0.5 x 0.5 x 3.14159 = 0.785
Therefore a 1" diameter circle has an Area of 0.785 sq. inches
Pressure x Area = Force
EXAMPLE: 100 psi line pressure, on a servo with an area of 2 square inches = force
So, 100 psi line pressure x 2 sq in = 200 pounds of force.
Force divided by Area = Pressure
EXAMPLE: 200 lbs divided by 2" = 100 psi
Force divided by Pressure = Area
EXAMPLE: 200 lbs divided by 100 psi = 2 inches
THINGS WE CAN DO WITH THESE FORMULAS:
EXAMPLE: A 700 R4 has 62 psi of line pressure at Idle.
The PR spring weighs 6.5 lbs
The tip (reaction end) of the PR valve has a diameter of 0.365" (0.365 divided by 2 = 0.1825 radius) 0.1825 x 0.1825 x 3.14159 = 0.1046" area
We want 75 psi of line pressure at Idle
First, let's see if those numbers add up, using: Pressure x Area = Force
62 psi x 0.1046 = 6.48, or 6 1/2 lb PR Spring
We want 75 psi:
Pressure x Area = Force (Spring) 75 psi x 0.1046 = 7.85 lb spring
What if we put in an 8 lb Spring? Force divided by Area = Pressure
8 lbs divided by 0.1046 = 76.48 or 76 1/2 line pressure
Now, let's look at RATIO.
Ratio is the relationship in quantity, amount or size, between two or more things.
In our example ratio is: How many psi each pound of spring will add.
1982 Volvo 240 L4-2127cc 2.1L SOHC B21F Copyright ? 2013, ALLDATA 10.52SS Page 64
Pressure divided by Force = Ratio
EXAMPLE: 62 psi divided by 6.5 lbs = 9.5 ratio Each pound of spring will increase pressure 9.5 psi
Force x Ratio = Pressure
EXAMPLE: 6.5 lbs x 9.5 = 61.75 or 62 psi
(Let's add 1 lb of spring, and see if we get 9.5 more psi.)
Force x Ratio = Pressure
EXAMPLE: 7.5 lbs x 9.5 = 71.25
New pressure Old pressure = Pressure difference
71.25 minus 61.75 = 9.5 psi change (by adding 1 lb of spring)
Once you know the ratio, a lot can be determined. Pressure divided by Ratio = Force
62 psi (actually 61.75) divided by 9.5 = 6.5 lb spring
The ratio never changes. This means that if I know that line pressure is 55 psi at idle, in a 700 R4, the the PR spring must be 5.78 lbs.
Pressure divided by Ratio = Force
So, 55 psi divided by 9.5 = 5.78 lbs.
Now, let's look at a math formula for shift speeds.
Suppose we had shift speeds of 15 mph and 20 mph, for the 1-2 & 2-3 shifts on a transmission. 20 mph may be too early for the 2-3 shift. If we
adjust TV modulator, we will move both shifts. We don't want to do that because the 1-2 shift is fine, so let's work with just the 2-3 shift spring.
EXAMPLE: Original spring divided by Original MPH = Ratio
As, 4 lbs divided by 25mph = 0.2
Ratio x Desired MPH = New Spring
0.2 x 25 mph = 5 lb spring
A 5 lb spring will raise the shift on this transmission to 25 mph.
All you need to know is -- Where is it shifting now (at MINIMUM throttle) and what does the spring weigh.
This formula will get you very close, but may be a "tad" off, because we are not accounting for TV pressure helping the spring. This is why you
want to check it at minimum throttle, so TV has the least effect.
Speedometer Ratios
Finally, let's look at speedometer ratios.
Suppose we put an exchange transmission in a car, and now the speedometer is off, because the speedometer drive gear has a different tooth count.
What do we have to do to the driven gear to correct it?
Let's say the old drive gear had 7 teeth and the old driven gear had 21 teeth. The exchange unit had 8 teeth on the drive gear.
Old Drive Gear divided by the New Drive Gear = Ratio
7 teeth divided by 8 teeth = 0.875
Old Driven Gear divided by Ratio = New Driven Gear
21 teeth divided by 0.875 = 24 teeth
A 24 tooth driven gear will correct the speedometer error.
Let's do one more speedometer change. This time the old drive is 9, and the new drive is 10. The old driven gear is still 21.
Old Drive Gear divided by New Drive Gear = Ratio
1982 Volvo 240 L4-2127cc 2.1L SOHC B21F Copyright ? 2013, ALLDATA 10.52SS Page 65
9 tooth divided by 10 tooth = 0.9
Old Driven Gear divided by Ratio = New Driven Gear
21 tooth divided by 0.9 = 23.33 teeth
We can't get a 23.3 tooth count so we round it off to 23 teeth. Now the speedometer will be close, but not exact, because we had to round off the
No comments:
Post a Comment